Res. Popul. Ecol. (1973) 15, 50--63.

THE DEVELOPMENT OF SAMPLING TECHNIQUES FOR

POPULATIONS OF THE TARNISHED PLANT BUG,

LYGUS LINEOLARIS (HEMIPTERA: MIRIDAE) 1

M.K. MUKERJI

Ottawa Research Station, Canada Department of Agriculture, Ottawa, Canada

INTRODUCTION

The tarnished plant bug, Lygus lineolaris (BEAuV.), is cosmopolitan in distribu-

tion, attacking a large number of field, vegetable, and fruit crops. Legumes such

as alfalfa, red clover, and birdsfoot trefoil are favoured hosts and form the epicentres

of damaging outbreaks. During the early part of the growing season, the adults and

nymphs suck the sap from terminals, floret buds, and blossoms of forage crops and

release a toxin that causes distortion and blasting of the new growth. Later in the

season, the bug attacks the green seed pods, causing them to shrivel. Heavy

damage reduces seed yield as well as the nutritive value of the crop when fed to

livestock.

The object of the present study was to devise suitable sampling techniques for

estimating population density during the various life history stages of the tarnished

plant bug on birdsfoot trefoil. These estimates are essential in detecting population

losses between stages and in determining the effects of various factors on temporal

and spatial changes in abundance. The development of sampling techniques has been

approached through a study of the spatial distribution because this is a population

attribute that warrants attention in any sampling program.

HABITS OF THE PEST

In eastern Ontario, the tarnished plant bug has at least two generations annually,

the winter being passed in the adult stage (GUPPY, 1958; BEIRNE, 1972). The over-

wintered female lays its eggs in the late spring and early summer. These hatch

and develop through five nymphal instars into adults from late June to mid-July, at

which time many migrate to vegetables and fruits. Nymphs of the second generation

complete tkeir development at mid-September and the adults seek hibernation in the

forage stubble and in woodlots under refuse and dead leaves.

DESCRIPTION OF STUDY AREA

The study was carried out from May to September, 1971, at Richmond, Ontario,

i Contribution No.380, Ottawa Research Station

51

�9 : i :.:::.: ::!::-.::: : : ~:*: .:::. ~ v ' : ! : : g;:7::!::::: ,i-i::i!: :~: ======================================

Fig. 1. Diagrammatic view of the experimental field of birdsfoot trefoil, Richmond, Ontario.

15 miles sou thwes t of the Central Expe r imen ta l F a r m , Ot tawa. The expe r imen ta l

field, 147 ft • ft (Fig. 1), was par t of a one acre s tand of b i rdsfoot t refoi l (var ie ty ,

Empire) tha t had been p lan ted the prev ious summer . I t was sparse ly in te rmingled

wi th a wide var ie ty of common weeds and was borde red on the nor th by an alfalfa

field, on the eas t by a cabbage field, and on the south and west by fields of corn.

The te r ra in , of sandy loam, was fiat and well d ra ined ; a t no t ime were insect ic ides

used in the area.

SAMPLING PROCEDURE

The sample unit adopted for e s t ima t ing number s of L. lineolaris was a 3 sq. ft.

a rea of foliage and subst ra te . Th is unit, which satisfied the cr i ter ia of MORRIS

(1955) was s table and contained all of the nympha l s tages as well as adul t s of the

species. To compare var ia t ion be tween samples , the exper imen ta l field was d iv ided

into four b locks of equal size. Each block was fur ther d ivided by means of a 2 •

gr id into four equal plots. Each of the 16 plots measured 30 f t • ft and was

separa ted by a 9 ft path.

Popula t ion densi t ies were es t ima ted by vacuum sampl ing. The sampler (D-Vac

Vacuum Insec t Ne t -Mode l 11) was a t t ached to a p la t form at the end of a 40 ft long

boom mounted on a t ruck (Plate I) . The boom was manoeuverab le hor izonta l ly in

any di rec t ion wi th in a rad ius of 25 ft. A t each sampling, the t ruck was dr iven

between the plots and the boom lowered to wi th in 18 inches of the ground. This

procedure was adopted to avoid t r amp l ing the crop and d i s tu rb ing the insect. T w o

samples were selected at r andom from each plot.

Popula t ions of the five nympha l s tages and adu l t s were es t imated twice weekly.

1 D-Vac Company, P.O. Box 2095, Riverside, California 92506.

52

Plate I. The truck with boom and vacuum sampler. Note location of platform just above foliage.

The vacuum samples contained var ious types of a r th ropods and debr is mixed wi th

the plant bug. Samples were placed in plast ic bags and s tored in a cold room at

app rox ima te ly 33~ pending examina t ion in the labora tory . A t the t ime of examina-

tion, each sample was exposed to CO2 and shaken thorough ly and divided into four

quar te r s ; counts were made for each quar ter by hand sort ing.

RESULTS AND DISCUSSION

Detection of aggregation pattern

For ana lyz ing the aggrega t ion pa t t e rn of r andom quadra ts , LLOYD (1967) proposed

the parameter , 'mean c rowding ' (m), which is defined as the mean number per

individual of other indiv iduals in the same quadra t ; rn is de r ived as :

* 0-2 m = m + (~----1) (1)

where m represen ts the populat ion mean and a 2, the variance. IwAo (1968) found

that changes in m wi th m could be fitted to a l inear regress ion in var ious types of

d i s t r ibu t ion models and may be expressed as:

m=oz + ~m (2)

where vz and ~ are cons tants charac te r i s t i c to var ious theore t ica l d is t r ibut ions , e .g . ,

vz-O, ~ = 1 for r andom (Poisson) d i s t r ibu t ions and oz=O, ~ - 1 + 1 / k for the negat ive

binomial wi th a common k. The in tercept of the regress ion (6) has been t e rmed

"index of basic contagion" because it indicates whe ther the basic component of

d i s t r ibu t ion is the single individual or g roup of individuals ; the regress ion coefficient

(/~), the "dens i ty contagiousness coefficient", indicates how these components are

53

distributed in space.

The m - m relationship for each population count of the five nymphal stages and

adults of L. lineolaris are illustrated in Fig. 2. Regression lines fitted to the plotted

points show that 9 for each stage is significantly greater than unity, indicating the

overdispersed nature of the data.

7.00-

6.00-

5.oo-

4~O0-

G 3.00-

2.00-

1.00-

0.00.

9.00-

8.00-

7.00-

6.00-

5.00-

4.00-

3.00-

2.00"

1.00-

0.00-

14.~0-

,12.00-

10.0[~.

8.00-

6.00-

4.00"

2.00-

0.00.

IST INSTAR / , 14.00" �9 �9 b : 1.20 m: 55+ 1 20m ~ / b :

(~ .06) (+~ ,16) * / 12.00- r : ,966 i /

/ /m~: 1.oo lO.O0-

, / 8.GO-

6,0C-

�9 / 4.00-

// 2.00"

3'.0o 4'00 s'oo ' o.oo

mRD INSTAR / � 9 : .57 i- 1.40m �9 (• (~.13) r , ~ i

t : .929 �9 �9 �9

/ i/X:1oo ,ooo �9 / i / 8.00-

y * // 6.oo-

/ : ; / .o- / 2.oo-

. 0,00 Loo Loo ~.oo 4'.oo ~.oo ~.oo

"~ "IT'1 INS'TAR 14.00-

= -.18 + 1.6.~ (*_.60) (+_ .17) / 12.(~0-

r = .927 �9 ~ - L 6 S ~.0~"

/ / / 8.~C"

�9 / �9 //b ~ 1.oo 6.oo-

::: oo 4;00 s00-6;00 7.bo so�9

m

lIND INSTAR

~: .11 + 1.53m (_* .34) (*-.13)

r : .951

j . .

�9 /

t " /

i ~ i i i i "' 0 1.00 2.00 3.00 4.00 5.00 6.00

18-00 t ~TH INSTAR ~n = -.41 + 1.83m

16.00 (*_ .45) (*-.~5) r = .947

14.007 �9

12.00-

/ �9 �9 /.~+

/ / ~ _ ~ _ v ~ �9 ~ T ~ / / , ..... ~ ~ ,

1.00 2.00 3.00 4.00 S.00 6.00 7.00

ADULT �9

r : .927 ~ b = L32 �9 f /

�9 /t42oo

1'.~o-23~ :'c~ 4'.cc" 's'.oo 6.'00 s a'.oo "' .. ~ 9.00 m

Fig. 2. Relation of mean crowding (m) to mean density (m) for counts of six stages of L. lineolaris. Each point plotted is based on 32 samples.

54

T h e values for /~ in Fig. 2 showed that aggrega t ion increased g r adua l l y f rom the

first to the four th instar , then decreased th rough the adul t stage. The values of

were posi t ive for first- to th i rd - ins ta r n y m p h s and adul ts , however , for the four th- and

f i f th- instar nymphs , oz values were negat ive.

Acco rd ing to IwAo (1968), a posi t ive value of a m a y r e s u l t f rom the insect ' s

hab i t of l ay ing eggs col lect ively or f rom posi t ive in terac t ion be tween individuals ,

whereas a negat ive value may resul t f rom repuls ive in terac t ion be tween individuals .

When ~r is near fy equal to zero, it m a y re la te to the fact tha t females lay thei r eggs

singly. However , since ~r ca lcula ted f rom a set of observed counts is undoub ted ly

affected by sampl ing er ror , etc., a smal l devia t ion f rom zero may be safely d i s regarded .

Detection of density dependence in the operation of mortality processes IwAo and KuNo (1971) proposed a r - i n d e x to de tec t local dens i ty dependence

in the opera t ion of m o r t a l i t y processes on biological populat ions. I t is expressed

as :

m mo ~" = ~ - - - (3)

m m0

where mo and m0 denote the mean c rowding and mean for the init ial populat ion and

m and m are those of the populat ion af ter opera t ion of some m o r t a l i t y processes.

P rov ided tha t l i t t le or no m o v e m e n t between quadra t s t akes place, the value of ~- is

un i ty when the mor t a l i t y is independent of local dens i ty or random, is g rea te r than

un i ty when its act ion is inverse ly dens i ty dependent , and less than un i ty if it is

dens i ty dependent .

1.60-

1.40 -

1.20 -

E-.'

1.00

.80

.00

�9 (N,~N ~)

Q (N4/N 3)

@ (Ns/N4)

(Ns/N 1)

�9 (N3/N 2)

' ' N .J0 .10 .20 MORTALITY

Fig. 3. Density dependence as indicated by ~ in the operation of mortality processes during the~ intervals of successive stages (I-V instar) of L. lineolaris, generation two, 1971.

55

To es t ima te the amoun t of mor t a l i t y f rom f i r s t - t o f i f th-instar n y m p h s of

L. lineolaris, popula t ion samples were in tegra ted by using to ta l s obta ined a t peak

occurrence combined wi th forms present to which the s tage had a l r eady given rise.

Mor t a l i t y was thus based on the difference be tween e s t ima tes of successive stages.

T h e index r Was appl ied to the da ta for second genera t ion in 1971 to de tec t the

dens i ty dependence of m o r t a l i t y factors . Fig. 3 shows the values of v for the successive

age intervals . Mor ta l i t i e s that occur red in the first- and th i rd - ins ta r n y m p h s were

inverse ly dens i ty dependent . On the con t ra ry , the mor t a l i t y processes tha t opera ted

dur ing the second ins tar were dens i ty dependent and that in the four th- ins tar , dens i ty

independent . The overal l m o r t a l i t y process f rom the first- to f i f th- instar was inverse ly

dens i ty dependent .

Analysis Of variance

Since the var iance of counts of L. lineolaris changes wi th mean densi ty , it is

necessary to s tabi l ize the var iance pr ior to fu r the r a s sessmen t of the data. Accord ing ly ,

a t r ans fo rma t ion of the fo rm f (x ) :- s inh -1 ~ x ( IwAo and KuNo 1971, p. 508)

was used, de r ived f rom the m - m re la t ionship for each deve lopmenta l s tage.

An ana lys i s of var iance (i. e., Tab le 1) was car r ied out to assess the con t r ibu t ion

to total var ia t ion associa ted wi th blocks, plots per block, samples per plot, and

qua r t e r s per sample. Tab le 2 shows tha t var ia t ion be tween b locks was s t a t i s t i ca l ly

Table 1. Analysis of variance of counts of fifth-instar nymphs of L. lineolaris (6th sampling).

Source of variation df Expected mean square Observed F mean square

Blocks 3 aq 2+4as ~+8ap ~+32ao ~ .7018 3.85* Plots within blocks 12 aq~+4as2+Sap 2 .1832 0.05 Samples within plots 16 aqe+4as 2 .3517 3. 08** Quarters within samples 96 aq 2 .1140

* Significant at the 5 per cent level ** Significant at the 1 per cent level

s ignif icant i n 18 of the 55 sampl ings , and var ia t ion be tween plots, in but 10.

Differences be tween b locks were pa r t i cu la r ly pronounced in the adu l t s tage ; this is

not su rp r i s ing since the s tand of b i rdsfoot t refoi l was sparse ly in t e rming led wi th

common weeds. The ana lys i s also indica ted tha t var ia t ion be tween samples was

signif icant in 30 cases and tha t such var ia t ion was the major source of sampl ing

var iance in popula t ions of L. lineolaris.

Sampling considerations

In o rde r to use var iance componen t s in de t e rmin ing combina t ions of n~ (number

of samples per plot) and n~ (number of quar t e r s per sample) tha t will p rovide equal

sampl ing precision, we mus t next de te rmine the var iance of the overal l mean for the

5 6

T a b l e 2. S i g n i f i c a n c e o f v a r i a t i o n d u e t o b l o c k s , p l o t s a n d s a m p l e s , e s t i m a t e s o f

v a r i a n c e c o m p o n e n t s i n s a m p l e s , a n d o p t i m u m n u m b e r s o f q u a r t e r s ( n . ) p e r

s a m p l e r e q u i r e d f o r s a m p l i n g L. l ineo lar i s .

S t a g e S a m p l i n g S i g n i f i c a n c e o f v a r i a t i o n ( F - v a l u e ) V a r i a n c e C o m p o n e n t s N o . B l o c k s P l o t s S a m p l e s sq z ss 2 nq

1 s t i n s t a r 1 - - - - 2.58**

H 2 - - - -

H 3 - - - - - -

n 4 - - 2 . 9 9 *

2 n d i n s t a r 1 - - 2 . 5 6 * - -

# 2 - - - - - -

3 - - - - 2 � 9

# 4 5 � 9 - - - -

# 5 - - - - 3.21"*

# 6 - - - - 2 , 3 1 " *

# 7 - - 6 . 7 6 * * - -

3 r d i n s t a r 1 - - - - 2 . 2 5 * *

# 2 - - - - 4 . 4 0 * *

# 3 6 . 3 6 * * - - - -

# 4 - - - - 2 . 8 0 * *

# 5 3 � 9 - - - -

# 6 - - - - 2 . 5 5 * *

# 7 4 . 2 3 * - - 2 . 3 1 " *

8 - - 4 . 1 8 " * - -

4 t h i n s t a r 1 - - - - 1 . 7 5 "

# 2 - - - - 1 . 8 8 *

# 3 - - - - 2.10"

4 - - - - 2 . 1 6 "

# 5 1 0 . 1 6 " * - - - -

# 6 4 . 3 6 * - - - -

7 6 . 5 1 " * - - - -

# 8 - - - - 1 . 9 7 "

# 9 - - - - 1 . 9 7 "

n 10 - - - - 1 . 7 5 "

# 11 - - - - 2 . 9 1 " *

# 12 - - 3 . 6 7 * * - -

5 t h i n s t a r 1 - - 3 � 9 - -

# 2 - - - - 1 . 9 7 *

# 3 - - - - 1 . 9 4 *

# 4 4 . 6 2 * - - 1 . 8 8 *

# 5 - - - - 1 . 8 4 "

# 6 3 . 8 5 * - - 3 . 0 8 * *

# 7 - - - - 2 . 6 6 * *

# 8 - - 2.53* - -

# 9 4 . 7 2 * - - 1 . 9 6 "

# 10 - - - - 2 . 5 0 * *

# 11 1 2 � 9 - - - -

# 12 - - 3 � 9 - -

# 13 3 . 5 3 * - - 2 � 9

Adult 1 - - 7.72** - -

# 2 - - - - 2 . 4 8 * *

# 3 - - 2 . 5 9 * - -

# 4 5 . 1 6 " - - - -

# 5 7.15"* - - - -

# 6 3 . 6 1 " - - 1 , 7 5 "

# 7 - - - - 3 . 4 9 *

# 8 5 . 4 3 * - - - -

H 9 3 . 6 3 * - - - -

# 10 4 � 9 - - 3 . 7 7 * *

�9 0 3 2 1

�9 0 5 7 7

�9 0 3 3 4

�9 0 3 1 7

�9 0 2 2 6

�9 0 7 5 6

. 1 2 7 7

�9 1 5 3 6

�9 1 6 6 8

�9 0 9 6 2

�9 0 6 9 3

�9 0904

. 0 4 3 3

�9 0 4 3 7

�9 0 5 2 6

�9 0 8 0 0

�9 0 9 4 6

�9 1 0 2 4

. 0 7 4 9

�9 0 6 0 5

2 7 2 5

2 3 5 6

2 6 8 0

2 1 9 3

2 0 1 8

2 0 1 0

2 4 9 7

2 9 5 3

2 9 8 7

3 0 6 7

2 4 2 6

2 1 2 2

2 3 3 5

1 4 4 9

1 5 9 2

1 6 9 8

1 1 3 6

1 1 4 0

1 8 1 5

1 9 1 7

1 6 6 2

1 7 7 4

1 8 9 9

2 4 6 3

1 3 4 1

0 8 5 9

0 7 4 6

0 7 6 5

�9 0 9 5 1

�9 0 7 8 7

�9 0 5 8 2

�9 0 6 9 6

. 0 8 5 2

�9 0 8 9 9

. 0 5 5 5

0127 1

0060 2

0053 2

0000 1

0021 2

0049 2

0062 2

0550 1

0000 1

0533 1

. 0 2 7 7 1

. 0 0 0 0 1

. 0 1 3 4 1

. 0 3 7 2 1

. 0 0 6 4 2

. 0 3 5 9 1

�9 0 1 3 3 2

0 3 9 7 1

0 2 4 6 1

0000 1 0 4 8 7 2

0 5 2 2 1

0 7 4 0 1

0 3 5 1 2

0 5 8 7 1

0 2 1 3 2

0 3 9 3 2

0 3 2 3 2

0 7 2 3 1

0528 2

1162 1

0 0 0 0 1 0 0 0 0 1 0 3 5 1 1

, 0 3 7 6 1

0 3 7 3 1

0 2 3 8 1

0 5 9 5 1

0 7 5 3 1

0 1 2 6 2

0 3 9 9 1

0 6 6 5 1

0 0 7 6 3

0 0 0 0 1

0 5 0 0 1

0000 1 0 2 7 7 1

0 0 1 5 4

0 0 1 2 4

0008 1

0101 2 0 4 3 4 1

0 0 8 3 2

0 0 8 2 2

0 3 8 5 1

* S i g n i f i c a n t a t t h e 5 ~ l e v e l

** S i g n i f i c a n t a t t h e 1 ~ l e v e l

57

required degree of precision. In terms of the sampling units, the s tudy area as a

whole formed a finite population of samples which were grouped into plots and

blocks. The variance of the mean per quarter of a sample is therefore:

v a r ( ~ ) = ( -lnb l b ) a ~ + ( - 1 N@N;)a'~+( n~n.n,1 1 ) ~s 2 nbnv NbN.N, ,

1 (4) + ( 1 N~N.~Nq ) a 2 nbn~nsnq

where Nb, N., N., and Nq are respectively the total populations of blocks, plots per

block, samples per plot, and quarters per sample, and rib, n., n., and nq are respec-

tively the numbers of blocks, plots, samples, and quarters actually sampled. If

nb=Nb and n.~N., i.e., if samples are taken from all plots, then the variance

components for blocks and plots need not be included in the calculation of variance

of the overall mean. Hence for the design used in the present work, i.e., 4 blocks,

4 plots per block, 2 samples per plot, and 4 quarters per sample, equation (4)

reduces to:

E( k) Since n,~Ns, then 1/N, can be ignored so that equation (5) simplifies to:

1 1 ag~)

1 ( ~ + m a . 2 ) (6) -- 16-r

Table 2 lists the est imates of inter- and intra-sample variances. For each stage,

est imates of mean densities per quarter together with their s tandard errors are listed

in Table 3; also listed are the confidence limits of the mean at the 70 and 80 per

cent probability. For mos t stages, the s tandard er ror was 15 per cent of the mean

or less ; it exceeded 20 per cent in but four cases (II instar : 6th sampling ; I I I

instar : 1st and 2nd samplings ; V instar : 6th sampling).

Optimum sample size and cost function Decision as to the opt imum numbers of quarters per sample, nq, was based on

the ratio of inter- (ss 2) and intra- (sq ~) sample variance components, and on the cost

of taking a population sample as compared to the cost of examining each quarter

(LERoux and REIMER, 1959). na values for each sampling, are listed in Table 2,

derived f rom the formula nq=v'(sq~/s, ~) (c,/ca), where c, was the cost of taking a

population sample ( = 3 man-mins.) and ca was the cost of examining each quarter

(=15 man-mins.). When the inter-sample variance was est imated as zero, the value

of nq was considered to be one. Str ict ly speaking, if s, 2 is nil, one sample is sufficient

and the value of nq may be calculated in a similar way to equation (7) below.

However , it was assumed that a, 2 could not be zero. Since na was equal to one

5 8

T a b l e 3. E s t i m a t e s a n d conf idence i n t e r v a l s

s a m p l e fo r L. lineoloris of m e a n dens i t i e s pe r q u a r t e r of a

S t a g e S a m p l i n g s 1 7 7 E. n o . L o w e r

l i m i t

Conf idence l im i t s 70%

U p p e r L o w e r l imi t l imi t

80% U p p e r l i m i t

1st i n s t a r N

N

H

N

2nd i n s t a r N

H

N

#

N

H

3rd i n s t a r N

H

N

N

N

H

H

4th i n s t a r N

H

N

N

N

N

N

N

N

H

H

5 th i n s t a r N

N

N

N

H

N

N

H

N

N

N

N

A d u l t H

N

N

N

H

N

H

N

H

1 . 1 4 6 6 • 2 . 2 5 4 7 • 3 . 1 3 9 4 • �9 4 �9 • �9 5 . 0 7 1 8 • 0141 1 . 1 8 3 0 • 2 . 2 5 8 9 • 3 . 5 4 0 8 • 0538 4 . 4 2 1 2 • 5 . 2 6 4 5 • 0489 6 . 1 5 5 0 • 0360 7 . 2 O 8 3 • 1 . 1 3 3 5 • 0282 2 . 1 6 8 4 • 0387 3 . 1 7 8 6 • 0244 4 .2418 • .0412 5 . 4 5 6 9 • .O346 6 . 4 2 4 5 • .0447 7 .3051 • 8 . 2 0 9 9 • .0223 1 . 4 0 7 5 • 0608 2 . 3 5 3 3 • 0591 3 . 4 9 0 6 • 0663 4 . 3 1 2 3 • 0529 5 . 3 2 2 6 • 583 6 . 2 4 5 8 • .0469 7 . 3 9 7 3 • 8 . 4 8 9 6 • 9 . 8 7 5 0 • �9

10 . 9 1 6 9 • .0632 11 . 7 7 7 3 • .0741 12 .2908 •

1 .5028 • 0424 2 .2863 • 0469 3 .3734 • 4089 4 . 4 1 6 9 • .O500 5 . 2 0 6 3 • 0400 6 . 2 3 3 4 • 0519 7 . 4 0 5 2 • 8 . 5 8 3 5 • .0435 9 . 7 6 2 7 • .0500

10 . 6 7 2 0 • 0591 11 .6461 • 0412 12 . 5 0 8 8 ! . 0 4 3 5 13 .3811 •

1 . 5 8 7 2 • 0264 2 . 5223• .0374 3 .4191 • 4 . 3 1 3 9 • 5 . 2 4 7 5 • 0244 6 . 1 9 9 9 • .0282 7 .3149 • 8 .3110 • .0300 9 . 3 6 4 4 • 0316

10 . 6 2 2 9 •

1193 2276 1173 1012 0551 1538 2219 4829 3825 2118 1171 1798 1040 1269 1521 1970 4205 3761 2657

.18O6 �9 �9 �9 �9 �9 �9 �9 �9 �9 .8488 �9 �9 �9 �9 �9 .3634 .1630 .1772 .3394 .5369 .7087 .6090 .6017 .4618 .3264 .5595 �9 �9 �9 .2209 �9 .2682 �9 �9 .5796

�9 1739 �9 2818 �9 1615 �9 1350 .0885 �9 2122 �9 2959 �9 5987 �9 4599 �9 3172 �9 1929 �9 2368 �9 163. �9 2099 �9 2051 �9 2866 �9 4933 �9 4729 .3445 �9 2332 .4722 �9 4164 �9 5617 �9 3691 �9 3851 �9 2964 �9 4577 �9 5513 �9 9476 �9 9850 �9 8569 �9 3344 �9 5485 �9 3369 �9 4261 �9 4704 �9 2496 �9 2896 �9 4710 �9 6301 �9 8167 �9 7350 �9 6905 �9 5558 �9 4358 �9 6149 �9 5631 �9 4463 �9 3438 �9 2741 �9 2296 �9 3616 �9 3436 �9 3976 �9 6662

�9 1126 �9 2209 �9 1118

0971 0510 1465 2128 4686 3729 1988 1077 1728 0967 1166 1456 1859 4115 3641 2559 1808 3267 2745 4019 2414 2445 1826 3219 4126 7844 8319 6779 2364 4457 2232 3076 3502 1523 1633 3231 5254 6952

�9 5933 �9 59O6 �9 4502 �9 3128 .5526 �9 4714 3852 2765 2143 1628 2566 2703 3230

�9 5688

.1806

.2885

.1670 �9 .0926 �9 �9 �9 .4695 �9 .2023 .2438 .1703 .2202 .2116 .2977 .5023 .4849 .3543 .2390 .4883 .4321 .5793 .3832 .4007 .3090 .4727 .5666 .9656

1.0019 .8767 .3452 .5599 .3494 .4392 .4836 .2603 .3035 .4873 .6416 .8302 .7507 .7016 .5674 .4494 .6218 .5732 .4530 .3513 .2807 .2370 .3732 .3517 �9 �9

59

more often than any other value (Table 2), it was decided to set nq as one when

s~ ~ was e s t ima ted as zero.

An app rox ima t ion procedure was used to es t imate the number of samples , n,,

r equ i red for a given level of precision. If d is the marg in of e r ro r a l lowed in

e s t ima t ing the populat ion mean, then

t~ ~ n~= ~ - (s~/n~+ s, 2) (7)

where t~ is the 1 - ~ / 2 percentage point of S tuden t ' s t d i s t r ibut ion . Since the t rue

populat ion means a r e not known, d is expressed as a f ract ion of sample means, i.e.,

d=p2, for 0~=.05, .10, . 20, .30, and p - . 10, . 15, .20. Fo r each stage, n~ requi red

per plot for th ree levels of m a r g i n of e r ror a t two levels of significance for the

es t ima t ion of mean dens i ty a re l i s ted in Table 4.

Equat ion (6) for ca lcula t ing var (~) assumes tha t N~ was large compared wi th

n,. For the sampl ing design employed in the presen t work, each plot measured 900

sq. ft. Th i s is equiva lent to 300 s a m p l e s ; when nq=l, it was possible to ignore

1/N, as n, was not l a rger than 60, or when n~=2, ns was not l a rger than 30, and

so on. W i t h large n~, the consequence of omi t t ing the t e rm l /N8 in ca lcula t ing

va t (2) was an overes t imat ion of n~ ca lcula ted f rom equat ion (7). However , th i s

was a p rob lem only in a few cases at low densi t ies (Figs. 4D, E).

Fo r the p resen t sampl ing design, cost per plot was expressed by a cost funct ion

as fo l lows;

C ~ 68~8 ~- Cqn~q

n8 (3 + 15nq) (8)

The values of C for three levels of marg in of e r ro r a t two levels of s ignif icance for

the es t ima t ion of mean dens i ty of each s tage of L. lineolaris are l is ted in Tab le 4.

SUGGESTED SAMPLING PLAN

The sugges ted sampl ing plan is i l lus t ra ted in Fig. 4. Because we wish to use

mean dens i ty based on the scale of or ig inal va r ia tes r a the r than on the t r a n s f o r m e d

scale, i t is necessa ry to es tabl i sh the re la t ionship be tween the t r a n s f o r m e d and

or iginal da ta (Fig. 5A). F o r nymphs and adu l t s of L. lineolaris, the effect of dens i ty

on the number of samples requi red for a g iven s t anda rd e r ror a t the . 30, . 20, .10,

and . 05 levels of significance is shown respec t ive ly in Figs . 4B, C, D, and E. The

sample size r equ i red is inverse ly propor t iona l to popula t ion densi ty , a fact tha t is

not su rp r i s ing since the d i s t r ibu t iona l pa t t e rn of the insect is of the contagious type.

S imi lar ly , the cost of sampl ing per plot is inverse ly propor t iona l to popula t ion dens i ty

(Figs. 4F, G, H, I) .

The sampl ing plan should be appl icable to fields tha t a re s imi la r in size and

shape to tha t encounte red in the p resen t s tudy. The cost funct ion m a y be used in

two ways. If the size of the sampl ing crew cannot be increased, then C is a f ixed

60

Tab l e 4. N u m b e r s of s a m p l e s (n,) and cost of s a m p l i n g in m a n - m i n s (C) for t h r e e levels of m a r g i n of e r ro r at the . 30 and . 20 levels of s igni f icance for the e s t i m a t i o n of m e a n dens i t y for L, lineolaris.

STAGE S a m p l i n g .30 No. p_=_20o~ P = 1 5 o ~

ns C n8 C

Level of Signif icance

.2O P = 1 0 % P-=20% P-=15% P = 1 0 % n~ C ns C ns C ns C

1st i n s t a r H

H

H

H

2rid in s t a r H

H

H

H

H

#

3rd in s t a r H

H

H

H

H

H

H

4th in s t a r H

H

H

H

H

H

H

H

H

H

5th in s t a r H

U

H

H

H

H

H

H

H

H

H

H

Adul t M

#

H

H

H

H

H

H

H

1 2 3 4 5 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9

10 11 12

1 2 3 4 5 6 7 8 9

10 11 12 13

1 2 3 4 5 6 7 8 9

10

4 72 7 126 1 33 2 66 2 66 4 132 5 90 8 144 5 165 9 297 3 99 5 165 2 66 4 132 2 36 3 54 2 36 3 54 4 72 7 126

15 270 6 108 11 198 24 432 4 132 2 66 3 99 6 198 9 297 4 132 6 198 13 429

17 306 7 126 12 216 26 468 19 627 8 264 13 429 29 957 10 330 4 132 7 231 15 495 8 264 3 99 6 198 12 396 6 108 2 36 4 72 8 144 7 126 3 54 5 90 11 198

16 288 6 108 11 198 24 432 7 126 13 234 28 504 11 198 19 342 43 774 4 72 7 126 15 270 6 108 11 198 24 432 6 108 11 198 23 414 9 162 16 288 36 648 6 108 10 180 21 378 8 144 15 270 32 576 2 66 4 132 8 264 3 99 6 198 12 396 4 72 7 126 15 270 6 108 10 180 23 414 1 33 1 33 3 99 1 33 2 66 4 132 2 36 3 54 6 108 3 54 4 72 9 162 2 36 4 72 8 144 3 54 6 108 12 216 3 54 5 90 10 180 4 72 7 126 16 288 2 66 4 132 8 264 4 132 6 198 13 429 5 90 8 144 17 306 7 126 12 216 26 468 3 54 5 90 11 198 4 72 8 144 3 99 5 165 11 363 5 165 8 264 5 90 8 144 18 324 7 126 13 234 4 132 7 231 15 495 6 198 10 330 2 66 4 132 8 264 3 99 6 198 2 66 3 99 6 198 3 99 4 132 1 18 2 36 4 72 2 36 3 54 1 33 1 33 2 66 1 33 2 66 2 36 2 36 5 90 2 36 3 54 5 90 8 144 18 324 7 126 13 234 2 36 3 54 7 126 3 54 5 90 4 72 7 126 16 288 7 126 11 198 3 54 5 90 11 198 4 72 7 126 3 54 4 72 9 162 4 72 6 108 6 108 11 198 24 432 9 162 16 288 6 108 ii 198 23 414 9 162 16 288 3 54 5 90 12 216 5 90 8 144 1 33 i 33 3 99 1 33 2 66 1 18 2 36 3 54 1 18 2 36 i 18 2 36 4 72 2 36 3 54 1 48 1 48 2 96 1 48 1 48 2 36 3 54 7 126 3 54 5 90 3 54 4 72 10 180 4 72 7 126 1 18 1 18 1 18 2 36 1 63 1 63 1 63 1 63 3 54 5 90 2 66 4 132 2 36 4 72 1 33 2 66 1 33 2 66 1 18 i 18

2 36 1 18 2 36 3 54 1 18 2 36 1 63 1 63 1 63 2 126 1 63 2 126

10 180 4 72 7 126 7 231 3 99 5 165 9 162 4 72 6 108 4 132 2 66 3 99 3 99 2 66 2 66 2 36 1 18 2 36

16 288 17 561 28 504 23 759 12 396

9 297 6 108 3 99 7 126

28 504 11 198 25 450 16 288 14 252 37 666 36 648 18 324

4 132 4 72 6 108 2 96

11 198 15 270 3 54 5 9O 2 126 3 189

15 270 11 363 13 234 6 198 5 165 3 54

61

1.00 i A

~t:3 ~ U ~ ~ .8~ IV rNSTAR ADULT 4:{ U'J v INSTAR OOC .6C OCE) II INSTAR

. >-4 .40- i._~: IIi INSTAR V- m .20 -

.00 - - -

,20 .40 ,60 .80 1.00 1.20 1,40 1.60 1.80 2.00 2.20 2.40

DENSITY PER QUARTER - UNTRANSFORMED

40- loro

20- ~s%

2o%

~) - - - r - - - I i r

B 1oo-

80- 2

60-

40-

20- ~o%

0

8OO

600-

400 -

200- =

'~ 0-

.~ 2000-

1600-

8 12oo-

800-

~o

i i i -

400-

0 0.00

i I

5%

2

T

.20 .40 .60 .80

20

~ J

Io% I

1 5 % ~

20

.20 .40 .60 .80 DENSITY PER QUARTER - TRANSFORMED

Fig. 4A. Relationship of mean density per quarter between t ransformed and original scale for six stages of L. lineolaris. Figs. 4B, C, D, and E, relationship between population density and required number of samples to be taken per plot for three levels of margin of error at the .30, .20, .10, and .05 levels of significance, respectively, when nq= l . Figs. 4F, G,H, and I, relationship between population density and cost of sampling per plot for three levels of margin of error at t h e . 30, . 20, . 10, a n d . 05 levels of significance, respectively.

62

quant i ty and the funct ion may be solved by accepting any precision that can be

obtained with such a fixed resource. However, if C is flexible but a specified level

of precision mus t be achieved, we can est imate the resource required.

SUMMARY

The relat ionship of 'mean crowding ' to mean densi ty showed that counts of

nymphs and adults of the tarnished plant bug, Lygus lineolaris (B~Auv.), on birds-

foot trefoil were aggregated and that the index of basic contagion approached zero

for each developing stage. Aggregat ion increased gradual ly from the first to the

fourth instar and then decreased through the adult stage. The mor ta l i ty process

from the first to the fifth instar was inversely densi ty dependent.

In ter-sample variance was the major source of populat ion variance al though

significant variance was occasionally associated with blocks and plots owing to

heterogenei ty of the host stand. The most appropriate sample uni t was a 3 sq. ft.

area of foliage and substrate. This was divided into four q u a r t e r s ; application of

the variance component technique indicated that in most cases one quar ter d rawn at

r andom was optimal for sampling different stages. The number of samples required

to a t ta in a given level of precision varied inversely with populat ion density. The

cost funct ion for sampl ing was de termined for specified levels of precision.

ACKNOWLSDGMBNTS : The author wishes to thank Dr. C.S. SHIn, Statistical Research Service,

Ottawa, for his suggestions on methods of estimating sample size, and Dr.D.G. HARcOURT, Re-

search Station, Ottawa, for his critical review of the manuscript. He is also grateful to Mr.L.

M. CASS for suggesting use of the boom and sampling platform.

REFERENCES

B~mNE, B.P. (1972) Pest insects of annual crop plants in Canada. IV Hemiptera-Homoptera, V

Orthoptera, VI Other group. Mere. Ent. Soc. Can. No.85.

GUPPY, J.C. (1958) Insect surveys of clovers, alfalfa, and birdsfoot trefoil in eastern Ontario.

Can. Enl. 90: 523-531.

IwAo, S. (1968) A new regression method for analyzing the aggregation pattern of animal popu-

lations. Res. Popul. Ecol. 10: 1-20.

IwAo, S. and E. KuNo. (1971) An approach to the analysis of aggregation pattern in biological

populations. In Statistical Ecology (Ed. by G.P. PATIL el al.) 1: 461-513.

LERoux, E.J. and C. REIMgR. (1959) Variation between samples of immature stages, and of morta-

lities from some factors, of the eye spotted budmoth, Spilonota ocellana (D.& S.) (Lepido-

ptera: Olethreutidae), and the pistol casebearer, Coleophora serratella (L.) (Lepidoptera:

Coleophoridae), on apple in Quebec. Can. Ent. 91: 428-449.

LLOYD, M. (1967) 'Mean crowding'. J. Anim. Ecol. 36: 1-30.

MORRrS, R.F. (1955) The development of sampling techniques for forest insect defoliators, with

particular reference to the spruce budworm. Can. J. Zool. 33: 225-294.

63

J ~ ~ ~ ,~ r "~�9 1 ~ Lygus lineolaris � 9 1 6 9

M. K. Mug~zx

"TLt~JC~a~l,~/~-~'~l~@~.. '~ ~a ~ r L,?,,." ~ C7~, ~ birdsfoot trefoil ( ' ~ - ~ _ - ~ ) J2~:~