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CHAPTER 4

MODELLING THE IMPACT OF LARVAL BROWSING

ON E. NITENS SHOOT GROWTH

4.1 INTRODUCTION

This chapter describes models for predicting the loss of leaf area due to larval

browsing, aggregated to the shoot level, given an initial egg population density.

Given an estimate of the average number of eggs per shoot, obtained from routine

population monitoring (cf. Fig. 1.4), the reduction in new season’s foliage expressed

as percent defoliation, P, can then be predicted. This predicted P is a key input for

the decision support system for the leaf beetle IPM described in Chapter 7.

Only a few studies have examined the growth impact at the leaf or shoot level of

feeding by a phytophagous insect in eucalypts (Cremer, 1972; Fox and Morrow,

1983) and models that can be used to predict these growth impacts are completely

lacking. The most extensive modelling of the effects of phytophagy on growth for a

broadleaf tree species is that for feeding by the gypsy moth (Lymantria dispar (L.))

on deciduous hardwoods, particularly commercially important oak species (Quercus

spp.) (Valentine et al. 1976; Valentine and Talerico, 1980; Valentine, 1983).

A rigorous and elegant method of estimating growth impacts of phytophagous insects

is to : (a) measure or estimate insect consumption rates in the laboratory or field, (b)

independently measure aliquot leaf expansion rates, (c) dynamically model growth

impacts at the leaf level, and (d) aggregate these impacts to the shoot, tree, or stand

level (Reichle et al. 1973; Valentine and Talerico, 1980). However, a limitation of

this approach is that it assumes expansion rates are uniform over the leaf lamina

(Goldstein and Van Hook, 1972) or alternatively, the pattern of feeding over the leaf

lamina is random. This last assumption is clearly unrealistic. In addition, if expansion

rates vary between different coexisting phenological classes of leaves (e.g. age

classes) then models of larval feeding preference and consumption rate for each leaf

class (Reichle et al. 1973) are required.

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For oak/gypsy moth phytophagy the assumption of uniform within and between-leaf

spatial pattern of leaf expansion, as in Valentine and Talerico (1980) and Valentine

(1983), is probably an adequate approximation. This is because for deciduous

broadleafs such as oaks : (a) a new set of leaves is produced each year, (b) budbreak

is often well synchronised for a given species and location (Longman and Coutts,

1974; Valentine, 1983; Nizinski and Saugier, 1988; Collet and Frochot, 1996) so that

the majority of leaves have a similar phenology, and (c) there is evidence that

expansion rates are uniform across the leaf blade (Goldstein and Van Hook, 1972;

Reichle et al. 1973). Valentine (1983) discussed the impact of non-synchronous

budbreak on predictions of defoliation based on accumulative leaf consumption.

However, for eucalypts the situation compared to oaks is very different with leaves

retained typically for 3 years and new leaves produced continuously through the

growing season. This results in a range of leaf ages and sizes being held on the shoot

at any given time (Jacobs, 1955; Pederick, 1979). In addition, eucalypt leaf expansion

rates vary greatly as a function of leaf (physiological) age and size as was seen in

Chapter 3. Combined with this extra complexity in leaf phenology, the feeding

preferences of paropsine larvae, particularly those of early instars, are known to be

highly dependent on leaf phenology in eucalypts (Ohmart et al. 1987; Larson and

Omhart, 1988; Omhart, 1991; Omhart and Edwards, 1991). In the case of within-leaf

spatial variation in expansion rates, no published information could be found for

eucalypts.

Due to the lack of data on feeding preferences of C. bimaculata larvae on E. nitens,

construction of a dynamic model incorporating feeding/leaf expansion interactions

was not possible. In the absence of such data, if incorrect assumptions on feeding

preferences were used then predictions of growth impact based on the consumption

rate data of Baker et al. (1999) and the leaf expansion models in Chapter 3 could be

subject to large errors. As a result, two simple, empirical shoot-level models were

fitted and compared in terms of their ability to predict observed growth losses from

larval browsing. These were: (i) fitting a simple response-surface regression model

using data from a caged-shoot feeding trial, and (ii) a simple process model

144

incorporating the leaf expansion models described in Chapter 3 and calibrated in part

using the same data as that in (i).

However, before describing these two models in detail it is worth outlining how they

fit into a general theoretical framework in terms of the dynamic models mentioned

above. It is shown how the models in (i) and (ii) provide estimates of the combined

loss of leaf area due to (a) accumulative consumption by larvae and, (b) the loss of

potential leaf area caused by the consumption of actively expanding leaf tissue. The

total of (a) and (b) corresponds to what Valentine (1983) defines as ‘apparent

defoliation’.

4.2 DYNAMIC MODELS OF THE IMPACT OF PHYOPHAGOUS FEE DING

ON LEAF AND SHOOT GROWTH

Valentine (1980) defined (apparent) percent defoliation resulting from gypsy moth

feeding on red oak from the time from budbreak, 0t , to the time of pupation, pt , as

( ) ( ) ( )( )p

ppp tF

tFtFtP

*

100−

= (4.1)

where ( )ptF is the foliage biomass (kg ha-1) that would have been present at time pt

if insect consumption had not occurred and ( )ptF * is the foliage biomass at time pt

when larval feeding has ceased. Time, pt , was measured in day-degree units.

Here, leaf area per shoot (cm2) is modelled instead of foliage biomass but conversion

between leaf area and leaf weight is straightforward using the specific leaf area (SLA)

(cm2 g-1) for each leaf age class. Conversion to total canopy leaf area per unit ground

area (i.e. Leaf Area Index, LAI) is more difficult. However, prediction of LAI was not

required here since the impact of larval feeding on growth was required only at the

shoot level (Section 7.4).

145

Valentine (1980) estimated ( )ptF * by integrating the following differential equation

from time 0t to pt ,

( ) ( )( )

( ) ( )dt

tdCa

dt

tdF

tF

tF

dt

tdF −=**

(4.2)

where ( )tC is the accumulative consumption (kg ha-1) of the larval population since

time 00 =t and a is a constant which is the ratio of dry weight of foliage both

dropped and consumed by the larvae to the dry weight consumed. Further, the

average consumption for an individual larva, ( )tC1 (mg larva-1), is related to ( )tC by

the rate function

( ) ( ) ( )dt

tdCtN

dt

tdC 1610−=

where ( )tN is population size at time t (number ha-1).

Riechle et al. (1973) used a similar dynamic model to estimate insect consumption

rates in yellow poplar using measurement of leaf holes over the growing season.

Average, population-level, insect consumption, ( )tC j , in units of leaf area (cm2)

consumed to time t, for leaves in leaf class j was estimated from the average area of

leaf holes, ( )tH j [ ( )tF *= ], after adjusting for the expansion of the holes. This

expansion was modelled as proportional to the expansion of the average, gross, leaf

blade area, ( )tG j [ ( )tF= ]. The following first-order differential equation was used

to estimate the average consumption rate per leaf, ( ) dttdC j / ,

( ) ( ){ }( ) ( ) ( )

dt

tdCtH

td

tGd

dt

tdH jj

jj −=ln

(4.3).

Though each of the above approaches has a different objective and operates at a

different scale, they both rely on a common underlying dynamic model for ( )ptF * at

146

the individual leaf level. This model can be applied to each leaf age or canopy class

separately, as in Riechle et al. (1973), but for the moment the j subscript will be

suppressed. Using Valentine’s notation to refer to leaf area rather than biomass, this

underlying model of leaf area during feeding to time t is given by

( ) ( ) ( ) ( ) ( )tdt

tdL

dt

tdC

dt

tdF

dt

tdF δ

+−=

*

(4.4)

where

( ),otherwise;

tttt;t ps

0

1 0

=

<≤≤=δ

( )tL is the potential leaf area lost due to consumption by time t (i.e. the equivalent

expanded leaf area at time t that the area consumed to time t would have produced),

and st is the time at the start of feeding. If it is assumed that the rate of expansion of

( )tL is proportional to the rate for the equivalent unbrowsed leaf then

( )( )

( ) ( ) ( ){ }tCtLdt

tdF

tFdt

tdL += 1 (4.5).

Substituting (4.5) into (4.4) gives

( ) ( ) ( ) ( )( )( )

( ) ( )ps ttt

dt

tdC

dt

tdF

tF

tCtLtF

dt

tdF <≤−

+−= ;

*

from which model (4.2) can be obtained given that ( ) ( ) ( )tCtFtF ** −= , where

( ) ( ) ( )tCtLtC +=* , and a=1. Therefore the quantities ( )ptF and ( )ptC * , where

( )ptC * is apparent defoliation, are of greatest interest here since together they allow

prediction of percentage apparent defoliation, ( )ptP , at the time when feeding has

been completed using (4.1).

147

The same model can be derived from equations (1), (2) and (3) of Riechle et al.

(1973). Riechle et al. (1973) also showed that given these models of leaf expansion

and consumption rates then for leaf age class j

( ) ( ) ( )( )

ττ

ττ

= ∫ dd

dC

FtFtC

pt

t

j

jpjpj

0

1* (4.6).

Therefore, given a sample of E. nitens shoots measured at time 0t , with leaf classes

determined by factors such as leaf age and time of leaf set, apparent defoliation,

( )pj tC * , for leaf class j can be predicted using (4.6). This requires estimates of (a)

( )tF j which can be obtained from models (3.1) and (3.5) (Chapter 3) and (b)

( ) ( )tCtC j = (i.e. assuming a common consumption rate across leaf classes) which

can be predicted by a consumption rate model. The model for ( )tC can be

constructed by combining average consumption rate with larval development rate

(Chapter 6) for each instar. Average consumption rate for each larval instar was

measured by Baker et al. (1999) in a laboratory experiment using a single

temperature regime and feeding on harvested E. regnans and E. nitens leaves.

However, there is a serious difficulty in using this approach to estimate ( )∑ j pj tC *

(i.e. the aggregate of the individual leaf values) for E. nitens shoots since this

quantity depends on the consumption rates for different leaf classes and the

assumption that ( ) ( )tCtC j = is unrealistic.

Eucalypts, because their growth habit is evergreen and indeterminate (Jacobs, 1955),

at any one time hold leaves with markedly different phenologies (for example leaf

ages of 0, 1, 2, or 3 years with corresponding range of leaf toughness and size) on the

same shoot with each having different expansion rates. Therefore, the feeding

preferences of the larvae for leaves with differing phenologies need to be

incorporated in model (4.5). Data on survival of neonate larvae on E. nitens leaves of

varying leaf toughness, (B. Howlett, unpublished data), showed that these larvae can

only successfully feed on newly flushed foliage but there is currently no information

148

on feeding preferences for older larvae. The L3 and L4 larvae are capable of

successfully feeding on a much wider range of leaf toughness than L1 larvae. Since

these older larvae account for almost 90% of total consumption (Greaves, 1966;

Baker et al. 1999) then modelling their feeding preference is essential in order for

model (4.6) to give realistic predictions of ( )∑ j pj tC * .

As well as variation between leaves in expansion rates, these rates at any point in

time can vary spatially over the leaf lamina. The models described above assume that

leaf expansion is uniform over the leaf lamina. Hsiao et al. (1985) refer to studies on

broadleaf species from the Xanthium, Curcubita (squashes), and Vitis (grapes) genus

which indicate greater growth rates in the basal or interior regions compared to apical

portions of the leaf. Lowman (1987) observed that expansion of holes punched in the

basal region of the leaf was proportional to overall leaf expansion for each of five

Australian rainforest canopy tree species. Coleman and Leonard (1995) reported

twice the final leaf area for tobacco (Nicotiana tabaccum) leaves that had a 3.5 cm2

hole punched in the tip compared to leaves that had the same area removed in their

base where the treatments were carried out on young leaves at 20-30% of full

expansion. The reduction in final leaf area was four times greater than for mature

leaves (80-100% expanded) which had the same area removed from either the tip or

base compared to the young leaves with hole punched in the base.

Figure 4.1 demonstrates the effect of three, (a) to (c), hypothetical spatial patterns of

leaf expansion and feeding for leaves of the same initial size, )( 0tF , at time 0t , and

gross final leaf area, )( ptF . To more easily demonstrate apparent defoliation, feeding

was assumed to have finished after a short time interval, t∆ , relative to the period,

0tt p − . Therefore at time tt ∆+0 the area loss is due almost entirely to accumulative

consumption ( )ttC ∆+0 while the total area loss at time pt corresponds to ( )ptC * . It

can be seen in Fig. 4.1 that although the values of ( )ttC ∆+0 and )( ptF have been

constrained to take approximately the same values in (a) to (c) the values of ( )ptC *

are very different. Similar comparisons can be made between leaves, for example

between fully-expanded and actively-expanding leaves, with similar results.

149

(a) (b) (c)

Actively expanding

Total area loss at time t

growth

f

F(t0)=n

unbrowse

browsed

F(tpF(t0

tt0

t0 t∆

tt0

t0 t∆

growth growth tt

t0 t∆

Figure 4.1 Effect of three different combinations of within-leaf spatial pattern of leaf expansion (E) and larval feeding (F) on final leaf area, (a) basal (E), apical (F), (b) uniform (E), apical,marginal (F), (c) apical (E), apical (F). Common assumed values of initial leaf area, F(t0), final leaf area, F(tp), and leaf area consumed with total ‘apparent defoliation’ given by total area loss at time tp. Leaf area at time t0 is made up ofn unit areas of size f0 . Browsing is assumed to have ceased at time .0t t+ ∆

150

Using the jn small sub-areas of size 0f at time 0t , representing the area of the jth

leaf, as in Fig. 4.1, to generalise (4.4) to the ith sub-area of the jth leaf gives

( ) ( ) ( ) ( ) ( ) dttdt

tdL

dt

tdC

dt

tdFtF

m

j

n

i

t

ttij

ijijijp

j p

∑ ∑ ∫= = =

δ

+−=1 1

*

0

(4.7).

The extra degree of complexity involved in generalising model (4.4) to (4.7) is

required if there is systematic spatial variation in within-leaf expansion rates

combined with non-random within-leaf feeding patterns. There are no published

studies of within-leaf spatial pattern of expansion in eucalypts and no quantitative

studies have been made of within-leaf feeding pattern of C. bimaculata. Given the

above difficulties alternative, simpler methods of estimating ( ) ( )∑=ij pijp tCtC ** ,

)( ptF , and therefore )(*ptF and ( )ptP , were required.

Expressing (4.7) as an explicit function of the number of larvae feeding per shoot, N,

the impact of browsing on shoot total leaf area is given by

( ) ( ) ( )ppp tCNtFtNF ** , −=− (4.8)

where ( )ptC * is denoted the ‘effective leaf area loss per larva’ (ELAL) in units of

cm2 larva-1. Therefore, total apparent defoliation, as an explicit function of N, is given

by ( ) ( )pp tCNtNC ** , = . Model (4.8) does not incorporate time-dependent mortality

(i.e. N as a function of t) because consumption was not modelled here as a dynamic

process. In fact, the consumption component of ( )ptNC ,* is not explicit in (4.8).

Therefore, N must be set to either the starting cohort size for the shoot (i.e. number of

eggs), 0N , or the number of larvae successfully completing development, pN . Both

methods redistribute the total consumption across the N larvae. Using 0N attributes

extra consumption to those larvae that fail to complete development and

correspondingly reduces that attributable to those that feed to pre-pupal stage.

Alternatively, using pN attributes all consumption to the surviving larvae. Therefore

151

ELAL is a notional value applicable for average survival corresponding to the data

used to calibrate (4.8). Since total consumption is the same in each case, ( )ptC *

depends on the value of N used in (4.8). The implication of using ELAL to predict

growth impact of feeding is discussed later.

Given values of ( ) ( )pp tFtNF ,,* , and N for a sample of shoots, then ( )ptC * can be

estimated by fitting (4.8) as a linear regression through the origin. However, both

( )ptNF ,* and ( )ptF cannot be observed on the same shoot. To overcome this a

field experiment was used in which visually-matched shoots on a sample of trees

were selected and one of the shoots ‘loaded’ with an egg batch of size N (treatment

shoot) while the control shoot was protected from browsing. Different levels of N

were randomly assigned to trees and the shoots were harvested after feeding finished.

The treatment shoots provided measurements of( )ptNF ,* while the control shoots

provided measurements of ( )ptF allowing regression equation (4.8) to be fitted.

This is method (i) mentioned in the introduction and will be called the ‘response

surface’ regression method for the following.

An alternative method, method (ii), was used in order to : (a) reduce the variability in

the estimates of ( )ptC * from method (i) caused by variation in growth between

different shoots and (b) explicitly account for losses due to disbudding (i.e. removal

of leaf buds). This involved the use of a simple process model to predict ( )ptF for

the treatment shoots and then estimate ( )ptC * using a profile-likelihood.

Explicitly accounting for disbudding is potentially useful since the interaction of leaf

expansion and feeding is qualitatively different for damage to, or consumption of,

leaf buds compared to feeding on existing, actively expanding leaves. This is because

a very small amount of consumption is involved in disbudding. Therefore, even

though complete disbudding of a shoot can be achieved by only a few larvae it can

result in a relatively large loss of potential leaf area. In this case the effect of

disbudding, if not incorporated separately, would invalidate the assumed linear

152

functional relationship between ELAL= ( )ptC * , and total apparent defoliation

( )ptNC ,* in model (4.8). The models of spruce budworm defoliation given by

Sheehan et al. (1989) account for these two causes of lost potential foliage : (a) that

due to killed buds and (b) that due to damaged shoots (see pages 28 and 41 of

Sheehan et al. 1989). These correspond here to (a) disbudding, and (b) browsing of

actively expanding leaves.

The caged-shoot feeding trial is described next along with the response surface

method of estimation after which the process model is described. Estimates of

( )ptC * and ( )ptNP , , expressing P as an explicit function of N, are the key quantities

of interest. For the following reference to the time over which consumption takes

place will be assumed to be from time stt =0 to time pt so dependence on pt is

assumed [i.e. ( ) ( ) ( ) ( ) FtFNFtNFtCC ppp === ,,, **** , and ( ) ( )NPtNP p =, ].

4.3 RESPONSE SURFACE MODEL : THE CAGED-SHOOT EXPERIMENT

4.3.1 Materials and Methods

Site and stand description

The trial was established in December 1992 in Gould’s plantation, an ex-pasture site

near Dover, in Southern Tasmania (Appendix 5). The site has a north-easterly aspect

and altitude of 100 m with a gentle to steep slope. The site was planted in September

1990 with E. nitens using seedling stock of a Mount Toorongo seedlot of the Upper

Toorongo provenance (Pederick 1979). Details of plantation establishment can be

found in Pinkard (1997,1998).

Experimental design and structures

A sample of 18 trees was selected at random in December 1992 from a gently sloping

area of approximately one hectare. Only trees which had at least 50% of their height

from the top of the tree down consisting of adult foliage were selected for treatment

consisting of attaching cages and introducing C. bimaculata egg batches onto the

enclosed foliage. Figures 4.2(a) and (b) show typical examples of the selected trees.

Tree height range was 4 - 6 m.

153

On each tree, three first or second order branches were selected to be evenly spaced

around the mid-crown and similar in appearance in terms of total leaf area of adult

foliage, number of shoots, number of buds, and amount of new season’s flush

foliage. The visually matching attempted to sample foliage typical of such branches

in the mid-crown across, as well as within, trees. Only branches on which all

previous seasons leaves were of the adult form, and thus new leaves were all of this

form, were selected. For some selected branches, near the stem, some leaves were

intermediate between juvenile and adult form (Fig. 1.1). These leaves were included

in the cages and measured but were later excluded from analyses. The cages enclosed

leaves from the apical bud of the first order branch inwards towards the bole until

juvenile foliage was encountered. The aggregate of these shoots enclosed in the cage

defines the within-tree experimental unit (EU) which will simply be called the

‘shoot’, unless the context implies a single shoot, or ‘shoot EU’ if ambiguous. The

three shoots were marked with flagging tape. Each of three treatments was randomly

assigned to one of the shoot EUs, the trees thus representing ‘blocks’ in the usual

experimental design sense. The treatments were a caged control (C), an uncaged,

sprayed control (S), and a caged treatment (T) shoot. Figure 4.2 shows experimental

trees with attached cages.

The cages were made of welded aluminium pipes and were firmly attached to a

hardwood plank driven into the ground and supported by stakes. The bags, made of

nylon mesh, were designed to be attached to the cage and tied-off around the base of

the branch. A flap, secured on 3-edges with Velcro®, was incorporated in the bags to

allow easy access to the shoots. The bags were designed to keep the larva contained

and protected from predators but still allow light to filter into the cage as seen in

Figure. 4.2(c,d). To keep the leaves from sticking to the bags when wet the branch

was supported inside the cage by means of elastic tape so that there was little if any

contact between the bag and the foliage.

154

(c) (d)

(a) (b)

Figure 4.2 Experimental structures : (a) typical sample tree, (b) cages attached in mid-crown, (c) and (d) cages showing suspended shoots and access flap. The neighbour tree in (b) is typical of those trees rejected because more than 50% of the height of the crown consists of juvenile foliage.

unsuitabletree

(c) (d)

(a) (b)

Figure 4.2 Experimental structures : (a) typical sample tree, (b) cages attached in mid-crown, (c) and (d) cages showing suspended shoots and access flap. The neighbour tree in (b) is typical of those trees rejected because more than 50% of the height of the crown consists of juvenile foliage.

unsuitabletree

155

Cages were set up between the 9th and 20th of December and egg batches collected

from E. regnans plantations in the Florentine Valley were introduced to the treatment

cages on the 24th and 29th of December. This was done by stapling the E. regnans

leaf section with the egg batch to a suitable leaf within the treatment cage (Fig. 4.3a).

At a second level of randomisation, each tree was randomly assigned one of three

batch sizes of 10, 20, or 30 eggs. Feeding was allowed to progress normally

(Fig. 4.3).

The uncaged shoot was protected from leaf beetle browsing by spraying with the

synthetic pyrethroid, cypermethrin (Dominex 100®), if required taking care that there

was no drift of spray onto the cages with eggs and larvae. A backback sprayer was

used with the equivalent rate of 10 g active ingredient ha-1 (Elliott et al., 1992). There

was very little natural browsing damage through the summer and spraying with

cypermethrin was only carried out once in January 1993.

Leaves on the treatment shoots were numbered with permanent black marker pen

near the base of each leaf large enough to be numbered without significantly

affecting the leaf’s food quality. When surviving larvae had finished feeding and

dropped off the shoots, pre-pupae and pupae were collected from the bottom of the

cage and counted (Fig. 4.4) on the 19th and 27th of January. The cages were removed

and treatment and control shoots harvested on the 26th February.

A late summer repeat of the above trial was carried out on a separate set of nearby

trees with cages established and shoots measured between 12th and 18th of February,

egg batches introduced on the 25th of February, pre-pupae and pupae collected on the

12th of April, and shoots harvested on the 12th of May. The difference between this

trial and the earlier trial is that in this trial only 9 trees (i.e. 3 replicates per batch size)

were used. The early and late trials will be denoted by the factor ‘TIME’ with classes

of ’early’ and ‘late’ while the factor ‘TREATMENT’ will denote the control shoots

as well as the shoots with introduced eggs. In this last case these treated shoots will

be denoted ‘batch-size’ treatments.

156

(a) (b)

(c)

Figure 4.3 Browsing damage showing : (a) attached (dead) leaf section used to introduce eggs, (b) leaves eaten down to midrib, and (c) manna produced on leaf margins where feeding has occurred. The leaves in (a) and (b) are tender enough for young larvae to feed while those in (c) are not. Manna produced by the leaf during and after feedin shown in (c).

manna

(a) (b)

(c)

Figure 4.3 Browsing damage showing : (a) attached (dead) leaf section used to introduce eggs, (b) leaves eaten down to midrib, and (c) manna produced on leaf margins where feeding has occurred. The leaves in (a) and (b) are tender enough for young larvae to feed while those in (c) are not. Manna produced by the leaf during and after feedin shown in (c).

manna

157

(a)

(b)

pupa

Pre -pupa

instar IV

Figure 4.4 Recovered pupae, pre-pupae, and final instar larvae (a) in the bottom of a cage and (b) collection of those recovered at one field visit in March.

pupa

(a)

(b)

pupa

Pre -pupa

instar IV

Figure 4.4 Recovered pupae, pre-pupae, and final instar larvae (a) in the bottom of a cage and (b) collection of those recovered at one field visit in March.

pupa

158

Measurements

Before the cages were positioned each leaf on each of the 3 shoot EUs was measured

for length from the base of the leaf (i.e. excluding the petiole) to the tip and for width

at the widest point using a plastic ruler to an accuracy of 1 mm. Last season’s leaves,

where these could be identified, where designated ‘O’ for ‘old’. Buds were

designated as ‘B’, ‘SB’, or ‘TB’ for a naked bud on a branch stem, a bud in the axil

of a leaf, and the terminal naked bud respectively.

All leaves on each harvested shoot were then measured for leaf area using a

T∆ AREA METER® (DELTA-T-DEVICES, Cambridge U.K; accuracy 0.1 cm2). In

addition, for a random sample of shoots, intact leaves were measured for length and

width in the same way as the pre-treatment measurements and recorded along with

the measured individual leaf areas. From the leaf area, length, and width data a

regression model predicting leaf area from the length and width measurements was

developed to allow prediction of leaf area at the pre-treatment measurement.

Temperatures were recorded every 15 minutes from the 8th December 1992 until 12th

May 1993 using a STARLOG Data Logger® (UNIDATA Australian, O'Connor

W.A.) with a temperature thermistor. Unfortunately the data recorded before 19th

March 1993 were unusable. However, daily minimum and maximum temperature

recorded at the same site using max-min thermometers and a thermohygrograph, each

placed in a Stevenson Screen, were obtained from Dr C.Beadle (CSIRO FFP) for the

period 1st August 1992 until 30th March 1993. Using the daily minimum and

maximum temperatures and cubic spline interpolation, as described in Section

3.2.1.1, for the period 1st August 1992 until 18th March 1993, and logged

temperatures for the remaining period to the 12th May, the day-degrees for each of

temperature thresholds 0 to 15oC were calculated from the 1st August to each day in

the period.

Some treatment shoots, particularly for the February treatment, produced large

amounts of manna along the margins of leaves that had been browsed (Fig. 4.3c).

Manna is a saccharine secretion exuded from stems and leaves following injury

159

caused by insects (Steinbauer, 1996). Figures 4.5, 4.6, and 4.7 show the leaves

recovered from three harvested batch-size treatment shoots for TIME=’late’ with

batch sizes of 10, 20, and 30 respectively. These photographs understate the damage

from feeding since leaves that were completely consumed are obviously absent.

4.3.2 RESULTS

Figure 4.8 shows observed and fitted leaf area for the leaves sampled from the

harvested shoots and Table 4.1 gives the parameter estimates for the regression based

on the allometric relationship (von Bertalanffy, 1968, p.64) between individual leaf

area (ILA) (cm2), leaf length (LL) (cm), and width (LW) (cm) given by

( ) ( ) ( )LWLLILA lnlnln 210 β+β+β= (4.9).

Observed leaf areas for harvested shoots and predicted leaf areas at initial

measurement of the shoot were accumulated to give a total for each of the three shoot

EUs for each of the 18 early and 9 late sample trees. Old (‘O’) and intermediate

leaves were excluded from the calculation of total shoot leaf area.

Table 4.1 Leaf area (cm 2) allometric regression parameter estimates, standard errors and fit statistics .

Parameter

0β 1β 2β

Estimate -0.0455 0.8829 1.0475

s.e. (0.0344) (0.0161) (0.0150)

Sample size 744

RMSa 0.01286

%errorb 11.3

R2 0.9797

a Residual mean square on the logarithmic scale b Prediction error as a percentage of leaf area ≅ 100 RMS

Table 4.2 gives the mean percentage of the nominal egg batch sizes recovered as

pupae or pre-pupae for each batch size and time. There was complete failure of some

batches due to the inability to induce feeding past the L1 larval instar stage because

160

(a)

(b)

(c)

Figure 4.5 Dried leaves recovered from the harvested treatment shoot for tree 1 for the late time showing leaves from each of three second order branches (a)-(c). The treatment was a 10 egg batch.

(a)

(b)

(c)

Figure 4.5 Dried leaves recovered from the harvested treatment shoot for tree 1 for the late time showing leaves from each of three second order branches (a)-(c). The treatment was a 10 egg batch.

161

(a)

(b)

(c)

Figure 4.6 Dried leaves recovered from the harvested treatment shoot for tree 4 for the late time showing leaves from each of three second order branches (a)-(c). The treatment was a 20 egg batch.

(a)

(b)

(c)

Figure 4.6 Dried leaves recovered from the harvested treatment shoot for tree 4 for the late time showing leaves from each of three second order branches (a)-(c). The treatment was a 20 egg batch.

162

(a)

(b)

(c)

Figure 4.6 Dried leaves recovered from the harvested treatment shoot for tree 4 for the late time showing leaves from each of three second order branches (a)-(c). The treatment was a 20 egg batch.

(a)

(b)

(c)

Figure 4.6 Dried leaves recovered from the harvested treatment shoot for tree 4 for the late time showing leaves from each of three second order branches (a)-(c). The treatment was a 20 egg batch.

163

-1 0 1 2 3 4 5 6

predicted ln(leaf area)

-1

0

1

2

3

4

5

6

ln(leaf

area)

0 30 60 90 120 150

predicted leaf area (cm2 )

0

30

60

90

120

150

leaf area (cm

2)

Figure 4.8 Observed and fitted values for allometric relationship between leaf area and leaf length and width (a) ln-ln scale (b) natural scale.

(a)

(b)

-1 0 1 2 3 4 5 6

predicted ln(leaf area)

-1

0

1

2

3

4

5

6

ln(leaf

area)

0 30 60 90 120 150

predicted leaf area (cm2 )

0

30

60

90

120

150

leaf area (cm

2)

Figure 4.8 Observed and fitted values for allometric relationship between leaf area and leaf length and width (a) ln-ln scale (b) natural scale.

(a)

(b)

164

of a lack of foliage of sufficiently low toughness for neonate (i.e. freshly hatched)

and older first instar larvae to feed. However, even these failed batches were

observed to damage and partially consume leaf buds. Also, the number of recovered

pre-pupae and pupae is not a completely reliable measure of the number of larvae

successful feeding since mortality or unexplained losses occurred but could not be

quantified due to : (a) the small size of young larvae especially when dead and

desiccated, and (b) the difficulty of keeping an accurate count as the experiments

progressed. The analyses in this section use the nominal batch sizes and thus use

0NN = in model (4.8).

Table 4.2 Number of recovered pupae and pre-pupae b y batch size and

time .

TIME Batch

size1

Reps2

Mean

number

recovered3

Standard

deviation

Range

min,max

Mean percent

Recovered

(s.e.)

Early 10 6 5.67 3.20 1, 9 56.7

20 6 11.50 6.63 0,19 57.5

30 6 17.67 10.41 0,30 58.9

Mean 18 57.7 (7.5)

Late 10 3 5.33 4.51 1,10 53.3

20 3 13.67 6.11 7,19 68.3

30 3 22.33 10.79 10,20 74.4

Mean 9 65.2 (11.3)

Mean 27 60.2 (6.2)

1 Potential number of pupae when feeding by larvae is complete. 2 Number of trees for each batch-size treatment.

3 Number of pre-pupae and pupae collected after completion of

feeding.

4.3.2.1 Response variables

The initial (LAI) and final leaf areas (LAF) for each shoot were obtained (as

described above) and absolute growth, calculated as LAILAFAG −= , used as the

response variable. An alternative response variable, relative growth (RG) defined as

)LAIln()LAFln(RG −= was also constructed. All the analyses reported below

165

were carried out on both response variables but since similar conclusions were drawn

in each case only the results for AG will be reported.

The comparison of growth of treatment and control shoots is given by the contrasts of

the form CT AGAG − where the ‘T’ subscript represents a batch-size treatment shoot

and ‘C’ the control shoot. If the initial leaf areas are the same for both shoots on the

tree [i.e. ( )0tFLAI = ] then this contrast gives ( ) ( )ppCT tFtFAGAG −=− * which is

the response variable in model (4.8). Adjusting for differences in LAI between

matched shoots is a way of reducing non-informative variability in AG. In the

calibration of the process model described later this adjustment is not required since

the treatment shoot is used as its own ‘control’ so by definition LAI is the same for

both ‘shoots’.

4.3.2.2 Individual treatment effects

Before estimating *C from these contrasts, initial analyses to investigate the growth

response for each treatment separately, including controls, are described. In these

analyses means are estimated from the fit of the linear mixed model (LMM) so that

they account for the use of trees as random ‘block effects’. Each treatment is

considered separately while the modelling of treatment contrasts is left to the next

section.

Initial leaf area and control shoot growth

To determine if any effects other than the five treatments have influenced the

response variables, in particular effects due to initial leaf area (LAI) or caging, the

following analyses were carried out.

First, the estimated mean LAI was tested for significant TREATMENT, TIME, or

TREATMENT x TIME effects. Then the variable AG was restricted to the two

control shoots on each tree and tested for TREATMENT, TIME, or

TREATMENT x TIME where TREATMENT in this case excludes the batch-size

treatments and is equivalent to a Control(S) versus Control(C) contrast. These

analyses were carried out using the linear mixed model (LMM) fitted using the

166

GENSTAT (Genstat 5 Committee, 1997) REML directive with fixed effect model

TREATMENT * TIME (which in GENSTAT is expanded to main effects plus

interaction) and random effect of TREE representing the 27 sample trees in the

experiment. These random tree effects are assumed normally, independently, and

identically distributed, NIID(0, 2tσ ), with mean zero and variance 2

tσ ; the between-

tree variance.

Table 4.3 gives the mean LAI for TREATMENT within, and pooled across each

TIME. Similarly, means for the two controls are given for AG. The significant

differences were determined, as recommended by Giesbrecht and Burns (1985), by

comparing differences in means to the standard error of the difference multiplied by

the 95% point of the t-distribution (two-sided test) with degrees of freedom

calculated using Satterthwaite’s approximation (Snedecor and Cochran, 1980, p.97,

325). These approximate degrees of freedom ranged from 30 to 70, so in effect the

t(95%) can be taken as 2. Note also that the standard error of the difference depends

on the particular comparison, whether between batch-size treatments, between batch-

size treatment and a control, or between controls and also whether the comparison is

made within a time, between times, or combined across times. Table 4.4 shows the

Wald tests from GENSTAT’s REML analysis of LAI.

From Tables 4.3 and 4.4 it can be seen that the main difference in LAI was between

early and late shoots with the early shoots having a significantly larger mean. There

was also a significant difference between mean LAI for the two control shoots at the

early treatment with the caged control (C) having a lower mean LAI. This difference

was of opposite sign for the late treatment but was not significant (P>0.1). In the

REML analysis which produced the control means for AG in Table 4.3 (Wald tests

not shown) the TREATMENT x TIME interaction and the corresponding main

effects were all non-significant (P>0.1).

The sprayed control shoots had a greater average leaf area growth than the caged

controls but this difference was not statistically significant (P>0.1) (Table 4.3). From

Table 4.3 it can be seen that, although most of these effects were not statistically

significant, if the two controls are combined then the absolute growth AG is greater

167

for TIME=early. The early shoots had a larger area made up of large leaves that were

at, or near, full expansion compared to the late shoots (Fig 4.9).

Table 4.3 Mean initial leaf area for TREATMENT and TIME and growth response for control treatments and TIME.

TIME TREATMENT Reps Means

LAI (cm2) AG (cm2)

Early T10 9 1010.5ab

(December) T20 9 934.2ab

T30 9 915.4ab

S (sprayed control) 18 1036.7b 431.6a

C (caged control) 18 834.4a 365.2a

Mean 54 956.3A

Mean (controls) 36 398.4A

Late T10 3 439.8a

(February) T20 3 602.0a

T30 3 673.6a

S (sprayed control) 9 525.8a 346.8a

C (caged control) 9 577.1a 166.8a

Mean 27 563.7B

Mean (controls) 18 256.8A

Pooled T10 18 821.3ab

T20 18 823.5ab

T30 18 833.8ab

S (sprayed control) 27 866.4b 403.3a

C (caged control) 27 748.7a 299.1a

ab TREATMENT means with the same superscript are not significant at the 5% level with comparisons only made within, or combined across, TIME.

AB TIME means with the same superscript are not significant at the 5% level.

The main effect of larval browsing is on the growth of rapidly expanding leaves so

although the mean initial leaf area per shoot was significantly lower at the late

treatment this was compensated by the greater proportion of total shoot leaf area that

could rapidly expand.

168

0 30 60 90 120 150

Initial (predicted) leaf area (cm2)

0

30

60

90

120

150Frequency

0 30 60 90 120 150

Initial (predicted) leaf area (cm2)

0

40

80

120

160

200

240

Frequency

(a)

(b)

Figure 4.9 Frequency histogram for individual leaf area at initial measurement for all shoots combined at each of the (a) early (b) latetreatments.

0 30 60 90 120 150

Initial (predicted) leaf area (cm2)

0

30

60

90

120

150Frequency

0 30 60 90 120 150

Initial (predicted) leaf area (cm2)

0

40

80

120

160

200

240

Frequency

(a)

(b)

Figure 4.9 Frequency histogram for individual leaf area at initial measurement for all shoots combined at each of the (a) early (b) latetreatments.

169

Table 4.4 Wald tests and their statistical signific ance based on

REML analysis of TREATMENT,TIME, and TREATMENT x TI ME effects for

LAI, LAF, and AG.

Factor Df LAI LAF AG

TREATMENT 4 11.6* 21.7** 27.6**

TIME 1 21.6** 11.5** 1.2ns

TREATMENT x TIME 4 16.4** 1.8ns 0.9ns

Between-tree

variance σ ts (s.e.)

25 35216

(11725)

104934

(39250)

60245

(23327)

Between-shoot

variance σ ss (s.e.)

46 16803

(3503)

89448

(18644)

58422

(12176)

** P<0.01 * P<0.05 ns P>0.10

It is unclear from Table 4.3 if caging has had a negative effect on growth given the

larger LAI for the sprayed control (S) at the early treatment. When early and late

TIMES were pooled there was no significant difference between the two controls

(Table 4.3). There may be a cage effect which causes a reduction in shoot growth due

to shading but such an effect was not consistently detected either across times or

growth variables. The significantly larger average LAI for the sprayed control shoots

at the early treatment did not result in significantly higher growth rates (Table 4.3).

Final leaf area and growth of batch-size treatment and control shoots

Table 4.4 also gives Wald tests from the REML analyses of LAF and AG for

TREATMENT (including the batch-size treatments) and TIME main effects and their

interaction. For LAF both main effects were significant but the interaction was not

significant. Only the TREATMENT main effect was significant for AG.

For the following analyses the two times will be pooled to emphasize the batch-size

treatments. This pooling can be justified to a degree by the non-significant

TREATMENT x TIME interaction for AG and the need to increase replication due to

the variability in growth response for similarly treated shoots. However, given the

170

difference in shoot phenology between early and late shoots it would have been

preferable to treat early and late shoots separately. This was not possible here because

of the small number of replicates, especially for TIME=’late’. In Section 4.4 the

difference in phenology between early and late shoots is explicitly accounted for.

Figure 4.10 shows box and whisker plots and mean values with standard error bars

for AG for each treatment with trees from both treatments pooled. The standard errors

are based on the between-tree residual variance obtained separately for each

treatment (i.e. the pooled residual variance was not used) and 27 replicates for each

of the controls and 9 replicates for each of the three batch-size treatments. The trends

are largely as expected with decreasing growth rate with increasing batch size.

Variances about the means, reflected in the standard error bars and box and whisker

plots, are large.

4.3.2.3 Treatment contrasts

Since the experimental design involves matched shoots within trees, two control

shoots per tree, and a different sample of trees for each batch-size treatment, there are

three possible methods of estimating the differences between the controls and each

batch-size treatment. Two of these methods use a weighted combination of within-

tree and between-tree contrasts with only one of the control shoots used to calculate

the contrast, the natural choice being the caged-control (C). The information in the

sprayed (S) control shoot is therefore not exploited. However, a third method can be

used which does exploit this information.

To understand the difference between the three methods the following notation is

required. Denote the response variable, AG, for each treatment as variables kTz for

tree k and corresponding batch size T=10, 20, 30, Sz for the sprayed control, and Cz

for caged control so that the 81 length response vector z is the catenation given by

( )CSTT z,z,z

k=z . Also let ( )CST z,z,z

k represent the means over all trees in which the

treatment occurs (i.e. 9 trees for each of the batch-size treatments and 27 trees each

171

S C 10 20 30

Treatment

-5

0

5

10

15

20

Absolute grow

th (LA

F-LAI) (cm

2x 100)

S C 10 20 30

Treatment

-1

0

1

2

3

4

5

Absolute grow

th (LA

F-LAI) (cm

2 x 100)

Figure 4.10 Absolute growth (AG) of treatment and control shoots showing (a) box and whisker plots and (b) means and standard error bars. S=sprayed control, C=caged control.

(a)

(b)

median

outlier

Inter-

quartile

range

(IQR)

Largest data value

within 1.5 x IQR

S C 10 20 30

Treatment

-5

0

5

10

15

20

Absolute grow

th (LA

F-LAI) (cm

2x 100)

S C 10 20 30

Treatment

-1

0

1

2

3

4

5

Absolute grow

th (LA

F-LAI) (cm

2 x 100)

Figure 4.10 Absolute growth (AG) of treatment and control shoots showing (a) box and whisker plots and (b) means and standard error bars. S=sprayed control, C=caged control.

(a)

(b)

median

outlier

Inter-

quartile

range

(IQR)

Largest data value

within 1.5 x IQR

172

for the two control treatments). The treatment contrasts are then simply CS zz − for

the sprayed versus caged control contrast and )30,20,10(, =− kCT Tzzk

for batch size

versus the caged control contrasts. To simplify the notation for the remainder the

subscript k representing the particular tree is not explicit but inferred where

necessary. Now let )10( =TCz represent the mean of caged control shoots for trees

which have been allocated a batch size of 10, and define means similarly for the other

two batch sizes. Also let )10( ≠TCz represent the mean of caged control shoots for trees

which have not been allocated a batch size of 10 and define means similarly for the

other two batch sizes.

Let the contrasts of interest be ( )543 ,, α−α−α− given by

ααααα

µµ µ

µ µµ µµ µ

1

2

3

4

5

10

20

30

=−

−−−

=

=

=

C

C S

C T

C T

C T

where the µ ’s are the expected values of the treatment means. The parameters

( )21,αα are not of direct interest but are required to express the model for the

response variable, z, as a linear mixed model.

The first two methods of estimating the contrasts ( )543 ,, α−α−α− are simply

differently weighted combinations of the within-tree and between tree contrasts.

These can be expressed for the 10, 20, and 30 batch-size treatments respectively, as

( ) ( )( )

( ) ( )( )

( ) ( )( ) .1ˆ

1ˆ

1ˆ

)30(30)30(305

)20(20)20(204

)10(10)10(103

≠===

≠===

≠===

−−+−=α−

−−+−=α−

−−+−=α−

TCTTCT

TCTTCT

TCTTCT

zzwzzw

zzwzzw

zzwzzw

173

The first and simplest method is to only use the within-tree contrasts obtained by

setting w=1, so that only the caged control shoots for the same 9 trees as the batch-

size treatment are used to calculate the contrast. The other method is that derived

from the simple, unbalanced, one-way ANOVA and is obtained by setting 2718=w . In

this case the ANOVA method is simply the mean of the batch-size treatment minus

the caged-control mean of all 27 sample trees. The means used in these contrasts are

those used in Fig. 4.10(b).

The third method corresponds to estimated the means for the unbalanced ANOVA

incorporating the ‘block structure’ (i.e. ‘blocks’=trees) of the experiment obtained

using GENSTAT’s REML directive. These contrasts (4.10) correspond to

generalised least squares (GLS) estimates using a linear mixed model formulation for

the experimental design. The one-way ANOVA estimates correspond to ordinary

least squares (OLS) estimates from the linear model. The three sets of estimated

contrasts are denoted ‘within-tree’, OLS, and GLS respectively.

Explicitly, the GLS method calculates the contrasts as

( )

+−

+ρ−

ρ−−=α− === 22ˆ1

ˆ2~ )10()10(103

SCTSTCCT

zzzzzz

( )

+−

+ρ−

ρ−−=α− === 22ˆ1

ˆ2~ )20()20(204

SCTSTCCT

zzzzzz (4.10)

( )

+−

+ρ−

ρ−−=α− === 22ˆ1

ˆ2~ )30()30(305

SCTSTCCT

zzzzzz

where 22

2

ˆ3ˆ

ˆˆ

t

t

σ+σσ=ρ , and 2ˆ tσ and 2σ are the estimated ‘between-tree’ and ‘within-

tree’ variances, respectively.

The GLS estimate of α2 , 2~α , is shown in Appendix A6 to be identical to the OLS

estimate, and this value is also equivalent to the estimated within-tree contrast. This

makes intuitive sense since both controls are present on all sample trees. The

estimated treatment contrasts (4.10) can be seen to be the OLS estimates minus an

174

adjustment. This adjustment is a scaled difference of the average of both the controls

on the trees to which the particular batch-size treatment was applied and the average

of all control shoots. The scaling factor is ( ) 1ˆ1ˆ2 −ρ−ρ which can take values between

0 and 1 depending on the relative magnitude of 2σ and 2ˆ tσ . If 2σ is very large

relative to 2ˆ tσ then ρ is close to zero so than the adjustment to the simple mean

difference or OLS estimate is small. If 2ˆ tσ is very large relative to 2σ then ρ is close

to 1/3 so that the adjustment to the OLS estimate is the full value of the mean of

controls for trees with the particular batch-size treatment minus the overall control

mean. If ρ is zero then the OLS and GLS estimates are identical. This adjustment

therefore incorporates the extra information in both the control shoots on trees that

do not have the particular batch-size treatment in proportion to the magnitude of 2ˆ tσ .

If the controls show that the trees allocated to this treatment have grown more than

the average of all trees then the growth loss for this treatment is decreased compared

to the OLS estimate. The reverse occurs when these controls have grown less than

the average.

This adjustment is similar to that obtained using ‘recovery of inter-block’

information in incomplete block designs (Cochran and Cox, 1957, p.382). The

adjustment in (4.10) is not identical to that in the incomplete block design since two

of the ‘treatments’, that is the caged and sprayed controls, occur in every ‘incomplete

block’. Note that (4.10) gives unbiased estimates of the contrasts ( )543 ,, α−α−α−

irrespective of whether or not there is a real effect of caging since if

( ) ( ) ω+= CS zEzE , where 0≠ω is an average ‘cage effect’, then ω is eliminated

from (4.10) because ( ) ( )SkTS zEzE == )( and ( ) ( )CkTC zEzE == )( .

Table 4.5 gives the estimated treatment means and these three sets of estimated

contrasts and Appendix A6 formally derives the OLS and GLS estimates.

Bartlett’s test of homogeneity of variances (Neter and Wasserman, 1974, p.509) for

the within-tree variance was calculated using the within-tree contrasts since these

contrasts are subject to only within-tree variance. The hypothesis of homogeneity of

175

variances was accepted (P>0.10). The means and standard errors for the contrast

estimates (4.10) are given in Table 4.5 where these standard errors are unbiased

estimates given the assumed LMM is correct (Appendix A6). The standard errors for

the OLS estimates, as mentioned earlier, are biased. The standard errors for the

within-tree-only contrasts in Table 4.5 are smaller than those for the GLS estimates

because they do not include the variance of the caged versus sprayed control contrast

and are based on within-tree variance alone.

Table 4.5 Estimated treatment mean growth response ( AG) and batch

size versus caged control contrast using each of AN OVA, ANOVA/REML,

and Within-tree method of analysis.

Method Mean or Treatment Contrast (cm2)

(s.e. contrast)

C S T10 T20 T30

Reps 27 27 9 9 9

ANOVA

(OLS)

Mean 299 403 191

36 -26

Contrast 104

(93)

-108

(131)

-263

(131)

-325

(131) ANOVA/

REML

Mean 299 403 97 66 38

(GLS) Contrast 104

(64)

-202

(98)

-233

(98)

-261

(98) Within

-tree

-234

(93)

-196

(93)

-265

(93)

The three methods of estimation give quite different results as seen in Table 4.5. For

example there was a greater growth loss for 10-batch treatment compared to the 20

for ‘within-tree’ estimation while this did not occur for the other two methods. The

GLS estimates are used for estimating the regression of growth response on nominal

batch size given next since these estimates exploit all the relevant information in the

experimental data.

176

Figure 4.11 shows the GLS estimated contrasts ( )5432~,~,~,~ α−α−α−α− , corresponding

to nominal batch sizes of (0,10,20,30) respectively, and their 95% LSD confidence

intervals. The degrees of freedom for the t-statistic used to calculate these LSD

intervals was estimated using Satterthwaite’s approximation (Snedecor and Cochran,

1980, p.97, 325).

4.3.2.4 Response surface models

To be able to interpolate the predicted response to egg batch sizes between 10 and 30,

or extrapolate outside this range two forms of regression model were fitted to the

means given in Fig 4.11 where both models logically giving a zero response for zero

batch size. These models were a linear model

0* Ny τ−= (4.11)

and nonlinear model

-5

-4

-3

-2

-1

0

1

2

3

Absolute grow

th difference (cm

2 x100)

0 10 20 30 40

Batch size

Figure 4.11 Mean difference of treatment versus control(0=sprayed control) versus batch size for absolute growth(AG) with 95% confidence bars based on GLS (REML)estimates of means and standard errors and approximatedegrees of freedom for the t-statistic. Fitted linear andnonlinear response surface models shown. Estimate ofELAL for the linear model shown.

36.1030/8.310ˆ ==τ

177

1)exp( 0* +τ−= βNy (4.12)

where 0N is the nominal batch size, τ and β are regression parameters,

( )543* ~,~,~ α−α−α−=y is the estimated growth loss given by (4.10) with 0N taking

corresponding values of 0N =(10,20,30). From models (4.8) and (4.11), *C=τ , the

mean effective leaf area loss per larva (ELAL) defined for 0NN = , is less than the

value obtained if the values for pNN = (Table 4.2) were used in (4.11).

Model (4.12) was transformed to linearity and fitted as a simple linear regression

given by

( )[ ]{ } ( ) ( )0* lnln1lnln Ny β+τ=−− .

The least squares estimate of τ in model (4.11) and τ and β in model (4.12) are

given in Table 4.6. The fitted relationships are shown in Fig. 4.11.

Note that the standard errors in Table 4.6 are based on the variance of the contrasts,

*y obtained from REML (Table 4.5) since the usual error variance has only 2 degrees

of freedom for model (4.11) and single degree of freedom for model (4.12). An

approximate 95% confidence interval for τ = *C in (4.11) is 4 to 16.7 cm2 larva-1.

Table 4.6 Fitted linear and nonlinear models to gro wth variable

contrasts ( )543~,~,~ α−α−α− for batch sizes of 10, 20, and 30 eggs

Parameter estimate (s.e.)

Model (4.11) Model (4.12)

τ = *C

(cm2larva-1)

τ

( )τln

β

10.36 (3.18) 4.8222 0.0421 (0.0993)

1.5732 (0.2970)

178

4.4 A PROCESS/SIMULATION MODEL

4.4.1 Introduction

Model (4.7) expresses the processes of (a) leaf expansion, (b) larval feeding, and (c)

their interaction that determine the impact of browsing on leaf growth, (and shoot

growth after aggregation to the shoot level) in a completely general way. However,

modelling interaction (c) is not trivial and, as mentioned earlier, requires data to

quantify the between and within-leaf spatial feeding behaviour and the within-leaf

spatial pattern of expansion.

These data were not available to this study so a simpler approach was adopted. This

involved empirically determining the value of *C for the sample of shoots and larval

cohorts used in the caged-shoot trial described above. This estimation differed from

that obtained for model (4.7) in that some of the processes in (a), (b), and (c) were

modelled without directly incorporating consumption rate data or models (Baker et

al., 1999). Explicitly, disbudding behaviour, feeding mortality [i.e. pNN = in model

(4.8)], and leaf expansion were included in the modelling/simulation procedure.

Using the data from the caged-shoot experiment, *C in model (4.8) was estimated

using a profile-log likelihood by predicting the final leaf area, LAF, of the batch-size

treatment shoots in the absence of feeding and comparing this to the observed LAF

[i.e. corresponding to F and ( )NF * in model (4.8) respectively].

An outline of the process model

The process model employed can be summarised in the first three steps given below

with the final two steps describing the use of the model to simulate browsing on all

the shoots in the caged-shoot experiment given the initial measurements of leaf

attributes (i.e. before feeding began on treated shoots).

1. Predict growth of shoots in the absence of browsing by aggregating the predicted

growth of individual leaves using initial individual leaf areas and the models

described in Chapter 3. Re-calibration of some of the parameters in these models

was carried out using the observed growth of the control shoots.

179

2. Estimate leaf area loss of existing leaves per surviving larva, as the total of both

consumption and potential loss as κ== *CELAL , (i.e. total ‘apparent

defoliation’ is given by *CN p ) using the observed and predicted growth of

treatment shoots where predicted growth is calculated both with and without

larval browsing.

3. Incorporate the effect of disbudding as the loss of newly recruited leaves which is

assumed to occur when there are at least 5 neonate larvae present. Therefore, for

practical purposes a minimum population size of 5 eggs per shoot was assumed.

4. Apply the models in (1) and ELAL in (2) in simulations using the initial state of

all 81 shoots in the caged-shoot experiment for a range of population sizes

ranging from 5 to 50 eggs per shoot.

5. Calculate average growth impacts for this sample of 81 shoots.

Note that ELAL (= *C ) has been denoted above by the parameter, κ , to distinguish it

from the estimate, τ , of ELAL in model (4.11) which used nominal batch sizes (i.e.

total ‘apparent defoliation’ given by *0CN ).

Figure 4.12 summarises the simulation model used to carry out Steps (1) to (5) as a

flowchart with description of the individual simulation model components given in

detail below.

4.4.2 Process/simulation model components and validation using Gould’s Block

caged-shoot experiment

4.4.2.1 Predicting the final leaf area of control shoots using leaf expansion models

Leaves existing at initial measurement

Each leaf, other than ‘O’ leaves, on each of the 54 control shoots was grown to the

harvest date using the initial leaf area as estimated by (4.9) from the initial, pre-

treatment (or establishment) measurements of leaf length and width and accumulated

day-degrees using the following steps:

C1) Exclude previous season’s (i.e. old, ‘O’) leaves.

180

Predict leaf area at harvest (steps C3 to C7)

At establishmentExclude old ('O') leaves (step C1)Determine largest individual leaf area (step C2)

Select shoot i

Select leaf j

Sum leafareas for

shoot

Predict area of leaf pair at

harvest ( steps C4 to C7)

Sum leafareas for

shoot

Predict totalarea of new

season's leaves at harvest for shoot i

(Step C9 or T3)

Grow leaves and total shoot leaf area using steps C1 to C7

(step T1)

Using batch size, proportion surviving,

and ELAL predict loss of leaf area

(step T2)

Assume no recruitedleaves due to

disbuddingso set additional leaf

area to zero(step T3a)

Subtract from control leaf area

(step T3b)

Recruit new leaf pair

k(Step C8)

Figure 4.12 Flowchart of a process/simulation model of the impact ofbrowsing by C. bimaculata larvae on E. nitens shoot growth. ELAL is the 'effective leaf area loss per larva'.

j=j+1

k=k+1

i=i+1

Growth without larval feeding(control shoots)

Growth with larval feeding(treatment shoots)

181

C2) Determine the largest area for an individual leaf for the shoot, Lmax, which will

be assumed to be for a fully expanded leaf (see Section 3.2.2).

C3) For each leaf estimate the time of leaf initiation x6 in terms of day-degrees

from the 1st August with a 6oC lower threshold temperature where

{ }[ ]( )x T c l L c be e6 61 11= + − − −− −

, maxexp ln ln / ,

le is the leaf area at initial measurement, predicted using length and width

measurements and (4.9), 6,eT (=DD[6]) is the day-degrees from 1st of August to

the establishment date, and parameters b and c are given by b = −20364. and

c=2.2774. This estimate of x6 is based on (3.5) (Section 3.3.1) but note that

there the estimates of b and c in Table 3.4 are for the optimum threshold of

3oC. The 6oC threshold was used here so that time of leaf initiation was

compatible with the time scale used to predict maximum FELA [see (3.1) in

Section 3.2.2]. The estimates of b and c used here were also obtained by the

RC/LMM estimation procedure (Section 3.2.3).

C4) Scale x6 using a separate ‘shrinkage’ parameter for each of the early and late

treatments but common to all shoots at the particular time. The estimation of

these parameters will be describe below but they operate by shrinking x6

towards the ‘mean’ value of x6 based on the Weibull ‘distribution’ described

by (3.1) to give *6x

x x x x6 6 6 6* ( )= + −λ

where

)1( 106

−α+Γθ+= Xx ,

00 =X , estimates of θ and α are given in Table 3.2, and λ is the shrinkage

parameter. An alternative was to replace 6x in the above by the time, also

calculated in DD[6] units, to peak proportion of maximum FELA (see Fig. 3.6)

which corresponds to the mode of the Weibull distribution. This approach gave

considerably poorer predictions, when combined with the rest of the algorithm,

than using the mean as was found in Section 3.2.3.

182

C5) Predict the fully expanded leaf area (FELA), L, for each leaf using (3.1) with

x6* replacing x.

C6) Predict day-degrees from 1st August to leaf initiation using a 3oC threshold as

{ }[ ]( )x T c l L c be e3 31 11= + − − −− −

, exp ln ln /

where Te,3 is the day-degrees with 3oC threshold, DD[3], from 1st of August to

the establishment date and parameter estimates for b and c given in Table 3.4

as b = −30003. and c=2.3045.

C7) Using (3.4) predict individual leaf area at the harvest date, lh , as

{ }[ ]l L T x bh hc c= − − − ′1 3 3exp ( ) /,

where ( ) bcb 1ln −−=′ . If the harvest leaf area was predicted to be less than that

at establishment, l lh e< , then lh was set equal to le .

Leaves recruited during the period between initial measurement and harvest

C8) Recruit and grow new leaves. The number of recruited leaves per shoot was

calculated as the difference between final number of leaves harvested and the

number of leaves measured on the control shoots for the particular tree at the

initial measurement. This number was averaged over the two control shoots for

each tree, divided by two, and finally rounded to the nearest integer to give an

estimate of the number of recruited leave pairs, n. This reflects the way in

which new leaves are recruited from the naked bud in pairs (Jacobs, 1955,

p.21). This estimate of recruitment of new leaf pairs is subject to measurement

error since recruitment is inferred from the difference in the final number of

leaves compared to the initial number of leaves on each control shoot.

However, there were some control shoots for which this difference was

negative but generally these negative values were small with -1 being a

common value and the largest negative value being -7. These can be explained

as small leaves that were naturally shed during the above period. For the caged

control such small, shed leaves would have desiccated and so be

indistinguishable from the general frass in the bottom of the cage control. Also

there could have been unintentional losses of leaves at harvest. These negative

values were reset to zero. If shed leaves were mostly newly recruited then the

above estimate of recruitment can be considered the net gain in new leaves so

183

that the contribution these leaves make to the predicted leaf area at harvest

should be a realistic value. Note that at harvest, leaf area due to newly recruited

leaves cannot be determined separately to the leaf area of leaves existing at

initial measurement. The number of day-degrees with threshold 3oC between

establishment and harvest, T Th e, ,3 3− , was divided by n to give the average

interval between recruitment of new leaf pairs. This process was repeated for

the 6oC threshold. Therefore the time of initiation of each simulated leaf pair,

in terms of day-degrees from 1st August for each of thresholds 3 and 6oC was

known so that steps (C4) to (C7) could then be repeated for these new leaves.

Predicted total leaf area for the shoot at harvest

C9) The predicted total leaf area for the shoot at harvest (excluding ‘O’ leaves)

could then be calculated as the sum of ‘grown on’ leaf areas for leaves existing

at establishment plus twice the sum of ‘grown on’ leaf areas for leaf pairs

recruited between establishment and harvest. This predicted total leaf area was

then compared with the actual leaf area at harvest.

Calibration of the simulation algorithm for control shoot growth

To predict growth in leaf area for control shoot leaves the above simulation algorithm

was calibrated by estimating the ‘shrinkage’ parameter λ in step (C4). It is clear

from Section 3.2.2 that to predict the growth of leaves accurately, good estimates of

FELA are required. Unfortunately, the observed values of FELA were predicted with

poor precision as seen in Fig. 3.6. In addition, the specification of the starting date for

day-degree accumulation as input to (3.1) is somewhat arbitrary but reasonable since

it occurs within the winter period when growth is at a minimum. However, by using a

day-degree scale with lower development threshold and starting day-degree

accumulations from sometime in the winter dormancy period allows a greater

generality in the use of (3.1) than simply using Julian days for the time scale. Even

so, with temperatures exceeding the 6oC threshold for some of this period then

accumulating day-degrees from different dates in this winter period will give

different values for DD[6]. The underlying problem is the unknown time of onset of

the physiological processes which initiate leaf development at both the Esperance

sites in 1985 and the Gould’s Block site in 1992.

184

In an attempt to overcome this problem (3.1) was calibrated to the Gould’s Block

experiment by estimating a ‘shrinkage’ parameter λ for the day-degree time scale.

For this calibration and to simplify the calculation of day-degree accumulations

between the various dates in the above algorithm, X 0 in step (C4) was set to zero so

that all day-degree accumulations start from 1st August.

The calibration of the growth prediction algorithm for control shoots used a profile

log-likelihood for the unknown λ in step (C4). This log-likelihood was calculated

assuming the sum of squares, over the control shoots, of the residuals for relative

growth rate (RG) for given λ , RSS( λ ), is distributed as a scaled chi square statistic

with single degree of freedom, 21

2χσ where the scale parameter 2σ is the variance of

the residuals This approach was used at the individual leaf-level in Section 3.2 to

adjust the leaf expansion model. Since the initial leaf area (LAI) for the shoot used in

to calculate RG is the observed LAI then

{ } { }[ ]RSS LAF LAFC S( ) ln ln ɵ ( ),λ λ= −∑2.

Using a grid of values for λ the profile likelihood was calculated separately for each

of the early and late treatments by calculating RSS( ) /λ σ2 using the 36 control

shoots in the early treatment and then separately for the 18 control shoots at the late

treatment. The value of λ which gives the smallest value of 2/)( σλRSS is the

maximum profile likelihood estimate (MPLE), λ . The estimate ofσ2 is

RSS E( ɵ ) /λ 35 for the early treatment, where ɵλ E is the MLPE estimate, and similarly

for by 17/)ˆ( LRSS λ for the late treatment. For the early treatment the MLPE estimate

was ɵ .λ E = 019 while for the late treatment as ɵ .λ L = 0 28. These estimates are similar

to that obtained in Section 3.2 of 0.2. Figure 4.13 shows the profile log-likelihood

and approximate 95% support intervals based on a 21χ .

To compare predictions to actual total shoot leaf areas, measured leaf area at harvest

LAF can be compared to )ˆ(ˆ λFAL . However, Fig. 4.14 shows that a large proportion

185

0 0.1 0.2 0.3 0.4

0

4

8

12

16

20

Shrinkage factor

-2 x profile log-likelihood

Figure 4.13 Profile log-likelihood for shrinkage factor for early (solid line) and late (hashed line) treatments with approximate 95% confidence intervals shown with the offset for clarity and to reflect the smaller sample size for the late treatment.

95% confidence

intervals

0 3 6 9 12 15 18

Initial leaf area (LAI) (cm2 x 100)

0

10

20

30

40

Final leaf area (LAF) (cm

2 x 100)

Figure 4.14 Final versus initial total leaf area for control shoots for early (+) and late ( ) treatments with 1:1 line shown.

0 0.1 0.2 0.3 0.4

0

4

8

12

16

20

Shrinkage factor

-2 x profile log-likelihood

Figure 4.13 Profile log-likelihood for shrinkage factor for early (solid line) and late (hashed line) treatments with approximate 95% confidence intervals shown with the offset for clarity and to reflect the smaller sample size for the late treatment.

95% confidence

intervals

0 3 6 9 12 15 18

Initial leaf area (LAI) (cm2 x 100)

0

10

20

30

40

Final leaf area (LAF) (cm

2 x 100)

Figure 4.14 Final versus initial total leaf area for control shoots for early (+) and late ( ) treatments with 1:1 line shown.

186

of LAF is made up by LAI so that a more informative comparison of fit is that based

on predicted growth in leaf area, that is by comparing relative growth

( ) ( )LAILAFRG lnln −= to { } ( )LAIFALRG ln)ˆ(ˆln)ˆ( −λ=λ (Fig. 4.15a) or

alternatively absolute growth LAILAFAG −= to LAIFALAG −λ=λ )ˆ(ˆ)ˆ(

(Fig. 4.15b). The predictions given by )ˆ(ˆ λFAL were obtained using the ML

estimates ɵλ E and ɵλ L for early and late treatments respectively. The regression line,

fitted through the origin, of observed growth on predicted growth is shown in each of

Figs. 4.15(a) and (b).

Figure 4.15 shows that the algorithm gives unbiased and reasonably precise

predictions of the growth in total leaf area for the control shoots.

4.3.2.2 Predicting final leaf area of batch-size treatment shoots using leaf

expansion models, larval survival, and effective leaf area loss per larva

The next stage was to model the impact of larval browsing on shoot growth. This

model is calibrated using the 27 treated shoots with 9 trees of each nominal batch

size. The steps involved were:

T1) Grow the treated shoots from initial measurement of leaves to the harvest date

assuming no losses due to larval browsing using the same steps, (C1) to (C9),

used to grow the control shoots.

T2) Predict the ‘effective’ number of larvae feeding on the leaves and buds using

one of the following two methods

a) Simply use the recorded number of larvae, pre-pupae, or pupae recovered

for the particular shoot after the finish of feeding when the larvae drop to

the bottom of the cage summarised in Table 4.2.

b) (i) Assume all eggs in the batch hatch, (ii) the total area of leaves which

have a toughness below 35 mg cm-2 at initial measurement is calculated

where leaf toughness is predicted from leaf area and predicted leaf age,

(iii) the leaf area calculated in (ii) is divided by the leaf area of 0.244 cm2

larva-1 required for neonate larvae to progress to L2 stage (Baker et al.,

1999) and the lesser of this figure and the nominal batch size is taken to

be the number of neonate larvae progressing to L2 stage, (iv) all neonate

187

larvae which progress to L2 stage are assumed to survive to the

completion of feeding.

T3) Estimate the total shoot leaf area at harvest as that obtained from step (T1)

minus (a) the leaf area attributed to newly recruited leaves in step (C8) (i.e.

assumed to have been removed at the bud stage) and (b) the number of larvae

completing development, pN , multiplied by ELAL denoted by the parameter

*C=κ .

ELAL is the leaf area that is lost due to larval feeding on existing leaves including (i)

the leaf area actually consumed by a larva plus (ii) the potential leaf area growth

which is the increase in leaf area that would have occurred if there had been no larvae

feeding (i.e. the leaf area from expansion forgone by the shoot due to the

consumption of actively expanding leaves). ELAL ( *C= ) was given earlier by

equation (4.8). However, the loss of leaf area expressed in ELAL is attributed to those

larvae which survive to complete development to prepupal stage (i.e. total apparent

defoliation is given by *CN p where κ=*C ).

The complication of potential leaf area loss due to disbudding was not explicitly

incorporated in the model (4.8). Here, the potential leaf area loss due to disbudding in

(ii) is incorporated in the process model as additional to the growth loss expressed by

*CN p . Disbudding is assumed to depend on larvae being present, rather than the

actual number of larvae feeding, the natural recruitment rate and growth rate of new

leaves. Therefore it is assumed that all treatment shoots are completely disbudded

(buds damaged or removed by larvae) irrespective of the number of surviving larvae

(i.e. even for failed batches where all larvae died during the L1 stage it is assumed

that the larvae disbudded the shoot before dying). This assumption is simplistic but

reasonably realistic based on direct observation of treatment shoots that consumption

of buds or browsing at their base, which results in the death of the bud, can be

achieved by only a few L1 larvae.

188

Figure 4.15 Comparison of observed and predicted (a) relative, and (b) absolute growth for early (+) and late ( ) treatments using control shoot total leaf area excluding ‘O’ leaves. The solid line is the fitted regression while the dotted is the 1:1 line. R 2 calculated using the total sum of squares unadjusted for the mean.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Predicted log(LAF/LAI)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Observed log(LAF/LAI)

0 4 8 12 16

Predicted LAF - LAI (cm2 x 100)

0

4

8

12

16

20

24

Observed LA

F -LA

I (cm

2x 100)

R 2=74.8%

R 2=78.6%

(b)

(a)

Figure 4.15 Comparison of observed and predicted (a) relative, and (b) absolute growth for early (+) and late ( ) treatments using control shoot total leaf area excluding ‘O’ leaves. The solid line is the fitted regression while the dotted is the 1:1 line. R 2 calculated using the total sum of squares unadjusted for the mean.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Predicted log(LAF/LAI)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Observed log(LAF/LAI)

0 4 8 12 16

Predicted LAF - LAI (cm2 x 100)

0

4

8

12

16

20

24

Observed LA

F -LA

I (cm

2x 100)

R 2=74.8%

R 2=78.6%

(b)

(a)

189

Prediction of leaf toughness and its impact on survival of neonate larvae

The critical leaf toughness for survival of neonate larvae is based on the work of

B. Howlett who provided the author with data from feeding studies of C. bimaculata

on a number of eucalypt species including E. nitens. Howlett recorded the survival of

neonate larvae fed E. nitens leaves with a range of leaf toughness from 22 to

42 mg cm-2 where leaf toughness was measured by a penetrometer. The penetrometer

value is the weight required to puncture the leaf when applied to a needle of given

cross sectional area and is recorded in units of mg per cm2. A probit model was fitted

to Howlett’s data on survival as a function of leaf toughness. However, it was

difficult to implement this model here since given a selection of leaves of leaf

toughness low enough for efficient feeding then larvae will obviously select such

leaves. Also, as survival dropped sharply from 100% at leaf toughness of 33 mg cm-2

to 0% at 37 mg cm-2 it was considered sufficiently accurate here to assume 100%

survival for a leaf toughness below 35 mg cm-2 and 0% survival above this value.

Since the error in predictions of leaf toughness obtained from the model outlined

below are much larger than this 33 to 37 mg cm-2 range it would be unreasonable to

try and predict intermediate values of survival based on predictions of leaf toughness.

A model to predict leaf toughness at initial measurement of the leaves on each shoot

was developed from data provided by B.Howlett. Howlett’s data involved

measurement of leaf toughness using the above penetrometer for samples of E. nitens

leaves at two sites in central Tasmania over a 5 month period from early October

1996 to early March 1997. This gave data on leaf toughness over the leaf

development period from soon after leaf recruitment when leaves were of measurable

size to well after full expansion. The model predicted penetrometer value as a

function of days from the estimated date of leaf set and leaf area as a proportion of

the FELA. For Howlett’s data the FELA of each leaf modelled was known from

measurement but in applying the model here FELA was predicted (Step C5). This

model is not described here since it was not found useful in Step T2 in predicting

mortality due to the inability of L1 larvae to feed due to leaf toughness above

35 mg cm-2. The reasons for this are explained later. The model may be of some

interest in studying the progression of leaf toughening but since it is an empirical

190

model that does not directly account for the effect of temperature on the process of

toughening it was decided not to report it here.

Calibration of the simulation algorithm for treatment shoot growth

The calibration of the growth prediction algorithm for the treatment shoots was

carried out in a similar way to that for the control shoots using a profile log-

likelihood to estimate κ in step (T3). This log-likelihood was calculated in the same

way as that described for estimating λ from the final total leaf area for the control

shoots. As for the control shoots, since the initial leaf area (LAI) for the shoot used in

the prediction is the observed LAI then

{ } { }[ ]RSS LAF LAFT( ) ln ln ɵ ( ), ,κ κ= −=∑ 10 20 30

2.

Using a grid of values for κ , the profile log-likelihood was calculated separately for

each of the early and late treatments by calculating RSS( ) /κ σ2 using the 18

treatment shoots in the early treatment and then separately for the 9 treatment shoots

at the late treatment. The value of κ that gives the smallest value of RSS( ) /κ σ2 is

the maximum profile likelihood estimate (MPLE), κ . The estimate of σ2 is

RSS E( ɵ ) /κ 17 for the early treatment for MPLE ɵκ E and RSS L( ɵ ) /κ 8 for the late

treatment for MPLE ɵκ L . Combining both early and late treatments, κ was estimated

as 12.6 cm2 larva-1. However, due to the small number of treatment shoots at the late

treatment, the pooled estimate σ2 given by { }RSS RSSE L( ɵ ) ( ɵ ) /κ κ+ 26 was used.

Figure 4.16 shows the profile log-likelihoods and approximate 95% support intervals

based on the chi square statistic with single degree of freedom. It is clear from

Fig. 4.16 that there is little advantage in using separate estimates of κ for each time.

Therefore, the 95% support interval for ɵκ can be approximated, using the above

pooled estimate of σ2 , by the range 9-16 cm2 larva-1.

191

The above results were obtained for option (a) in step (T2) since it was found that

using option (b) gave unrealistic predictions of neonate larval survival. The model of

leaf toughness when used to predict the toughness of each leaf gave 100% survival of

neonate larvae for all shoots. This was because for each shoot the predicted leaf area

with toughness below the toughness threshold of 35 mg cm-2 at initial measurement

was more than adequate for all neonate larvae of each nominal batch size to develop

to L2 stage.

Despite considerable effort in modelling leaf toughness the imprecision of

predictions from the model, based on inputs of estimated leaf age and leaf area as a

proportion of estimated FELA, resulted in the inability of the model to realistically

predict neonate mortality. Even with an accurate estimate of leaf age and known

FELA, as for the calibration dataset, the approximate 95% confidence interval for

predictions was estimated to be ± 32% of the prediction which gives ± 11.2 mg cm-2

for a prediction of 35 mg cm-2. These errors would be significantly larger here given

Figure 4.16 Profile log-likelihood for ELAL for early (solid line) andlate (dashed line) trials with approximate 95% confidence intervalsshown. The dotted line is the combined early and late curve. For thelate curve the scale parameter was taken as the pooled estimate of theresidual variance.

4 6 8 10 12 14 16 18 20

Effective leaf area loss, ,(cm2 larva-1)

0

4

8

12

16

-2 x Profile log-likelihood

early

early+late

late

95% confidence intervals

κ

192

the imprecision in the estimation of each of the age of each leaf and the leaf’s FELA

given by Steps C3 and C5 respectively.

It was not possible to record neonate mortality but for failed batches it was observed

that very few larvae reached L2 stage and for the shoots with poor survival this can

largely be attributed to the inability of these young larvae to feed successfully due to

excessive leaf toughness. Therefore using the observed survival in Step T2(a) was

considered the only available method of simulating overall survival.

To compare predictions to actual total shoot leaf areas, as for the control shoots,

observed growth, LAF-LAI, can be compared to predicted,LAFɵ ( ɵ )κ -LAI. However,

in the case of treatment shoots since larval browsing can not only reduce or eliminate

completely the growth in leaf area but also reduce leaf area to below its initial value,

LAI, then there is strong justification for comparing LAF to LAFɵ ( ɵ )κ to judge the

models predictive ability. Fig. 4.17(a) shows the comparison of LAF to LAFɵ ( ɵ )κ

while Fig. 4.17(b) shows the relationship of observed absolute growth LAF-LAI to

LAFɵ ( ɵ )κ -LAI. The regression line, fitted through the origin is shown in each of

Figs. 4.17(a) and (b).

Figure 4.17 shows that the algorithm for treated shoots underestimates the LAF and

growth, the regression coefficient for observed LAF on predicted LAF is 0.91

(s.e.=0.03) with 0.9752 =R and for observed growth on predicted growth is 0.60

(s.e.=0.16) with 0.5122 =R . This represents a 40% underestimation of observed

growth, though Fig. 4.17(b) shows that the 1:1 line gives as good a visual fit as the

fitted regression indicating that there are some highly influential data points in the

regression which is exacerbated by the small sample size. After considerable effort

using different approaches to predicting the LAF of the treatment shoots, mostly

involving changing the method of estimating the ‘effective’ number of larvae in step

(T2), no improvement in the predictive ability beyond that described above could be

achieved. The implications of possible underestimation of leaf area loss due to larval

browsing are discussed in Section 7.10.

193

0 4 8 12 16 20 24

Predicted LAF (cm2 x 100)

0

4

8

12

16

20

24

Observed LA

F (cm

2x 100)

-3 -1 1 3 5 7 9

Predicted LAF-LAI (cm2 x 100)

-3

-1

1

3

5

7

9

Observed LA

F-LAI (cm

2x 100)

Figure 4.17 Comparison of observed and predicted (a) final leaf area, and (b) absolute growth for early (+) and late ( ) treatment using total leaf area excluding ‘O’ leaves for the batch size treatment shoots. The solid line is the fitted regression while the dotted is the 1:1 line. R 2

calculated using the total sum of squares unadjusted for the mean.

R 2=51.2%

(b)

(a)

R 2=97.5%

0 4 8 12 16 20 24

Predicted LAF (cm2 x 100)

0

4

8

12

16

20

24

Observed LA

F (cm

2x 100)

-3 -1 1 3 5 7 9

Predicted LAF-LAI (cm2 x 100)

-3

-1

1

3

5

7

9

Observed LA

F-LAI (cm

2x 100)

Figure 4.17 Comparison of observed and predicted (a) final leaf area, and (b) absolute growth for early (+) and late ( ) treatment using total leaf area excluding ‘O’ leaves for the batch size treatment shoots. The solid line is the fitted regression while the dotted is the 1:1 line. R 2

calculated using the total sum of squares unadjusted for the mean.

R 2=51.2%

(b)

(a)

R 2=97.5%

194

4.3.2.3 Predicting the final leaf area after simulation of larval feeding on all

shoots for a range of batch sizes

As mentioned earlier, the main objective of constructing the ‘calibrated’ simulation

model is to allow all 81 shoots across the 2 times to be used to estimate growth loss

for a range of batch sizes. Here, 10 different batch sizes ranging from 5 to 50 eggs in

increments of 5 were simulated. Separate results were obtained for each time using

the 54 early and 27 late shoots. Using the initial measurements of the shoot and each

of the nominated batch sizes from 5 to 50 the predicted LAF of each shoot (both

control and treatment shoots) was obtained from steps (T1) to (T3). For step (T2a)

the ‘effective’ number of larvae was obtained by simply multiplying the proportion of

the actual batch size for that tree recovered by the simulation’s nominal batch size.

The LAF for each shoot was predicted both with and without simulated browsing for

each nominal batch size and of ELAL, ɵ .κ = 126 cm2 larva-1. Since LAI was obviously

the same for each shoot the difference in these predicted leaf areas gives the

predicted difference in absolute growth, CT AGAG − .

Figure 4.18 shows the relationship between CT AGAG − and batch size. Standard

errors of the predictions are also shown for the means in Fig. 4.18 where the

calculation of these standard errors takes into account the nesting of shoots within

trees. However, these standard errors do not account for the component of prediction

error due estimation error for κ . To incorporate this source of error the 95%

confidence bands shown in Fig. 4.18 were based on the sum of the variances

attributed to (a) prediction error in ELAL= κ and (b) variance in the mean predictions

conditional on ɵ .κ = 126. The variance in (a) was approximated by 20

2 )6.0(ˆ Nσ

where 0N is the nominal batch size, 0.6 is the average proportion surviving (Table

4.2), and 84.3/5.3)ˆ(ˆ 2 ≅κ=σ Var . The variance (b) was simply the square of the

standard errors shown in Fig. 4.18. Thus the confidence bands shown in Fig. 4.18

were obtained as the square root of the sum of variances (a) and (b) which was

multiplied by an approximate 95% critical value of the t-distribution of 2.0.

195

Figure 4.18 Difference between simulated and control absolute growth versus batch size based on the simulation using all shoots for (a) early, (b) late treatments. The black solid line corresponds to the mean ELAL=12.6 cm2 larva-1, with s.e.(mean) bars and 95% c.b.’s shown. The purple dotted lines show the means and 95% c.i.’s from the REML analysis, and the purple solid line shows the fitted linear model (4.11).

(b)

(a)

AG

T-A

GC (cm

2x 100)

AG

T-A

GC (cm

2x 100)

0 10 20 30 40 50

-6

-5

-4

-3

-2

-1

0

0 10 20 30 40 50

Batch size

-6

-5

-4

-3

-2

-1

0

Figure 4.18 Difference between simulated and control absolute growth versus batch size based on the simulation using all shoots for (a) early, (b) late treatments. The black solid line corresponds to the mean ELAL=12.6 cm2 larva-1, with s.e.(mean) bars and 95% c.b.’s shown. The purple dotted lines show the means and 95% c.i.’s from the REML analysis, and the purple solid line shows the fitted linear model (4.11).

(b)

(a)

AG

T-A

GC (cm

2x 100)

AG

T-A

GC (cm

2x 100)

0 10 20 30 40 500 10 20 30 40 50

-6

-5

-4

-3

-2

-1

0

-6

-5

-4

-3

-2

-1

0

0 10 20 30 40 500 10 20 30 40 50

Batch size

-6

-5

-4

-3

-2

-1

0

-6

-5

-4

-3

-2

-1

0

196

For comparison, the corresponding means and 95% confidence intervals from the

REML analysis are also shown in Fig. 4.18 though note that these means are the

same for both early and late times.

Figure 4.19 shows the relationship between proportional growth difference,

CT PGPG − and batch size obtained by dividing CT AGAG − by CLAF . Note that

100/PPGPG CT −=− where P is percent defoliation given by (4.1). The standard

errors shown in Fig. 4.19 were obtained from the variance of the 54 early and 27 late

shoots for each simulated batch size in the same was as those given for absolute

growth. The 95% confidence bands were obtained by calculating the variance of the

ratio CCT LAFAGAG /)( − given the means, variances, and covariances of

CT AGAG − and CLAF , and the formula for the variance of a ratio given by equation

(10.17) of Kendall and Stuart (1963). The variance for CT AGAG − was taken as the

sum of the variances (a) and (b) used above. Again the t-distribution critical value of

2.0 was used.

Since Fig. 4.19 expresses proportion defoliation as a function of batch size it is the

key result for this chapter. To enable this relationship to be incorporated in the

economic analyses described in Chapter 7, regressions were fitted for each of the

mean and upper and lower confidence lines shown in Fig. 4.19. These regressions

were fitted as CT PGPG − on (Batch size -5) (i.e. for economic simulations the

minimum batch size considered was 5). The absolute value of the regression

parameter estimates therefore gives the relationship between P/100 and (Batch size -

5). The absolute value of the regression parameter estimates are given in Table 4.7.

Note that since means are linear in (Batch size -5) the regressions gave a perfect fit.

This linearity is due to the fact that CT AGAG − , after adjusting for the effect of

disbudding, is simply κ− ˆ6.0 0N .

197

Figure 4.19 Difference between simulated and control proportional growth versus batch sizes based on the simulation using all shoots for (a) early, (b) late treatments. The solid lines correspond to the mean ELAL=12.6 cm2 larvae-1, with s.e.(mean) bars and 95% confidence bands incorporating variance in estimate of ELAL and the additional variance due to the other major sources of prediction error.

Batch size

(b)

(a)

PG

T-P

GC= -

P/100

PG

T-P

GC =-P/100

0 10 20 30 40 50

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

-0.8

-0.6

-0.4

-0.2

0.0

0 10 20 30 40 50

Figure 4.19 Difference between simulated and control proportional growth versus batch sizes based on the simulation using all shoots for (a) early, (b) late treatments. The solid lines correspond to the mean ELAL=12.6 cm2 larvae-1, with s.e.(mean) bars and 95% confidence bands incorporating variance in estimate of ELAL and the additional variance due to the other major sources of prediction error.

Batch size

(b)

(a)

PG

T-P

GC= -

P/100

PG

T-P

GC =-P/100

0 10 20 30 40 500 10 20 30 40 50

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

-0.8

-0.6

-0.4

-0.2

0.0

-0.8

-0.6

-0.4

-0.2

0.0

0 10 20 30 40 500 10 20 30 40 50

198

Table 4.7 Absolute values of slope ( b) and intercept ( a) for the

regression of simulated proportional growth loss, PGT- PGC, on (batch

size-5) to give the decrease in PG and corresponding increase in

P/100 for a given batch size of a + b(batch size-5).

Time Regression

Parameter

Estimate1

PGT-PGC

( κ =12.6)

PGT-PGC

(upper band)2

PGT-PGC

(lower band)2

Early b 0.0060 0.0052 0.0068

a 0.0867 0.0612 0.1122

Late b 0.0102 0.0086 0.0118

a 0.0760 0.0453 0.1066

1 Absolute values of regression parameter estimates,

a=|Intercept|,b=|Slope|. 2 Regression through upper and lower 95% confidence bands.

Note that a larger growth loss for batch size of 5 is predicted for the early compared

to the late treatment (Figs. 4.18, 4.19). This is explained by the assumption that a

batch size as low as 5 is capable of disbudding the shoot. The recruitment of new

leaves was greater for the early treatment and therefore expansion of newly recruited

leaves gave a larger contribution to growth for the early compared to the late

treatment. The control shoots recruited on average 3.25 new leaves at the early

treatment with a range of 0 to 19 and with 58% of these shoots recruiting no new

leaves. For the late treatment the average was 2.11, the range of 0 to 28, and the

percentage of shoots with no recruitment was 78%. For each of early and late times

the average per tree of number of new leaves recruited by the two control shoots

combined was used in step (C8). Negative values of recruitment were set to zero as

mentioned earlier. As a result, the effect of disbudding on growth is greater for the

early treatment. Note that κ does not include potential leaf area loss due to

disbudding which is included separately in the simulation model in part (a) of

step (T3).

In contrast, P increases with batch size at a greater rate for the late treatment

compared to the early treatment. Since absolute growth loss is the same for both (i.e.

due to a common value of ELAL and proportion surviving for both times) this

199

difference is due to the greater mean value of CLAF for the early treatment shoots

with mean of 1326.3 cm2 per shoot (s.e. 70.7) compared to the late shoots with mean

828.8 cm2 (s.e. 54.7).

4.5 DISCUSSION

Comparison with laboratory feeding trials

In the laboratory study of Baker et al. (1999) fresh, new season’s leaves of each of

E. nitens and E. regnans were harvested and fed to replicate cohorts of each

C. bimaculata larval instar. Leaves were weighed before and after feeding when

replacing leaves every two days. The difference in leaf weight resulting from feeding

were adjusted for moisture loss and wet leaf weights were converted to green leaf

area using the specific leaf area (SLA) for a sample of E. nitens leaves typical of those

fed to the larvae. The average wet area of the leaves fed to L1 to L4 larvae ranged

from 9.44 to 35.9 cm2 respectively but the corresponding SLAs were similar for

leaves fed to L1 to L3 instars with mean of 28.5 while the SLA dropped slightly to

27.4 cm2 g-1 for L4 larvae. Overall, the SLA averaged 28.05 cm2 g-1. The total

consumption per surviving larva (i.e. the total for L1 to L4 stages) was 0.2345 and

0.3158 g larva-1 for E. nitens and E. regnans respectively.

These green weights and leaf areas consumed per larva were calculated as the total

consumed for the cohort divided by the number of surviving individuals at the end of

each feeding period. The total larval mortality was 22.8% and 69.1% for E. nitens

and E. regnans respectively so that the individual weight and leaf area consumed per

larva is inflated by the amount eaten by individuals that died during the feeding

period similarly to the estimate of total apparent defoliation given by κ .

For E. nitens, given the above SLA, this corresponds to 6.6 cm2 of green leaf area

consumed per surviving larva. This corresponds to ( )ptC where ( ) ( )ppp tCNtC =

and ( )ptC is total consumption for the cohort given in model (4.5). Using the total

consumption of the 10 cohorts fed on E. nitens leaves in the Baker et al. (1999)

laboratory trial the 95% confidence interval for ( )ptC , ignoring variability in SLA,

was calculated here as 6.0 to7.2 cm2 larva-1.

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Elek and Beveridge (1999) report a laboratory trial to measure mortality and

consumption by C. bimaculata L1, L2 and L3 larvae when fed E. nitens foliage

sprayed with the biotic insecticide Bacillus thuringiensis subsp. tenebrionis. For the

unsprayed (i.e. control) foliage, consumption from L1 to the end of L4 stages

averaged 3.4 cm2 (95% confidence limits of 2.6 to 4.1 cm2) per surviving larva.

Control survival was 33%, which is substantially lower than that obtained here

(Table 4.2) and that obtained by Baker et al. (1999), and is attributed to the poor

quality of the foliage (N.Beveridge FT, pers. comm.).

The average leaf area loss per larva, excluding the effect of disbudding, was

estimated here as ɵ .κ = 126 cm2 larva-1 which is almost double the loss estimated

from the study of Baker et al. (1999) of ( )ptC =6.6 cm2 larva-1.

The above laboratory study of Baker et al. (1999) gave relatively precise estimates of

green leaf weight and area consumed by each larval instar for a wide range of leaf

sizes but narrow range of leaf toughness as measured by SLA. However, to obtain an

estimate of leaf area loss at the shoot level, notwithstanding the problem of

estimating potential losses, these results would need to be applied to typical shoots

and development times for each larval instar in combination with models of feeding

behaviour. Also the impact of disbudding cannot be estimated by applying the

laboratory results to the field.

The estimate of ELAL obtained here is applicable for shoots similar to the sample of

shoots used here, with their inherent distribution of leaf size and leaf phenology, and

for actual larval feeding behaviour using a reasonably close approximation to the

natural environment. Therefore, although the laboratory trial of Baker et al. (1999)

gives an accurate estimate of consumption rate it does not provide by itself realistic

data on overall feeding impact. In contrast, the feeding observed in the caged-shoot

trial is a realistic representation of feeding effects. However, because growth impact

was only measured at the aggregate shoot level rather than the individual leaf level,

development of a more realistic simulation model was not possible. Instead the

201

estimate of ELAL as ɵ .κ = 126 cm2 larva-1 is a compromise taking into account actual,

but unobserved, feeding behaviour on existing leaves and assumed disbudding

behaviour both aggregated to the shoot level. Even after excluding the impact of

disbudding on growth, the value of 6.12ˆ* =κ=C is almost double that of

consumption 6.6=C cm2 larva-1 so that loss of potential leaf area is significant and

needs to be incorporated in prediction of defoliation as in Valentine’s (1980)

‘apparent defoliation’.

Comparison of predictions of growth impact using the ANOVA/response surface and

process/simulation models

Excluding the effect of disbudding, both the linear model (4.11) fitted to the batch-

size means and the process/simulation model with the estimated value of ELAL

applied to the sample of shoots, give similar relationships between growth loss and

population size (Figs. 4.18 and 4.19). The main difference between model (4.11) is

that the process/simulation model gives a greater absolute growth loss at the early

treatment due to the impact of disbudding. The disbudding effect accounts for the

greater apparent defoliation at low population levels than that predicted from (4.11).

An indication of the effect of disbudding on shoot growth can be obtained from

Fig. 4.18 using a population size of five. After feeding mortality of some 40% [i.e.

)4.01(0 −= NN p ] the remaining three larvae consume on average 3x12.6=37.8 cm2

green leaf area. Therefore, from Fig. 4.18 and a loss of leaf area of approximately

134 and 66 cm2 for early and late times respectively, the corresponding losses due to

disbudding alone are 96 and 28 cm2 per shoot.

Direct comparison of κ and τ is complicated by the indirect incorporation of the

pooled (i.e. across times) disbudding effect in τ as well as the different definitions of

N used in each case. If τ (Table 4.6) is scaled by multiplying by pNN /0 (i.e. using

average survival given in Table 4.2 as 60%) then the value obtained is 17.5 cm2

larva-1. However, this value also includes the pooled, disbudding effect.

The direct incorporation of the effect of disbudding in the process/simulation model

is a more robust method than that implied by either model (4.11) or the nonlinear

202

model (4.12). Although the disproportionate growth loss at the 10-batch size was

predicted by model (4.12) (Fig. 4.11), no distinction was possible between this effect

at the early compared to late time due to the necessity of pooling the two times. Note

also that the process model gives better predictions of batch means that model (4.11)

especially for the early time as seen in Figs. 4.18 and 4.19. For the early time the

process model predicts the growth loss for the 10-batch size as intermediate between

models (4.11) and (4.12) (i.e. compare Figs. 4.11 and 4.18). Since model (4.12) is

purely an empirical, nonlinear interpolation of the means in Fig. 4.11 the generality

of this model is limited.

A further difference is the increasing size of the confidence bounds on predictions

with population size, seen in Figs. 4.18 and 4.19, as a result of applying the

confidence bounds obtained for κ in the simulation algorithm. These ‘proportional’

bounds are more ‘natural’ than the fixed-size confidence intervals for the REML

means (Figs. 4.11, 4.18, and 4.19).

For the above reasons, the economic analyses described in Chapter 7 apply the

regression of growth loss or equivalently apparent proportional defoliation, P/100, on

population size using the coefficients based on the process/simulation model given in

Table 4.7.

Generalisations of the process/simulation model

Different feeding behaviour, particular with respect to disbudding, will give different

growth impacts. Since the impact of disbudding is considered independently of

growth losses for existing leaves as quantified using ELAL, if different assumptions

on the prevalence and degree of disbudding are made then the above simulation

model can be re-run with these assumptions and growth impacts re-estimated. For

example it may be assumed or predicted that a given proportion of browsed shoots

are not disbudded and/or a given proportion of buds on browsed shoots are left intact.

Apart from the way disbudding is incorporated, the extra generality possible in

application of the above process/simulation model resides mainly in its ability to

predict shoot growth in the absence of browsing using steps (C1) to (C9). Growth of

leaves and thus shoots can be simulated for any part of a growing season using the

203

day-degree-driven leaf expansion model and the initial phenology of the shoot’s

leaves. However, more general models of leaf recruitment need to be incorporated in

step (C8). These leaf recruitment models would need to predict not only recruitment

of new leaf buds but also natural bud mortality where this is mortality due to the

physiological process of shedding buds rather than removal by invertebrate browsing.

Observations suggest that natural mortality of leaf buds is highly variable and can be

substantial (J. Elek FT, pers. comm.).

4.6 SUMMARY

Apparent defoliation was modelled as the sum of two components : (a) the combined

total of leaf area lost directly from consumption and indirectly from consumption of

actively expanding leaves, and (b) loss of potential leaf area due to removal of buds

(i.e. disbudding). A general dynamic model of leaf expansion and larval feeding was

used to provide a framework for the development of empirically models of apparent

defoliation calibrated using data from a caged-shoot feeding trial. Two models were

used : (i) an ANOVA/linear response surface model which gave a combined estimate

of losses due to (a) and (b), and (ii) a process/simulation model which estimated (a)

and (b) separately.

The caged-shoot trial used 9 replicate shoots of each nominal egg batch sizes of 10,

20, and 30 eggs with each replicate located on a different tree. Visually matched

control shoots, a caged-control and an uncaged (sprayed) control, were also allocated

to each of the 27 sample trees. The 27 sample trees in the trial were divided across

two times, 18 trees in December (early) and 9 in February (late). The two times were

pooled for the ANOVA/response surface method. This method compared treatment

to control shoot growth to estimate apparent defoliation.

Estimation using the linear mixed model was used to extract the maximal amount of

information in the trial on the contrast of treatment and control growth in order to

estimate the mean apparent defoliation for each batch size. Unfortunately,

imprecision in these estimates due to variation in growth between matched shoots,

variation in feeding success, and the small number of replicates meant that

204

predictions from the linear response surface model were subject to a large amount of

uncertainty.

The process model was used to estimate apparent defoliation by comparing growth of

the treatment shoots both with (actual) and without (predicted) feeding using the leaf

expansion models described in Chapter 3. Growth losses were estimated using a

profile log-likelihood to estimate ‘effective leaf area loss per larva’ (ELAL) for

existing leaves, combined with the observed number of surviving larvae, and the loss

of potential leaf area due to the loss of newly recruited leaves (i.e. disbudding). The

use of the process/simulation model overcame some of the difficulties mentioned

above for the ANOVA method but the estimate of ELAL was also subject to

considerable uncertainty.

The two methods gave similar estimates of losses for late (February) but for the early

(December) population the process/simulation model predicted greater losses at low

population levels (<20 eggs per shoot) due largely to the explicit modelling of losses

due to disbudding. Even after excluding the impact of disbudding, apparent

defoliation estimated using an ELAL of 12.6 cm2 larva-1 (95% confidence

interval=9,16 cm2 larva-1) for larvae successfully completing development (i.e.

mean=60%) was almost double the green leaf area consumed in a laboratory feeding

trial. Therefore, the loss of potential leaf area was significant and was incorporated in

prediction of defoliation as a function of population size.

Percent defoliation, including the effect of disbudding, for populations at or above 5

eggs per shoot was predicted from simulation of defoliation in December using the

process model and the sample of 54 shoots. Defoliation was estimated at 8.7% plus

0.6% for each unit increase in number of eggs per shoot above 5. The corresponding

figures for late (February) defoliation using the sample 27 shoots were 7.6% and a

1% increase per unit increase in population size above 5. Simulating populations

below 5 eggs per shoot was not considered since these are well below any possible

economic threshold.

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CHAPTER 5

MODELS OF THE IMPACT OF SIMULATED BROWSING ON

TREE DIAMETER AND HEIGHT GROWTH

5.1 INTRODUCTION

The qualitative impact of the wide range of insect herbivours of eucalypts is

reasonably well documented (see reviews by Ohmart and Edwards, 1991 and

Landsberg and Cork, 1997). A number of studies have also looked at the effect of

leaf attributes, such as essential oils, secondary compounds such as tannins, phenols,

and surface waxes on feeding efficiency and survival of leaf-feeding insects (Ohmart

and Edwards, 1991; Li et al., 1995, 1996). However, Abbott et al. (1993) noted that

the impact of insect defoliation on tree growth in eucalypts is poorly understood. Few

studies have quantified the effect of insect herbivory on tree growth even in the

relatively simple and common case of leaf chewing (phytophagous) insects.

Artificial or manual defoliation is commonly used in studies to simulate the impact

of insect phytophagy on plant growth. Using manual stripping of leaves, designed

experiments can be employed to study the impact of intensity, timing, and frequency

of defoliation on tree growth. Intensity is the amount or proportion of leaf biomass

removed in a single defoliation, timing is the time of year when insect defoliations

are simulated to take place, for example spring, early summer, late summer or

autumn, and frequency is the number of consecutive years of defoliation. In addition

to manually removing existing leaves, new leaves and leaf buds can be periodically

removed for a pre-determined proportion of the growing season. This is described by

the term disbudding (Candy et al., 1992).

Measurement of the growth of single-tree experimental units after replicated and

randomised artificial defoliation treatments allows comparison of the effect of these

treatments and calibration of models of growth impact. Studying natural defoliation

does not allow such experimental control of defoliation apart from the ability to

completely exclude defoliation from control experimental units using insecticide

(Elliott et al., 1993).

206

However, the disadvantage of studying insect herbivory using artificial defoliation is

that it only approximates the way that insects defoliate trees. For example, manually

stripping of leaves is usually carried out on a single day but may be meant to

represent feeding of immature stages over their development period that often takes

several weeks. Plant growth responses can be sensitive to such differences between

simulated and actual defoliation (Baldwin 1990).

A number of studies have examined the effect of insect herbivory in eucalypts using

artificial defoliation to simulate the defoliation caused by an individual or suite of

pest species. These studies and summarised in Table 5.1.

Of these studies, only Candy et al. (1992) and Abbott et al. (1993) develop

quantitative relationships of the effects of one or more of intensity, timing and

frequency of defoliation on tree growth. Abbott et al. (1993) compared the relative

impact on sapling diameter growth in jarrah, E. marginata, regrowth forests of five

intensities of defoliation (0% =control, 25%, 50%, 75%, and 100%) for frequencies

of one, two, or three consecutive defoliations (i.e. one per season). The final diameter

measurement was taken in the 4th summer. They calculated a cumulative defoliation

index (e.g. three consecutive 25% defoliations gave an index of 75) and for each of

measurement years 1988 to 1990 regressed diameter on this cumulative index. Also,

for each of the 25%, 75%, and 100% intensities they regressed the final diameter on

frequency. They then inferred from these latter regression models that the total

impact on growth of frequent, low intensity defoliations is greater than that for a

single high intensity defoliation. These models help quantify some attributes of the

growth impact of defoliation but they are not sufficiently general to be useful in

determining economic injury levels needed for deciding whether or not to control the

insect population (the jarah leafminer, see Table 5.1) artificially.

Candy et al. (1992) developed quantitative relationships of the effects of each of

three intensities, two timings, and two frequencies of defoliation on tree height

growth for E. regnans plantations using a single model. They also included a

treatment factor that repeated defoliation of the same intensity in the same season,

207

Table 5.1 Artificial defoliation studies in Eucalyptus spp.

Host species Age (stage)

forest type Pest species simulated Defoliation

Treatments Measurements Reference

E. regnans Pole stage

regen. (35-year old)

phasmatid (Didymuria violescens )

Complete & partial over 3 seasons in May or Jan

DBHob to winter of 3rd season

Mazanec (1966)

E. regnans 3-year old natural regen.

chrysomelid beetle (C. bimaculata )

Remove top 40cm of green crown and/or once or weekly disbudding

Shoot elongation for up to 12 weeks after treatment

Cremer (1972,1973)

E. grandis 2-year old plantation

christmas beetles (Anoplognathus porosus A. chloropyrus )

3 trials: control, 90-95% 70-75%, and 3, 30% defoliations for a range of timings in a single season

Height in following winter

Carne et al . (1974)

E. regnans 3 (Trial A) and 6-year old (Trial B) plantations

chrysomelid beetle (C. bimaculata )

Control, 66, 100% defoliation by 2 timings, over 1 or 2 seasons and/or regular disbudding

Height, DBHob for 4 seasons (Trial A), height for a single season (Trial B) after 1st defoliation

Candy et al . (1992)

E. marginata Sapling, regrowth

Jarrah leafminer (Perthida glyphopa )

0,25,50,75,100% defoliation over 1, 2, or 3 seasons

Diameter (30cm above ground) over 4 years from year 1 defoliation

Abbott et al . (1993)

E. globulus 1-year old plantation

spring beetles (Scarabaeidae), grasshoppers (Phaulacridium vittatum , Chortoicetes terminifera ) autumn gum moth (Mnesamplea privata )

0, 50, 100% defoliation in 1 year at 1 of 3 timings (Sept,Dec,Mar)

Height from spring defoliation to following spring

Abbott and Wills (1996)

208

that is, an early and late summer defoliation in the same summer. Their model used

as reference or baseline growth, the growth of the undefoliated controls which

allowed the model to be applied to, if not validated for, other growing seasons and

stands of different ages and site qualities to those measured. They used the

predictions from this model to provide input to individual-tree height and diameter

growth models for E. globulus (Goodwin and Candy, 1986) that was then used to

predict the impact of a range of simulated defoliation scenarios on harvested timber

volume and net present value. The net present value of the harvested volume was

calculated with and without control of the hypothetical populations, that if left

uncontrolled, would cause the simulated defoliation. These and other simulated

scenarios have been used to assist forest entomologists in setting a general, forest-

estate-wide, economic injury level (EIL) for E. regnans plantations in Tasmania

(D. Bashford, FT pers. comm.)

Here, a similar approach to that of Candy et al. (1992) is used to develop a model of

the impact of defoliation on the growth of each of diameter at breast height (DBH)

and total tree height for E. nitens. Two artificial defoliation trials were used to

simulate larval browsing in order to provide data for model calibration and

validation. The trial used for model calibration incorporated a greater range of

defoliation treatments that the trial used for model validation. The main difference

between these trials and those described in Candy et al. (1992) is that here there is no

repetition of defoliation in the same summer; that is, there is no combined ‘early and

late’ treatment. For both trials, tree growth was measured for a long enough period

after treatments were imposed to determine the level of persistence of treatment

effects. In Chapter 7, these defoliation/tree growth models are linked to later-age

growth models for E. nitens plantations calibrated from growth data collected in

Tasmania and New Zealand (Candy, 1997b). The input or ‘driving variable’ for the

models described here is percentage of new season’s foliage removed, P, provided by

the models described in Chapter 4.

209

5.2 ARTIFICIAL DEFOLIATION TRIALS 1

5.2.1 Blue Gum Knob trial

Site and stand characteristics

This trial was established in a 2-year old E. nitens plantation at ‘Blue Gum Knob’

(BGK) (Appendix 5). The stand was planted with seedlings from the Torongo

provenance (Pederick 1979) after clearfall of the previous crop of Pinus radiata. The

site was gently sloping with a south-westerly aspect (Fig. 5.1a) at an altitude of

430 m. Trees were planted at a 2 x 4 m spacing, giving 1250 stems ha-1, and were

fertilised at planting with 100 g of triple superphosphate per tree. The site index of

the stand, which is defined as the mean dominant height at age 15, was estimated

from the control mean height measured in 1998 and the site index model in Candy

(1997b) as 27.2 m. This indicates that the site quality is moderate to good (Candy and

Gerrand, 1997). Treatments were established in fifteen replicates.

Experimental materials and methods

Tree selection and experimental design

Trees were selected for treatment in October 1994 (i.e. age 2) with the following

attributes : (1) a single main leader with no low forks or multiple leaders, (2) height

in the range 4 to 5.3 m for the single main leader stem, (3) adult foliage visually

estimated to comprise greater than 5% of the total leaf area, and (4) greater than 20%

of total tree height consisting of adult foliage. Treatments were randomly assigned to

tree numbers within replicate areas prior to tree selection where these areas can be

considered ‘blocks’ in the usual experimental design sense.

Defoliation and disbudding methods

The percentage foliage removed was estimated visually based on the leaf area

removed rather than the number of leaves. As described in Candy et al. (1992),

defoliation commenced at the top of the tree and branch tips and continued towards

the centre of the crown so that the youngest leaves were removed first and the

remaining current season’s leaves of progressively greater maturity were removed.

1 These trials were established, measured, and maintained by Forestry Tasmania. The author was primarily responsible for experimental design but also assisted with establishment and measurement.

210

Figure 5.1 Artificial defoliation trials (a) Blue Gum Knob site, (b) Arve site (with heavy treatment tree in foreground), (c) manually stripping leaves to treatment specification, and (d) pulling in suitable foliage to strip by hand.

(a) (b)

(c) (d)

Figure 5.1 Artificial defoliation trials (a) Blue Gum Knob site, (b) Arve site (with heavy treatment tree in foreground), (c) manually stripping leaves to treatment specification, and (d) pulling in suitable foliage to strip by hand.

(a) (b)

(c) (d)

211

Manual defoliation involved drawing a closed hand along the shoots to strip off

leaves as described by Carne et al. (1974) (Fig. 5.1c,d). Foliage was removed from

the top of the tree using an extendable pole-pruner in order to avoid the risk of

snapping off branches caused by pulling the branch within reach when stripping

leaves by hand (Fig. 5.1d). Using this method twigs were removed as well as leaves

and buds; however, only new shoot material was removed (i.e. material that would

not have grown under continuous browsing of shoot tips by larvae). For foliage that

could be reached by hand disbudding was carried out by plucking off the buds and

newly emergent, small leaves.

Figures 5.2 and 5.3 give examples of natural and artificial defoliation. Figure 5.2d

gives an example of refoliation of a shoot two months after it was artificially

defoliated. The ‘heavy’ artificial defoliations shown in Fig. 5.3 (a,c,d) are similar in

overall appearance to the natural defoliations shown in Fig. 5.2 (a,b,c).

Description of treatments

Each replicate contained one of each of the following treatments shown in Table 5.2.

Note that the treatment combinations incorporating a repeat of the disbudding

treatment in the second year (i.e. 1995) were not carried out in the trial.

Table 5.2 Treatment codes. Code Treatment

Intensity Disbud Timing Frequency

CONTROL - - - - LDE1 Light (50%) D (yes) Early (Dec) 1 (Yr 1) L_E1 - (none) L_E2 - (none) 2 (Yrs 1,2) LDL1 D (yes) Late (Feb) 1 (Yr 1) L_L1 - (none) L_L2 - (none) 2 (Yrs 1,2) HDE1 Heavy(100%) D (yes) Early (Dec) 1 (Yr 1) H_E1 - (none) H_E2 - (none) 2 (Yrs 1,2) HDL1 D (yes) Late (Feb) 1 (Yr 1) H_L1 - (none) H_L2 - (none) 2 (Yrs 1,2)

212

Figure 5.2 Examples of natural defoliation of E. nitens in (a)-(c) with(c) showing typical ‘broom top’ appearance before re-foliation and (d)showing the extent of re-foliation of a shoot two months after artificialdefoliation.

(a) (b)

(c) (d)

Figure 5.2 Examples of natural defoliation of E. nitens in (a)-(c) with(c) showing typical ‘broom top’ appearance before re-foliation and (d)showing the extent of re-foliation of a shoot two months after artificialdefoliation.

(a) (b)

(c) (d)

213

(a) (b)

(c) (d)

Figure 5.3 Examples of artificially defoliated trees (a) heavy treatment,(b) light treatment in 1995 at Blue Gum Knob, (c) and (d) heavy treatmentin 1993 at Arve showing height pole in (c) and crown width measurementin (d).

(a) (b)

(c) (d)

Figure 5.3 Examples of artificially defoliated trees (a) heavy treatment,(b) light treatment in 1995 at Blue Gum Knob, (c) and (d) heavy treatmentin 1993 at Arve showing height pole in (c) and crown width measurementin (d).

214

Intensity: For the ‘Heavy’ intensity treatment 100% of the current season’s growth of

adult foliage suitable for consumption by C. bimaculata larvae was removed. For

‘light’ defoliation, 50% of this foliage was removed by visual estimation in terms of

leaf area rather than the volume defined by the outline of the crown (Fig. 5.3a,b).

Timing: The timing of the ‘early’ and ‘late’ treatments aimed to parallel naturally

occurring defoliation by C. bimaculata L3 and L4 larvae. ‘Early’ defoliation was

performed in December. ‘Late’ defoliation was performed in February, with the

disbudding treatment occurring between late February and the end of March.

Frequency: ‘Year 1’ - defoliation was performed in the summer of 1994/95 while for

‘Year 1&2’ defoliations were performed in both the summers of 1994/95 and

1995/96.

Disbudding: Disbudding involved removal of new foliage, as the shoots refoliated

after defoliation, at approximately fortnightly intervals. The period over which

disbudding was carried out was chosen to simulate feeding behaviour: approximately

one month for the ‘early’ timing treatment to simulate browsing of expanding shoots

by larvae, and two months for the ‘late’ treatment to simulate browsing by both

larvae and newly emerged adult beetles.

Untreated controls: All replicates contained at least one untreated control (CONT). In

addition to this control tree some replicates ended up with additional control trees

since these extra controls were selected as potential replacements for any trees which

had there main leaders broken by the first defoliation. In addition, one of the

untreated trees from each replicate was destructively sampled as a biomass tree (see

below). Therefore, there were differing number of controls per replicate with a

minimum of one, a maximum of three, and a total over all replicates of 50. All

control trees were used in the analyses since this resulted in an improvement in the

precision of control versus treatment contrasts at the cost of introducing a small

degree of imbalance into the experimental design.

Biomass trees

In the first summer, one tree in each of the fifteen replicate blocks was cut down and

leaves were removed to determine total leaf biomass. Leaves were separated into the

following categories for weighing (green weight):

215

1. leaves visually assessed to make up 50% of ‘new season’s edible adult leaves’

(NSEL) (i.e. from the outer part of the tree crown)

2. remaining new season edible adult foliage

3. remaining adult foliage

4. juvenile foliage.

Figure 5.4 shows this progressive removal of adult foliage (i.e. up to step 3) for one

of the biomass trees at the Arve trial described later.

Tree measurements

The initial pre-treatment measurement was carried just prior to the first year

treatments in December 1994. Annual measurements were then carried out in the

winter of each of the years 1995 to 1998 (Fig. 5.5a). Diameter at breast height over

bark, DBH, was measured with a steel diameter tape with breast height point taken at

a standard 1.3 m above ground (Fig. 5.5b,c). Tree height was measured to the

topmost live foliage using a telescopic height pole and laser hypsometer (accuracy

2.5%) when trees were taller than 8 m (Fig. 5.5d). The breast height point was moved

upwards by up to 30 cm if necessary to avoid any irregularities in the stem. By the

final measurement in winter 1998 the trees were six years old. Coding of these

measurements was as follows: DBH94 and Height94 will refer to DBH and height

measured in 1994 and so on for the other years of measurement.

Protection

Trees were protected in the summer of 1995/96, due to a high egg population, by

aerial spraying of cypermethrin. No protection of the trees was required in the other

summers.

5.2.2 Arve trial

Site and stand characteristics

This trial was established in a plantation near Geeveston (Arve compartment

AR022E) in southern Tasmania (Appendix 5). The stand was established primarily as

a blackwood (Acacia melanoxylon) plantation with inter-planting of Eucalyptus

nitens as a ‘nurse crop’ (Fig. 5.1b). Planting was carried out in winter 1991 after

216

Figure 5.4 Destructive sampling of biomass tree 74 at the Arve site showing: (a) harvested tree before defoliation, (b) after removal of the nominal 50% of NSEL, (c) 100% removal of NSEL, and (d) removalof all adult leaves. Differences in appearance of the tree apart from thatdue to artificial defoliation are due to the different angles from whichphotographs were taken.

(a)

(d)(c)

(b)

Figure 5.4 Destructive sampling of biomass tree 74 at the Arve site showing: (a) harvested tree before defoliation, (b) after removal of the nominal 50% of NSEL, (c) 100% removal of NSEL, and (d) removalof all adult leaves. Differences in appearance of the tree apart from thatdue to artificial defoliation are due to the different angles from whichphotographs were taken.

(a)

(d)(c)

(b)

217

(a)

(c) (d)

(b)

Figure 5.5 Measurement of the Blue Gum Knob trial in August 1998(age 6) four growing seasons after the 1994 defoliation showing :(a) a defoliation treatment tree (yellow flagging tape), (b) and (c)measurement of DBH, and (d) measurement of height using a laserhypsometer.

(a)

(c) (d)

(b)

Figure 5.5 Measurement of the Blue Gum Knob trial in August 1998(age 6) four growing seasons after the 1994 defoliation showing :(a) a defoliation treatment tree (yellow flagging tape), (b) and (c)measurement of DBH, and (d) measurement of height using a laserhypsometer.

218

clearfall of native forest, windrowing, and burning. The E. nitens seedlings were

from the Torongo provenance and were fertilised at planting using 235 g per tree of

NP pasture fertiliser with N:P ratio of 11:5. The stand was planted with 3 m row

spacing with alternate rows of each species. The inter-row spacings were 4 m and

2 m for A. melanoxylon and E. nitens respectively giving corresponding stockings of

400 and 800 stems ha-1. The altitude of the compartment is approximately 260 m

with a gentle to moderately sloping south-easterly aspect. A similar site index to that

at BGK was estimated with a value of 27.6 m.

Experimental methods

Sixty E. nitens trees were selected late in the summer of 1992/93, with a height range

4 - 5.5m and adult foliage estimated visually to comprise between 5 and 25% of the

total tree leaf area. Trees were allocated to one of five classes depending on the

percentage of foliage that consisted of adult leaves (i.e. 5-10%, 10-15%, 15-20%, 20-

20%, >25%). The four treatments, including a control, were randomly allocated to

the trees in a way that gave (close to) equal representation of each treatment in each

of the above five classes. Each treatment besides the control consisted of 15 trees

while there were 18 control trees. There was no ‘blocking’ of replicate trees as was

carried out for the Blue Gum Knob trial.

Treatments

The treatments other than the control were:

1. ‘Light’ - Removal of 50% of the NSEL from each branch

2. ‘Heavy’ - Removal of 100% of the NSEL

3. ‘Heavy with disbudding’ - removal of 100% of the current season's adult

foliage, followed by three disbuddings performed fortnightly.

The treatments were carried out in late January 1993 and there were no repeat

treatments in 1994/95. For simplicity and to be able to combine the results from this

trial with those from the Blue Gum Knob trial, the above three treatments can be

considered to correspond, in the order given above, to the L_L1, H_L1, and HDL1

treatments in Table 5.2.

219

Protection

In 1993 trees were stem injected with Nuvacron 400 (CIBA-GEIGY Australia Ltd,

Pendle Hill, NSW) systemic insecticide, diluted 50% with water, at the rate of 2 ml

per cm DBHob. No insecticide treatment was employed in subsequent years.

Tree measurements

The initial pre-treatment measurement was carried out just prior to the application of

the treatments in 1993 and then measured annually for five years by which time they

were seven years old. Tree height and DBH were measured in the same way as

described for the BGK trial.

Biomass trees

Two biomass trees were used to examine the percentage of foliage removed by the

manual treatments. Trees were sequentially stripped of foliage and green weight

determined at each of the stages (1) to (4) described above for the BGK trial.

Figure 5.4 shows this progressive removal of adult foliage (i.e. up to step 3) for one

of the biomass trees at the Arve site.

5.3 RESULTS

5.3.1 Blue Gum Knob trial

5.3.1.1 Biomass sampling

Table 5.3 gives the mean, minimum, maximum and standard deviation of green

weight for each foliage component obtained from the 15 biomass sample trees. The

visual estimate of 50% slightly over-estimated the actual percentage of total green

weight of NSEL with a corresponding value of 42.75%. Total adult foliage and NSEL

averaged 30% and 25% of total leaf biomass respectively (Table 5.3).

5.3.1.2 Diameter (DBH) and Height growth response over time

Figures 5.6, 5.7, and 5.8 show the mean DBH, Height, and Height/DBH ratio (HDR)

respectively over the five years of measurement for the control and each defoliation

treatment. The means given for 1994 are pre-treatment values. The standard error

bars in Figs. 5.6 to 5.8 are based on the residual mean square from the TREExYEAR

stratum in the ‘split-plot-in-time’ ANOVA (Diggle et al., 1995, p.128) and

220

Table 5.3 summary of results of the biomass tree sa mpling at Blue Gum Knob and Arve trials.

Leaf Mass (g) Height

(m)

DBHob

(cm)

Height

(m) to

Adult

foliage

Total Nominal

50%

NSEL 1

Residual

NSEL 1

Residual

adult

Juvenile

Nominal 50%

as percent

of Total

NSEF

Blue Gum Knob trial : 15 biomass trees, 1 per replicate

Maximum 6.27 8.1 3.25 18903 2607 2790 1219 14603 50.03

Minimum 4.86 5.0 2.35 5533 239 373 122 3756 36.00

Mean 5.56 6.8 2.75 11991 1307 1680 625 8378 42.75

Std. Dev. 0.41 1.0 0.29 3797 631 652 380 3496 4.05

Arve trial : 2 biomass trees

Tree 74 12689 2308 2981 586 6814 43.64

Tree 47 9728 1729 2201 271 5527 43.99

Mean 11209 2018 2591 429 6171 43.82

1 New season edible adult leaves (i.e. leaves visually judged to be suitable for feeding by at least L4 larvae).

221

Year

Figure 5.6 DBH at measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown. Note that the s.e bars are under-estimates for late and over-estimates for early measurements due to the variance increasing with Year.

Year

DBH (cm

)DBH (cm

)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

Year

Figure 5.6 DBH at measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown. Note that the s.e bars are under-estimates for late and over-estimates for early measurements due to the variance increasing with Year.

Year

DBH (cm

)DBH (cm

)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

222

Year

Year

Height (m)

Height (m

)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

Figure 5.7 Height at measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown though these are under-estimates for late and over-estimates for early measurements due to the variance increasing with Year.

Year

Year

Height (m)

Height (m

)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

Figure 5.7 Height at measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown though these are under-estimates for late and over-estimates for early measurements due to the variance increasing with Year.

223

Figure 5.8 Height/DBH ratio at measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

Height/D

BH (m cm

-1)

Height/D

BH (m cm

-1)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

Year

Figure 5.8 Height/DBH ratio at measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

Height/D

BH (m cm

-1)

Height/D

BH (m cm

-1)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

Year

224

therefore only allow comparisons between treatments within a year. Since post-1994

measurements were positively correlated with the pre-treatment measurement for

each of the response variables, the pre-treatment measurement was removed from the

response variable and included as a covariate in the above ANOVA. In addition, the

within-treatment variance for DBH and Height tended to increase with age. Bartlett’s

test statistic (Steele and Torrie, 1960, p.347), calculated using the residuals from the

above ANOVA and the 52 treatment by year combinations (excluding 1994), gave a

the chi square statistic (df=51) of 340.23 for DBH and 107.13 for Height with

P < 0.01 in each case. This variance heterogeneity results in the standard error bars in

Figs. 5.6 to 5.8 being under-estimates for the late and over-estimates for the early

measurements. For HDR, Bartlett’s test statistic of 93.91 (P < 0.01) also indicated

heterogeneous variance though this was due to differences in variance between

treatments.

Comparison of treatments versus control

To investigate more directly the differences between individual treatments and the

control, Figs. 5.9, 5.10, and 5.11 show trellis plots of the difference between

treatment and control means for each treatment for DBH, Height, and HDR

respectively using covariate-adjusted values. The covariate-adjusted values are given

by

)(ˆ94,94,94

*94 TCii yyyy −λ+= ++

where y represents either a tree DBH, Height, or HDR with subscript T representing

any one of the treatments and C the control, y i94+* is the covariate-adjusted value

where the i subscript, i=1…4 represents the post-1994 measurements, yC ,94

represents the control mean value at the pre-treatment measurement, and λ is the

estimated regression coefficient for the covariate. Due to the problem of variance

heterogeneity both across years and between treatments the 95% confidence intervals

around zero in Figs. 5.9, 5.10, and 5.11 were calculated using internal (i.e. within

treatment) sample variances and weighted Student’s t-distribution critical values, t ′ ,

as follows (Steele and Torrie, 1960, p.81)

225

Figure 5.9 Trellis plot of treatment mean DBH minus control mean DBH (adjusted for 1994 mean DBH) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean treatm

ent -

Mean c ontrol D

BH (cm

)

Year Year

Figure 5.9 Trellis plot of treatment mean DBH minus control mean DBH (adjusted for 1994 mean DBH) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean treatm

ent -

Mean c ontrol D

BH (cm

)

Year Year

226

Figure 5.10 Trellis plot of treatment mean Height minus control mean Height (adjusted for 1994 mean Height) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean treatm

ent -Mea

n c ontrol H

eight (m )

Year Year

Figure 5.10 Trellis plot of treatment mean Height minus control mean Height (adjusted for 1994 mean Height) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean treatm

ent -Mea

n c ontrol H

eight (m )

Year Year

227

Figure 5.11 Trellis plot of treatment mean Height/DBH ratio (HDR) minus control mean (adjusted for 1994 mean HDR) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean trea

tment -

Mean control H

DR (m cm

-1)

Year Year

Figure 5.11 Trellis plot of treatment mean Height/DBH ratio (HDR) minus control mean (adjusted for 1994 mean HDR) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean trea

tment -

Mean control H

DR (m cm

-1)

Year Year

228

TC

TTCC

ww

twtwt

++

=′

where w sC C= 2 50/ and w sT T= 2 15/ , sC2 and sT

2 are the estimated variance for the

control and particular treatment respectively, and tC and tT are the 95% (two-sided)

Student’s t critical values with 49 and 14 degrees of freedom respectively.

Wald tests of TREATMENT and YEAR effects

Formal tests of significance are given in Table 5.4 using Wald tests obtained from the

fit of the linear mixed model (LMM) for each of DBH and Height, again including

the pre-treatment measurement as a covariate as estimated by GENSTAT’s REML

directive.

The LMM incorporated fixed effects TREAT, YEAR and their interaction

(TREAT x YEAR), a covariate of either DBH94 or Height94, and block effects

(REPS). Variance heterogeneity was handled by estimating a separate variance

parameter for each year. A number of models of the between-year correlation were

tried including a first order autoregressive model [=AR(1)], uniform correlation, and

an unstructured correlation matrix (Diggle et al. 1995; Genstat 5 Committee 1997b).

Only the uniform correlation structure, or ‘split-plot-in-time’ model (Diggle et al.,

1995, p.128), gave satisfactory results probably because of the short length of the

time series in the case of the AR(1) model. Table 5.5 gives the estimates of variance

parameters and covariate regression parameter for each of DBH and Height.

Table 5.4 Wald tests for the ‘split-plot-in-time’ m odel of

DBH and Height with variance heterogeneity over yea rs

Fixed term d.f. Wald statistica

DBH Height

YEAR 3 4650.9b 8419.3b

TREAT 12 192.4b 72.8b

TREAT x YEAR 36 122.0b 74.8b

Covariate (1994) 1 2095.1b 92.6b

REP 14 46.6b 34.7b

a. Distributed asymptotically as a chi square

b. P<0.001

229

The significance of each fixed effect term given by the Wald test is dependent on the

order in which the term is fitted (i.e. the significance of a term is conditional on those

terms appearing above it in Table 5.4). The TREAT x YEAR is significant for both

DBH and Height and the Wald chi square values were larger than those in Table 5.5

if DBH94 or Height94 were fitted before the TREAT and YEAR terms. The order of

terms in Table 5.4 demonstrates that the REP effect is of minor importance if the

covariate DBH94 or Height94 is already included in the model.

Table 5.5 Covariate regression and variance paramet ers for the mixed

‘split-plot-in-time’ model with variance heterogene ity over time for

DBH and Height

Parameter DBH Height

Estimate s.e. Estimate s.e.

Covariate 1.0790 0.0242 1.0340 0.1070

Residual variance 2σ 0.0943 0.0054 0.1807 0.0102

Correlation ρ 0.999 * 0.999 *

Scaled variances iγσ2

1γ (1995) 1.84 0.31 0.724 0.166

2γ (1996) 11.63 1.42 2.468 0.365

3γ (1997) 25.94 3.07 4.558 0.612

4γ (1998) 42.50 4.96 7.059 0.909

DBH and Height increment and relative growth

Figures 5.12 and 5.13 show the mean annual DBH and Height increments

respectively for each treatment where these are not covariate-adjusted values. The

within-treatment variance significantly increased with year only for Height

increment. Bartlett’s test statistic for all 52 treatment by year combinations was 60.8

(P > 0.1) for DBH and 103.1 (P < 0.001) for Height. The standard error bars were

obtained in the same way as described above for DBH and Height with a caveat on

their relevance over time for Height due to the heterogeneous error variance.

230

Year

Figure 5.12 Annual DBH increment to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

DBH increm

ent (cm

)DBH increm

ent (cm

)(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

Year

Figure 5.12 Annual DBH increment to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

DBH increm

ent (cm

)DBH increm

ent (cm

)(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

231

Year

Figure 5.13 Annual height increment to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

Heigh

t increment (m)

Height incremen

t (m)

(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

Year

Figure 5.13 Annual height increment to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

Heigh

t increment (m)

Height incremen

t (m)

(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

232

Figures 5.14 and 5.15 were obtained in a similar way and show the mean relative

annual DBH and Height growth respectively for each treatment where relative

growth over the period of year i–1 to i is given for DBH at year i by

)ln()ln( 1−− ii DBHDBH and is similarly defined for Height. The standard error bars

were obtained in the same way as described above and again a feature of the residuals

was variance increasing with year but this time for DBH. Bartlett’s test statistic for

all 52 treatment by year combinations was 117.6 for DBH and 64.54 for Height

giving P<0.001 and P=0.096 respectively.

Key results

At this point it is worth noting the key results from the above analyses as background

to the development of the model of growth impact for each of DBH and Height.

For DBH these results are:

1. The late treatments produced a greater loss in increment than the early treatments.

2. As expected, the repeat (year 2) treatments had a greater negative impact on

growth than the single year treatments, though this was only obvious for the

heavy treatments.

3. Most importantly for the following model development, by 1998 (at age 6 or

three full growing seasons subsequent to the first-year defoliation treatments) the

relative growth rates for all treatments had recovered to that of the control. The

possible exception to this is the H_L2 treatment (Fig. 5.14). Although the mean

growth rate for this treatment recovered rapidly it was still slower that the control

and other treatments at the last measurement. Although this difference was not

statistically significant, given the standard error bars shown in Fig. 5.14, the

difference is likely to be real but small enough for practical purposes to ignore.

The variance heterogeneity makes the statistical significance of some of these

comparisons unclear. However, there is strong a priori grounds for expecting real

growth losses that increase with intensity and frequency of defoliation so that

carrying out tests of significance is less important than obtaining estimates of the

magnitude of the mean growth losses and their variability. This situation is less clear

for the timing treatment.

233

Year

Figure 5.14 DBH relative growth to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

DBH relative grow

th

DBH relative grow

th(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

Year

Figure 5.14 DBH relative growth to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

DBH relative grow

th

DBH relative grow

th(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

234

Year

Figure 5.15 Height relative growth to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Height relative grow

th

Height relative grow

th

(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

Year

Year

Figure 5.15 Height relative growth to measurement year for (a) heavy and (b) light treatments for Blue Gum Knob artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Height relative grow

th

Height relative grow

th

(a)

(b)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

Year

235

The key results from the above analyses for Height are similar to those for DBH

except that the negative effect of the treatments on growth is far less pronounced. In

fact with the exception of the H_L2 treatment, Figs. 5.13 and 5.15 indicate that the

response to defoliation can be an increase in height growth after an initial growth loss

in the first year after treatment. This can be seen clearly in Fig. 5.15 where, after

lower growth in 94/95 compared to the control, all treatments with the exception of

H_L2 and L_L2 increased their relative height growth compared to the control in

95/96 and 96/97. By the end of the first growing season after the second year

treatment (i.e. winter 1996) the height increment of treated trees was generally

greater than the control but by the end of the third growing season (i.e. winter 1998)

all treatments had very similar relative height growth rates to the control.

Height to diameter ratio

The response of the Height/DBH ratio to the treatments can give insights that are

more difficult to obtain by considering DBH and Height independently. Figure 5.8

shows that for the control trees there was a sharp drop in the mean of this ratio

between 1995 and 1996 reflecting the increase in DBH increment between 94-95 and

95-96 (Fig. 5.12) relative to a decrease in Height increment (Fig. 5.13). The ‘light,

early,once’ treatment (L_E1) can be seen to closely follow the same trend as the

control (Fig. 5.8b) indicating the generality of this trend when there has been little or

no defoliation. The overall trend for heavier defoliation is that Height/DBH ratio

increases relative to the control after treatment. This is more clearly seen in the trellis

plots in Fig. 5.11. Although most of the treatment versus control differences fall

within 95% confidence bounds about zero, taking all trends together, there is an

obvious increase in the ratio for all but the least severe treatments. This reflects the

greater effect of defoliation on DBH relative to Height as noted above.

Recovery of growth

In terms of modelling the growth impact of defoliation the key result from the above

is as follows. By the third growing season after the first year defoliation, given at

most one repeat defoliation, the relative growth of all treatments for both DBH and

Height had fully recovered (or had almost fully recovered in the case of H_L2 for

DBH) to that of the control.

236

5.3.2 Arve trial

Table 5.3 gives the green weight for each foliage component obtained from the two

biomass sample trees. The average percentage of actual green weight for the nominal

50% of NSEL was very similar to the average for the 15 biomass trees from BGK,

these being 43.8% and 42.8% respectively. For the following the percentage for the

Arve trial used in model (5.2) will be taken as that for BGK of 42.8% due to the

greater sample size of biomass trees for BGK.

The statistical methods used here are the same as those described for the Blue Gum

Knob trial with the exception that in this trial there are no replicate ‘block’ (=REP)

effects. Figure 5.16 shows each of mean DBH and mean Height over the six years of

measurement for the control and each defoliation treatment. The means for 1993 are

pre-treatment values. Figure 5.17(a) shows means similarly calculated for

Height/DBH ratio. The split-plot-in-time ANOVA with 1993 measurement as a

covariate was carried out for DBH and Height as was done for BGK. Bartlett’s test

statistic for residuals from the ANOVA for the 19 treatment by year combinations

was 173.34 for DBH and 30.19 for Height giving P<0.001 and P=0.0495

respectively. Table 5.6 gives the Wald tests from REML after the fit of the linear

mixed models with covariate and variance parameters given in Table 5.7. The only

difference in the results here compared to Blue Gum Knob, is that the continuous-

time AR(1) model was successfully fitted for Height and was superior in fit to the

uniform correlation model. Therefore the correlation between years 92+i and 92+i+j

for height is given by jρ rather than ρ for the uniform correlation model.

Figures 5.18(b) and 5.19 give trellis plots for the treatment versus control

comparison, adjusted for the 1993 measurement, for each of Height/DBH ratio,

DBH, and Height respectively. Figures 5.19 and 5.20 show mean absolute and

relative growth, respectively, for DBH and Height.

237

Year

Figure 5.16 Mean (a) DBH and (b) Height at measurement year for Arveartificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

Height (m)

DBH (cm

)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

Year

Figure 5.16 Mean (a) DBH and (b) Height at measurement year for Arveartificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Year

Height (m)

DBH (cm

)

2 x se(C)

2 x se(T)

2 x se(T)

2 x se(C)

(a)

(b)

238

Year

Height/D

BH ratio (m cm

-1)

Figure 5.17 Mean Height/DBH ratio (HDR) : (a) mean HDR versus year and(b) Trellis plot of HDR for treatment mean minus control mean (adjusted for mean 1993 HDR) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars. Standard error bars for the control (C) and treatments (T) are shown in (a).

(a)

(b)

Year

Mean treatm

ent -Mea

n Con

trol HDR (m cm

-1)

2 x se(C) 2 x se(T)

Year

Height/D

BH ratio (m cm

-1)

Figure 5.17 Mean Height/DBH ratio (HDR) : (a) mean HDR versus year and(b) Trellis plot of HDR for treatment mean minus control mean (adjusted for mean 1993 HDR) versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars. Standard error bars for the control (C) and treatments (T) are shown in (a).

(a)

(b)

Year

Mean treatm

ent -Mea

n Con

trol HDR (m cm

-1)

2 x se(C) 2 x se(T)

239

Table 5.6 Wald tests for the mixed ‘split-plot-in-t ime’

model with variance heterogeneity over time for DBH and

Height

Fixed term d.f. Wald statistica

DBH Height

Covariate (1993) 1 289.6b 25.2b

YEAR 4 709.8b 1358.3b

TREAT 3 3.7c 79.6b

TREAT x YEAR 12 24.7d 11.3c

a. Distributed asymptotically as a chi square

b. P<0.001

c. P>0.1

d. P<0.025

Table 5.7 Covariate regression and variance paramet ers for the mixed

‘split-plot-in-time’ model with variance heterogene ity over time for

DBH and Height

Parameter DBH Height

Estimate s.e. Estimate s.e.

Covariate (1993) 0.9543 0.0581 0.8209 0.1586

Residual variance 2σ 0.1932 0.0184 0.1076 0.0353

Correlation ρ 0.999 * 0.8745 0.0301

Scaled variances iγσ2

1γ (1994) 3.45 0.86 2.40 1.30

2γ (1995) 13.76 2.79 7.72 3.35

3γ (1996) 28.38 5.50 24.29 9.36

4γ (1997) 44.86 8.53 32.22 11.84

5γ (1998) 66.20 12.45 34.78 12.66

Key results

The trends described in Figs. 5.16 to 5.20 generally confirm the trends observed for

the BGK trial. Although the range of treatments is greatly restricted compared to

BGK the main results are :

1. A significant effect of TREAT or TIME.TREAT interaction on DBH and Height.

240

Mea

n treatm

ent D

BH -Mean Control DBH (cm

)

Year

Figure 5.18 Trellis plot of (a) DBH and (b) Height for treatment mean minus control mean adjusted for mean 1993 measurement versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean treatm

ent H

eight -Mean Control Height (m)

Year

(a)

(b)

Mea

n treatm

ent D

BH -Mean Control DBH (cm

)

Year

Figure 5.18 Trellis plot of (a) DBH and (b) Height for treatment mean minus control mean adjusted for mean 1993 measurement versus measurement year. Approximate 95% confidence intervals for the difference are shown as the bars.

Mean treatm

ent H

eight -Mean Control Height (m)

Year

(a)

(b)

241

Year

DBH increment (cm

)

2 x se(C) 2 x se(T)

Year

Figure 5.19 Annual (a) DBH and (b) Height increment to measurement year for Arve artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Height increm

ent (m)

2 x se(T)2 x se(C)

(a)

(b)

Year

DBH increment (cm

)

2 x se(C) 2 x se(T)

Year

Figure 5.19 Annual (a) DBH and (b) Height increment to measurement year for Arve artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Height increm

ent (m)

2 x se(T)2 x se(C)

(a)

(b)

242

Year

DBH relative grow

th(a)

2 x se(C) 2 x se(T)

Year

Figure 5.20 Relative (a) DBH (b) Height growth to measurement year for Arve artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Height relative grow

th

2 x se(T)2 x se(C)

(b)

0.0

Year

DBH relative grow

th(a)

2 x se(C) 2 x se(T)

Year

Figure 5.20 Relative (a) DBH (b) Height growth to measurement year for Arve artificial defoliation trial. Standard error bars for the control (C) and treatments (T) are shown.

Height relative grow

th

2 x se(T)2 x se(C)

(b)

0.0

243

2. At the end of the fourth growing season after the growing season in which

treatments were applied, the mean relative growth rate for all defoliation

treatments were not significantly different to that of the control for both DBH and

Height.

3. The Height to DBH ratio increased with time for the treated trees after an initial

decline with this effect more obvious for the ‘heavy’ intensity treatments. These

trends when considered alone were not significant but when combined with the

results for BGK they indicate that there is a delayed but more sustained impact of

defoliation on DBH growth compared to that for height growth.

4. The impact of ‘heavy’ intensity treatments on Height growth (Fig. 5.18b) is

greater than that for BGK ( 5.10).

5.4 A MODEL OF THE GROWTH IMPACT OF DEFOLIATION

To develop a model to predict the impact on DBH and height growth of a given level

of defoliation the model described by Candy et al. (1992) was employed and

subsequently modified. The model was calibrated using the data from the BGK trial

and validated using the Arve trial data. Only the final measurement in 1998 was

modelled given that the results above indicate that the impact of defoliation was fully

expressed by that time.

The model of the effect of defoliation of new season’s foliage is

( ) ( )[ ]ERREexpPDy 321211 τ+τ+τβ+β−α= γ (5.1)

where y is the response variable (either DBH98 or Height98) for the individual trees

and as in Candy et al. (1992), D is an indicator variable for disbudding (D=1 for

disbudding, 0 otherwise), P is the proportion of new season’s foliage removed, E

indicates early season defoliation (E=1 early, E=0 late), R indicates repeat of the first

years treatment in the following year (R=1, 0 otherwise), and 2121 ,,,,, ττγββα and 3τ

are parameters to be estimated. As in Candy et al. (1992), an estimate of α is taken

as the mean value of the controls yC . Note that a separate parameter for late season

244

defoliation is not estimated as in Candy et al. (1992) since in this trial there was no

treatment combination of early and late defoliation in the same season. Here, if we

set D,E,R=0 then β2 defines the baseline effect for late defoliation so that the effect

of early defoliation is 21)exp( βτ . Alternatively, the baseline parameter β2 could

have been set for the early defoliation. As a further modification to the model of

Candy et al. (1992) it was found that incorporating initial measurements of the

response value (i.e. before treatments were applied) as a covariate greatly improved

the fit of the model for both individual-tree DBH and height. Carne et al. (1974) also

found it necessary to predict control tree height growth using initial height as a

covariate. Model (5.1) then becomes

( ) ( )[ ] 0321211 yERREexpPDyy C λ+τ+τ+τβ+β−θ= γ (5.2)

where 0y is the response variable at the initial measurement of the tree (i.e. DBH94

or Height94) and θ λ, are additional parameters to be estimated. Models (5.1) and

(5.2) were fitted using GENSTAT’s FITNONLINEAR directive which uses

numerical derivatives. Estimation of the parameters involved iterating between a

nonlinear fit for those parameters that appear nonlinearly in (5.2) and a linear fit for

the θ λ, parameters. However, the ordinary least squares (OLS) fit using

FITNONLINEAR ignores the nesting of sampling units (i.e. trees) within replicates

(REP). REP is a random effect factor since in the application of (5.2) the REP effects

are unknown and part of the random variation about the regression. For this reason

(5.2) was fitted as a nonlinear mixed model (NLMM) (Lindstrom and Bates, 1990;

Vonesh and Carter, 1992; Schabenberger and Gregoire, 1995; Candy, 1997b) with

REP included simply as an additive random effect in the model error. To facilitate

estimation (5.2) was reparameterised as

( ) ( ) iPCP

ijCij

bERREPDyD

yyy

+τ+τ+τ+′γ+δβ′+β′++θδ+−

λ+θ=

32121

0

lnlnlnexp

(5.3)

where the i subscript represents the replicate number and j the tree within replicate,

)ln(),ln( 2211 β=β′β=β′ , 1=δP if P is greater than zero and zero otherwise, P′ is

245

PP δ+⌣

where Pδ⌣

is the complement of Pδ (i.e. 1=δP

⌣ if 0=δP and zero

otherwise), and ib is a random replicate effect with variance 2bσ . The variables Pδ

and P′ are introduced in (5.3) to allow predicted values for the controls to be

correctly handled, that is to give a zero value for the third term on the RHS of (5.3).

The NLMM fitting method for (5.3) used here follows along the lines of Appendix 1

of Candy (1997b) and involves linearizing (5.3) using a first-order Taylor series

expansion and iteratively fitting the resulting linear mixed model. Since the random

effects appear in the additive error in (5.3) there is no difference between population-

average (PA) and subject-specific (SS) parameter estimates (Zeger et al. 1988;

Schabenberger and Gregoire 1996; Candy 1997a). The estimates of the regression

parameters from the fit of the NLMM are also generalised least squares (GLS)

estimates.

It was clear from the fit of model (5.3) using GLS that the following parameter

values could be assumed, 0;1 3 =τ=γ , with t-statistics for the hypothesis of no

departure from these values of 0.711 and 0.248 respectively for DBH98 and 0.086

and 0.061 respectively for Height98. Even under non-conservative degrees of

freedom of 224 (i.e. ignoring the presence of random REPS effects) these hypotheses

can be accepted at P>0.1. For the remainder, reference to either parameterisation of

(5.2) or (5.3) will assume 0;1 3 =τ=γ .

Model Results of the fit of model (5.3) using both OLS and GLS are given for

DBH98 in Table 5.8 and for Height98 in Table 5.9. From Tables 5.8 and 5.9 it can be

seen that the OLS and GLS parameter estimates and their standard errors are of

similar size. The differences, though, are worth noting even in the case of Height98

where the random REPS effects variance can be considered not significantly different

from zero if the quoted standard error is accurate. For both DBH98 and Height98 the

random REPS effects variance is small relative to the between-tree variance. The

OLS parameter estimates are preferred over the GLS estimates for reasons explained

below.

246

Table 5.8 Regression parameter estimates (s.e.) for model (5.3) for DBH98 from OLS and GLS fits .

Term, parameter OLS GLS

Defoliation, θ 0.506 (0.043)

0.533 (0.044)

Covariate, λ 1.499 (0.125)

1.473 (0.119)

D, 1β′ , 1β -2.320, 0.0983 (0.524)

-2.772 (0.706)

P’ , 2β′ , 2β -1.607, 0.2005 (0.295)

-1.470 (0.221)

E, 1τ -0.608 (0.237)

-0.539 (0.164)

R, 2τ 0.678 (0.276)

0.467 (0.157)

REPS, 2bσ - 0.692

(0.341)

Trees/REPS, 2σ 3.770 3.165

(0.309)

Table 5.9 Regression parameter estimates (s.e.) for model (5.3) for Height98 from OLS and GLS fits . Term, parameter OLS GLS

Defoliation, θ 0.486 (0.082)

0.452 (0.080)

Covariate, λ 1.496 (0.231)

1.606 (0.225)

D, 1β′ , 1β -3.083, 0.0458 (0.945)

-3.695 (1.816)

P’ , 2β′ , 2β -2.712, 0.0664 (0.730)

-2.309 (0.467)

E, 1τ -1.830 (1.170)

-1.680 (0.838)

R, 2τ 1.319 (0.675)

0.887 (0.348)

REPS, 2bσ - 0.131

(0.082)

Trees/REPS, 2σ 1.390 1.288

(0.126)

Figures 5.21 and 5.22 show regression diagnostics for OLS residuals for DBH98 and

Height98 respectively using Genstat’s RCHECK procedure (Payne et al.,1997) which

gives a histogram of residuals, scatterplot of residuals versus fitted values (with fitted

cubic smoothing spline), normal, and half-normal residual plots. Homogeneity of

variance of residuals across the 13 treatment combinations gave Bartlett statistics

247

Figure 5.21 Regression diagnostics for OLS residuals from the fit of model (5.3) to DBH at 1998.Figure 5.21 Regression diagnostics for OLS residuals from the fit of model (5.3) to DBH at 1998.

248

Figure 5.22 Regression diagnostics for OLS residuals from the fit of (4.3) to Height at 1998.Figure 5.22 Regression diagnostics for OLS residuals from the fit of (4.3) to Height at 1998.

249

(df=12) of 8.29 for DBH98 and 32.3 for Height98 with corresponding probabilities

of P=0.7621 and P=0.0012 respectively.

Apart from the three outliers for Height98 seen in Fig. 5.22 as two extreme negative

residuals and one extreme positive residual, the residuals appear to be adequately

described by a normal distribution with homogeneous variances. When these outliers

were removed Bartlett’s statistic reduced to 2.52; (P=0.9981). There is a slight

degree of nonlinearity in the Height98 normal plot in Fig. 5.22.

Figures 5.23 and 5.24 show the treatment means and standard errors for DBH98 and

Height98, respectively, versus fitted values along with the line of perfect fit. These

means were sorted in rank order in terms of the OLS fitted values for model (5.3).

The complete set of treatments has been divided onto two separate graphs to improve

clarity. The corresponding figures to 5.23 and 5.24 obtained for the GLS fit of model

(5.3) are not given since they were very similar (but see Section 5.5).

Both observed and fitted (or predicted) means have been adjusted for the covariate

regression of DBH98 and Height98 on DBH94 and Height94 respectively using the

mean of the 1994 measurements. The adjustment to the observed means is given by

( )00ˆ

TCTT yyyy −λ+=′

where Ty′ is the adjusted 1998 individual tree value for a treatment, say treatment

‘T’, 0Cy is the 1994 control mean, and 0Ty is the 1994 mean for treatment T. The

same adjustment was carried out for the fitted values from model (5.3) so that Ty′ and

Ty are replaced by Ty ′ and Ty respectively in the above equation.

5.4.2 Validation of model (5.3) using the Arve trial data

Due to the small number of treatments the model given by (5.3) was not fitted

separately to the Arve trial data. Instead, the model calibrated from the BGK 1998

measurement for each of DBH and Height was validated using the four treatments at

the Arve trial. However, it was necessary to re-calibrate the parameter λ of model

250

Mean DBH (cm

)Mea

n DBH (cm

)

Fitted values

Fitted values

Figure 5.23 Observed and fitted (OLS) mean DBH at 1998, adjusted for DBH94, showing treatment codes and standard error bars.

H_L2

L_L2

H_L1 HDE1

LDE1

L_L1

CONTROL

HDL1

LDL1

H_E2

L_E2H_E1

L_E1

CONTROL

Mean DBH (cm

)Mea

n DBH (cm

)

Fitted values

Fitted values

Figure 5.23 Observed and fitted (OLS) mean DBH at 1998, adjusted for DBH94, showing treatment codes and standard error bars.

H_L2

L_L2

H_L1 HDE1

LDE1

L_L1

CONTROL

HDL1

LDL1

H_E2

L_E2H_E1

L_E1

CONTROL

251

Mean He igh

t (m)

Fitted values

Fitted values

Figure 5.24 Observed and fitted (OLS) mean Height at 1998, adjusting for Height94, showing treatment codes and standard error bars.

H_L2

L_L2

H_L1

HDE1

LDE1

L_L1

CONTROL

HDL1

LDL1

H_E2

L_E2

H_E1

L_E1CONTROL

Me an Height (m)

Mean He igh

t (m)

Fitted values

Fitted values

Figure 5.24 Observed and fitted (OLS) mean Height at 1998, adjusting for Height94, showing treatment codes and standard error bars.

H_L2

L_L2

H_L1

HDE1

LDE1

L_L1

CONTROL

HDL1

LDL1

H_E2

L_E2

H_E1

L_E1CONTROL

Me an Height (m)

252

(5.3) to account for the younger age for the initial, pre-treatment measurement (i.e.

one and a half growing seasons from planting compared to two for BKG). The other

parameters were fixed at the OLS estimates given in Tables 5.8 and 5.9. Therefore,

the only inputs that differed from those used in the fit to the BGK data were, y, Cy ,

and 0yλ . The regression was therefore of y on 0y without a regression intercept but

with the other terms in (5.3), using the parameter estimates in Tables 5.8 or 5.9,

included as an ‘offset’ in the linear predictor (McCullagh and Nelder, 1989, p.206).

Figures 5.25 and 5.26 show regression diagnostics from RCHECK for DBH98 and

Height98 respectively. The residuals appear reasonably well described by a normal

distribution with no obvious bias with respect to fitted values (though these residual

plots do not identify treatments). Figure 5.27(a) and (b) show the fit of (5.3) to the

four treatment means for DBH98 and Height98, respectively, after adjustment using

the 1993 measurement as a covariate. The method of adjustment was the same as that

used for Figures 5.23 and 5.24 for BGK. The prediction of the adjusted treatment

means for DBH98 are unbiased and reasonably precise but those for Height98 tend to

under-estimate the adjusted means for the control and light intensity treatments while

over-estimating that of the heavy treatments.

5.5 MODEL PROPERTIES AND APPLICATION

For the following it is simpler to refer to the parameterisation of the model as (5.2)

rather than the fitted form of (5.3). As in Candy et al. (1992), the main use of

model (5.2) is to determine the economic impact of different levels of defoliation.

This requires estimation growth loss as a function of defoliation level (or intensity),

as quantified by (5.2), where defoliation level is expressed as the percentage of new

foliage removed. Only three levels of defoliation were carried out in the above trials

being nominal defoliation intensities of 0, 50, and 100% and corresponding actual

intensities of 0, 42.75, and 100%. Model (5.2) allows interpolation to any value of

percent defoliation and extrapolation to different ages to that at the final

measurement age used in the trial.

253

Figure 5.25 Regression diagnostics for OLS residuals from the fit of model (5.3) to DBH at 1998 for the Arve trial.Figure 5.25 Regression diagnostics for OLS residuals from the fit of model (5.3) to DBH at 1998 for the Arve trial.

254

Figure 5.26 Regression diagnostics for OLS residuals from the fit of model (5.3) to Height at 1998 for the Arve trial.Figure 5.26 Regression diagnostics for OLS residuals from the fit of model (5.3) to Height at 1998 for the Arve trial.

255

Mea

n He igh

t (m)

Mean DBH (cm

)

Fitted values

Fitted values

Figure 5.27 Observed and fitted (OLS) mean (a) DBH and (b) Height at 1998, adjusted for 1993 pre-treatment measurement, showing treatment codes and standard error bars for the Arve trial.

H_L1

L_L1

CONTROL

HDL1

CONTROL

HDL1

H_L1

L_L1

Mea

n He igh

t (m)

Mean DBH (cm

)

Fitted values

Fitted values

Figure 5.27 Observed and fitted (OLS) mean (a) DBH and (b) Height at 1998, adjusted for 1993 pre-treatment measurement, showing treatment codes and standard error bars for the Arve trial.

H_L1

L_L1

CONTROL

HDL1

CONTROL

HDL1

H_L1

L_L1

256

To allow extrapolation to other ages Candy et al. (1992) simply defined model (5.1)

as the height of defoliated trees relative to that of the control by dividing both sides

of (5.1) by the mean control height, yC .

Model (5.2) needs to be modified to allow its general application due to the inclusion

of the term 0yλ involving initial DBH or Height, 0y . This modification involves

averaging both sides of the equation for trees with same timing, frequency, and level

of defoliation and presence or absence of disbudding treatment, and applying the

following logical constraint for controls (i.e. D,P=0),

0CCC yyy λ+θ=

where 0Cy is the mean of the initial value of DBH or Height for control trees. This

gives

CC yy )1(0 θ−=λ (5.4).

Since, it can be assumed that 000 yyy CT == , when the RHS of (5.4) is substituted

for 0yλ in the averaged form of (5.2) the following model of relative DBH or height

of defoliated to control trees is obtained

( ) ( )ERREPDy

y

C

T32121 exp1 τ+τ+τβ+βθ−= γ (5.5).

To obtain (5.5) the constraint (5.4) on the parametersλ and θ was imposed and this

gives an alternative estimate of λ , λ~ , to that obtained from the fit of (5.3) where

0

)ˆ1(~

C

C

y

yθ−=λ

257

and θ is the estimate from the fit of (5.3). Given as λ the simultaneous estimate

from the fit of (5.3) (Tables 5.8 and 5.9), it was found that the OLS fit gave a value

for λ~ that was closer to λ compared to those from the fit using GLS for each of

DBH and Height. That is, for DBH98 and OLS the pair ( λ ,λ~ ) was (1.499,1.509)

while for GLS it was (1.473,1.425). For Height98 the difference between λ and λ~

was not as great with values of (1.606,1.586) for OLS while GLS gave (1.496,1.487).

The effect of the difference between λ andλ~ can be seen for OLS in Figs. 5.23 to

5.24 since the 1:1 line based on λ does not pass exactly through the control mean

whereas if λ~ is used instead the agreement is exact.

Generally, the GLS parameter estimates would be recommended over the OLS

because they are more efficient and standard errors are more reliable (Dielman,

1983). Here the OLS estimates are preferred since : (1) the REP variance is relatively

insignificant, (2) model parameters are judged to have a similar degree of

significance (based on t-tests of estimate divided by standard error) whether OLS or

GLS is used, and (3) the pair (λ ,λ~ ) is more consistently estimated using OLS. It

would be possible to incorporate constraint (5.4) into the OLS and GLS fitting

procedures but this would worsen the fit and thus make the estimates of the

parameters of interest, given in (5.5), less accurate.

Note that the RHS of (5.5) is independent of the initial value of DBH or Height at the

age of defoliation. This allows (5.5) to be applied to stands of different age at the

defoliation episode and/or stands of different site quality to that of BGK. Note also

that, for this reason, it was necessary to provide values of 0y and re-calibrate model

(5.2) for the λ parameter to make the model relevant to the Arve trial. By relevant, it

is meant that, given that the model is correct, then re-calibrated it gives unbiased

predictions of growth losses due to defoliation. In application of the model for

predicting such impacts in stands in which C. bimaculata populations are monitored

(Section 7.4) the data required to carry out this ‘re-calibration’ are not available.

Therefore, it was necessary to sacrifice some predictive power of (5.2) by eliminating

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the term 0ˆyλ from the fitted model in order to be able to apply the model in the form

of (5.5).

Comparison with model (1) of Candy et al. (1992) for E. regnans

The OLS parameter estimates of )]exp([ 11 β′=β and )]exp([ 22 β′=β in model (5.3)

for Height98 of 0.046 and 0.066 after scaling by 486.0=θ are considerably smaller

than those obtained by Candy et al. (1992) of 0.056 and 0.042 for E. regnans height

growth for a model of the form of (5.5) but with 1=θ . These parameter estimates for

DBH98 of 0.098 and 0.200 respectively, obtained after scaling by 506.0=θ , reflect

the greater impact of defoliation on DBH growth compared to height growth. Note

that with these scaled values for DBH98 the effect of 50% actual defoliation

corresponds to very close to the effect of a disbudding. Comparisons of the other

terms in the model of Candy et al. (1992) to model (5.6) are complicated by the

presence of θ in model (5.5), the significant ER interaction, and the ability to include

both an early and late defoliation in the same season in model (1) of Candy et al.

(1992).

Comparison of early versus late defoliation

The equivalence of the fixed effect model parameterisations of (5.2) or (5.3) can be

seen if the term EP 12 τ+δβ′ in (5.3) is replaced by LP 112 )( τ′+δτ+β′ where L is

defined as 1 if timing is ‘late’ and 0 otherwise (i.e. ‘early’) and 11 τ−=τ′ . This

corresponds to setting the zero reference, or baseline, level to ‘early’ rather than ‘late’

so that '1τ gives the impact of L relative to the zero effect of E. From the fit of model

(5.2) it was determined that the ER interaction was not significant (i.e. the hypothesis

03 =τ was accepted). Model (5.5) can be expressed, after dropping non-significant

terms, as

( ) ( ) ( )REPDy

y

C

T2121 expexp1 ττβ+βθ−=

which demonstrates the full multiplicative nature of the model.

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Given the above, a comparison of the relative effect of early versus late treatments

can be made using the parameter estimates in Tables 5.8 and 5.9. The late defoliation

has a greater negative impact on growth than early defoliation at the same intensity

for both DBH and Height since 1τ is negative (i.e. and thus 1τ′ is positive) in each

case. In contrast, Candy et al (1992) found for E. regnans that a single early

defoliation had a greater impact than a late defoliation. However, given the parameter

estimates and their standard errors reported in their Table 7, that difference would not

be considered statistically significant.

5.6 DISCUSSION

Accuracy of manual defoliation in simulating defoliation caused by C. bimaculata

The manual stripping of leaves in these trials was carried out for a given tree on a

single day while disbudding was carried out over a period of one to two months. This

was because it is impractical in an artificial defoliation trial to reproduce the ‘bite-by-

bite’ defoliation caused by phytophagous insects. Baldwin (1990) reviewed the

ability of artificial defoliation experiments to accurately mimic natural defoliation.

The deficiencies in artificial defoliation relate mostly to the inability of the simple

manual leaf stripping process to adequately mimic the complex nature of the natural

processes involved in feeding. These include the nature of tissue shearing, the

amount, timing and spatial distribution of tissue removal, the introduction into the

plant tissues of fungi, saliva or other contaminants, and the plant’s response to these

damaging processes. Baldwin (1990) concluded that in the absence of the ideal

simulated herbivory experiment, ecologists need to proceed with caution since

mechanical damage does not adequately simulate true herbivory.

The objective of this study is prediction of the impact of defoliation at a level of

accuracy that is adequate for decision-making for the control of monitored

populations. Therefore, despite the crudeness of the simulation of the impact of

natural defoliation on tree growth using artificial defoliation experiments, the use of

model (5.5) should be adequate for this purpose (Section 7.4). However, artificial

defoliation studies cannot be sufficiently accurate to be useful for developing an

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understanding of the complex processes involved in the interaction of phytophagy

and the physiological response of the tree such as the production of manna

(Fig. 4.3c). Fundamental research is required to determine the role of manna as a

possible deterrent to browsing and the physiological cost to the tree of its production.

It is not possible here to rigorously determine the level of accuracy of the growth

impacts of artificial relative to actual defoliation but some general observations can

give some encouragement on the usefulness of the models as follows:

1. Disbudding was carried out progressively as new shoots developed over a period

which approximated the feeding period for larvae (1 month) for the early

defoliation and larvae and newly emerged adults (2 months) for the late

defoliation.

2. The L3 and L4 instars account for 87% of the total leaf biomass consumed (i.e.

green weight) (Baker et al., 1999) by an individual from L1 larval to pre-pupal

stages. The total development time for L3 and L4 instars is approximately 9 days

assuming an average daily temperature of 15o C and the day-degrees required for

development (see Table 6.2). This period is much closer to the single day period

for artificial defoliation than the corresponding total period of feeding by an

individual, under these conditions, of approximately 28 days.

3. Although disbudding was simulated as an ‘all-or-nothing’ process, observations

from the caged-shoot feeding trial (Chapter 4) indicated that when larvae disbud a

shoot all buds are eaten or damaged. In addition, since the growth impact of

removal of newly emerged leaves should be similar to that for bud removal and

these leaves are preferentially browsed, then these leaves are likely to be

completely removed during the feeding period if they were not removed at the

bud stage.

Simplifying the complex growth responses to defoliation

The split-plot-in-time analyses of all annual measurements, given in Table 5.4 for the

BGK trial and Table 5.6 for the Arve trial, demonstrate the complex response of both

DBH and Height over time to defoliation treatments as indicated by significant

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TREAT x YEAR interaction and covariate effects. However, despite this complexity

it was possible to simplify the model by taking advantage of the substantial number

of annual measurements taken after the initial defoliation. It was observed that

relative growth for all treatments had recovered to that of the control by the end of, or

prior to, three growing seasons subsequent to the season in which the defoliation was

carried out. This allowed a simple model of the impact of defoliation to ignore the

complex dynamic processes involved in the tree’s response to defoliation over

subsequent growing seasons. These processes depend on a number of complex

interactions including those examined here of defoliation intensity, timing and

frequency. This simplification was achieved by : (a) modelling the cumulative effect

of treatments at the end of the third growing season subsequent to the season of the

defoliation and (b) representing the treatment mean DBH or Height as a proportion of

the control mean.

Linear relationship between growth impact and defoliation intensity

Kulman (1971) in reviewing published artificial defoliation studies (mostly in

northern hemisphere pines, spruces, and hardwoods) found a proportional (i.e. linear)

relationship between growth impact and intensity of defoliation. This was also found

to be the case here. This can be seen by taking the control mean as fixed and varying

intensity, P, in model (5.2) with the nonlinear parameter γ set to unity. Since it was

found for both DBH98 and Height98 that the estimate of γ was not significantly

different from unity, the hypothesis of the linearity of this relationship is empirically

supported here.

Comparison with growth impacts of green pruning and plant compensation for insect

herbivory

Considerable research has been carried out on the effects on tree growth caused by

green pruning (O’Hara, 1989) (i.e. pruning branches from the ground up into the live

crown) though very little of this work has been carried out in eucalypts (Pinkard,

1997). Since green pruning is a form of artificial defoliation it is useful to compare

research results for these two forms of defoliation to gain some insights into general

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tree responses to defoliation. In 1994 Pinkard (Pinkard, 1997; Pinkard et al., 1998)

applied three green pruning treatments to four year old E. nitens trees at two sites,

one of which was the Gould’s Block site described in Chapter 4. At these two sites,

the number of experimental trees were 60 and 30, respectively, with mean heights of

9.5 m and 7.5 m, mean DBHs of 11.6 cm and 9.7 cm, and mean live crown ratios (i.e.

the ratio of length of green crown to total tree height) of 0.95 and 0.97 respectively.

The three treatments applied were an unpruned control, removal of 50%, and 70% of

green crown height from below corresponding to 0, 55% and 88% removal of foliage

biomass.

The major difference between such green pruning and artificial defoliation simulating

leaf beetle defoliation is that the majority of the foliage type removed by the green

pruning described by Pinkard (1997) was old (>2 years) and mature (< 2 years but

fully expanded) leaves while apical foliage was left largely intact. Pinkard’s ‘apical

foliage’ corresponds approximately to the majority of the new season edible foliage

(NSEL) removed in the artificial defoliation trials at BGK and Arve.

Trumble et al. (1993) noted that arthropod herbivory can change canopy structure

resulting in a reduction in the light extinction coefficient. That is, the removal of

leaves at the edge of the tree crown will expose the previously shaded inner crown to

more light. This inner crown is largely made up of mature (or fully expanded) leaves.

Pinkard et al. (1998) showed that it was this foliage class that consistently gave the

greatest increase in CO2 assimilation (a measure of photosynthetic activity) after

green pruning.

The effect of green pruning on height and DBH growth obtained by Pinkard et al.

(1998) are similar to those here with DBH growth exhibiting a greater negative

impact of defoliation than height growth and a barely detectable height growth loss

for light (i.e. their 50% treatment) defoliation. However, direct comparisons of

growth loss as a function of defoliation level is not possible due to the radically

different nature of the two types of defoliation. However, their results provide a

useful qualitative explanation of the relatively minor impact on growth of low levels

(i.e. 50% removal of NSEL) of simulated herbivory observed in this study. The

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increase in photosynthetic activity of foliage remaining after defoliation, if

independent of the type of defoliation, will offset to some degree the loss of leaf area

from simulated herbivory and the loss of corresponding photosynthate as discussed

by Trumble et al. (1993).

Influence of neighbouring trees on DBH and height growth response to defoliation

The prediction of growth impacts of defoliation using models (5.2) and (5.5) consider

each tree in the stand independently. Therefore, no account is taken of the effect of

the level of defoliation of neighbouring trees on the subject tree. If initial pre-

treatment measurement of DBH or height can be taken as a relative measure of tree

vigour within the particular stand, then model (5.2) does implicitly incorporate the

tree’s competitive position in the stand up to the time the treatments were applied.

The large influence of this initial measurement on growth even after severe

defoliation treatments were applied, as quantified by model (5.2), reflects the

importance of tree vigour in compensating for defoliation impacts on growth.

However, the applied form of the model, (5.5), does not incorporate this information.

Even with this information, the spatial arrangement of neighbours that have been

defoliated at different intensities and times may influence the growth of the subject

tree.

In the BGK and Arve trials defoliated treatment trees were surrounded by a mixture

of undefoliated controls and non-experimental trees. These non-experimental trees

were excluded because they were either too tall for treatment, too short compared to

the required height range, or did not contain a sufficiently large proportion of adult

foliage. Therefore, it is realistic to assume that the treatment trees were surrounded

by a range of dominant, co-dominant, and sub-dominant neighbours. Also the full

range of defoliation levels, timings, and frequencies were imposed within the area

occupied by a REP in the BGK trial. These sources of variation are probably a more

realistic, though exaggerated, representation of the spatial variation of natural

defoliation levels compared to that obtained if each treatment had been applied at the

REP level. Therefore, if there are important inter-tree components of the effect of

defoliation on growth, the data used here should take their average effect into

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account. The most obvious inter-tree effects that may arise are : (a) the change in

light availability due to the defoliation of a neighbour that is competing for light and

(b) the reduced root competition from a defoliated neighbour as it allocates carbon to

refoliation at the expense of root development. Vranjic and Gullan (1990) in a study

of the effect of infestations of the scale insect Eriococcus coriaceus on glasshouse

seedlings of Eucalyptus blakelyi found that the reduction in root dry weight due to

sap-sucking by E. coriaceus was greater than that for shoots. Since the stands of

interest here are those from age 2 to canopy closure and defoliation is only partial, the

effect of variable defoliation on inter-tree competition for light is probably not large.

Root competition between trees may be more significant especially where below-

ground resources are limited by site conditions, drought, or high stocking levels.

It is beyond the scope of this study to account for inter-tree effects of defoliation but

it should be noted that in practice model (5.5) is applied at the stand-average level

(Section 7.4). Therefore, as long as the trial sites and stands at BGK and Arve22E are

reasonably representative of the general site quality and planting spacings of existing

and future plantations, then model (5.6) should be adequate to predict the growth

impact of defoliation at the stand level. Note also that the growth models of Candy

(1997b) do not explicitly include inter-tree competition effects on growth. This is a

common feature of growth models for plantations due to the regular spatial

arrangement of the trees and relatively low stocking compared to native forests

(Clutter et al., 1983, ch.4).

5.7 SUMMARY

DBH and Height growth response to artificial defoliation

To summarise the results :

1. The impact of defoliation on DBH growth was delayed but greater and more

sustained compared to that for height growth.

2. Height growth under all but the most severe treatments (i.e. H_L2 at BGK and

HDL1 at Arve) was not significantly lower than that of the controls and there is

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an indication that height growth can actually increase relative to the controls after

light defoliation.

3. The relative growth of all treatments was close to, and not significantly different

from, the controls at or before the end of three growing seasons subsequent to the

season of the first year defoliation.

4. The Height to diameter ratio generally increased relative to the control due to the

greater decrease in DBH growth and/or increase in height growth.

5. Disbudding had a substantial impact on DBH and height growth approximately

equivalent to a 50% removal of new season’s foliage for DBH and 70% for

height.

6. Late defoliation had a greater negative impact on growth than early defoliation at

the same intensity for both DBH and Height.

The model of defoliation impact on E. nitens DBH and Height growth

1. A model that incorporates interactions of intensity and frequency of defoliation

effects on DBH and height growth was fitted to data obtained from a large

artificial defoliation trial.

2. The growth impact measured at the end of the third growing season subsequent to

the first-year defoliation was an appropriate response variable given (3) above.

3. The impact of defoliation intensity on growth was adequately modelled by a

linear function.

4. The model incorporated effects for time (early versus late season) of defoliation

and disbudding.

5. Growth impacts were moderated by initial pre-defoliation DBH or height and

inclusion of a model term to incorporate this effect substantially improved the fit

of the model. However, to make the model generally applicable it was necessary

to ‘averaged-out’ the effect of initial tree DBH or height from the model.

6. The growth-impact model was validated using a separate trial with a smaller set

of defoliation treatments. The model was found to fit the DBH growth data from

this trial quite well. For height growth the model under-predicted defoliation

impact but predictions were within statistical confidence bounds for treatment

means.

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7. The model can be applied to stands of age and site quality which differ to those of

the artificial defoliation trials used for model calibration and validation.

However, the accuracy of predictions for such stands cannot be ascertained

without permanent growth plots that measure annual growth of DBH and Height

along with regular assessments of defoliation level for each growing season.