allometric growth and allocation in forests: a perspective from fluxnet

Ecological Applications, 21(5), 2011, pp. 1546–1556� 2011 by the Ecological Society of America

Allometric growth and allocation in forests:a perspective from FLUXNET

ADAM WOLF,1 CHRISTOPHER B. FIELD, AND JOSEPH A. BERRY

Department of Global Ecology, Carnegie Institution for Science, Stanford, California 94305 USA

Abstract. To develop a scheme for partitioning the products of photosynthesis towarddifferent biomass components in land-surface models, a database on component mass and netprimary productivity (NPP), collected from FLUXNET sites, was examined to determineallometric patterns of allocation. We found that NPP per individual of foliage (Gfol), stem andbranches (Gstem), coarse roots (Gcroot) and fine roots (Gfroot) in individual trees is largelyexplained (r2¼ 67–91%) by the magnitude of total NPP per individual (G). Gfol scales with Gisometrically, meaning it is a fixed fraction of G (;25%). Root–shoot trade-offs were manifestas a slow decline in Gfroot, as a fraction of G, from 50% to 25% as stands increased inbiomass, with Gstem and Gcroot increasing as a consequence. These results indicate that afunctional trade-off between aboveground and belowground allocation is essentially capturedby variations in G, which itself is largely governed by stand biomass and only secondarily bysite-specific resource availability. We argue that forests are characterized by strongcompetition for light, observed as a race for individual trees to ascend by increasingpartitioning toward wood, rather than by growing more leaves, and that this competitionstrongly constrains the allocational plasticity that trees may be capable of. The residualvariation in partitioning was not related to climatic or edaphic factors, nor did plots withnutrient or water additions show a pattern of partitioning distinct from that predicted by Galone. These findings leverage short-term process studies of the terrestrial carbon cycle toimprove decade-scale predictions of biomass accumulation in forests. An algorithm forcalculating partitioning in land-surface models is presented.

Key words: allocation of biomass; allometry; data assimilation; FLUXNET; forest stand biomass; land-surface model; net primary productivity, NPP; partitioning of photosynthesis products; tree biomasscompounds; tree plasticity.

INTRODUCTION

The central challenge in modeling the land surface of

the Earth is translating the theoretical and empirical

understanding gained from small-scale process studies

into a model that describes the state and change of

physical quantities at much larger scales. The scaling

problem for terrestrial carbon-cycle science is that

photosynthesis, growth, and mortality are directly

observable only at small spatial scales, such as individual

leaves or trees, and at short temporal scales, especially

for process studies, but the scale of vegetation’s

interaction with climate-change impact is global and

long term. Direct measurement of photosynthesis takes

place on individual leaves or branches in cuvettes, but

grid-cell-scale modeling of photosynthesis requires some

scaling approach to translate leaf-level observations of

fluxes to the canopy scale, such as the widely used ‘‘big

leaf’’ approach to accommodate light gradients within

the canopy (Sellers et al. 1997). The accumulation of

biomass in forest stands is also a challenge to model

because secondary succession can extend well past a

century (Wirth et al. 2009) but process studies of

growth, allocation and turnover typically span a year

or less (Luyssaert et al. 2008), and even forest-inventory

programs rarely have observations extending past a few

decades. Current thought on the terrestrial carbon cycle

(Schulze 2005) suggests that the processes that are most

prominent in the short term, such as photosynthesis or

leaf growth and senescence, are less important determi-

nants to the long-term carbon budget than are processes

that are slow or infrequent, such as decomposition of

coarse woody debris (Harmon et al. 1986) or gap-phase

dynamics (Moorcroft et al. 2001).

We argue in a companion paper (A. Wolf, P. Ciais, V.

Bellassen, N. Delbart, C. B. Field, and J. A. Berry,

unpublished manuscript) that the treatment of vegetation

growth in land-surface models (LSMs), namely the

selective allocation of photosynthate toward different

organs (Fig. 1), has really not adequately addressed the

scaling of biomass from that of individual trees into

stands. The simulation of biomass in LSMs is an

important diagnostic because it represents the realism

of long-term integrals of land–atmosphere carbon fluxes

Manuscript received 16 June 2010; revised 17 September2010; accepted 19 October 2010. Corresponding Editor: D. S.Schimel.

1 Present address: Department of Ecology and EvolutionaryBiology, Princeton University, Princeton, New Jersey, USA.E-mail: [email protected]

1546

that are central to uncertainty in future feedbacks in the

carbon cycle (Friedlingstein et al. 2006). A. Wolf, P.

Ciais, V. Bellassen, N. Delbart, C. B. Field, and J. A.

Berry (unpublished manuscript) found that simulated

biomass in most LSMs is at odds with the large body of

empirical and theoretical work on forest allometry

(West et al. 1999).

Allometry can also play a constructive role in linking

LSMs with remote sensing to constrain estimates of

biomass (Wolf et al. 2010). Many of the forest attributes

that show the strongest allometric interrelationships

with biomass—such as height, population density, and

crown radius—also impact lidar and radar retrievals

(Sun and Ranson 2000, Goodwin et al. 2007) and multi-

angle optical remote sensing (Chopping et al. 2008).

Improving links between modeled and remotely sensed

biomass estimates, such as those from forthcoming

DESDynI, Carbon-3D, and BIOMASS missions (Hese

et al. 2005, Dubayah et al. 2010), would allow improved

monitoring of the state of the biosphere in a rapidly

changing world. However, for this interaction to

proceed, we need stand-level models that can accom-

modate these individual-level data in a self-consistent

manner without bias.

Allometry is a quantitative approach that character-

izes trees in forest stands (e.g., their size, mass, number,

and growth rate), using scaling laws to describe the

properties that emerge as a consequence of the

biophysical constraints of being a tree competing for

survival in a forest. The important concept to gain from

this scaling argument is that size matters: the proportion

of leaf, trunk, and coarse- and fine-root masses in a tree

is not fixed, but changes as the body size of the tree

changes (Enquist and Niklas 2002), and as a forest

matures the number of trees decreases as the mass of the

trees in the stand increase (Enquist et al. 1998, West et

al. 2009). While real forests experience crowding that

results in competition for resources, mortality of

branches and leaves that underperform (‘‘self-pruning’’),

and death of whole trees that have negative carbon

balance (‘‘stand self-thinning’’), LSMs generally lump

these processes into allocation and turnover of abstract

pools that represent the aggregate biomass of the entire

stand. While no model behaved perfectly with the

respect to the observations, the models that did best,

including Orchidee (Bellassen et al. 2009) and ED

(Moorcroft et al. 2001), were those that made the

attempt to treat stands as collections of individuals

subject to allometric constraints.

While the study by A. Wolf, P. Ciais, V. Bellassen, N.

Delbart, C. B. Field, and J. A. Berry (unpublished

manuscript) identified a bias in the biomass patterns

simulated by a variety of global models, it suggested no

means for fixing the problem. Accumulation of biomass

over time is an outcome of both the carbon devoted to

the growth and maintenance of those pools, and the loss

of carbon from those pools by respiration or mortality.

The rate of loss can be conceptualized using a turnover

rate following first-order kinetics. Discerning the frac-

tional allocation of photosynthate to different plant

parts is not easily accomplished from observations of

biomass alone, because the turnover of the pools (leaf,

wood, and fine roots) is different. We will use the term

‘‘partitioning’’ in this paper to refer to the fractional

distribution of a plant’s net primary productivity (NPP)

among different plant parts, where NPP includes both

biomass accumulation and subsequent mortality, but

excludes respiration for growth or maintenance. As

Friedlingstein et al. (1999) point out, woody and

herbaceous vegetation could in principle partition

biomass equally, but the longevity of lignified wood

results in the predominance of the stem pool in forest

biomass. In addition, biomass data alone are inadequate

for estimating partitioning because partitioning is

unlikely to be constant over the life of a tree, due to

the fractal nature of the branches needed to physically

FIG. 1. The role of net primary productivity (NPP) partitioning schemes for biomass component growth in land-surface models.‘‘R’’ stands for respiration, and ‘‘hetero’’ for heterotrophic. Partitioning schemes that determine fractional allocation include (1)fixed proportion, (2) root/shoot competition for resources; (3) seasonal phenology, and (4) size dependent (allometry); seeIntroduction for discussion of partitioning schemes.

July 2011 1547GROWTH ALLOMETRY FROM FLUXNET

support the leaves and fine roots (Mohler et al. 1978,

West et al. 1999).

Friedlingstein et al. (1999) identified several additional

impediments to applying the existing literature on

partitioning to a scheme appropriate for LSMs. The

process-level understanding of partitioning, to the extent

it is understood at all, is essentially at the level of the

individual (Levin et al. 1989, Cannell and Dewar 1994,

Bartelink 1998, Lacointe 2000, Poorter and Nagel 2000,

Ogle and Pacala 2009). Superimposed on this uncer-

tainty of individual partitioning are additional phenom-

ena that are evident at the stand level, such as self-

pruning, self-thinning, and change in species composi-

tion. These community-level phenomena enhance the

mortality of whole trees and tree organs (e.g., branches

and coarse roots) while changing the size distribution of

individuals in the remaining growing tree stock. Such

larger-scale processes do not have to be represented in

models intending to simulate short-term flux data, but

are essential to modeling the carbon budget of a forest

stand that extends for years or decades. Although an

individual-level representation of forest biomass was

discarded decades ago by LSMs to speed up computa-

tion (Running and Gower 1991), it is not necessary (or

reasonable) to discard the allometric constraints or

functional balance of the individual in the pursuit of a

model representing growth and biomass distribution at

the stand level (Purves and Pacala 2008). We base this

on a line of evidence that the scaling of individuals into

stands follows some general ‘‘rules’’: the competition of

individuals for space in a stand leads to predictable

patterns of self-thinning (Enquist et al. 1998), growth

(Niklas and Enquist 2002), and resultant biomass

(Enquist and Niklas 2002) that emerge as a consequence

of structural and vascular constraints imposed on

individuals (West et al. 1999). Because large databases

of stand-level forest inventory repeatedly corroborate

these individual-level scaling patterns, they should be

amenable to use in LSMs that also operate at the stand

level. However, we do not currently have a way of

incorporating these scaling rules into a LSM.

A good partitioning scheme should possess a few key

attributes. First, the partitioning should honor the scale

dependence of partitioning, i.e., that partitioning de-

pends on the characteristic tree size in a stand, and that

the balance of biomass in different organs must conform

to observed allometries. Second, a partitioning scheme

should also distinguish between above ground and

belowground wood, because aboveground wood is

widely measured by forest inventory and facilitates

validation against data and use in data assimilation.

Third, a partitioning scheme must represent fine roots,

because this pool is globally important in the carbon

cycle (Jackson et al. 1997, Matamala et al. 2003), but

largely neglected by allometric scaling theory (Enquist

and Niklas 2002, Niklas and Enquist 2002). Finally,

because most models represent some sort of functional

competition of allocation between leaves and fine roots

in response to limitations in light, water, or nutrients

(e.g., Tilman 1988, Running and Gower 1991), we must

address the relative importance of allometry (i.e., size

dependence of mechanical support) vs. resource limita-

tion in driving variation in partitioning.

The goals of the present study are to use a recently

compiled database on component net primary produc-

tivity (NPP) collected at FLUXNET sites (Luyssaert et

al. 2007), and to use these data to develop a partitioning

scheme that obeys the allometric scaling observed in

nature for use in LSMs. There are several motivations

for adding this study to the literature on allocation and

partitioning. This study is the largest we are aware of to

separately analyze fine roots as a component of

partitioning (cf. Litton et al. [2007] and Enquist and

Niklas [2002]). Fine roots are functionally distinct from

coarse roots because of their dramatically higher

turnover rate, and are generally modeled as a separate

biomass pool in LSMs, so understanding partitioning to

fine roots is essential to be relevant for these modeling

efforts. Also, this study considers the role of stand

thinning in apparent allocation by separately controlling

population density from individual allocation in scaling

from individuals to stands. Finally, we hope that

synthesizing the literature on growth allometry

(Enquist and Niklas 2002) with that of partitioning in

LSMs will give improved confidence that LSMs

realistically represent long-term integrals of forest–

atmosphere carbon flux, which could reduce this source

of uncertainty in predictions of future climate (Fung et

al. 2005, Friedlingstein et al. 2006).

MATERIALS AND METHODS

The FLUXNET program synthesizes data that have

been collected at a large number of sites (.400 sites)

where net ecosystem exchange (NEE) between the

terrestrial biosphere have been intensively measured

and pooled to permit synthesis activities (Baldocchi et

al. 2001, Baldocchi and Valentini 2004, Luyssaert et al.

2007). A subset of these sites were summarized in a

database presented by Luyssaert et al. (2007; hereafter

‘‘the Luyssaert database’’), which compiled annual

fluxes of component net primary productivity (NPP)

separated by foliage, branch, trunk, coarse roots, and

fine roots whenever available. The NPP of these

components includes growth that was subsequently lost

to mortality (e.g., litterfall), such that summing compo-

nent NPP and ecosystem respiration should in principle

equal the NEE measured by eddy covariance; the

closure between bottom-up and top-down estimates is

generally within 5%. Because the Luyssaert database is

compiled from a large number of studies, methods

employed to estimate component NPP vary between

sites, and not all components are available for all sites.

For the purposes of this paper, we included only sites

where all components of NPP (foliage, branch, trunk,

coarse root, fine root) are reported, and where stand

density N is also reported (n ¼ 95 sites). Total NPP per

ADAM WOLF ET AL.1548 Ecological ApplicationsVol. 21, No. 5

individual (G, in kg dry matter�tree�1�yr�1) was calcu-

lated as the sum of all component NPP (kg C�ha�1�yr�1)divided by stand density N (trees/ha): G ¼ (NPPfol þNPPtrunk þ NPPbranch þ NPPcroot þ NPPfroot)/N

with appropriate unit conversions from kilograms C to

kilograms dry matter (DM). Similarly, each component

NPP was calculated from the component NPP per

individual: Gfol ¼ NPPfol/N; Gstem ¼ (NPPtrunk þNPPbranch)/N; Gcroot ¼ NPPcroot/N; Gfroot ¼NPPfroot/N. Total biomass per individual (M, in kg

C) and component biomass per individual (Mfol,

Mstem, Mcroot, Mfroot) was calculated analogously.

Woody biomass is calculated an aggregate of stem and

coarse-root biomass such that Mwood ¼ Mstem þMcroot and Gwood ¼ Gstem þ Gcroot. The conversion

of stand-level values of NPP and biomass to an

individual basis using the stand density (N) follow

Enquist and Niklas (2002) and Niklas and Enquist

(2002) for their allometric analysis of the Cannell (1982)

database. While this approach elides the variation within

stands of tree size and size-related growth, it facilitates

comparison between stands differing in population

density on the basis of the biomass and growth of the

‘‘average’’ tree.

Among the 95 useable sites, 27 sites are dominated by

angiosperms (Fig. 2: open circles), and 68 sites are

dominated by gymnosperms (Fig. 2: solid circles). The

sites are generally located at temperate (n¼ 71 sites) and

boreal (n ¼ 20 sites) regions, with few in tropical (n ¼ 3

sites) and Mediterranean (n ¼ 1 site) regions. The sites

were given a variety of codes to characterize manage-

ment of the stands; most stands were managed forests (n

¼48 sites), many were natural forests (n¼20 sites), some

stands were categorized as recently disturbed (n ¼ 8

sites), a small number were given fertilizer or irrigation

(n¼ 9 sites), and for some no information was available

(n¼10 sites). For the sake of comparison, of the 63 plots

from Litton et al. (2007), only 14 plots are included here:

3 plots from Ryan et al., (1996), 4 plots fromMaier et al.

(2004), 2 plots from Law et al. (2001), and 5 plots from

Curtis et al. (2002). The remainder either lacked data on

fine roots or were unavailable for reference as Master’s

theses or book chapters. The Maier et al. (2004) and

Ryan et al. (1996) studies represent seven of the nine

fertilization/irrigation plots included in this study, with

the remaining two control and treatment plots reported

in Linder and Agren (1998) and Gower et al. (2001),

respectively. The fertilized and irrigated plots are

included with all other plots in the regression analysis,

but their departures from the mean slope will be

additionally discussed as the only direct measure of the

impact of nutrient and water additions on partitioning.

Direct measurements of soil nutrients are not otherwise

available in the Luyssaert database. Finally, in one study

(Gielen et al. 2005), three irrigated control plots

included in the regression calculation have three

corresponding CO2-enriched plots, which will be shown

for comparison.

A range of techniques were employed to measure fine

root NPP, including ‘‘higher quality’’ measurements of

biomass and in situ turnover using minirhizotrons or

root windows (n¼ 54 sites), ‘‘modest quality’’ techniques

such as biomass with an assumed turnover rate (n ¼ 18

sites) or root ingrowth techniques (n ¼ 3 sites), and

‘‘lower quality’’ techniques based on sequential coring (n

¼ 16 sites). Some sites used techniques for fine-root NPP

that were ambiguous from the study text (n ¼ 4 sites).

The majority of studies to estimate coarse-root NPP

were derived from allometric considerations (n ¼ 64

sites), with the remaining sites deriving coarse-root NPP

from biomass and in situ turnover observations (n ¼ 9

sites), ingrowth techniques (n¼4 sites), sequential coring

(n ¼ 17 sites), and one site with unknown methodology

(n ¼ 1 site). Because the coarse-root biomass and NPP

are largely derived from allometric relationships with

stem biomass and NPP, readers should be cautious in

interpretating Gcroot and Mcroot separately from

Gstem and Mstem. Readers are encouraged to refer to

Luyssaert et al. (2007) for more detail on the methods

used to compile the data hierarchically, as well as for all

citations to the original data comprising the database.

The world forest-production database compliled by

Cannell (Cannell 1982; hereafter ‘‘the Cannell data-

base’’) is included here as a benchmark database to

facilitate comparison with other work in this area. The

Cannell database reports stand biomass and NPP, with

additional details on stand age, diameter, height,

density, and basal area where available. Biomass and

NPP are reported separately for foliage, branches, bark,

stem, reproductive structures, and roots. NPP whenever

possible accounts for mortality such as litterfall. Note

that the Cannell database does not distinguish growth or

mass of fine roots from coarse roots, so Mroot and

Groot in the Cannell database reflects the mass and

growth rate, respectively, of the aggregate root pool.

Global relationships with climate were evaluated

using the CRU (Climate Research Unit) high-resolution

climatology from 1961–1990 used in the IPCC AR3

(Intergovernmental Panel on Climate Change, Third

Assessment Report [2001], available online)2 (also see

Mitchell and Jones 2005). These data include mean

monthly maximum, minimum, and average tempera-

ture, wet days, frost-free days, precipitation, water

vapor content, diurnal temperature range, and cloud

cover. These data were converted to representative

annual values expressing climate limitations, including

annual maximum vapor pressure deficit, minumum

annual relative humidity, annual frost-free days, annual

precipitation, and Thornthwaite’s aridity index (P –

PET)/PET, where P is precipitation and PET is

potential evapotranspiration calculated using the

Thornthwaite equation (Thornthwaite 1948). Soil tex-

ture was used as an integrated measure of soil resources

2 hhttp://www.ipcc-data.org/obs/cru_ts2_1.htmli


such as nutrients and aeration. Texture data were

gathered from the 0.0833 degree IGBP (International

Geosphere–Biosphere Programme) soil database

(Global Soil Data Task Force 2000).

Allometric scaling employs a power-law relationship

of the form Y ¼ aXb. Taking the logarithm to this

function yields the equation log(Y )¼ log(a)þ blog(X ),

whose parameters can be solved by linear regression.

The scaling parameters were estimated using Type II

(reduced major axis [RMA]) regression (Sokal and

Rohlf 1995: section 14.13). Most of the scaling relations

explored in this paper represent the scaling of NPP of a

component of a tree in relation to the whole, for

example Gfol } G. In this case, the solved parameters

represent the fractional allocation of net primary

productivity to that component, i.e., the partitioning.

Due to noise in the data, the parameters estimated in

this way do not sum identically to 1 (i.e., fractions of

total annual NPP), and were therefore renormalized.

RESULTS

The results presented below show first the scaling of

component NPP (net primary productivity) to total

NPP (G) using regression analysis, then an analysis of

the residuals against climatic and edaphic factors. We

then compare the allometry drawn from the Luyssaert

FIG. 2. Partitioning toward (A) foliage, (B) stem (i.e., trunk and branches) (C) fine roots, and (D) coarse roots. Both Type I(solid line: least squares, LS) and Type II (dashed line: reduced major axis, RMA) regressions are shown. G is total NPP (netprimary productivity) per individual (in kg dry matter [DM]�tree�1�yr�1).


database (Luyssaert et al. 2007) with those from the

benchmark Cannell database (Cannell 1982). Finally we

integrate the partitioning results at the individual level

to the stand level using G : M (where M is total biomass

per individual [in kg C]) andM : N allometry (where N is

stand density [in trees/ha]). The results conclude with an

algorithm for calculating partitioning in land-surface

models (LSMs).

The partitioning of G among the different biomass

pools is plotted in Fig. 2 (abbreviations: fol, foliage;

croot, coarse roots; and froot, fine roots). The linear

regressions on log-transformed variables assume that the

component NPP follows a power law that falls to 0 as G

goes to 0, a functional relationship that is widely used in

the allometry literature, and is intended to capture

changes in the response variable over several orders of

magnitude. Gfol is isometric with G (bGfol ¼ 1.106 6

0.054, r2 ¼ 0.914, n ¼ 95 sites). Isometric scaling means

that the scaling exponent is not significantly different

from 1, and that Gfol and G vary in a fixed proportion,

as predicted by Niklas and Enquist (2002). By contrast,

allocation toward woody biomass pools (Gstem and

Gcroot) increases with G (bGstem ¼ 1.165 6 0.045, r2 ¼0.942, n¼95 sites; bGcroot¼1.310 6 0.045, r2¼0.953, n¼95 sites). Note that the scalings of Gstem and Gcroot are

not significantly different from one another, indicating

that the ratio of partitioning to aboveground and

belowground woody biomass does not change with G.

The fraction of Gwood (i.e., GstemþGcroot) devoted to

Gstem is estimated as 0.808 (Gstem¼0.8083Gwood0.987

(r2 ¼ 0.995, n ¼ 95 sites; 0.822 ¼ 10�0.085). As a

consequence of the increase in partitioning to Gwood,

the partitioning to Gfroot drops as G increases (bGfroot¼0.987 6 0.078, r2 ¼ 0.821, n ¼ 95 sites).

The regressions of each component G against G show

that the majority (70–93%) of all variation can be

explained by the magnitude of G itself. The residuals of

component G (Gfol, Gstem, Gcroot, Gfroot vs. G) had

no significant or systematic relationship with nutrient or

water additions within the studies that had these

treatments (two-sided t tests nonsignificant), although

G itself increased in all plots with resource additions as

would be expected (Fig. 3). The study that included a

CO2 enrichment treatment (Gielen et al. 2005) showed a

slight increase in fine-root allocation, but this study had

some of the largest residuals overall (Fig. 3B–D),

perhaps because these data were collected from a 1–2

year old plantation of Populus spp. grown with drip

irrigation on agricultural land, which was considerably

different from the other forests in terms of age and

management. The residuals were regressed against

climate variables from the CRU (Climate Research

Unit) data set (Mitchelll and Jones 2005), and against

the aridity index, and none were found to be signifi-

cantly related to the unexplained variation in compo-

nent G. Likewise, the residuals were not significantly

related to soil texture. The residuals of log(Gfol) and

log(Gfroot) were uncorrelated with one another (r2 ¼

0.03). Together these results suggest that there is not a

trade-off in partitioning toward foliage and fine roots,

and that this putative trade-off, at the stand level, is

furthermore not related to climatic resources such as

aridity, season length, or light availability, nor soil

resources linked to texture. Other attributes of stands

such as taxonomic affiliation (angiosperm vs. gymno-

sperm), site management (managed vs. unmanaged), and

stand age were not significantly related to the unex-

plained variation in component G. The strong relation-

ship of partitioning with G itself, and the independence

of partitioning from climate and taxon indicate that at

the resolution of this study, partitioning is a relatively

conservative, non-plastic attribute, and is consequently

generalizeable for trees of given NPP.

The allometric scaling of mass and NPP among

different biomass components is not significantly differ-

ent in the Luyssaert database from the Cannell database

(Appendix Table A1), suggesting that the essential

features of allometry in the Luyssaert database are

consistent with previous studies (Enquist and Niklas

2002, Niklas and Enquist 2002). Although labile

biomass components (Mfol and Mfroot) have scaling

exponents against woody biomass (Mstem and Mcroot)

that are significantly less than 1 (Appendix Table A1),

the fractional distribution of mass among different

biomass components is fairly constant with total tree

size M because all biomass components asymptote fairly

quickly (Fig. 4A and D; regressions shown in Appendix

Fig. A1). After an initial condition dominated by labile

components of biomass, the stands quickly transition to

a state where the overwhelming majority of biomass is

woody. Mstem and Mcroot scale in fixed proportion of

approximately 3:1 (Mcroot ¼ 0.246 3 Mstem1.014, r2 ¼0.99, n ¼ 37 sites), although it should be cautioned that

most of the coarse-root biomass data in the Luyssaert

database is allometrically derived from stem-biomass

data.

The rates of component G at the stand level were

estimated by estimating M as a function of G (M¼5.357

3G1.575, r2¼ 0.70, n¼ 40 sites) and N as a function of M

(N ¼ 18 793 3 M�0.552, r2 ¼ 0.67, n ¼ 42 sites), which

invert metabolic rate–body size allometry and self-

thinning allometry, respectively. Note that the correla-

tion between G and M, and M to N is not nearly as

strong as the correlations between component G (Gfol,

Gstem, Gcroot, Gfroot) and G, so stand biomass is a

weaker predictor of partitioning than G, and therefore

factors that impact G, such as favorable soils or climate,

have a stronger influence on partitioning than does tand

biomass per se. Nevertheless, the consequence of

upscaling to the stand level by including the strong

decline of population density with mass accumulation

(Fig. 4C and F) is to enhance the drop-off of

partitioning to fine roots for stands of modest biomass

(300–500 MG DM/ha), which creates stronger differ-

ences among stands for biomass devoted to fine roots.


By contrast, partitioning to foliage at the stand level is

nearly constant for all stand sizes.

These results suggest the hypothesis that an algorithm

for calculating partitioning in land-surface models

(LSMs) would take the following form:

1) Calculate NPP.

2) Calculate N (population density). If N is not

simulated in the model, diagnose N from M 3 N by

inverting the self-thinning relationship (equations in

previous paragraph).

3) Calculate G ¼NPP/N.

4) Calculate Gfol, Gstem, Gcroot, Gfroot from G

(equations in Fig. 2).

5) Renormalize Gfol, Gstem, Gcroot, Gfroot so that

they sum to G.

DISCUSSION

This paper synthesizes the partitioning data from a

large, detailed database of component net primary

productivity, NPP, with an emphasis on identifying the

scale dependence of component NPP and trade-offs in

NPP among various plant organs, particularly fine

roots, and explicitly accounting for stand self-thinning

in accounting for variation among stands. Particular

results presented above are in agreement with a variety

of previous studies, but which have not been synthesized

in a form useful for application to efforts to model the

FIG. 3. Residuals of component growth from the RMA regressions of Fig. 2, emphasizing studies with fertilizer, water, or CO2

additions: (A) foliage, (B) stem (i.e., trunk and branches), (C) fine roots, (D) coarse roots. Original units for G (individual NPP)are kg DM�tree�1�yr�1; RMA stands for reduced major axis; r is a correlation coefficient, n is sample size. FACE refers to studiesincluding free-air carbon enrichment (e.g., Gielen et al. 2005). Symbol color identifies the data sources: brown, Maier et al.(2004); blue, Ryan et al. (1996); red, Gielen et al. (2005); green, Lender and Agren (1998) and Gower et al. (2001). The small solidgray circles represent studies with no manipulation.


global biosphere. For example, the component allome-

try from this study is not significantly different

(Appendix Table A1) from the component mass

allometry in Enquist and Niklas (2002) or the compo-

nent allometry of NPP in Niklas and Enquist (2002).

However, neither of those studies considered fine-root

mass or growth, which greatly limits their applicability

in carbon-cycle science because this pool is critically

important in the global carbon cycle (Jackson et al.

1997). The estimate of partitioning to Gfroot estimated

here is similar to the value of 1/3 estimated globally by

Jackson et al. (1997), but their value was not based on

direct measurement, but inferred from biomass and an

assumed turnover rate of once per year.

The results of our present study are likewise consistent

with the findings of Litton et al. (2007), who also

presented a synthesis of stand-level partitioning (Fig. 4C

and F), with the caveat that few of the studies they cite

include fine-root data, so they were compelled to group

fine roots and coarse roots as an aggregate ‘‘below-

ground’’ pool. Litton et al. (2007) found that stand-level

individual-tree foliage, Gfol, was fixed at ;25% for

stands of all sizes, which is supported by the data here.

Also, Litton et al. (2007) show a trade-off in partitioning

between Gstem and belowground components (GcrootþGfroot): stands with low NPP partitioned ;50% of their

NPP belowground and ;25% to Gstem, and with higher

stand-level NPP, this proportion flipped to 25%belowground and 50% Gstem. Our results show that

fast-turnover fine roots (‘‘froot’’) and woody coarse

roots (‘‘croot’’) are functionally distinct in this context,

and that the trade-off is apparently between Gwood and

Gfroot (Fig. 4C), and not Gstem and Groot as suggested

by Litton et al.’s (2007) results. This result is intriguing

because it suggests that in forests, the functional trade-

off for aboveground and belowground resources that is

so widely postulated (Tilman 1988), is manifest not as a

trade-off between root and shoot allocation per se (e.g.,

Levin et al. 1989), nor between foliage and fine roots

(e.g., Friedlingstein et al. 1999, Poorter and Nagel 2000),

but as a trade-off between the woody shoot and roots.

The Gfroot�Gwood trade-off appears to be a basic

feature of forest stand ontogeny, largely explained by

changes in the magnitude of G, which generally increases

as a forest accumulates biomass. Only secondarily does

this trade-off appear to be driven by changes in G that

FIG. 4. (A, D) Fractional distribution of mass and (B, C, E, F) fractional partitioning of growth. Upper plots are modeleddistributions of fractional component mass per individual, fractional component growth per individual, and fractional componentgrowth vs. stand biomass, and were developed from power-law relationships. Lower plots show original data with modeledfunctions superimposed.


are mediated by site resources independently from forest

size. To the extent that climate, site resources, and even

fertilization and irrigation change partitioning, we found

no evidence that these factors have effects beyond those

attributable to their impact on G itself (Fig. 3).

Clearly, plants in general are hugely plastic in their

partitioning towards roots, shoots, and foliage, resulting

in wide differences in root : shoot ratios as an adapta-

tion to local site conditions (Mokany et al. 2006), which

corroborates the basic validity of the functional trade-

off hypothesis (Tilman 1988). Nevertheless, our present

study found that the pattern of partitioning responds

consistently to the large variety of site conditions that

could enhance or reduce NPP, including fertilizer and

irrigation, which suggests that forests are fairly con-

strained in the variety of partitioning strategies that are

successfully employed. Why should this constrained set

of strategies basically consist of increasing partitioning

to stem and reducing partitioning to fine roots when

NPP is large? The net primary productivity of forests is

well above the mean NPP of terrestrial biomes

worldwide (Baldocchi and Valentini 2004, Luyssaert et

al. 2008). That is, forests are a biome that occurs in

places that are relatively free of growth constraints

climatically and edaphically. The findings in this study

indicate that in such a rich resource environment,

competition for light is likely driving trees to allocate

evermore photosynthate toward the woody stem in a

race to ascend. In this context, more foliage per se is

apparently not as important as lofting the foliage into

the sunlit canopy, because the allocation toward foliage

itself is a constant fraction of NPP. Therefore, while

stem biomass (Mstem) per se has no ‘‘functional’’ benefit

in terms of resource capture, it is critically important in

helping to realize the potential resource capture of the

foliage. Indeed, the biomass scaling of Mfol } Mstem3/4

(Enquist and Niklas 1998) shows that trees need to

create an ever larger amount of woody stem to support a

given amount of foliage: Mstem } Mfol4/3. This observa-

tion has been borne out in a number of studies using

different datasets (e.g., Wolf et al. 2010, Cheng and Niklas

2007), but importantly all of these studies are derived from

stand-level inventory data. The Mfol :Mstem scaling in

these studies is therefore only partly a consequence of the

vasculature and mechanical support needed to maintain a

given mass of leaves, and indeed the mass of branches is a

small fraction of total aboveground woody biomass

(Mwood). The stands in this study (and forests generally)

become taller over the course of stand development (H

[height] scales positively withM ), even though the mass of

leaves is constant at the stand level. It is perhaps significant

in this context that althoughWest et al. (1999) predict that

H should scale to the ¼ power of M, but instead grow

substantially taller in the Cannell database for a given

biomass:H } Mstem0.346 (95% CI: 0.321–0.373, r¼0.82, n

¼ 315 sites). We conclude from this that the allometric

scaling of biomass (Enquist andNiklas 1998) is only partly

a consequence of the vascular arguments made in that

paper, but largely a consequence of competition between

trees leading to major investments in stem biomass.

Together, the results presented above indicate that

incorporation of an allometrically sound partitioning

scheme in LSMs is straightforward, because the com-

plications introduced by differences in site potential and

other factors that may affect partitioning but that are

not represented in LSMs are essentially captured by

variations in NPP, which is ubiquitous in LSMs. This is

an incremental step in reconciling the biomass allometry

simulated in land-surface models with that seen in nature

(A. Wolf, P. Ciais, V. Bellassen, N. Delbart, C. B. Field,

and J. A. Berry, unpublished manuscript). However, this

still leaves open the issue of representing population

density in LSMs, because few models have any

representation of an individual. In addition, the recon-

ciliation of mass allometry between models is not made

possible simply by coming up with an allometric

partitioning scheme, because the turnover times of

leaves, wood, and fine roots is an additional free

parameter that may be in error in LSMs. The turnover

times (M/G from Appendix Fig. A1 divided by Fig. 2)

for fine roots and gymnosperm foliage in the Luyssaert

database is consistent with literature values, and has a

mean of ;3 years (Appendix Fig. A2). The woody

biomass, by contrast, shows a large increase in turnover

times of 15–45 years without reaching an asymptote.

This could be interpreted as a decrease in the lability of

woody tissue as branches and trunks become coarser in

size and decrease in rate mortality as the stand matures

(e.g., Ishii and McDowell 2002). Regardless, the absence

of a constant turnover time for woody tissue makes the

goal of simulating a forest with the proper biomass

allometry a greater challenge than simply calculating the

partitioning correctly, as implemented by the algorithm

presented in the Results. For the given partitioning

scheme to result in the patterns of biomass in Appendix

Fig. A2, a model would need to adjust the turnover

times in order to keep on the biomass accumulation

trajectory shown in the regressions. To this end, it might

be possible to implement a version of data assimilation

that adjusted the turnover times of biomass pools

dynamically, in order to align better with the inventory

data, as summarized by their allometric scaling equa-

tions. Finally, our conclusion that partitioning is

essentially predicted by total NPP places a premium on

understanding controls on NPP, about which there is

still considerable uncertainty among LSMs (Beer et al.

2010).

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APPENDIX

A table comparing regression coefficients for allometric relationships between tree biomass components in different databases, afigure showing regressions for scaling of component mass with total tree mass, and a figure showing turnover times for componentsof biomass from the Luyssaert database (Ecological Archives A021-072-A1).


allometric growth and allocation in forests: a perspective from fluxnet

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