JEC 657.fm Page 251 Tuesday, March 19, 2002 7:39 AM Primary and secondary stem growth ... · 2007-01-11 · Primary and secondary stem growth in arctic shrubs: implications for community

Journal of Ecology

2002

90

, 251–267

© 2002 British Ecological Society

Blackwell Science Ltd

Primary and secondary stem growth in arctic shrubs: implications for community response to environmental change

M. SYNDONIA BRET-HARTE, GAIUS R. SHAVER† and F. STUART CHAPIN III

Institute of Arctic Biology, Room 311 Irving I Bldg., University of Alaska, Fairbanks, AK 99775 USA; and

†

The Ecosystems Center, Marine Biological Laboratory, 7 MBL St., Woods Hole, MA 02543 USA

Summary

1

Shrubs are among the tundra plants most responsive to environmental change. Wemeasured primary and secondary stem growth in a retrospective analysis of ramets ofthree codominant shrubs (

Betula nana

,

Salix pulchra

, and

Ledum palustre

ssp.

decum-bens

) exposed to long-term field treatment with greenhouses and N + P fertilizers atToolik Lake, Alaska.

2

Ramets of

Salix

had the greatest primary stem growth under control conditions,because of their relatively high branching rate. Under fertilization, however,

Betula

produced much more primary stem growth than the other species, because axillarybuds that would have grown as short shoots in control ramets were instead stimulated toproduce long shoots (structural branches). There appeared to be a trade-off betweenallocation to length per stem segment and number of stem segments produced in agiven year, for both

Betula

and

Ledum

.

3

Although secondary growth in stems is the largest component of above-ground netprimary production in forests, it is often ignored in shrub-dominated ecosystems. Wederived an expression for secondary growth in shrubs based on distributions of stemmass and length with age, and allowing for experimentally induced changes in second-ary growth rate.

4

There was good agreement between measured ramet stem mass and calculated valuesfor all three species, validating our mathematical analysis of secondary growth.

5

Fertilization greatly increased the relative rate of secondary growth only in

Betula

,consistent with observed accumulations of its stem mass in ecosystem-level quadratharvests. Secondary growth of

Betula

was a major component of ecosystem NPP infertilized plots and probably contributes significantly to ecosystem carbon storage.

6

The increase in its secondary growth enabled

Betula

to become dominant under fer-tilization, whereas the inability of older stems of

Ledum

to respond in this way preventedit from growing into the canopy.

Key-words

: arctic tundra,

Betula nana

, carbon storage, elevated temperature, nitrogenand phosphorus fertilization

Journal of Ecology

(2002)

90

, 251–267

Introduction

The slow-growing, clonal, and long-lived growth pat-terns seen in many arctic plants may be advantageousfor survival in a harsh physical environment (Callaghan1988). Recruitment of seedlings into mature life stagesis rare, however (McGraw & Shaver 1982; McGraw &

Fetcher 1992), and vegetation response to changingenvironmental conditions is often driven by the differ-ential growth of individual plants. Analysis of growthmay therefore give insight into the mechanisms under-lying ecosystem response to environmental perturbation.

Anthropogenically induced climate change is ex-pected to be most pronounced at high latitudes(Houghton

et al

. 1996). Their potential to respond toclimate change makes arctic shrubs of particularimportance for tundra ecosystems. Tundra responds

Correspondence: M. S. Bret-Harte (fax 907-474-6967; [email protected]).

JEC_657.fm Page 251 Tuesday, March 19, 2002 7:39 AM

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M. S. Bret-Harte, G. R. Shaver & F. S. Chapin III

© 2002 British Ecological Society,

Journal of Ecology

,

90

, 251–267

strongly to manipulations of nutrient availability andtemperature that simulate climate change, in both eco-system properties such as net primary production andin the growth of individual species (Chapin

et al

. 1995;Chapin & Shaver 1996; Bret-Harte

et al

. 2001). InAlaskan moist tussock tundra, increased dominance of

Betula nana

is one of the most striking changes underincreased nutrient availability (Fig. 1; Bret-Harte

et al

.2001; Chapin

et al

. 1995).

Betula

’s dominance resultsfrom increased growth of individuals present at thestart of the experiment, rather than recruitment of newindividuals (Bret-Harte

et al

. 2001). Although morenutrients were added in this experiment (four times theannual N requirement for above-ground vascular pro-duction and 20 times the annual P requirement in thissite (Shaver & Chapin 1991)) than would be expected tobe associated with climate change over the short term,

Betula

did increase on the Alaskan North Slope duringthe last warm period, about 9000

, as seen in long-term pollen records (Brubaker

et al

. 1995).Ecologists have successfully applied a demographic

approach to retrospective analysis of plant growth in

individuals of a variety of species (e.g. Svensson & Cal-laghan 1980; Maillette 1982; Callaghan

et al

. 1986;Maillette 1987; Ebert & Ebert 1989). Although thisapproach gives insight into the patterns of growth andmortality of populations of meristems, it does not pro-vide a direct measure of changes in biomass with timeor under an experimental treatment. In particular, onecannot easily address changes in secondary growth bywoody species, such as tundra shrubs, using this method.

Secondary growth of woody stems is essential to sup-ply mechanical strength for supporting an aerial can-opy and for hydraulic transport of water to foliage. Insingle trees and forests, secondary growth usuallygreatly exceeds primary stem growth and leaf produc-tion (Grier

et al

. 1981; Whittaker

et al

. 1979) and isoften used to estimate forest biomass and production(e.g. Phillips

et al

. 1998). For shrubs and mixed vegeta-tion of low stature, however, secondary growth is stillfrequently considered negligible or is ignored. Forexample, a recent calculation of carbon-13 exchangesbetween atmosphere and biosphere ignored the con-tribution of wood in tundra ecosystems (Fung

et al

.

Fig. 1 Photographs of vegetation in the experimentally treated plots. Control tundra is visible outside the greenhouses in Fig. 1(b,c). (a) Plot fertilized withN and P, showing dominance of Betula nana; (b) greenhouse treatment plot; (c) greenhouse plus fertilizer (N + P) treatment plot, showing dominance ofBetula nana inside the fertilized greenhouse.


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Journal of Ecology

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, 251–267

1997), even though shrubs are a major component oftundra vegetation, particularly in the low Arctic (Bliss& Matveyeva 1992), and previous work (Shaver 1986)suggested that secondary growth can represent a sig-nificant part of net primary production in tussocktundra.

In the only previous attempt to estimate the con-tribution of secondary growth to shrub production inarctic tundra, Shaver (1986) determined distributionsof mass per unit length with age, for stem segments oftundra shrubs. This approach assumed a constant relativerate of secondary growth and could not accommodateany changes in growth caused by experimental mani-pulations. Also, it used terminal bud scars to determinethe age of stem segments, and thus excluded speciessuch as

Betula nana

, which do not produce these per-sistently visible markers, from being analysed.

In this study, we retrospectively analysed the prim-ary and secondary growth of

Betula nana

and twoother common tundra shrubs exposed to long-termmanipulations of nutrient availability and temperature.We expanded Shaver’s (1986) approach and used amathematical analysis to derive an expression forsecondary growth that could be evaluated from distri-butions of mass and length with age. Our derivationtook into account the geometry of stem growth and theeffects of experimental treatment on secondary growth.Our objectives were (1) to quantify primary and secon-dary stem growth in these species; (2) to understandhow primary and secondary growth change under alteredenvironmental conditions; and (3) to understand howthe patterns of growth of

Betula nana

allow it to achievedominance under increased nutrient availability. Ouranalysis gives insight into the contribution of second-ary growth to shrub growth and response to environ-mental change.

Materials and methods

We conducted this study in moist tussock tundra (Bliss& Matveyeva 1992) near Toolik Lake at the arcticLong-term Ecological Research (LTER) site in thenorthern foothills of the Brooks Range of arctic Alaska(68

°

38

′

N, 149

°

34

′

W, elevation 760 m). Vegetationon the site is characterized by approximately equalbiomass of graminoids (mainly

Eriophorum vaginatum

and

Carex bigelowii

), deciduous shrubs (mainly

Betulanana

, with less

Salix pulchra

), evergreen shrubs (mainly

Ledum palustre

ssp.

decumbens

and

Vaccinium vitis-idaea

),and mosses (mainly

Hylocomium splendens

,

Aula-comnium turgidum

,

Dicranum

spp.

and Sphagnum

spp.)(Shaver & Chapin 1991). Nomenclature follows Hultén(1968).

Detailed information on the experimental treat-ments and their environmental effects is given by Bret-Harte

et al

. (2001) and Chapin

et al

. (1995). Briefly, in1988 we established four replicate blocks in homogene-

ous tussock tundra on a gentle (5%), north-facingslope. Each block contained ten 5

×

20 m plots separ-ated by 2-m buffer strips. Of those plots, three in eachblock were randomly assigned to the following treat-ments: (1) control (no manipulation); (2) fertilizationwith commercial N and P fertilizers once annually; and(3) greenhouse treatment to raise soil and air temper-ature during the growing season, with and without fer-tilization. Two greenhouses were erected on each plotin treatment (3), with one unfertilized (treatment 3a)located at least 2 m uphill from the other, which was fer-tilized (treatment 3b). This ensured that the unfert-ilized greenhouse would not be affected by any nutrientsleaching from the fertilized greenhouse. Greenhousetreatments were regarded as independent in statisticalanalyses. The separation between the greenhouses andbetween the other treatments has been shown to be suf-ficient to isolate the treatments from each other (Shaver& Chapin 1986; Chapin

et al

. 1995; Shaver & Chapin1995; Bret-Harte

et al

. 2001). Remaining plots in theblock received other treatments (e.g. shading, N alone,and P alone), results of which are not included in thepresent study.

Nitrogen and phosphate were applied to fertilizedplots annually in late May or early June, starting in1989. We applied N (as slow-release granular ammo-nium nitrate) at 10 g m

–2

y

–1

and P (as commercial gran-ular superphosphate, a mixture of calcium phosphates)at 10 g m

–2

y

–1

in the first year and 5 g m

–2

y

–1

in subse-quent years, as in previous work (Bret-Harte

et al

.2001; Shaver & Chapin 1980; Shaver & Chapin 1986;Chapin

et al

. 1995; Chapin & Shaver 1996).Greenhouses, first put in place in June 1989, had per-

manent, rectangular (2.46

×

4.92 m) wooden frameswith a gable roof 65 cm above the ground at the sidesand 130 cm at the centre line (Fig. 1). The roof and allfour sides were covered with transparent 0.15 mm (6mil) UV-resistant clear polyethylene sheeting (Cloud 9commercial greenhouse plastic; Monsanto, St. Louis,MO). Greenhouse frames remained in place year-round, but the plastic was put in place at the beginning(May 25–June 5), and removed at the end (August 20–25), of each growing season.

As described in detail previously (Bret-Harte

et al

.2001; Chapin

et al

. 1995), we monitored air tempera-ture, soil temperature, relative humidity, and photosyn-thetically active radiation in greenhouse and controlplots. Values were recorded continuously with a data-logger. Environmental data are available at http://www.mbl.edu/html/ECOSYSTEMS/lterhtml/arc.html.The primary effect of the greenhouse was to increasedaytime air temperature during the growing season byan average of 3.7

°

C, leading to a 37% average increasein thawing degree-days and increasing depth of soilthaw by an average of 9 cm. Fertilization increasednutrient availability and slightly reduced depth of thaw,probably because of increased canopy development inthis treatment. The main unintended effects of green-house treatment were a 20% reduction in light intensity


254

M. S. Bret-Harte, G. R. Shaver & F. S. Chapin III


Journal of Ecology

,

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, 251–267

and a 17% average decrease in relative humidity duringJune, when the sun was highest in the sky. This 20%light reduction is less than the 30% reduction recordedby Chapin

et al

. (1995), who used a different plastic tocover the greenhouses. Greenhouses did not decreasesoil moisture (Chapin

et al

. 1995). Consequences ofthese unintended effects were evaluated by McKane

et al

. (1997).

In 1995 we analysed branches from two deciduous andone evergreen shrub species (

Betula nana

,

Salix pul-chra

, and

Ledum palustre

ssp.

decumbens

) for growthperformance prior to and during the experiment. Theseshrubs are long-lived and grow clonally; their support-ing branches are largely prostrate and become progres-sively covered by moss, after which they produceadventitious roots. It is thus difficult to identify geneticindividuals in the field. Three ramets (large, rootedbranches) of each species were chosen randomly fromeach treatment in each block, giving 12 ramets pertreatment except for

Salix

in the greenhouse-plus-fertilizer treatment. In that treatment, there was onlyenough

Salix

to collect one ramet from each of threeblocks. The stem and attached branches of each rametwere pulled up and the stem was cut underground. Inthe laboratory, the most apical 12–15 years of growthwere analysed for branch structure, mass, and length.Thus, ramets had grown for up to 9 years before theexperiment began, then for another 6 years underexperimental treatment. Ramets were harvested frommid-June to early August. We analysed one ramet ofeach species from all treatments in all blocks beforecollecting subsequent ramets. Changes in growth ormortality that occurred over the harvest period werethus averaged across the season in all treatments.

To determine distributions of branch number, stembiomass, and stem length with age in each ramet, a map(drawing) was made of the branch structure and ages ofthe most apical 12–15 years of growth, counting 1995as year 0. Ages of branches in ramets of

Salix

and

Ledum

were determined by counting terminal budscars (Shaver 1986), which are visible for many years.

Betula

does not form persistent bud scars, so branchages were determined by cutting thin stem cross-sectionsby hand with a razor blade. Annual growth rings instem cross-sections were counted at 50

×

or 100

×

magnification under a compound microscope, afterstaining with 1% phloroglucinol in 20% HCl (Fig. 2).Whenever possible, at least two stem cross-sectionswere cut within each year of growth. Where a stem indic-ated different ages at the apical and basal ends of theclosest cuts, mass and length values were evenly dividedamong the age classes in that piece.

Betula

has long/short shoot dimorphism. Long shootsundergo extensive primary and secondary growth, andprovide many opportunities for branching by produc-ing buds in each leaf axil. In contrast, short shoots have

little internodal elongation or subsequent secondarygrowth, few leaves, and usually produce only one viablebud for growth in the following season; thus, they donot lead to further branching. Short shoots occasion-ally convert to long shoots, and secondary growth isalso triggered following the conversion. Because shortshoots do not branch or produce much wood, we definea ‘structural branch’ for

Betula

to include only longshoots and short shoots that have converted to longshoots. For

Salix

and

Ledum

, all branches are struc-tural, as these plants do not make short shoots.

For each 12–15 year-old ramet of each species, livestem segments of a given age were pooled, aggregatelengths were measured, and then stem segments weredried at 65

°

C for 48 h and weighed (Shaver 1986).Short shoots, converted short shoots, and long shootsof

Betula

were measured separately. Numbers ofbranch segments of a given age and shoot type weredetermined from the maps of each ramet. Values foreach ramet were averaged among the three individualswithin each block, and then among the four blocks foreach treatment. All values are presented as means

±

1 SE (

n

= 4 blocks). In age-distribution figures, valueswere plotted against the year that stem segments wereproduced; the age of a stem segment can be determinedby counting backward from 1995 (year 0). Data on cur-rent year’s shoots are not included here, because theirmass increased substantially between successive rametsampling times. Other parameters of the same rametshave already been reported (Bret-Harte

et al

. 2001),but not their distributions of mass and length with age.

Data were summarized and calculations of secondarygrowth were implemented using Excel spreadsheets(Microsoft 1998). Our calculations were based onmean values of length and mass/ length for stem seg-ments of each age class. We calculated secondarygrowth for the entire growing season, but assumed thatmeasured values of mass and length represented valuesafter half the current season’s growth had occurred,because ramets were harvested throughout the season.Different assumptions about the amount of growthexperienced before harvest had little effect on calculatedrelative rates of secondary growth (data not shown).

Our results were compared with two other estimatesof secondary growth, both of which assumed that therelative secondary growth rate is represented by theslope (

h

) of the log-transform of mass/ length vs. age(Shaver 1986). This method was developed using plantsthat did not experience a large change in environmentduring the period in which growth was analysed, buteach of our ramets contained stem segments that grewboth before and for 6 years after the experiment began(Fig. 2). To compare with our analysis, we thereforeapplied Shaver’s (1986) method by calculating

h

separ-ately for stem segments formed before and after the


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Stem growth in arctic shrubs


Journal of Ecology

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treatment began (‘Shaver 86a’), and also by calculating

h

only for stem segments formed after the treatmentsbegan, and applying that value to all stem segments(‘Shaver 86b’).

We estimate secondary growth in shrub ramets from amathematical analysis that uses empirical data on massand length of stem segments of different ages. Ourexpression for secondary growth is derived geometric-ally, assuming that a stem segment is cylindrical andthat the annual increment (

a

) in its radius (

r

) is constanton average; although the radial increment may varybetween years, we assume that its mean value does notchange systematically with age. Our analysis allows fora change in the radial increment following a persistentenvironmental alteration (see Experimentally inducedchange in rate of secondary growth, below). All sym-bols used in this analysis are defined in Table 1.

The value of

a

can be determined from the relation-ship between the age of stem segments and theirmass per unit length (

m/l

). From the formula for thevolume of a cylinder,

π

r

2

l

, mass/ length equals

πρ

r

2

where

ρ

is the density of stem biomass. The radius ofa cylindrical stem at time

t

equals the radius

a

1

atthe end of the segment’s first year of growth, plus theyears since then (

x

) times

a

. Taking the square root ofthis formula,

eqn 1

Therefore, if

a

is constant on average, the square root ofa segment’s mass/ length should increase linearly withage. Data for control ramets (Fig. 3) conform to thisexpectation in the shrubs we analysed, indicating that

a

is indeed relatively constant, on average, over 15 yearsof growth. If

α

is the slope of such a plot of (

m

/

l

)

1/2

vs.age, then

a

=

α

/ (

πρ

)

1/2

.We can find the increment in mass (

∆

m

) of a stem seg-ment due to secondary growth during a period

∆

x

(expressed in number of growing seasons and fractionsthereof ) from the radii at the beginning and end of theperiod

∆

x

. The beginning radius is

a

1

+

a

x

, the endradius is

a

1

+ ax + a∆x, and ∆m is the segment mass atthe end minus its mass at the beginning. Squaring theseradii, substituting them into the equation for mass/length above, multiplying by length to give mass, andsubstituting α / (πρ)1/2 for a, gives ∆m as

eqn 2

where c = a1(πρ)1/2. Since stem mass/ length after thefirst year of growth equals c 2, equation 2 can be evalu-ated from empirical data. However, equation 2describes the increment in mass for only one age classof stem segments over the time interval ∆x. The incre-ment in stem mass of the whole ramet (M ) due to sec-ondary growth is the sum over all age classes ofsegments,

Fig. 2 Micrograph of a cross-section through a 15-year-old stem of a Betula ramet from a fertilized plot, stained withphloroglucinol. Annual growth rings formed prior to fertilization are much closer together (white arrowheads) than those formedafter fertilization (black arrowheads). Bar = 500 µm.

( / ) ( )m l ax a1/2 1/2 1/2= +π ρ 1

∆ ∆ ∆ ∆m l x x x c x ( ( ) )= + +2 22 2 2α α α


256M. S. Bret-Harte, G. R. Shaver & F. S. Chapin III

© 2002 British Ecological Society, Journal of Ecology, 90, 251–267

eqn 3

where n is the age of the ramet, and i, the age of any par-ticular class of segments at the start of the interval,equals xi + 1 (from the definition of x, above).

The mass m of one age class of stem segments (neg-lecting the mass of any short shoots of Betula) is πlρ(ax+ a1)

2, and the stem mass of the whole ramet is thus

eqn 4

Comparing mass calculated from this equation withmeasured values of stem mass provides a check onour analysis (see Results). The fractional increase∆M/M in stem mass of the whole ramet due to second-ary growth over the time interval ∆x is equation 3divided by equation 4.

Experimentally induced change in rate of secondary growth

The shrub ramets that we analysed grew for 12–15years, the last 6 of which were under experimental treat-ments. Some of these treatments caused a dramaticincrease in secondary growth, even in stem segmentsformed before the treatment began (Fig. 2). To accountmathematically for an experimental treatment that

causes a step-change in the rate of secondary growth,we assume that the average value of the radial incrementprior to treatment (a) increases to a new value followingtreatment (b), which applies to stem segments of all ages.

For stem segments formed after the treatment beganto affect secondary growth, the previous analysisapplies because b can be substituted for a in equations1 and 2. Thus, for these segments, there should be a lin-ear relationship between the square root of mass/ lengthand age, and if β is the slope of that relationship,b = β(πρ)1/2. If ce = (πρ)1/2b1, and b1 is the stem radiusafter the first year of growth under the treatment(analogous to a1), then by equation 2,

eqn 5

For stem segments formed before the treatment began,let f be the number of years since the treatment began toaffect secondary growth, and g + 1 be the segment agewhen the treatment took effect. Thus x = g + f, andn = f + g + 1, where n is the age of the segment. Thestem radii at the beginning and end of the interval ∆xare then a1 + ag + bf and a1 + ag + bf + b∆x. As in thederivation of equation 2, ∆m can be calculated fromthese stem radii in terms of both a and b.

As before, we can use the empirical relationshipbetween mass/ length and age of stem segments to

∆ ∆ ∆ ∆M l x x x c xi ii

n

( ( ) )= + +=∑ 2 22 2 2

1

α α α

Table 1 Symbols used in the mathematical analysis and their definitions

Symbol Definition

a Annual radial increment under control conditions (mm y–1)a1 Radius of stem segment after 1st year of secondary growth (i.e. radius of primary growth + a · 1 year) (mm)b Annual radial increment under experimental conditions (mm y–1)b1 Radius of stem segment after 1st year of secondary growth under experimental conditions (i.e. radius of

primary growth + b · 1 year) (mm)c Square root of mass/ length of segments after 1 year of growth under control conditions (mg1/2 mm–1/2)ce Square root of mass/ length of segments after 1 year of growth under experimental conditions (mg1/2 mm–1/2)f Years since treatment began (y)g Age when treatment began minus 1 (y)h Slope of the natural log of (mass/ length) vs. agel Length of stem segments in a given age class (mm)m Mass of stem segment (mg)M, Mr Mass of whole ramet (mg)Me Old stem biomass per m2 (g m–2)n Age of the whole ramet (y)p Primary stem growth in the current year (g m–2)r Radius of stem segment (mm)R Relative rate of secondary growth compounded continuously (y–1)t Time (y)v Volume of a cylinder (mm3)x Age of stem segment minus 1 (y)z Stem biomass lost from the above-ground biomass compartment in 1 year due to mortality or engulfment by

moss (g m–2)α Slope of the square root of (mass/ length) vs. age for control stem segments (mg1/2 mm–1/2 y–1)αr Slope of the square root of (mass/ length) vs. age under experimental conditions for segments formed before

the treatment took effect (mg1/2 mm–1/2 y–1) β Slope of the square root of (mass/ length) vs. age under experimental conditions for segments formed after the

treatment took effect (mg1/2 mm–1/2 y–1)βr Yearly increment in square root of mass/ length under experimental conditions for stem segments formed

before the treatment took effect (mg1/2 mm–1/2 y–1) ρ Density of biomass in stem segments (mg/mm3)∆x Increment in time over which secondary growth is occurring (y)

M l x x c ci i ii

n

( )= + +=∑ α α2 2 2

1

2

∆ ∆ ∆ ∆m l x x x c xe ( ( ) )= + +2 22 2 2β β β


257Stem growth in arctic shrubs


obtain values to substitute for a and b. Because b is thesame for all age classes of stem segments, we can sub-stitute b = β(πρ)1/2, as above. For stem segments formedbefore the treatment began to affect secondary growth,m/l = πρ(a1 + ag + bf )2. Although f increases with timefollowing treatment, it is constant for all segments har-vested at the same time. Only g varies with age in thisequation, giving a linear relationship between squareroot of mass/ length and age, whose slope is α. Thus,a plot of square root of mass/ length vs. age for ra-mets from an experimental treatment should consistof two straight lines with slopes α and β, with thebreakpoint between the lines occurring when the treat-ment began to affect secondary growth. Data fromexperimentally treated ramets conform to this expecta-tion (Fig. 3).

Substituting α, β, and c as in the derivation ofequation 2 gives an expression for the increment inmass due to secondary growth in segments formedbefore the treatment took effect, that can be evaluatedfrom empirically determined mass/ length data.

eqn 6

Equation 6 reduces to equation 2 if α = β.The absolute increment in mass due to secondary

growth for the whole ramet is obtained by addingequations 5 and 6 and summing over all age classes ofstem segments.

eeqn 7

In this equation xi = i – 1, gi = i – f – 1, and ce = (πρ)1/2b1

is the square root of mass/length of 1-year-old-segments from experimentally treated ramets. Thefirst sum in equation 7 gives secondary growth in thecurrent year in segments formed after the treatmenttook effect, while the second sum gives secondary growthin the current year in segments formed before thetreatment took effect. Both c and ce must be known tocalculate ∆M from equation 7. We assumed that c fortreated ramets was the same as for control ramets.

The mass of stem segments formed after the treat-ment affected secondary growth (i.e. x < f ) is m =πlρ(bx + b1)

2. The mass of segments formed beforethe treatment took effect is m = πlρ(a1 + ag + bf )2.Expanding and modifying these expressions as in thederivation of equation 4, adding them together, andsumming over all age classes in a ramet gives its totalstem mass as.

eqn 8

where conventions for subscripts are the same as forequation 7. As before, this result may be compared withempirical values to check our analysis. The fractionalincrease in mass of the experimentally treated ramet causedby secondary growth is equation 7 divided by equation 8.

For both control and experimentally treated ramets,the fractional increase in biomass is calculated fora finite time interval. The true relative rate of secondarygrowth (compounded continuously), R = dM/Mdt, isrelated to a finite fractional change by

eqn 9

If the growth interval was one growing season, ∆ x = 1.

Fig. 3 Square root of mass/ length vs. year those segmentswere produced for stem segments from 15 years-old ramets.Experimental treatments began in 1989, 6 years before harvest.Treatments: C, control; F, fertilized with N + P; GH, treatedwith greenhouses; GHF, treated with greenhouses andfertilized with N + P. Stem segment age declines as year of stemsegment production increases; ramets were harvested in 1995,when segments formed in 1980 were 15 years old.

∆ ∆ ∆ ∆ ∆m l c x g x f x x ( ( ) )= + + +2 2 2 2 2 2β αβ β β

∆ ∆ ∆ ∆

∆ ∆ ∆ ∆

M l c x x x x

l c x g x f x x

i e ii

f

i ii f

n

( ( ) )

( ( ) )

= + + +

+ + +

=

= +

∑

∑

2 2

2 2 2

2 2 2

1

2 2 2

1

β β β

β αβ β β

M l x c x c

l c cg g cf g f f

i i e i ei

f

i i i ii f

n

( )

( )

= + + +

+ + + + +

=

= +

∑

∑

β β

α α β αβ β

2 2 2

1

2 2 2 2 2

1

2

2 2 2

1 + ∆ ∆MM

eR x =




Correction for reduced b in older segments

In experimentally treated ramets, the slope of squareroot of mass/ length vs. age of stem segments formedbefore the treatment took effect should equal α. If thatvalue, which we will call αr, is less than α in controlramets (e.g. F vs. C treatments, Fig. 3), either a orb must be less in older segments than in segmentsformed after the treatment began. Since a applies topre-treatment growth, it is more reasonable that b isless in older segments than in younger ones.

An average correction to b for older segments can becalculated as follows. Assume that b is constant for agiven age class of segments but declines with age; thisreduced average b in older segments will be called br.Mass/ length of older segments is m / l = πρ(a1 + ag+ br f )2. Substituting in α and c, and letting βr = (πρ)1/2br,the square root of mass/ length is

eqn 10

To find βr, let αr be the slope of the line through thesquare root of mass/ length vs. age for segments formedbefore the treatment took effect. The equation for thisline is

eqn 11

The first term in equation 11 is the mass/ length thatresulted from growth of older segments in the yearsbefore treatment. Since g is defined as age prior to treat-ment minus one, (g + 1) is the number of years thateach of these segments grew before the treatmentaffected their growth. The second and third terms inequation 11 together equal the square root of mass/length of segments formed in the first year that thetreatment took effect, which is the breakpoint of thecurve. Since ce is the square root of mass/ length afterthe first year of growth under treatment, these seg-ments grew for an additional ( f – 1) years, with resultsgoverned by coefficient β. Assuming that c and α arethe same as for control segments, we can set equations10 and 11 to be equal and solve for βr.

eqn 12

βr is substituted for β in the second sum terms in equa-tions 7 and 8.

Comparison of calculated results with ecosystem biomass accumulation

Relative rates of secondary growth calculated from ourmodel were compared to equivalent rates calculatedfrom quadrat harvest data on Betula abundance inlong-term fertilization experiments (Chapin et al. 1995;Bret-Harte et al. 2001; Shaver et al. 2001). To makethis comparison, we assumed that above-ground stemmass of Betula in control tundra is in a steady state, in

which addition of new stem material by primary andsecondary stem growth in one season is offset by anequal loss of stem mass. Stem loss occurs either bymortality or by engulfment of basal stems by upwardgrowth of moss, which does not kill the stems butremoves them from the above-ground stem compart-ment measured in these experiments. This assumptionis reasonable because, over time, biomass in controltundra fluctuates around a roughly constant value(Shaver et al. 2001). We assumed that stems in experi-mental treatments have the same proportional lossrate as in control tundra, and that secondary growthrates calculated for Betula ramets apply to the totalBetula stem mass in each treatment. We assumed thatprimary stem made up 14.8% of the current year’s pri-mary production for Betula in control and greenhousetreatments, and 25.2% in fertilizer and greenhouse plusfertilizer treatments (Shaver et al. 2001).

At peak season each year, stem mass measured inan ecosystem-level quadrat harvest includes old stemmass per m2 (Me) and new stem added by primarygrowth during that year ( p). This new stem becomespart of the old stem compartment in the followingyear. We calculated the net change in the old stem masscompartment from peak season of one year to thenext as

eqn 13

where ∆Mr/Mr is the fractional increase in mass of anaverage ramet due to secondary growth (from ourmodel), and z is the fraction of the total stem mass lostto mortality or engulfment by moss, assuming that oldstem mass in control plots is in a steady state. The pre-vious year’s primary growth (p) occurs twice in thisequation because it becomes part of the old stem masscompartment and undergoes secondary growth in thecurrent year. For experimental treatments, we deter-mined the gross gain in mass from equation 13 (neglect-ing the loss term) and expressed it as a true relative rate(equation 9). The expected relative rate of accumula-tion of old stem mass per m2 in an experimental treat-ment was calculated by expressing z as a true relativerate (equation 9) and subtracting this relative loss ratefrom the relative gain rate.

We compared expected relative rates of accumula-tion of stem mass calculated above with observed ratesof accumulation in the long-term experiments asfollows. When harvests from different years were avail-able (Shaver et al. 2001), we calculated an observedrelative rate of net increase in old stem mass betweenharvests as R = ( ln Me2 – ln Me1) /∆t, where Me2 is oldstem mass in the experimental treatment at time 2, Me1

is old stem mass in the experimental treatment at time1, and ∆t is the number of years between harvests.When only one harvest was available, we used the sameformula, but substituted old stem mass in control plotsfor Me1; ∆t was then the duration of the experimentprior to harvest.

( / ) /m l c g fr1 2 = + +α β

( / ) ( ) ( ) /m l g f cr e1 2 1 1= + + − +α β

β βα α α β

rr e rg c c

f

( ) = +

− + − + −

∆∆

M p M pM

MzMe e

r

re ( ) = + + −




Results

Primary stem growth in length is the product of lengthper stem segment times the number of stem segmentsformed in a given year. Under control conditions, Salixramets produced structural branches more rapidly(approximately doubling their number every 2–3 years)than ramets of Ledum and Betula (Fig. 4). For controlBetula ramets, structural branch number was nearlyconstant for long periods of time, because almost allaxillary buds that grew developed into short shootsrather than structural branches. Betula, and to a lesserextent, Ledum, responded to the two fertilization treatmentsby increasing the number of structural branches after

a 3-year lag, but ramets of Salix showed no signi-ficant change in branch number under any treatment(Fig. 4).

Average length per stem segment in control rametsvaried from year to year but showed no strong trendover time for any species (Fig. 5). Greenhouse treatmentdid not significantly increase length per stem segmentfor any species (Fig. 5). Both fertilization treat-ments strikingly increased the length of individual stemsegments of Betula and Ledum for several years, butby the time of harvest (6 years after treatment began),values had nearly returned to pre-treatment levels(Fig. 5). The decrease in length per stem coincidedwith the increase in branching (Fig. 4).

Total primary growth in length of each age class ofstems (length per stem segment times number of stemsegments) is needed to calculate secondary growth.Under control conditions, Salix showed the greatesttotal stem length per age class (Fig. 4b, insert), because

Fig. 4 Main graphs show average number of stem segmentsfor each age class of stem segments vs. year those segmentswere produced. Inserts show total length of stem segments ofa given age class vs. year those segments were produced (nota cumulative total over multiple age classes). Symbols as inFig. 3. Bars indicate SE between blocks (n = 4).

Fig. 5 Average length per stem segment for each age class ofstem segments vs. year those segments were produced. Conven-tions as in Figs 3 and 4.




of its greater branching rate. Under both fertilizationand greenhouse plus fertilization treatments, how-ever, there was a large progressive increase in totalstem length in Betula and Ledum with time (Fig. 4,insert). The factor of increase in total stem length withfertilization was much greater for Betula than for theother species (Fig. 4a, insert).

Empirical data support our key assumptions

A key assumption underlying our mathematical ana-lysis of secondary growth is that annual radial incrementdoes not change systematically with age under unchang-ing growing conditions, and this is supported by thelinear relationships in Fig. 3. As predicted, treatmentsthat changed secondary growth rate caused a breakin the plot of square root of mass/length vs. the yearthat stem segments were produced, with stem segmentsformed before and after the treatment took effectshowing different slope values (Fig. 3). This indicatesthat radial increment increased substantially in allstem segments following fertilization; the increase caneasily be seen in stem cross-sections from fertilizedBetula ramets (Fig. 2).

Correlation coefficients describing the linear fit ofsquare root of mass/ length with age (Fig. 3) for Betulawere greater than 0.99 for all segments formed after thetreatment began, and greater than 0.95 in all treatments(Table 2). This indicates that average inter-annualvariability in radial increment was very small in thepopulation of Betula ramets we sampled. The fit wasslightly poorer for Salix and worst for Ledum (Fig. 3),

but correlation coefficients were mostly greater than0.93 for Salix and 0.8 for Ledum (Table 2). Deviationsfrom constant radial increment in Ledum occurredbecause some stem segments grew consistently betterthan others. For example, control stem segments ofLedum produced in 1984 were heavier than segmentsproduced in 1981 and 1982 (Fig. 3), which could nothave resulted from poor growth throughout theramet in any year when all these stem segments werealive.

In all three species, fertilization with or withoutgreenhouse treatment increased the annual radial incre-ment, as indicated by differences between treatmentsin the slope of square root of mass/ length vs. year thesegments were produced (Fig. 3, Table 2). However,fertilization had a much greater effect on Betula thanon either Salix or Ledum. There was little differencebetween effects of greenhouse treatment and fertilizationfor Salix ramets (Fig. 3). Ramets of Betula andLedum from fertilizer and greenhouse plus fertilizertreatments showed a slightly less negative slope ofthe square root of mass/ length relationship for stemsegments formed before the treatment began thanwas seen for control ramets (Fig. 3). This indicatesthat radial increment increased slightly less with treat-ment in older stem segments than in ones formed afterthe treatment took effect (see Mathematical analysisof secondary growth).

Agreement with measured mass and mass/length data

A second test of our analysis is how well calculatedmass and mass/ length agree with empirical data. Cal-culated values of mass/ length mostly fell within the

Table 2 Slopes and correlation coefficients (R-values) from plots of square root of mass/ length vs. year segments produced.Correlation coefficients are calculated for a linear fit through square roots of mean values of mass/ length

Species and treatment

Pre-treatment Post-treatment

SlopeCorrelation coefficient Slope

Correlation coefficient

BetulaC –0.140 0.996F –0.087 0.954 –0.381 0.993GH –0.183 0.988 –0.186 0.995GHF –0.106 0.974 –0.575 0.997

SalixC –0.210 0.982F –0.193 0.975 –0.308 0.991GH –0.162 0.978 –0.270 0.976GHF –0.153 0.844 –0.328 0.930

LedumC –0.041 0.935F –0.027 0.805 –0.121 0.966GH –0.048 0.937 –0.049 0.971GHF –0.016 0.516 –0.121 0.941

Pre-treatment, stem segments formed before the treatment took effect; post-treatment, stem segments formed after the treatment took effect; C, control; F, fertilized with 10 g/m2 N and 5 g/m2 P; GH, warmed with plastic greenhouses; GHF, fertilized as in F and warmed with plastic greenhouses.




SEs of measured values for Salix, Betula, and Ledum(Fig. 6). The average difference between calculatedand measured values was within 0.1–9% of measuredvalues for different treatments of Ledum, within 1–15%for Salix, and within 5–12% for Betula.

Calculated mass for each age class of stem segmentsincorporates stem length. For Salix and Ledum, cal-culated mass was usually within the SEs of measuredvalues (Fig. 7), as it was for Betula, except for ramets fromthe greenhouse plus fertilizer treatment (Fig. 7). Here,the biggest difference was in the youngest age classesof Betula (Fig. 7), even though their calculated andmeasured mass/ length ratios agreed well (Fig. 6). Multi-plication of calculated mass/ length by very largelength values (Fig. 4a, insert) may have magnified smalldifferences between calculated and measured mass/length. For the whole ramet, calculated mass was within0.2–23% of measured mass for Betula, 0.8–21% forSalix, and 0.8–12% for Ledum.

The response of whole ramet mass to the two fert-ilization treatments in Betula was dominated by theyoungest age classes, because of extensive branching(Figs 4 and 7), even though mass/ length was greater inthe older age classes (Fig. 6). This was less true forSalix and Ledum.

Relative rates of secondary growth for control rametsranged from 8% y–1 for Ledum to 18% y–1 for Salix(Fig. 8). In both fertilizer and greenhouse plus fertilizertreatments, however, Betula experienced a greaterincrease in the relative rate of secondary growth (2.8–3.3-fold vs. 1.2–1.7-fold for Salix), making its second-ary growth by far the greatest under these conditions(Fig. 8). Although Ledum also responded to fertiliza-tion, its relative rate of secondary growth was so muchsmaller in control ramets that the 2–3-fold increase

Fig. 6 Agreement between calculated (open symbols) and the corresponding measured mass/ length (closed symbols of the sameshape) for each age class of stem segments. Bars indicate SE of measured values between blocks (n = 4).




only made it comparable with Salix (Fig. 8). For Salix,greenhouse treatment alone had a similar effect to fer-tilization on relative secondary growth rate (Fig. 8).

Comparison with previous methods of calculating secondary growth rate

Rates of secondary growth calculated for the wholeramet based on our analysis were fairly similar to thoseobtained with previous methods (Shaver 1986). Treatedramets showed the largest differences between the meth-ods (Table 3), as expected since treatment effects were notconsidered previously (Shaver 1986). Because squareroot (as used here) and natural log (as used in Shaver1986) plots are similar over a limited range of values, theirslopes are not very different, but the correlation coeffi-cients were higher in every case using our revised method.Assuming a constant relative rate of secondary growthamong all age classes of segments (Shaver 1986) requires

that the annual radial increment should increase as thesegment grows larger, which is not reasonable.

The amount of secondary growth indicated for dif-ferent age classes differed between our analysis and the

Fig. 7 Agreement between calculated and measured total stem mass for each age class of stem segments. Conventions as in Fig. 6.

Fig. 8 Relative rates of secondary growth for the whole rametin 1995.




previous method, particularly for stem segments formedbefore the treatment began (Fig. 9). In Betula rametsfrom both fertilization treatments, these segmentsmade up such a small proportion of the total stem mass

that their contribution to secondary growth of the wholeramet was minimal (Figs 7 and 9, Table 3). Any experi-mental treatment that increased the relative repres-entation of older segments would magnify differencesbetween the secondary growth predicted by our ana-lysis and by Shaver’s (1986) method.

Comparison with ecosystem biomass accumulation

A final test of our analysis is to compare the experi-mentally induced increases in secondary growth thatwe predict based on ramet growth with changes inBetula nana stem mass per m2 seen in the same exper-iment in 1996 (Bret-Harte et al. 2001), and in a previ-ous long-term fertilization experiment in tussocktundra (Chapin et al. 1995; Shaver et al. 2001). Wefocused on Betula because it becomes dominant in thefertilizer and greenhouse plus fertilizer treatments inthese experiments (Fig. 1). To make this comparison,we assumed that above-ground stem mass in thecontrol tundra was in steady-state and that the sameproportional stem loss rate occurred in the experi-mental treatments as in the control (see Mathematicalanalysis of secondary growth). The relative loss rateof old stem mass for Betula in control tundra was20.8% y–1, which is slightly higher than the secondarygrowth rate in control tundra because stem materialfrom primary growth in the current year is addedto the old stem compartment in the following year(equation 13).

Table 3 Relative rates of secondary growth (% y–1) for thewhole ramet from our analysis compared with rates calculatedas previously (Shaver 1986)

Species and treatment

Present analysis Shaver 86a Shaver 86b

BetulaC 15.8 16.5 16.5F 44.1 37.4 45.6GH 19.8 19.8 29.1GHF 51.8 46.2 55.4SalixC 18.1 19.4 19.4F 25.1 22.1 34.6GH 24.4 21.7 31.9GHF 29.8 21.3 37.0LedumC 7.9 8.0 8.0F 20.3 15.5 27.2GH 9.5 9.1 10.5GHF 21.7 18.6 25.9

Shaver 86a, pre- and post-treatment slopes of regressions of ln(mass/ length) vs. year segment produced were assumed to equal the relative secondary growth rates of those stem segments; Shaver 86b, post-treatment slopes of ln(mass/length) vs. year segments produced were assumed to equal the relative secondary growth rate of the whole ramet.

Fig. 9 Comparison of increase in mass/ length for each age class of stem segments of Betula ramets from our analysis (constantincrement), and from two alternative methods of calculating secondary growth (Shaver 86a and b; see Methods).




Expected relative rates of accumulation of old stemmass based on ramet data agreed reasonably well withobserved average relative rates calculated from the twoquadrat harvest data sets (Fig. 10). To compare ourresults with the older experiment (Shaver et al. 2001),we calculated the observed rates of relative increase inBetula stem mass in fertilized plots between harvests in1984 and 1989. We used these harvests because the mid-point of that period (6.5 years of treatment) was similarto the 6-year time point in the current study, on whichour ramet calculation was based. This average rate(Fig. 10; ‘LTER 1984-89’) was virtually identical tothe rate predicted by the model for fertilized Betula(Fig. 10; ‘Expected’). The greenhouse and greenhouseplus fertilizer treatments were not harvested in 1984,so it was not possible to do the same comparison forthose treatments (Shaver et al. 2001). The averagerate of accumulation of stem mass between 1989and 1995, i.e. between 9 and 15 years into the olderexperiment, was somewhat lower (data not shown),even as Betula biomass increased to over 12 times thatof the controls after 15 years of fertilization (Shaveret al. 2001).

In the present experiment, there were no quadratharvests of initial stem mass at the start of treatment in1989 (Bret-Harte et al. 2001). We estimated the averagerelative rate of increase in Betula stem mass over theseven years of this experiment by comparing experi-mental values in 1996 with control values in 1996,assuming that the control value was equivalent toinitial stem mass in experimental plots. This gavesomewhat lower rates than expected for Betula in fer-tilizer and greenhouse plus fertilizer plots (Fig. 10;‘1996 harvest’). One reason for the lower value may

be that the mid-point of the calculation is only 3.5years from the start of treatment. Accumulation ofBetula stem mass by secondary growth was probablylower in the early years of the experiment becausebranching rates did not increase until 3 years aftertreatment (Fig. 4). Secondary growth in youngerbranches contributes disproportionately to the sec-ondary growth of the whole ramet (Fig. 7). We alsomay have underestimated stem mortality in the fer-tilized plots by assuming it occurs at the same rate asin control plots.

Overall, this comparison reveals that the secondarygrowth rates we calculated for ramets are reasonablyconsistent with the measured accumulation of above-ground Betula stem mass at the ecosystem level. This istrue even though Betula in the field includes stems thatare much older than our ramets, which should decreasethe overall rate of secondary growth. Many older Bet-ula stems are prostrate and may have been covered bymoss, in which case they would not be included in theabove-ground stem mass sampled in the ecosystemmeasurements. If they are part of the above-groundstem mass, they probably comprise a very small frac-tion of the total.

Discussion

The increase over time in primary stem growth inducedby the two fertilization treatments in ramets of Betulaand Ledum results initially from increased stem elonga-tion, but beyond three years of fertilization it becomeslargely due to increased numbers of branches. In con-trast, Salix fails to increase primary stem growth verymuch under any treatment because it apparently has amore rigid branching programme. In Betula and Ledum,annual elongation per stem increases transiently withfertilization, but there appears to be a trade-offbetween increased numbers and length per branch,because as branch production increases, length perstem segment declines toward the control level (Figs 4and 5). Under fertilization, whole-plant photosynthesisis higher because of increased leaf area (Bret-Harteet al. 2001; Shaver et al. 2001). However, this increasedcarbon capture is apparently insufficient to allowallocation to both increased branch production andincreased length per stem segment for either Betulaor Ledum.

In Betula, production of long-shoot (structural)branches requires a much greater investment of bothnitrogen, in leaves, and carbon, in stems and leaves, thanproduction of short shoots does, although photosyn-thetic return from long shoots is higher than fromshort shoots (Maillette 1982; Bret-Harte et al. 2001).Betula normally grows along one or a few axes, each ofwhich results from continuing elongation of a singlelong shoot. Betula achieves its great increase in branchproduction under fertilization by inducing axillary

Fig. 10 Comparison of expected relative rates of net increasein Betula stem biomass per m2 from our analysis (‘expected’)with observed average relative rates of net increase calculatedfrom whole-vegetation quadrat harvests of two differentfertilization experiments. ‘1996 harvest’ was calculatedassuming the 1996 control value was equivalent to initialbiomass in 1989 in treated plots of the current experiment.‘LTER 1984-89’ was calculated comparing fertilized biomassin 1989 with fertilized biomass in 1984 (Shaver et al. 2001).The mid-point of the ‘1996 harvest’ calculation is 3.5 yearsafter treatment, the midpoint of the ‘LTER 1984-89’calculation is 6.5 years after treatment, and the ‘expected’calculation from the model is for ramets growing 6 years aftertreatment.




buds that would normally grow as short shoots togrow instead as long shoots (Bret-Harte et al. 2001).Maillette (1982) found that leader shoots in Betulapendula produce more long shoots than branches loweron the tree, possibly indicating that in that species also,better access to resources allows shoots to change thefate of their buds. However, unlike Betula nana, vegetativeterminal buds of long shoots in both Betula pendula andBetula cordifolia normally aborted after one season ofgrowth, indicating that their development was moreconstrained (Maillette 1982; Maillette 1987).

Clonal, perennial growth is often associated withslow-growing, deterministic plants that live in harshand nutrient-poor environments, where transfer ofnutrients and carbon from older modules to youngerones is important to their survival (Callaghan 1988;Jónsdóttir & Callaghan 1990). Although Betula nana isclonal, perennial, and relatively slow-growing in controltundra, developmental flexibility in the fate of its budsallows it to radically change its branching pattern whenresource limitation is removed, in contrast to manyother tundra species. Because Betula nana can hybridizewith tree species of Betula and shows introgressionwith other shrub Betula species where their rangesoverlap (Hultén 1968), introgression may have intro-duced genes for tree-like behaviour into populationsof Betula nana remote from the present occurrence oftrees.

Extensive theory exists on relative growth rate, in bothwhole plants (Hunt 1978), and in tissues and organs(Erickson & Sax 1956; Erickson 1976; Silk & Erickson1979). Usually, however, relative rates of whole plantgrowth are calculated only for annual plants, while rel-ative growth rates in tissues are calculated only forprimary growth. Here we present a mathematicalanalysis that allows calculation of relative rates ofsecondary growth in perennial plants. Our resultsindicate that secondary growth is a significant part ofbiomass accumulation by tundra shrubs under controlconditions. Under increased nutrient availability,secondary growth becomes the major component ofbiomass accumulation by tundra shrubs, as withforest trees.

Inclusion of our assessment of secondary growthgreatly increases our estimates of net primary produc-tion (NPP) in this fertilized ecosystem (Shaver et al.2001). The increase in secondary growth of Betulaunder fertilization leads to a continued increase in esti-mated NPP with time in fertilized tundra (Shaver et al.2001). Previously, vascular plant NPP was thought tojump up, under fertilization, to a larger but constantvalue over time, even though the relative contributions

to NPP by different species changed with time (Chapinet al. 1995).

Because wood has a much higher C : N ratio thanleaves, increased secondary growth by shrubs, especi-ally Betula, causes greater carbon storage per unit ofnitrogen in fertilized plots than in control plots (Shaveret al. 2001). There may be a threshold of nitrogenavailability below which ecosystem carbon storage isconstrained by the need to invest primarily in nitrogen-rich leaves. When the threshold is exceeded, secondarygrowth increases more than proportionally to increasesin nitrogen availability, and tundra behaves more likea forest with respect to carbon storage, in that the C : Nratio in accumulated biomass is high.

Anthropogenically induced increases in atmos-pheric CO2 concentration are expected to cause arcticand boreal regions to warm more than other parts ofthe globe (Houghton et al. 1996). Arctic and borealsoils contain roughly one-third of the global soil car-bon pool (Schlesinger 1977; Gorham 1991). Decom-poser activity is expected to increase as soils warm;since nutrients are mineralized from soil organic matterduring decomposition, soil nutrient availability shouldincrease (Hobbie 1996; Nadelhoffer et al. 1991). It isnot yet clear whether the release of CO2 by increaseddecomposition will be greater than nutrient-stimulatedincreases in plant production or vice-versa (Shaveret al. 1992; Goulden et al. 1998; Hobbie et al. 2000;Shaver et al. 2000). Our results suggest that, if warmingincreases soil nutrient availability, carbon storage inwoody biomass in tundra may be larger than previ-ously expected from NPP estimates that did notaccount fully for a changing allocation to secondarygrowth. Shrubs in arctic Alaska have already increasedin numbers and size as warming has occurred (Sturmet al. 2001).

A large increase in primary stem growth such as thatfound in Betula ramets under fertilization increasesboth total leaf area and the mass of the canopy (leavesplus stems). Secondary growth provides both conduitsfor water transport and the strength to meet themechanical demands of supporting the canopy. Mostwoody species operate near the tolerable limit of theirxylem’s hydraulic conductance, set by its vulnerabilityto gas embolisms (Tyree & Sperry 1989). Thus, hydrau-lic demands of an increased area of transpiring leavescould not be met by increased xylem tension, but requireincreased secondary growth to increase xylem area.

Mechanical support of a larger canopy also requiresincreased secondary growth. In control ramets of Betulaand Salix, both radial increment (Fig. 3) and lengthper stem segment (Fig. 5) were roughly constant, sobranch length scales in proportion to diameter; thus,they exhibit what is termed geometric self-similarity(King & Loucks 1978; Niklas 1995). Geometric




self-similarity is seen in tree saplings (King 1990; Alvarez-Buylla & Martinez-Ramos 1992; Coomes & Grubb1998), shrubs (Whittaker & Woodwell 1968), and non-woody plants (Niklas 1994). In contrast, large treesexhibit elastic or stress self-similarity (Niklas 1994), inwhich height scales as the 2/3 power or 1/2 power,respectively, of diameter (McMahon 1973; McMahon& Kronauer 1976; Niklas 1995). Bertram (1989) sug-gested that small branches of trees show geometric self-similarity because of hydraulic demands, whereas largerbranches and trunks exhibit elastic similarity becauseof greater mechanical demands. Even fertilized tundrashrubs need not meet the mechanical demands of treecanopies, so their growth allometry may be set bymaintenance of constant conductance for hydraulictransport, as in small tree branches.

Among the species studied, Betula responds to addednutrients most strongly, in both primary and secondarygrowth (Figs 4 (insert) and 8; Bret-Harte et al. 2001).Under both fertilization and greenhouse plus fertiliza-tion treatments, Betula dominates the community,whereas Salix and Ledum decline in abundance, eventhough ramets of all three species respond positively tofertilization (Bret-Harte et al. 2001). Betula’s responseresults from its ability to switch between producinglong shoots and short shoots (Bret-Harte et al. 2001).However, more primary growth would not be advanta-geous to Betula if its secondary growth could not alsobe increased to meet the hydraulic and mechanicaldemands of the extra leaf and stem tissue.

Salix and Ledum appear unable to increase their sec-ondary growth as much as Betula does (Fig. 8). Sec-ondary growth of treated Salix ramets does not differmuch from that of controls. Fertilization increasesLedum’s secondary growth only in the youngest stemsegments (Fig. 3). Its shoot length increases more thanin proportion to stem diameter, so Ledum does nothave even the limited mechanical reinforcement pro-vided by geometric self-similarity. Because Ledum doesnot acquire mechanical strength in its stems that wouldenable it to grow upward into the canopy, it becomesconfined to the understorey in both fertilization treat-ments, where its photosynthetic performance is light-limited by the Betula canopy and further growth isreduced (Bret-Harte et al. 2001). When nutrient avail-ability increases, Betula’s developmental plasticity insecondary growth and flexibility in the fate of its budscontribute to its dominance, whereas the way thatLedum’s secondary growth is regulated puts this speciesat a competitive disadvantage.

Acknowledgements

We thank Jill Johnstone, Jennifer Zoerner, JoannaWagner, Andreas Chavez, and Tad Gunkelman for

field assistance, and Dr Peter M. Ray for helpful dis-cussions and editorial assistance. We thank two anonym-ous referees for helpful comments. This work wasfunded by NSF grants OPP9896302, OPP9415411,OPP9907127, DEB9211775, and DEB0075669.

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Received 1 February 2001 revision accepted 29 August 2001


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