Competition is a major driver of carbon allocation to different
plant tissues (e.g., wood, leaves, fine roots), and allocation, in turn,
shapes vegetation structure. To improve their modeling of the terrestrial
carbon cycle, many Earth system models now incorporate vegetation
demographic models (VDMs) that explicitly simulate the processes of
individual-based competition for light and soil resources. Here, in order to
understand how these competition processes affect predictions of the
terrestrial carbon cycle, we simulate forest responses to elevated
atmospheric CO2 concentration [CO2] along a nitrogen availability
gradient, using a VDM that allows us to compare fixed allocation strategies
vs. competitively optimal allocation strategies. Our results show that
competitive and fixed strategies predict opposite fractional allocation to
fine roots and wood, though they predict similar changes in total net primary production (NPP) along
the nitrogen gradient. The competitively optimal allocation strategy
predicts decreasing fine root and increasing wood allocation with increasing
nitrogen, whereas the fixed strategy predicts the opposite. Although
simulated plant biomass at equilibrium increases with nitrogen due to
increases in photosynthesis for both allocation strategies, the increase in
biomass with nitrogen is much steeper for competitively optimal allocation
due to its increased allocation to wood. The qualitatively opposite
fractional allocation to fine roots and wood of the two strategies also
impacts the effects of elevated [CO2] on plant biomass. Whereas the
fixed allocation strategy predicts an increase in plant biomass under
elevated [CO2] that is approximately independent of nitrogen
availability, competition leads to higher plant biomass response to elevated
[CO2] with increasing nitrogen availability. Our results indicate that
the VDMs that explicitly include the effects of competition for light and
soil resources on allocation may generate significantly different
ecosystem-level predictions of carbon storage than those that use fixed
strategies.
Introduction
Allocation of assimilated carbon to different plant tissues is a fundamental
aspect of plant growth and profoundly affects terrestrial ecosystem
biogeochemical cycles (Cannell and Dewar, 1994; Lacointe, 2000).
Ecologically, allocation represents an evolutionarily honed “strategy” of
plants that use limited resources and compete with other individuals and
consequently drives successional dynamics and vegetation structure (De Kauwe
et al., 2014; DeAngelis et al., 2012; Haverd et al., 2016; Tilman, 1988).
Biogeochemically, allocation links plant physiological processes, such as
photosynthesis and respiration, to biogeochemical cycles and carbon storage
of ecosystems (Bloom et al., 2016; De Kauwe et al., 2014). Thus, correctly
modeling allocation patterns is critical for correctly predicting
terrestrial carbon cycles and Earth system dynamics.
Hierarchical structure of vegetation models.
In current Earth system models (ESMs), the terrestrial carbon cycle is
usually simulated by pool-based compartment models that simulate ecosystem
biogeochemical cycles as lumped pools and fluxes of plant tissues and soil
organic matter (Fig. 1a) (Emanuel and Killough, 1984; Eriksson, 1971;
Parton et al., 1987; Randerson et al., 1997; Sitch et al., 2003). In these
models, the dynamics of carbon can be described by a linear system of
equations (Koven et al., 2015; Luo et al., 2001; Luo and Weng, 2011; Sierra
and Mueller, 2015; Xia et al., 2013):
dXdt=AX+BU,
where X is a vector of ecosystem carbon pools, U is carbon input (i.e., gross
primary production, GPP), B is the vector of allocation parameters to
autotrophic respiration and plant carbon pools (e.g., leaves, stems and
fine roots), and A is a matrix of carbon transfer and turnover. In this
system, carbon dynamics are defined by carbon input (U), allocation (B), and
residence time and transfer coefficients (A). The allocation schemes (B) are
thus embedded in a linear system, or quasi-linear system if the allocation
parameters in B are a function of carbon input (U) or plant carbon pools
(X).
The modeling of allocation in this system (i.e., the parameters in vector
B) is usually based on plant allometry, biomass partitioning and resource
limitation (De Kauwe et al., 2014; Montané et al., 2017). The allocation
parameters are either fixed ratios to leaves, stems and roots, which may
vary among plant functional types (e.g., CENTURY, Parton et al., 1987; TEM,
Raich et al., 1991; CASA, Randerson et al., 1997), or are responsive to
climate and soil conditions as a way to phenomenologically mimic the shifts
in allocation that are empirically observed or hypothesized (e.g., CTEM,
Arora and Boer, 2005; ORCHIDEE, Krinner et al., 2005; LPJ, Sitch et al.,
2003). These modeling approaches either assume that vegetation is
equilibrated (fixed ratios) or average the responses of plant types to
changes in environmental conditions as a collective behavior. Thus, the
carbon dynamics in these models can be constrained by selecting appropriate
parameters of allocation, turnover rates and transfer coefficients to fit
the observations (Friend et al., 2007; Hoffman et al., 2017; Keenan et al.,
2013).
To predict transient changes in vegetation structure and composition in
response to climate change, vegetation demographic models (VDMs) that are
able to simulate transient population dynamics are being incorporated into
ESMs (Fisher et al., 2018; Scheiter and Higgins, 2009). Generally, VDMs
explicitly simulate demographic processes, such as plant reproduction,
growth and mortality, to generate the dynamics of populations (Fig. 1b).
To speed computations and minimize complexity, groups of individuals are
usually modeled as cohorts. With multiple cohorts and plant functional types (PFTs), VDMs can bring
plant functional diversity and adaptive dynamics into the system when
explicitly simulating individual-based competition for different resources
and vegetation succession and thus predict dominant plant trait changes
with environmental conditions and ecosystem development (Scheiter et al.,
2013; Scheiter and Higgins, 2009; Weng et al., 2015).
The combinations of plant traits represent the competition strategies at
different stages of ecosystem development. Evolutionarily, a strategy that
can outcompete all other strategies in the environment created by itself
will be dominant. This strategy is called an evolutionarily stable strategy
or a competitively optimal strategy (McGill and Brown, 2007). In VDMs,
competitively optimal strategies can therefore be reasonably predicted based
on the costs and benefits of different strategies (i.e., combinations of
plant traits) through their effects on demographic processes (i.e., fitness)
and ecosystem biogeochemical cycles (Fig. 1c) (e.g., Farrior et al., 2015;
Weng et al., 2015).
The dynamics of plant traits can substantially change predictions of
ecosystem biogeochemical dynamics since they change the key parameters of
vegetation physiological processes and soil organic matter decomposition
(e.g., Dybzinski et al., 2015; Farrior et al., 2015; Weng et al., 2017).
Therefore, the key parameters that are used to estimate carbon dynamics in
the linear system model (Eq. 1), such as allocation (B) and residence times
in different carbon pools (matrix A, which includes coefficients of carbon
transfer and turnover time) become functions of competition strategies that
vary with environment and carbon input. In addition, the turnover of
vegetation carbon pools becomes a function of allocation, leaf longevity,
fine root turnover and tree mortality rates, which change with vegetation
succession and the most competitive plant traits. These changes make the
system nonlinear and can lead to large biases within the framework of the
compartmental pool-based models as represented by Eq. (1) (Sierra et al.,
2017; Sierra and Mueller, 2015). Because of the high complexity associated
with demographic and competition processes, the model predictions are
usually sensitive to the parameters in these processes and are of high
uncertainty (e.g., Pappas et al., 2016).
In contrast to their implementation in the more complicated VDMs discussed
above, models of competitively dominant plant strategies using much simpler
model structures and assumptions can sometimes be solved analytically
(Dybzinski et al., 2011, 2015; Farrior et al., 2013, 2015). Although
simplified, such models can pinpoint the key processes that improve the
predictive power of simulation models (Dybzinski et al., 2011; Farrior et
al., 2013, 2015), allowing them to help researchers formulate model
processes and understand the simulated ecosystem dynamics in ESMs. For
example, the analytical model derived by Farrior et al. (2013) that links
interactions between ecosystem carbon storage, allocation and water stress
at elevated atmospheric CO2 concentration [CO2] sheds light on the
otherwise inscrutable processes leading to varied soil water dynamics in a
land model coupled with an VDM (Weng et al., 2015). Recognizing the benefit,
Weng et al. (2017) included both a simplified analytical model and a more
complicated VDM to understand competitively optimal leaf mass per area,
competition between evergreen and deciduous plant functional types, and the
resulting successional patterns.
In this study, we use a stand-alone simulator derived from the LM3-PPA model
(Weng et al., 2017, 2015) to show how forests respond to elevated [CO2]
and nitrogen availability via different competitively optimal allocation
strategies. The demographic processes of this model have been coupled into
the land model of the Geophysical Fluid Dynamical Laboratory's Earth System
Model (Shevliakova et al., 2009; Weng et al., 2015) and are being added to
NASA Goddard Institute for Space Study's Earth system model, ModelE (Schmidt
et al., 2014). Using this model, we simulate the shifts in competitively
optimal allocation strategies in response to elevated [CO2] at
different nitrogen levels based on insights from the analytical model
derived by Dybzinski et al. (2015). Dybzinski et al. (2015)'s model predicts
that increases in carbon storage at elevated [CO2] relative to storage
at ambient [CO2] are largely independent of total nitrogen because of
an increasing shift in carbon allocation from long-lived, low-nitrogen wood
to short-lived, high-nitrogen fine roots under elevated [CO2] with
increasing nitrogen availability. Here, we analyze the simulated ecosystem
carbon cycle variables (gross and net primary production, allocation, and
biomass) of separate monoculture and polyculture model runs. In the monoculture
runs, ecosystem properties are the result of the prescribed allocation
strategies of a given PFT. In the polyculture runs, competition between the
different allocation strategies results in succession and the eventual
dominance of the most competitive allocation strategy for a given nitrogen
availability and [CO2] level. Since everything else in the model is
identical, we are able to compare the predictions of single fixed strategies
with competitively optimal allocation strategies by comparing the ecosystem
properties of these two types of runs.
Methods and materialsBiomeE model overview
We used a stand-alone ecosystem simulator (Biome Ecological strategy
simulator, BiomeE) to conduct simulation experiments. BiomeE is derived from
the version of LM3-PPA used in Weng et al. (2017), and its code is available at
Github (https://github.com/wengensheng/BiomeESS, last access: 27 November 2019). In this
version, we simplified the processes of energy transfer and soil water
dynamics of LM3-PPA (Weng et al., 2015) but still retained the key features
of plant physiology and individual-based competition for light, soil water
and, via the decomposition of soil organic matter, nitrogen (Fig. 2 and
Supplement I for details). In this model, individual trees
are represented as sets of cohorts of similarly sized trees and are arranged in
different vertical canopy layers according to their height and crown area
following the rules of the perfect plasticity approximation (PPA) model
(Strigul et al., 2008). Sunlight is partitioned into these canopy layers
according to Beer's law. Thus, a key parameter for light competition,
critical height, is defined; all the trees above this context-dependent
height get full sunlight and all trees below this height are shaded by the
upper-layer trees.
Structure of BiomeE. (a) Vegetation structure: trees organize
their crowns into canopy layers according to both their height and their
crown area following the rules of the PPA model, which mechanistically
models light competition. (b) Biogeochemical structure and
compartmental pools. The green, brown and black lines are the flows of
carbon, nitrogen, and coupled carbon and nitrogen, respectively. The green
box is for carbon only. The brown boxes are nitrogen pools. The black boxes
are for both carbon and nitrogen pools, where X can be C (carbon) and N
(nitrogen). The C:N ratios of leaves, fine roots, seeds and microbes are
fixed. The C:N ratios of woody tissues, fast soil organic matter (SOM) and
slow SOM are flexible. Only one tree's C and N pools are shown in this
figure. The blue box and arrows are for water storage in soil and fluxes of
rainfall, evaporation and transpiration. The model can have multiple
cohorts of trees, which share the same pool structure. The dashed line
separates the aboveground and belowground processes.
Each tree consists of seven pools: leaves, fine roots, sapwood, heartwood,
fecundity (seeds), and nonstructural carbohydrates and nitrogen (NSC and
NSN, respectively) (Fig. 2b). The carbon and nitrogen in plant pools enter
the soil pools with the mortality of individual trees and the turnover of
leaves and fine roots. There are three soil organic matter (SOM) pools for
carbon and nitrogen: fast turnover, slow turnover and microbial pools,
along with a mineral nitrogen pool for mineralized nitrogen in soil. The
simulation of SOM decomposition and nitrogen mineralization is based on the
models of Gerber et al. (2010) and Manzoni et al. (2010) and described in
detail in Weng et al. (2017). The decomposition rate of a SOM pool is
determined by the basal turnover rate together with soil temperature and
moisture. The nitrogen mineralization rate is a function of decomposition
rate and the C:N ratio of the SOM. Microbes must consume more carbon in the
high C:N ratio SOM pools to get enough nitrogen and must release excessive
nitrogen in the low C:N ratio SOM pools to get enough carbon for energy
(Weng et al., 2017).
Plant growth and reproduction are driven by the carbon assimilation of
leaves via photosynthesis, which is in turn dependent on water and nitrogen
uptake by fine roots. The photosynthesis model is identical to that of
LM3-PPA (Weng et al., 2015), which is a simplified version of Leuning model
(Leuning et al., 1995). This model first calculates photosynthesis rate,
stomatal conductance and water demand of the leaves of each tree (cohort)
in the absence of soil water limitation. Then, it calculates available water
supply as a function of fine root surface area and soil water content. The
demand-based assimilation rate and stomatal conductance are adjusted if soil
water supply is less than plant water demand. Soil water content is
calculated based on the fluxes of precipitation, soil surface evaporation
and plant water update (transpiration) in three layers of soil to a depth of
2 m (see Supplement I for details).
Assimilated carbon enters into the NSC pool and is subsequently used for
respiration, growth and reproduction. Empirical allometric equations relate
woody biomass (including coarse roots, bole and branches), crown area and
stem diameter. The individual-level dimensions of a tree, i.e., height (Z),
biomass (S) and crown area (ACR), are given by empirical allometries
(Dybzinski et al., 2011; Farrior et al., 2013):
ZD=αZDθZ,SD=0.25πΛρWαZD2+θZ,ACRD=αcDθc,
where Z is tree height, D is tree diameter, S is total woody biomass carbon
(including bole, coarse roots and branches) of a tree, αc and
αZ are PFT-specific constants, θc=1.5 and θZ=0.5 (Farrior et al., 2013) (although they could be made
PFT-specific if necessary), π is the circular constant, Λ is a
PFT-specific taper constant, and ρW is PFT-specific wood density
(kgCm-3) (Table 1).
Model parameters.
SymbolDefinitionUnitDefault valueReferenceαZParameter of tree heightmm-0.536Farrior et al. (2013)θZDiameter exponent of tree height–0.5Farrior et al. (2013)ΛTaper factor–0.75Weng et al. (2015)ρWWood densityKgCm-3300Jenkins et al. (2003)αCParameter of crown areamm-1.5150Farrior et al. (2013)θCDiameter exponent of crown area–1.5Farrior et al. (2013)l∗Target crown leaf area layers (crown leaf area index)m2m-23.5–σLeaf mass per unit areakgCm-20.14Wright et al. (2004)γSpecific root area, calculated from root radius and densitym2kgC-134.5Pregitzer et al. (2002)ϕRLRatio of target fine root area to target leaf aream2m-2Varied with PFTs–αCSARatio of target sapwood cross-sectional area to target leaf aream2m-20.2×10-4McDowell et al. (2002)fU,maxMaximum mineral nitrogen absorption rateh-10.5–KFRRoot biomass at which the N-uptake rate is half of the maximumkgCm-20.3–CNL,0Target C:N ratio of leaveskgCkgN-176.5 (Function of LMA)Wright et al. (2004)CNFR,0Target C:N ratio of fine rootskgCkgN-160Magill et al. (2004)CNW,0Target C:N ratio of woodkgCkgN-1350Martin et al. (2015)CNF,0Target C:N ratio of seedskgCkgN-120Soriano et al. (2011)f1Supply rate of NSC and NSN at normal growth–1/(3⋅365)–f2Maximum fraction of NSC and NSN used for growth in a day–0.02–fLFR,maxMaximum fraction of available carbon allocated to leaves and fine roots–0.85–vFraction of carbon converted to seeds–0.1–rD/SNitrogen-limiting factor–Solved by the model (Eqs. 9 and 10)–
We set targets for leaf (L∗), fine root (FR∗) and
sapwood cross-sectional area (ASW∗) that govern plant allocation
of nonstructural carbon and nitrogen during growth. These targets are related by
the following equations based on the assumption of the pipe model
(Shinozaki et al., 1964):
L∗D,p=l∗⋅ACRD⋅σ⋅p(t),FR∗D=φRL⋅l∗⋅ACRDγ,ASW∗D=αCSA⋅l∗⋅ACRD,
where L∗(D,p), FR∗(D) and ASW∗D
are the targets of leaf mass (kg C per tree), fine root biomass (kg C per tree) and
sapwood cross-sectional area (m2/tree), respectively, at tree diameter
D; l∗ is the target leaf area per unit crown area of a given PFT;
ACR(D) is the crown area of a tree with diameter D; σ is
PFT-specific leaf mass per unit area (LMA); p(t) is a PFT-specific
function ranging from zero to one that governs leaf phenology (Weng et al.,
2015); φRL is the target ratio of total root surface area to
the total leaf area; γ is specific root area; and αCSA
is an empirical constant (the ratio of sapwood cross-sectional area to
target leaf area). The phenology function p(t) takes values 0 (nongrowing
season) or 1 (growing season) following the phenology model of LM3-PPA (Weng
et al., 2015). The onset of a growing season is controlled by two variables,
growing degree days (GDDs) and a weighted mean daily temperature
(Tpheno), while the end of a growing season is controlled by
Tpheno (see Supplement I for details of the
phenology model).
Nitrogen uptake
The rate of nitrogen uptake (U, gNm-2h-1) from the soil
mineral nitrogen pool is an asymptotically increasing function of fine root
biomass density (CFR,total, kgCm-2), following McMurtrie et al. (2012)
U=fU,max⋅Nmineral⋅CFR,totalCFR,total+KFR,
where Nmineral is the mineral nitrogen in soil (gNm-2),
fU,max is the maximum rate of nitrogen absorption per hour when
CFR,total approaches infinity, and KFR is a shape parameter (kgCm-2) at which the nitrogen uptake rate is half of the parameter
fU,max. The nitrogen uptake rate of an individual tree (Utree, kgNh-1tree-1) is calculated as follows:
Utree=U⋅CFR,treeCFR,total,
where, CFR,tree is the fine root biomass of a tree (kgCtree-1).
The nitrogen absorbed by roots enters into the NSN pool and then is
allocated to plant tissues through plant growth.
Allocation and plant growth
The partitioning of carbon and nitrogen into the plant pools (i.e., leaves, fine
roots and sapwood) is limited by the allometric equations, targets of
leaves, fine roots and sapwood cross-sectional area, and the stoichiometry
(i.e., C:N ratios) of these plant tissues. At a daily time step, the model
calculates the amount of carbon and nitrogen that are available for growth
according to the total NSC and NSN and current leaf and fine root biomass.
Basically, the available NSC (GC) is the summation of a small fraction
(f1) of the total NSC in an individual plant and the differences between
the targets of leaf and fine roots and their current biomass capped by a
larger fraction (f2) of NSC (Eq. 6a). The available NSN (GN) is
analogous to that of the NSC and meets approximately the stoichiometrical
requirement of plant tissues (Eq. 6b).
6aGC=min(f1NSC+L∗+FR∗-L-FR,f2NSC),6bGN=min(f1NSN+NL∗+NFR∗-NL-NFR,f2NSN),
where L∗ and FR∗ are the targets of leaves and fine roots,
respectively (see Eq. 3); L and FR are current leaf and fine roots biomass,
respectively; and NL∗ and NFR∗ are nitrogen of leaves
and fine roots at their targets according to their target C:N ratios. The
parameter f1 is the fraction of NSC (or NSN) for normal growth after
leaves and fine roots approach their targets, and f2 caps the maximum
daily availability of NSC (or NSN) during the period of leaf flush at the
beginning of a growing season. The parameter f1 is much smaller than
f2. We let f1=1/(365×3) and f2=0.02 in this study.
The allocation of the available NSC (i.e., GC) to wood (GW), leaves
(GL), fine roots (GFR) and seeds (GF) follows the equations
below (Eq. 7). These equations describe the mass growth of plant tissues
with nitrogen effects on the carbon allocation between high-nitrogen tissues
and low-nitrogen tissues (wood) for maximizing leaves and fine roots growth
(GL and GFR, respectively), optimizing carbon usage at given
nitrogen supply (GN) and keeping the tissues at their target C:N
ratios.
7aGC≥GW+GL+GFR+GF,7bGN≥GLCNL,0+GFRCNFR,0+GFCNF,0+GWCNW,0,7cFR+GFRγ(L+GL)/σ=φRL,7dGL+GFR=MinL∗+FR∗-L-FR,fLFR,maxGC,⋅rS/D,7eGF=GC-MinL∗+FR∗-L-FR,fLFR,maxGC,rS/D,⋅v⋅rS/D,7fGW=GC-MinL∗+FR∗-L-FR,fLFR,maxGC,rS/D,⋅(1-v⋅rS/D),
where CNL,0, CNFR,0, CNF,0, and CNW,0 are the target C:N ratios
of leaves, fine roots, seeds, and sapwood, respectively; γ is
specific root area (m2kgC-1); σ is leaf mass per unit
area (kgCm-2); fLFR,max is the maximum fraction of GC for
leaves and fine roots (0.85 in this study); v is the fraction of left carbon
for seeds (0.1 in this study); and rS/D is a nitrogen-limiting factor ranging
from 0 (no nitrogen for leaves, fine roots and seeds) to 1 (nitrogen
available for full growth of leaves, fine roots and seeds). The parameter
rS/D controls the allocation of GC and GN to the four plant
pools (Eq. 7a). It can be analytically solved as follows (Eqs. 8 and 9).
rS/D=Min1,Max0,GN-GC/CNWN′-GC/CNW,
where N′ is defined as the potential nitrogen demand for plant growth at
rS/D=1 (i.e., no nitrogen limitation),
N′≡γσFR+MinL∗+FR∗-L-FRfLFR,maxGC-φRLLγσ+φRLCNL+φRLL+MinL∗+FR∗-L-FRfLFR,maxGC-γσLγσ+φRLCNFR+vGC-MinL∗+FR∗-L-FR,fLFR,maxGCCNF+(1-v)GC-MinL∗+FR∗-L-FRfLFR,maxGCCNW,
when GN≥N′ (rS/D=1), there is no nitrogen limitation, all
the GC will be used for plant growth and the allocation follows the
rules of the carbon only model (Eq. 7d–f as rS/D=1). The excessive nitrogen (GN-N′) will be returned to the NSN pool (as
if they were never taken out). When GC/CNW,0<GN<N′ (i.e., 0<rS/D<1), all
GC and GN will be used in new tissue growth; however, the leaves and
fine roots cannot reach their targets at this step (i.e. they are
down-regulated). When GN≤GC/CNW,0 (rS/D=0), all
the GN will be allocated to sapwood and the excessive carbon
(GC-GNCNW,0) will be returned to NSC pool. This is a very rare
case since a low GN leads to low leaf growth, reducing GC before the
case GN<GC/CNW,0 happens. Therefore, in most cases, Eq. (7a) is GC=GW+GL+GFR+GF. Overall, this strategy
down-regulates leaf production under low nitrogen conditions while making
use of assimilated carbon in height-structured competition for light.
Allocation to wood tissues (GW) drives the growth of tree diameter,
height and crown area and thus increases the targets of leaves and fine
roots (Eq. 3). By differentiating the stem biomass allometry in Eq. (2) with
respect to time, using the fact that dS/dt equals the carbon allocated for wood
growth (GW), we have the diameter growth:
dDdt=GW0.25πΛρwαz(2+θz)D1+θZ,
This equation transforms the mass growth to structural changes in tree
architecture. With an updated tree diameter, we can calculate the new tree
height and crown area using allometry equations (Eq. 2) and targets of leaf
and fine root biomass (Eq. 3) for the next growth step.
Overall, this is a flexible allocation scheme and still follows the major
assumptions in the previous version of LM3-PPA (Weng et al., 2015, 2017).
This allocation scheme prioritizes the allocation to leaves and fine roots,
maintains a minimum growth rate of stems, and keeps the constant area ratio
of fine roots to leaves. Based on these allocation rules, the average
allocation of carbon and nitrogen to leaves, fine roots and wood over a
growing season are governed by the targets for the leaf area per unit crown
area (i.e., crown leaf area index, l∗) and fine root area per unit
leaf area (φRL). Since the crown leaf area index, l∗,
is fixed in this study, φRL is the key parameter determining
the relative allocation of carbon to fine roots and stems. A high φRL means a high relative allocation to fine roots and therefore low
relative allocation to stems and vice versa. Note that here ϕRL is fixed for
each PFT and will remain so for all the model runs.
The process of choosing a context-dependent competitively dominant
φRL will take place after finding the fitness of each
φRL in monoculture and in competition with other PFTs (i.e.,
different values of φRL). The competitively optimal strategy
is the one that can successfully exclude all others in the processes of
competition and succession, but it is not necessarily the one that maximizes
production in monoculture. For example, each φRL creates an
environment of light profile and soil nitrogen in its monoculture. Other
φRL PFTs may have higher fitness in this environment than the
one that creates it. Only the competitively dominant strategy has the
highest fitness in the environment it creates (Fig. 1c).
Site and data
Data pertaining to vegetation, climate and soil at Harvard Forest (Aber et
al., 1993; Hibbs, 1983; Urbanski et al., 2007) were used to design the plant
functional types (PFTs) and ecosystem nitrogen levels used in the simulation
experiments, to drive the model and to calibrate model parameters. Harvard
Forest is located in Massachusetts, USA (42.54∘,
-72.17∘). The climate of Harvard Forest is cool temperate with an
annual precipitation of 1050 mm, distributed fairly evenly throughout the year.
The annual mean temperature is 8.5 ∘C with a high monthly mean
temperature of 20 ∘C in July and a low of -7∘C in
January. The soils are mainly sandy loam with an average depth of around 1 m and
are moderately well drained in most areas. In forest sites, soil carbon is
around 8 kgCm-2 and nitrogen 300 gNm-2 (Compton and Boone,
2000). The vegetation is deciduous broadleaf (mixed) forest with its major species being
red oak (Quercus rubra), red maple (Acer rubrum), black birch (Betula lenta), white pine (Pinus strobus) and hemlock (Tsuga canadensis)
(Compton and Boone, 2000; Savage et al., 2013). The data used to drive our
model runs are gap-filled hourly meteorological data at Harvard Forest from
1991 to 2006, obtained from North American Carbon Program (NACP) site-level
synthesis datasets (Barr et al., 2013).
Simulation experiments.
TypeModel runsInitial PFT(s) φRLEcosystem total nitrogen levelsCO2 concentration [CO2]Monoculture runsOne model run per combination of PFT (φRL), nitrogen level and CO2 concentration.One of the following PFTs: φRL=1, 2, 3, 4, 5, 6, 7 or 8.Eight levels ranging from 114.5 to 552 gNm-2 at the interval of 62.5 gNm-2: (i.e., 114.5, 177, 239.5, 302, 364.5, 427, 489.5 and 552 gNm-2)Ambient: 380 ppm Elevated: 580 ppmPolyculture run IOne model run per combination of nitrogen level and CO2 concentration.All the PFTs (φRL=1–8) used in the monoculture runs.Polyculture run IIOne model run per combination of nitrogen level and CO2 concentration.Eight PFTs with φRL ranging from 4.5–0.5i to 8.5–0.5i at the interval of 0.5, where i denotes the eight nitrogen levels from 114.5 to 552 gNm-2.Simulation experiments
We set two atmospheric CO2 concentration ([CO2]) levels, 380
and 580 ppm, and eight ecosystem total nitrogen levels (ranging from 114.5 to 552 gNm-2 at the interval of 62.5 gNm-2) by
assigning the initial content of the slow SOM pool for our simulation
experiments (Table 2). This range covers the soil nitrogen contents across
the plots at Harvard Forest with different species compositions and land-use
history (200–300 gNm-2) (Compton and Boone, 2000;
Melillo et al., 2011) and represents the range from infertile to fertile
soils in temperate forests (Post et al., 1985; Yang et al., 2011). The
nitrogen cycles through the plant and soil pools and is redistributed among
them via plant demographic processes, soil carbon transfers and plant
uptake. In all the simulation experiments, we assume the ecosystem has no
nitrogen inputs and no outputs for convenience since we already have eight
total nitrogen levels to represent the consequences of different nitrogen
input and output processes at an equilibrium state. The PFTs were based on
an evergreen needle-leaved tree PFT with different leaf to fine root area
ratios, φRL, in the range from 1 to 8 (Table 2). Simply
stated, the PFTs we investigate only differ in parameter φRL.
We define the model runs started with only one fixed-φRL PFT
as “monoculture runs”, although the actual allocation of carbon to
different plant tissues varies with [CO2] and ecosystem nitrogen
availability. The model runs started with multiple PFTs are called
“polyculture runs” (eight PFTs with different φRL at the
beginning, although many are driven to extinction during a given model run).
We conducted one set of monoculture runs and two sets of polyculture runs
(Table 2).
In the monoculture runs, we run the full combinations of eight PFTs with
root/leaf area ratios (φRL) from 1 to 8, eight ecosystem total
nitrogen levels and two CO2 concentrations (380 and 580 ppm)
(Table 2). For the eight PFTs, only those with φRL≤6 survived at ambient [CO2] (380 ppm) because the carbon assimilated
by leaves could not meet the demand by plant tissues at φRL>6. The monoculture runs are for exploring the model
predictions of gross primary production (GPP), net primary production (NPP),
and allocation and biomass at equilibrium with fixed φRL at
different total nitrogen levels.
In polyculture run I, we used the same PFTs as in those monoculture runs,
where their φRL varied from 1 to 8 at the interval of 1.0 and
the ecosystem total nitrogen levels were the same as those used in the
monoculture runs (Table 2). This set of polyculture runs was used to explore
successional patterns at both ambient and elevated [CO2] (380 and
580 ppm, respectively). However, this set of model runs could not show the
details of equilibrium plant biomass and allocation patterns along the
nitrogen gradient because of the large intervals between the φRL values.
To achieve greater resolution in our competition predictions, we designed
the polyculture run II using a dynamic PFT combination scheme, according to
the ranges of φRL obtained from the polyculture run I that
could survive at a particular nitrogen level at both CO2
concentrations. For each nitrogen level, we set eight PFTs with φRL that varied in a range 3.5 (e.g., x∼x+3.5) at the
interval of 0.5, starting with the highest φRL of 8.0 at the
lowest N level (114.5 gNm-2) and decreasing 0.5 per level of increase
in ecosystem total N. We used i=1, 2, …, 8 to denote the eight
N levels from 114.5 to 552 gNm-2. The φRL of the eight
PFTs at each level were 5.0–0.5i, 5.5–0.5i, …, 8.5–0.5i (Table 2).
For example, at the nitrogen of 114.5 gNm-2 (i=1), the φRL of the eight PFTs were 4.5, 5.0, …, 8.0 and at 177 gNm-2 (i=2) they were 4.0, 4.5, …, 7.5.
For both monoculture and polyculture runs, visual inspection indicated that
stands had reached equilibrium after ∼1200 years. To be
conservative, we present equilibrium data by averaging model properties
between years 1400 and 1800. We compared simulated equilibrium GPP, NPP,
allocation (both absolute amount of carbon and fractions of the total NPP)
and plant biomass of the polyculture run II with those from the monoculture
runs. We used the results from one PFT (φRL=4) to highlight
the differences of plant responses with competitively optimal allocation
strategies obtained from the polyculture run II.
GPP, NPP, allocation and plant biomass at equilibrium state
simulated by monoculture runs. GPP: gross primary production; NPP: net
primary production; fNPP,x: the fraction of NPP allocated to x,
where x is root (fine roots), leaf (leaves in crown) or wood (including tree
trunk, stems and coarse roots). The data are from the averages of the model
run years from 1400 and 1800. Each model run is initiated with one PFT with a
fixed ratio of fine root area to leaf area (φRL).
Results
In the monoculture runs, GPP and NPP increase by a factor of 3 along the
gradient of nitrogen used in this study (114.5–552 gNm-2) at both
ambient (Fig. 3) and elevated [CO2] (Fig. S1 in the Supplement). The magnitude of
differences in GPP and NPP due to differences in fixed allocation within a
given nitrogen level is comparable to the magnitude of differences in GPP
and NPP due to nitrogen level within a given fixed allocation strategy (Fig. 3a and b) when φRL is in the range that allows plants to
grow normally (1–5 in the case of ambient [CO2]). As
prescribed by the definition of φRL, allocation of NPP to fine
roots increases with φRL in monoculture runs (Fig. 3c). As a
consequence, allocation of NPP to wood decreases as φRL
increases (Fig. 3d). Allocation to leaves does not change much with
φRL (Fig. 3e, note differences in scale).
Correspondingly, plant biomass at equilibrium decreases with φRL (Fig. 3f). The effects of nitrogen on the allocation of carbon to
fine roots and wood follow our allocation model assumptions because more
carbon is allocated to low-nitrogen woody tissues in our model when nitrogen
is limited. However, the amplitude of changes in GPP and NPP induced by
nitrogen availability is lower than the amplitude of changes resulting from
different values of φRL in the monoculture runs.
Successional patterns of polyculture run I at ambient and elevated
[CO2] concentrations. φRL is the fixed ratio of fine root
area to leaf area of a particular strategy.
We used two sets of polyculture runs to look for the φRL that
is closest to competitively optimal. In the polyculture run I, where
φRL ranges from 1 to 8 at all nitrogen levels, the winning
strategy (φRL) increases from 5 to 2 as the total nitrogen
increases from 114.5 to 489.5 gNm-2 at ambient
[CO2] (380 ppm) (Fig. 4a, c, g, e). Elevated [CO2] (580 ppm)
shifts the winning strategy to higher (φRL) at all the total
nitrogen levels. As shown in Fig. 4, the winning strategy shifts from
φRL=5 to φRL=8 at 114.5 gNm-2 and
from φRL=2 to φRL=4 at 489.5 gNm-2.
In some situations (e.g., Fig. 4g and Figs. S2 and S3), it takes a long
time for the most competitive PFTs to out-compete the previously dominant
PFTs because of the sequential replacement of dominant PFTs during the
course of succession and the slow growth rate of trees in understory.
Winning PFTs (φRL, a) in polyculture run II and
equilibrium gross primary production (GPP, b), net primary production (NPP,
c) and carbon use efficiency (NPP/GPP, d) at two CO2 concentrations
(aCO2: 380 ppm; eCO2: 580 ppm). The closed symbols with solid lines
represent polyculture runs. The open symbols with dashed lines represent
monoculture runs (only φRL=4 shown in this figure).
φRL is the fixed ratio of fine root area to leaf area of a
particular strategy.
Based on the shifts of the winning φRL from ambient [CO2]
to elevated [CO2] at the eight nitrogen levels, we designed the
polyculture run II with a high resolution of φRL and calculated
their GPP, NPP, allocation and plant biomass at equilibrium state. The of
φRL of the winning PFTs decreases from 5.5 to 2 at ambient
[CO2] and from 8.0 to 3.0 at elevated [CO2] as total nitrogen
increases from 114.5 to 552.0 gNm-2. The equilibrium GPP
and NPP increase with total nitrogen at values similar to those of the
monoculture runs (Fig. 5b and c). However, the CO2 stimulation of NPP
increases with total nitrogen in the polyculture runs more than it is in the
monoculture runs. Elevated [CO2] increases carbon use efficiency
(defined as the ratio of NPP to GPP in this study, NPP/GPP) in both the
monoculture and polyculture runs (Fig. 5d). Also, the dependence of
NPP:GPP ratio on nitrogen is higher in the polyculture runs than it is in the
monoculture runs (Fig. 5c).
Allocation to leaves, fine roots and wood tissues of the
competition and monoculture runs at the eight total nitrogen levels and two
CO2 concentrations (aCO2: 380 ppm; eCO2: 580 ppm). Panels (a), (c) and (e) show the NPP allocated to the tissues and panels (b), (d) and (f)
show the fractions of the allocation in total NPP. The closed symbols with
solid lines represent polyculture runs (Poly). The open symbols with dashed
lines represent monoculture runs (only φRL=4 is shown in this
figure, Mono). φRL is the fixed ratio of fine root area to
leaf area of a particular strategy.
Allocation of NPP to leaves increases with nitrogen in all conditions, i.e. both competition and monoculture at both ambient [CO2] and elevated
[CO2] (Fig. 6a). Foliage NPP is similar in these four model runs when
nitrogen is low. At high nitrogen (>400gNm-2),
polyculture runs have higher foliage NPP than the monoculture runs
generally. Allocation to leaves is relatively stable across the nitrogen
gradient at the two [CO2] levels (Fig. 6b). The fraction of NPP
allocated to leaves changes little with nitrogen (Fig. 6b) and it is
universally higher at ambient [CO2] than it is at elevated [CO2].
Fine root NPP does not significantly change with ecosystem total nitrogen in
polyculture runs, whereas it increases monotonically with increasing
nitrogen in monoculture runs (Fig. 6c). Elevated [CO2] increases fine
root allocation at low nitrogen in polyculture runs but decreases root
allocation irrespective of nitrogen in monoculture runs (Fig. 6c). The
fraction of NPP allocated to fine roots decreases with nitrogen at both
CO2 concentrations in polyculture runs, but it increases slightly in
monoculture runs (Fig. 6d). In monoculture runs, elevated [CO2]
reduces the fraction of NPP allocated to fine roots at all nitrogen levels.
In polyculture runs, fractional allocation to fine roots increases at
elevated [CO2] when nitrogen is low (e.g., 114.5–302 gNm-2) and
decreases at elevated [CO2] when nitrogen is high (e.g., 364–552 gNm-2).
In the reverse of the fine root response, NPP allocation to woody tissues
increases with total nitrogen in both competition and monoculture runs (Fig. 6e). In polyculture runs, the fraction of allocation to woody tissues
decreases at elevated [CO2] when ecosystem total nitrogen is low (e.g.,
114–245 gNm-2) and increases at elevated [CO2] when ecosystem
total nitrogen is high (e.g., 302–552 gNm-2).
Plant biomass responses to elevated [CO2] and nitrogen. Panel (a) shows the equilibrium plant biomass (means of simulated plant biomass from
model run year 1400 to 1800) in polyculture runs and monoculture runs (only
φRL=4 is shown as an example). Panel (b) shows the ratio of
simulated plant biomass at elevated [CO2] to ambient [CO2] for
both competition and monoculture runs. Panels (c) and (d) show the comparisons
with monoculture runs with φRL increasing from 1 to 6 at
ambient (c) and elevated [CO2] (d). The closed symbols with solid lines
represent polyculture runs. The open symbols with dashed lines represent
monoculture runs (φRL ranges from 1 to 6). φRL
is the fixed ratio of fine root area to leaf area of a particular strategy.
aCO2: 380 ppm; eCO2: 580 ppm.
As a result of the changes in competitively optimal φRL, plant
biomass increases dramatically with ecosystem total nitrogen in polyculture
runs compared with that in monoculture runs (Fig. 7a). The effects of
elevated [CO2] on plant biomass increase with nitrogen in polyculture
runs but are constant overall in monoculture runs (Fig. 7b). Compared with
the full spread of monoculture runs with φRL ranging from 1 to
6, polyculture runs have high root allocation at low nitrogen and low root
allocation at high nitrogen due to changes in the dominant competitive allocation strategy, which amplifies plant biomass responses to elevated
[CO2] with increasing nitrogen (Fig. 7c and d).
Discussion
Our simulations show that the predicted responses of individual plants to
elevated [CO2] can be significantly changed by explicit inclusion of
competition processes. Here, the major tradeoff for light- and N-limited
trees is the relative allocation between stems and fine roots (Dybzinski et
al., 2011). Although the wood allocation (and thus carbon sequestration
potential) of every PFT used in this study increases under elevated
[CO2] at all nitrogen levels (e.g., Fig. 6e, dashed lines), only those
PFTs that allocate more to fine roots (with lower carbon sequestration
potential) can survive competition under elevated [CO2] (Fig. 6c,
solid lines). Put together, explicit inclusion of competition processes
reduces the expected increase in biomass (and thus carbon sequestration
potential) under elevated [CO2] compared with simulations that do not
include competition processes (Fig. 7b).
Since there is a lack of direct observations or experiments to
quantitatively validate the long-term patterns predicted by our model, we
did not calibrate it to fit observations at Harvard Forest. In the following
section, we analyze the model processes in detail and validate our modeling
approach by comparing the general patterns from observations and experiments
with model predictions. These comparisons also shed light on the modeling of
allocation and vegetation responses to elevated [CO2].
Mechanisms of game-theoretic allocation modeling and simulation results
validation
In our model, the allocation of carbon and nitrogen within an individual
tree is based on allometric scaling (Eq. 2), functional relationships (Eq. 3) and optimization of resource usage (Eq. 7). Generally, the allometric
scaling relationships define the maximum leaf and fine root surface area at
a given tree size and the functional relationships define the ratios of
leaf area to sapwood cross-sectional area and fine root surface area. These
rules are commonly used in ecosystem models (Franklin et al., 2012) and have
been shown to generate reasonable predictions (De Kauwe et al., 2014;
Valentine and Mäkelä, 2012). These rules implicitly define the
priority of allocation to leaves and fine roots but allow for
structurally unlimited stem growth when resources (carbon and nitrogen in
this study) are available (i.e., the remainder goes to stems after leaf and
fine root growth) and NSC is not accumulated exaggeratedly when ecosystem
nitrogen is limited (Fig. S6).
We used a tuning parameter, maximum leaf and fine root allocation,
fLFR,max, to constrain the maximum allocation to leaves and fine roots
in order to maintain a minimum growth rate of wood in years of low
productivity. This is consistent with wood growth patterns in temperate
trees, where new wood tissues must be continuously produced (especially
early in the growing season) to maintain the functions of tree trunks and
branches (Cuny et al., 2012; Michelot et al., 2012; Plomion et al., 2001).
This parameter does not change the fact that leaves and fine roots are the
priority in allocation, since allocation ratios to stems are around
0.4–0.7 in temperate forests (Curtis et al., 2002; Litton et
al., 2007). With a value of 0.85, parameter fLFR,max seldom affects the
overall carbon allocation ratios of leaves, fine roots and stems. If
fLFR,max=1 (i.e., the highest priority for leaf and fine root
growth), simulated trunk radial growth would have unreasonably high
interannual variation because leaf and fine root growth would use all carbon
to approach to their targets, leaving nothing for stems in some years of low
productivity.
The simulation of competition for light and soil resources is based on two
fundamental mechanisms: (1) competition for light is based on the height of
trees according to the PPA model, which assumes trees have perfectly plastic
crown to capture light via stem (trunk) and branch phototropism (Strigul et
al., 2008), and (2) individual soil N uptake is linearly dependent on the
fine root surface area of an individual tree relative to that of its
neighbors (Dybzinski et al., 2019; McMurtrie et al., 2012; Weng et al.,
2017). These two mechanisms define an allocation tradeoff between wood and
fine roots for carbon and nitrogen investment in different CO2
concentrations and nitrogen environments. Including explicit competition for
these resources to determine the dominant strategies results in very
different predicted allocation patterns – and thus ecosystem level
responses – than those of strategies in the absence of competition. For
example, fractional wood allocation increases with increasing nitrogen
availability under competitive allocation but decreases – the opposite qualitative response – under a fixed
strategy (Fig. 6f). Consequently, equilibrium plant biomass is predicted
to increase much more with increasing nitrogen availability under a
competitive strategy (Fig. 4c, d). In nature, the effects of competition
on dominant plant traits may occur through species replacement or community
assembly (akin to the mechanism in our model) (e.g., Douma et al., 2012),
but it may also occur through adaptive plastic responses or in-place
subpopulation evolution of ecotypes (Grams and Andersen, 2007; McNickle and
Dybzinski, 2013; Smith et al., 2013).
Generally, the predictions from competitively optimal allocation strategies
predicted by our model can be found in large-scale forest censuses and
site-level experiments, such as that (1) high-nitrogen environments (i.e.,
productive environments) favor high wood allocation and low root allocation
(Litton et al., 2003; Poorter et al., 2012), (2) elevated [CO2]
increases root allocation (Drake et al., 2011; Iversen, 2010; Jackson et
al., 2009; Nie et al., 2013; Smith et al., 2013), (3) low nitrogen
availability limits vegetation biomass responses to elevated [CO2] as a
result of high root allocation or root exudation (Jiang et al., 2019a; Norby
and Zak, 2011), and (4) increases in vegetation biomass at elevated
[CO2] are largely due to high wood allocation (Norby and Zak, 2011;
Walker et al., 2019). These predictions emerge from the fundamental
assumptions of our model without tuning parameters to fit the data,
providing some confidence in the robustness of our approach.
The literature on experimental responses of plant community to elevated
[CO2] shows that the responses vary with site characteristics, forest
composition, stand age, plant physiological responses and soil microbial
feedbacks (Norby and Zak, 2011; Terrer et al., 2016, 2018). For example, in
the Duke Free Air CO2 Enhancement (FACE) experiment, where the major trees
are loblolly pine (Pinus taeda), increases in root production at elevated [CO2]
stimulated increased nitrogen supply that allowed the forest to sustain
higher productivity (Drake et al., 2011). However, in the Oak Ridge FACE, where
the major trees are sweetgum (Liquidambar styraciflua), increased fine-root production under
elevated [CO2] did not result in increased net nitrogen mineralization
and increases in root production declined after 8 years of CO2
enhancement (Iversen, 2010; Norby and Zak, 2011). In EucFACE (Jiang et al.,
2019a), where the major trees are Eucalyptus tereticornis and the soil is infertile, trees
significantly increased their root exudation under limited nutrient supplies
but had no significant increase in biomass in response to elevated
[CO2]. The BangorFACE experiment (Smith et al., 2013) found that
interspecific competition (Alnus glutinosa, Betula pendula and Fagus sylvatica) resulted in greater increases in root
biomass at elevated [CO2]. Leaf area index (LAI) responses to elevated
[CO2] are also highly varied. As summarized by Norby and Zak (2011),
low LAI (in this case, open-canopy) sites showed significant increases in
LAI and high LAI (in this case, closed-canopy) sites showed low increases or
even decreases in LAI. They concluded that LAI in closed-canopy forests is
not responsive to elevated [CO2] (Norby et al., 2003; Norby and Zak,
2011).
The nature of developing a model with generic assumptions and balanced
processes reduces its capability to predict all of these responses. For
example, plants have a variety of physiological mechanisms to deal with
excessive carbon supply when plant demand (i.e., “sink”) is relatively low
(Fatichi et al., 2019; Körner, 2006), such as down-regulating leaf
photosynthesis rate by the accumulated assimilates (Goldschmidt and Huber,
1992) or respiring excessive carbohydrates to regenerate substrates for
photosynthesis (Atkin and Macherel, 2009). But these mechanisms are
short-term physiological responses (minutes to hours, sometimes days) for
plants in situations of temporary nitrogen shortage, high irradiation or
drought stress. It is not “economically” sustainable in an infertile
environment to maintain highly productive leaves but often suppress their
photosynthesis or respire a large portion of their assimilated carbon.
Root exudation is a critical process for plants. It can stimulate soil
organic matter decomposition and nitrogen mineralization to facilitate soil
nitrogen supply at the expense of carbon (Cheng, 2009; Cheng et al., 2014;
Drake et al., 2011; Phillips et al., 2011). The process of root exudation
has been adopted by many models to couple with microbial processes in the
determination of soil organic matter decomposition (Sulman et al., 2014;
Wieder et al., 2014, 2015). Some carbon-only models, e.g., LM3 (Shevliakova
et al., 2009), the parent model of this one, and TECO (Luo et al., 2001),
incorporate root exudation to put extra carbon into the soil in order to
avoid down-regulating canopy photosynthesis or overestimating vegetation
biomass, both of which had been tuned against data. However, in a
demographic competition model like this one, individual plants cannot reap a
reward from root exudation as they do in nature when the microbial
activities are not fully coupled and the nitrogen in soil is assumed fully
accessible by roots of all individuals. Therefore, root exudation is not a
competitive strategy in the system defined by the assumptions of this model.
Since the purpose of this study is to explore long-term ecological
strategies in different but relatively stable environments, we did not
include these processes, especially since they present additional challenges
in balancing the complexity of the tradeoffs between modeled demographic
processes and plant traits. However, the lack of these processes does limit
the predictions of instantaneous responses to variation in environmental
conditions or resource supply and possibly of some long-term vegetation
characteristics as well. For example, our model predicts reduced LAI under
nitrogen limitation (Fig. S7) based on first principles, but it is
incidentally the only mechanism that reduces the whole-canopy photosynthesis
rate in our model. There are mechanisms that increase nitrogen use
efficiency at the expense of carbon by increasing LMA and therefore leaf
longevity to maintain high LAI and high canopy-level photosynthesis rates
(Aerts, 1995, 1999; Aerts and Chapin, 1999; Givnish, 2002). We did not
include these mechanisms in our simulations, although they are
well developed in this model (Weng et al., 2017), because we wished to focus
on the strategy of allocation. The clear descriptions of our model's
assumptions, its traceable processes, and inclusion of the tradeoffs
involved in aboveground and belowground competition provide a useful
benchmark from which to incorporate additional mechanisms and tradeoffs.
Root over-proliferation vs. wood allocation
The allocation strategy that maximizes site vegetation biomass allocates
very little to fine roots (Figs. 3 and S1). In contrast, the competitively
optimal strategy allocates more carbon to fine roots, termed “fine-root
over-proliferation” in the literature (Gersani et al., 2001; McNickle and
Dybzinski, 2013; O'Brien et al., 2005). It is the result of a competitive
“arms race”: while increasing fine root area under elevated [CO2]
does not result in more nitrogen for an individual, failing to do so would
cede some of that individual's nitrogen to its neighbors. Because most
nitrogen uptake is via mass flow and diffusion (Oyewole et al., 2017) and
because both of these mechanisms depend on sink strength, individuals with
relatively greater fine root mass than their neighbors take a greater share of
nitrogen, as was recently demonstrated empirically (Dybzinski et al., 2019;
Kulmatiski et al., 2017). Thus, fine roots may over-proliferate for
competitive reasons relative to lower optimal fine root mass in the
hypothetical absence of an evolutionary history of competition (Craine,
2006; McNickle and Dybzinski, 2013). This may also explain why root C:N
ratio is highly variable (Dybzinski et al., 2015; Luo et al., 2006; Nie et
al., 2013): a high density of fine roots in soil may be more important than
the high absorption ability of a single root in competing for soil nitrogen
in the usually low mineral nitrogen soils.
Root over-proliferation is still controversial in experiments. For example,
Gersani et al. (2001) and O'Brien et al. (2005) found that competing plants
generated more roots than those growing in isolation, whereas McNickle and
Brown (2014) found that competing plants generated comparable roots to those
growing in isolation. Compared to modeled roots, real roots are far more
adaptive and complex at modifying their growth patterns in response to soil
nutrient and water dynamics (Hodge, 2009). The root growth strategies in
response to competition also vary with species (Belter and Cahill, 2015).
The mechanisms of self-recognition of inter- and intra-roots can also lead
to varied behavior of root growth (Chen et al., 2012). However, all of the
aforementioned studies considered only plastic root over-proliferation, where
individuals produce more roots in the presence of other individuals than
they do in isolation, analogous to stem elongation of crowded seedlings
(Dudley and Schmitt, 1996). A portion of root over-proliferation may also be
fixed, analogous to trees that still grow tall even when grown in isolation.
Dybzinski et al. (2019) showed that plant community nitrogen uptake rate was
independent of fine root mass in seedlings of numerous species, suggesting a
high degree of fixed fine root over-proliferation. To improve root
competition models, more detailed experiments that control root growth
should be conducted to quantify the marginal benefits of roots in isolated,
monoculture and polyculture environments.
At high soil nitrogen, height-structured competition for light (also a
game-theoretic response, Falster and Westoby, 2003; Givnish, 1982) prevails
and trees with greater relative allocation to trunks prevail. The balance between
these two competitive priorities (fine roots vs. stems) can be observed in
our model predictions as a shift from fine root allocation to wood
allocation as soil nitrogen increases. The increases in the critical height
(i.e. the context-dependent height of the shortest tree in canopy layer in
the PPA) from low nitrogen to high nitrogen indicates a shift from the
importance of competition for soil nitrogen to the importance of competition
for light as ecosystem nitrogen increases (Fig. S8). Because the most
competitive type shifts from high fine root allocation to low fine root
allocation as ecosystem total nitrogen increases, increases in NPP and plant
biomass across the nitrogen gradient are greater than the increases in NPP
and plant biomass assuming allocation strategies in the absence of
competition (Fig. 3). This greatly reduces the carbon cost of belowground
competition as ecosystem total nitrogen increases. The decrease in the
fraction of NPP allocated to leaves at elevated [CO2] (Fig. 6b)
occurs because of increases in total NPP and nearly constant absolute NPP
allocation to foliage (Fig. 6a).
Model complexity and uncertainty
Compared with the conventional pool-based vegetation models that use pools
and fluxes to represent plant demographic processes at a land simulation
unit (e.g., grid or patch), VDMs add two more layers of complexity. The
first is the inclusion of stochastic birth and mortality processes of
individuals (i.e., demographic processes). These processes allow the models
to predict population dynamics and transient vegetation structure, such as
size-structured distribution and crown organization (e.g., Moorcroft et al.,
2001; Strigul et al., 2008). With changes in vegetation structure,
allocation and mortality rates can change, generating a different carbon
storage accumulation curve compared with those predicted by pool-based
models where vegetation structure is not explicitly represented (e.g., Weng
et al., 2015). The second is the simulated shift in dominant plant traits
during succession due to the shifting of competitive outcomes among
different PFTs, which changes the allocation between fast- and slow-turnover
pools and thus the parameters of allocation and the residence time of carbon
in the ecosystem.
Together, these mechanisms may alter long-term predictions of the terrestrial
carbon cycle due to changes in PFT-based parameters (Dybzinski et al., 2011;
Farrior et al., 2013; Weng et al., 2015). As described in the Introduction,
current pool-based models can be described by a linear system of equations
characterized by the key parameters of allocation, residence time and
transfer coefficients (Eq. 1) with the rigid assumption of unchangeable
plant types (Luo et al., 2012; Xia et al., 2013). In VDMs, however,
allocation, residence time, leaf traits, phenology, mortality, plant forms
and their responses to climate change are all strategies of competition
whose success varies with the environmental conditions and the traits of the
individuals they are competing against.
Many tradeoffs between plant traits can shift in response to environmental
and biotic changes, limiting the applicability of varying a single trait, as
we have in this study. For example, allocation, leaf traits, mycorrhizal
types and nitrogen fixation can all change with ecosystem nitrogen
availability (Menge et al., 2017; Ordoñez et al., 2009; Phillips et al.,
2013; Vitousek et al., 2013). The unrealistic effects of model
simplification can be corrected by adding important tradeoffs that are
missing. For example, the positive feedback between root allocation and SOM
decomposition plays a role in mitigating the effects of tragedies of the
commons of root over-proliferation (e.g., Gersani et al., 2001; Zea-Cabrera
et al., 2006). High root
allocation increases the decomposition rate of SOM and the supply of mineral
nitrogen because of the high turnover rate of root litter, which favors a
strategy of high wood allocation and reduces the competitive optimal fine
root allocation. This negative feedback indicates that the model structure
is flexible and that we can incorporate correct mechanisms step by step to
improve model prediction skills. Testing single strategies is still a
necessary step to improving our understanding of the system and prediction
skills of the models, though it could lead to unrealistic responses
sometimes.
We found that model predictions can differ significantly in response to
seemingly small variations in basic assumptions or quantitative
relationships. For example, our model predicts that the ratio of plant
biomass under elevated [CO2] relative to plant biomass under ambient
[CO2] should increase with increasing nitrogen due to the shift of
carbon allocation from fine roots to woody tissues. In contrast, the
analytic model of Dybzinski et al. (2015) predicts that the ratio of plant
biomass under elevated [CO2] relative to plant biomass under ambient
[CO2] should be largely independent of total nitrogen because of an
increasing shift in carbon allocation from long-lived, low-nitrogen wood to
short-lived, high-nitrogen fine roots under elevated [CO2] and with
increasing nitrogen. This significant difference between these two
predictions traces back to differences in how fine root stoichiometry is
handled in the two models. In the model of Dybzinski et al. (2015), the fine root
C:N ratio is flexible and the marginal nitrogen uptake capacity per unit of
carbon allocated to fine roots depends on its nitrogen concentration. Like
the model presented here, the model of Dybzinski et al. (2015) predicts
decreasing fine root mass with increasing nitrogen availability. Unlike the model
presented here (which has constant fine root nitrogen concentration), the
model of Dybzinski et al. (2015) predicts increasing fine root nitrogen
concentration with increasing nitrogen availability. As a result, there is
less nitrogen to allocate to wood as nitrogen increases in the model of
Dybzinski et al. (2015) than there is in the model presented here. These
countervailing factors even out the ratio of plant biomass under elevated
[CO2] relative to plant biomass under ambient [CO2] across the
nitrogen gradient in Dybzinski et al. (2015), whereas their absence amplifies
this ratio with increasing nitrogen in the model presented here. Our ability
to diagnose and understand this discrepancy highlights the utility of
deploying closely related analytical and simulation models (Weng et al.,
2017).
We conducted simulations only at one site for the purpose of exploring the
general patterns of competitively optimal allocation strategies and their
responses to elevated [CO2] at different nitrogen availabilities. We
can speculate about shifts in the competitively optimal allocation strategy
in different forest biomes by considering the effects of temperature on soil
nitrogen supply via the SOM's decomposition rate and its positive effect on
net nitrogen mineralization. For example, the SOM decomposition rate is
usually high in warm regions and low in cold regions (Davidson and Janssens,
2006) assuming there are no water limitations and SOM is equilibrated with
carbon input. According to our model, allocation to roots is high in low
nitrogen supply conditions (cold regions) and low in high nitrogen supply
conditions (warm regions). This pattern can be found from temperate to
boreal forest zones (Cairns et al., 1997; Gower et al., 2001; Reich et al.,
2014; Zadworny et al., 2016). Temperature also alters NPP, i.e., carbon
supply: as temperature goes down, NPP decreases and nitrogen demand
decreases, alleviating nitrogen limitation and leading to shifts of
allocation to stems. Therefore, the differences in temperature effects on
photosynthesis and SOM decomposition will determine competitive allocation
strategy. Since SOM decomposition is more sensitive to temperature than
gross primary production is at long-temporal and large spatial scales (Beer
et al., 2010; Carey et al., 2016; Crowther et al., 2016), our model suggests
that allocation will shift to wood in a warming world. Whether the carbon
stored in that wood is enough to offset the carbon released from increasing
soil respiration is a critical question.
Water is also a critical factor affecting allocation and its responses to
elevated [CO2]. Low soil moisture usually leads to high allocation to
roots (Poorter et al., 2012). Elevated CO2 can reduce transpiration (as
found in our study as well, Figs. S9–S11) and therefore
increase soil moisture, resulting in increases in allocation to stems and
aboveground biomass (Walker et al., 2019). A game-theoretic modeling study
using the PPA framework shows that the competitively optimal allocation
strategy shifts to high wood allocation at elevated [CO2] in
environments with water limitation (Farrior et al., 2015). This is the opposite
of the elevated [CO2] effects on allocation in nitrogen-limited
environments as simulated in this study. According to field experiments,
fine root allocation is more responsive to nitrogen changes than it is to soil
moisture changes (Canham et al., 1996; Poorter et al., 2012). Poorter et al. (2012) attribute the mechanisms to the optimal strategies in response to the
relative stable nitrogen supply and stochastic water input in soil. The
vertical distribution of roots and the contributions of roots in different
layers to water and nitrogen uptake also suggest that the uptake of soil
nutrients are dominant in shaping root system architecture (Chapman et al.,
2012; Morris et al., 2017), though root growth and turnover are flexible and
sensitive to nitrogen and water supply (Deak and Malamy, 2005; Linkohr et
al., 2002; Pregitzer et al., 1993).
Common principles for allocation modeling and implications
As shown in model intercomparison studies, the mechanisms of modeling
allocation differ very much, leading to high variation in their predictions
(e.g., De Kauwe et al., 2014). Calibrating model parameters to fit data may
not increase model predictive skill because data are often also highly
variable. Franklin et al. (2012) suggest that in order to build realistic
and predictive allocation models, we should correctly identify and implement
fundamental principles. Our model predicts similar patterns to those
predicted by the model of Valentine and Mäkelä (2012), which has
very different processes of plant growth and allocation. However, these two
models share fundamental principles, including (1) evolutionary or
competitive optimization, (2) capped leaves and fine roots at given tree
sizes, (3) structurally unlimited stem allocation (i.e., optimizing carbon
use) because the woody tissues can serve as unlimited sink for surplus
carbon, and (4) height–structure competition for light and root-mass-based
competition for soil resources. Principles 2 and 3 are commonly used in
models (De Kauwe et al., 2014; Jiang et al., 2019b). However, the different
rules of implementing them (e.g., allometric equation, functional
relationships, etc.) lead to highly varied predictions (as shown in De
Kauwe et al., 2014), though model formulations may be very similar.
In competitively optimal models, such as this study and also Valentine and
Mäkelä (2012), the competition processes generate similar emergent
patterns by selecting those that can survive in competition, regardless of the
details of those differences. The competition processes also make the
details of allocation settings for a single PFT and their direct responses
to elevated [CO2] less important because competition processes will
select out the most competitive strategy from diverse strategies in response
to changes in [CO2] and nitrogen. Our study and that of Valentine and
Mäkelä (2012) posit a fundamental tradeoff between light
competition and nitrogen competition via allocation based on insights gained
from simpler models (e.g., Dybzinski et al., 2015; Mäkelä et al.,
2008) for predicting allocation as an emergent property of competition. One
advantage of building a model in this way is that the vegetation dynamics
are predicted from first principles, rather than based on the correlations
between vegetation properties and environmental conditions. With these first
principles, the models can produce reasonable predictions, though the
details of physiological and demographic processes vary among models.
For vegetation models designed to predict the effects of climate change, the
important operational distinction is that the fundamental rules cannot or
will not change as climate changes. Nor, presumably, will the underlying
ecological and evolutionary processes change as climate changes. The
emergent properties can change as climate changes, however, and the models
built on the “scale-appropriate” unbreakable constraints and ecological
and evolutionary processes will be able to accurately predict changes in
emergent ecosystem properties (Weng et al., 2017). In our opinion, the
scientific effort to build better models is better served by understanding
unrealistic predictions than by “fixing” them with unreliable mechanisms
when there is a lack of data or theory to make them consistent with
observations. Validating assumptions and initial responses are critical, and
the long-term responses can be validated via spatial patterns.
This modeling approach also demands improvement in model validation and
benchmarking systems (Collier et al., 2018; Hoffman et al., 2017). As shown
in this study, allocation responses to elevated CO2 at different
nitrogen levels in monoculture runs are opposite to those in
competitive allocation runs. For example, in monoculture runs, elevated
[CO2] increases wood allocation and decreases fine root allocation at
low nitrogen; whereas in competitive allocation runs elevated [CO2]
leads to low wood allocation and high fine root allocation. Simply
calibrating our model against short-term observational data may improve the
agreement with observations but would not change the model's predictions
because the model's predictions emerge from its fundamental assumptions.
Conclusions
Our study illustrates that including the competition processes for light and
soil resources in a game-theoretic vegetation demographic model can
substantially change the prediction of the contribution of ecosystems to the
global carbon cycle. Allowing the model to explicitly track the competitive allocation strategies can generate significantly different ecosystem-level
predictions (e.g., biomass and ecosystem carbon storage) than those of
strategies in the absence of explicit competition. Building such a model
requires differentiating between the unbreakable tradeoffs of plant traits
and ecological processes from the emergent properties of ecosystems. Drawing
on insights from closely related analytical models to develop and understand
more complicated simulation models seems, to us, indispensable. Evaluating
these models also requires an updated model benchmarking system that
includes the metrics of competitive plant traits during the development of
ecosystems and their responses to global change factors.
Code and data availability
The model codes, simulated data and Python scripts used
in this study are available from Github
(https://github.com/wengensheng/BiomeE-Allocation, last access: 27 November 2019).
The supplement related to this article is available online at: https://doi.org/10.5194/bg-16-4577-2019-supplement.
Author contributions
All authors contributed to model design, results explanation and manuscript writing. EW and RD initially designed the simulation experiments. EW coded the model and implemented model runs and data analysis.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The authors thank Benjamin Stocker, Martin De Kauwe and other two anonymous referees for their insightful comments that greatly improved this paper. We also thank the USDA Forest Service Northern Research Station, Carbon Mitigation Initiative at Princeton University, and the University of Texas at Austin for their support. Earth system modeling at GISS is supported by the NASA Modeling, Analysis, and Prediction Program, and resources supporting this work were provided by the NASA High‐End Computing Program through the NASA Center for Climate Simulation (NCCS) at Goddard Space Flight Center.
Financial support
This research has been supported by the NASA Modeling, Analysis, and Prediction Program.
Review statement
This paper was edited by Sönke Zaehle and reviewed by Benjamin Stocker, Martin De Kauwe and two anonymous referees.
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