A mechanistic model of tree competition and facilitation for … · 2015. 9. 2. · Ecological...

Ecological Modelling 188 (2005) 76–92

A mechanistic model of tree competition and facilitation forMediterranean forests: Scaling from leaf physiology

to stand dynamics

M.A. Zavalaa,∗, R. Bravo de la Parrab

a Departamento de Ecologıa, Edificio de Ciencias, Universidad de Alcala, E-28871, Alcala de Henares, Madrid, Spainb Departamento de Matematicas, Edificio de Ciencias, Universidad de Alcala, E-28871, Alcala de Henares, Madrid, Spain

Available online 13 June 2005

Abstract

Mechanistic theories of plant competition developed to explain changes in community structure and dynamics along resourceavailability gradients have been mostly applied to temperate forests and grasslands where light and nutrients are the two mainlimiting resources. In contrast, the mechanisms underlying the structure and dynamics of water-limited plant communities havebeen little explored. Also previous mechanistic models rely either on complex simulators, which are difficult to interpret or onsimple conceptual models, which ignore too many critical details. In this study, we develop a model of stand dynamics for lightand water-limited forests of intermediate complexity and we provide an analytical framework for its analyses. The model is anindividual-based simulator that describes the feedback between transpiration, stomatal function and soil water dynamics withasymmetrical competition for light and water. Trees allocate carbon to three main compartments: shoot, stem and roots. We

the stand.lant-levelis tradeoff

adient. Atgradient.explored.

ns along

ilitation;

thes of

use the model to explore general patterns that may emerge across levels of biological organization from the leaf toModel predictions are consistent with a number of features of Mediterranean forests structure and dynamics. At the pthe leaf-based tradeoff between carbon gain and water loss expresses as a tradeoff between mortality and growth. Thexplains plant morphological changes in above-ground biomass and root to shoot allocation along a water availability grthe community-level, tradeoffs among carbon acquisition and water loss govern the sign of plant interactions along theCoexistence among morphological types was not observed for the range of parameters and environmental conditionsOverall the model provides an unifying explanation for the observed changes in the sign of plant to plant interactioenvironmental gradients as well as a process-based formulation that can be linked to empirical studies.© 2005 Elsevier B.V. All rights reserved.

Keywords: Mechanistic plant competition theory; Forest simulator; Partial differential equation; Tradeoffs; Drought; Root to shoot; FacCompetition

∗ Corresponding author.E-mail address: [email protected] (M.A. Zavala).

1. Introduction

A central goal of plant ecology is to understandmechanisms controlling the structure and dynamic

0304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2005.05.006

M.A. Zavala, R. Bravo de la Parra / Ecological Modelling 188 (2005) 76–92 77

plant communities (e.g.,Crawley, 1986; Tilman, 1988).It is generally accepted that community structure is anemergent property of species responses to resource gra-dients and interactions, such as competition. Gradientanalyses have shown spatial and temporal regulari-ties in community structure across sites with respectto resource variation, suggesting the existence of afew common underlying ecological mechanisms forall plant communities (Whittaker, 1975). Over the lastdecades, the development of mechanistic theories ofplant communities have allowed us to identify criti-cal ecological processes for explaining and predictingchanges in community structure along environmentaland disturbance gradients (Tilman, 1982; Smith andHuston, 1989). Chiefly, the mechanistic theory of plantcompetition developed byTilman (1988)is based on anindividual-based model (ALLOCATE) that describescommunity structure as a feedback between individualplant responses to resource availability and resourcedepletion by plants. In the model, species ability togather above- and below-ground resources is governedby an inevitable tradeoff between shoot-stem and rootallocations. According to ALLOCATE predictions, thistradeoff explains species relative positions along envi-ronmental gradients and a large number of successionaland segregation patterns along productivity gradients.The mechanisms controlling successional dynamics inplant communities have been explored only in a fewsystems, mainly in temperate regions, where light andnutrients are the main limiting resource. The constrainsa ow-e lantm longl thep iesw

anyp pro-c eh d thei ub-m iotica on-t Bothi ractd pe-c lantc tral

interactions. A large number of studies have focusedon plant functional responses and tradeoffs in responseto light and nutrient limitations (e.g.,Shugart, 1984;Brokaw, 1985; Chazdon, 1988; Tilman, 1988; Canham,1989; Grubb et al., 1996; Kobe et al., 1995). In contrast,whole-plant responses to combined gradients in lightand water availability are poorly understood and stud-ies on plant–water relations have typically focused onleaf-level ecophysiological processes (e.g.,Tenhunenet al., 1990). Shade and drought effects do not actindependently on plant performance (Holmgren et al.,1997; Sack, 2004) but rather show interactive effects,which are qualitatively different from those describedfor light and nutrient limitations. Similarly, as a resultof the interaction between irradiance and soil mois-ture, spatial and temporal distribution of soil moisturecan be qualitatively from temperate forests (e.g.,Joffreand Rambal, 1993; Kitzberger et al., 2000). All theseevidences suggest that water shortage results in qual-itatively different mechanisms of community assem-bly than nutrient limitations. Finally, another difficultyin developing mechanistic models of forest dynamicsis the existing compromise between model complex-ity and mathematical tractability. Mechanistic theoriesdeveloped so far rely either on simple analytical orheuristic models that omit too many critical biolog-ical details (e.g.,Tilman, 1982; Smith and Huston,1989) or on size-structured numerical models (e.g.,Shugart, 1984; Tilman, 1988; Mouillot et al., 2001)that are difficult to analyze and interpret from a bio-l e-t ver,c tions toe ual-b 95;L yt-i oal.

ndd andt tedf ribes eane tageb andsa rests ater

nd tradeoffs associated with water availability, hver, have not been explicitly incorporated in pechanistic theory despite the fact that water is a

ight and nutrients a critical resource influencingroductivity and composition of plant communitorldwide (Woodward, 1986; Stephenson, 1990).The development of a mechanistic model for

lant system requires understanding two separateesses (e.g.,Goldberg, 1990). First, we need to describow plants respond to resource heterogeneity an

nterspecific tradeoffs implied (plant performance sodel). Secondly, we need to understand how bnd abiotic processes interact dynamically to c

rol resource supply rates (resource sub-model).ndividual responses and resource variation inteynamically to determine the nature of the intersific mechanisms driving successional change in pommunities; e.g., competition, facilitation or neu

ogical point of view. Asymmetric resource compition in forest size-structured populations, howean be described through partial differential equaystems (Kohyama, 1991), which have been shownmerge from approximate aggregations of individased models (e.g.,Pacala and Deutschman, 19ischke et al., 1998). Thus, the development of anal

cal models of stand dynamics seems a feasible gIn this study, we develop a simulator of sta

ynamics that incorporates the main constrainsradeoffs experienced by plants in water-limiorests. The model is specifically suited to desctand structure and dynamics of Mediterranvergreen forests, which represent a transition setween northern more humid temperate forestsemi-arid vegetation (Archibold, 1995). The model issize-structured individual-based simulator of fo

tand dynamics coupled to a stochastic soil w

78 M.A. Zavala, R. Bravo de la Parra / Ecological Modelling 188 (2005) 76–92

balance. Individual tree performance is described by aphysiologically-based big-leaf model which describescarbon gain and transpiration as a function of climaticand edaphic conditions. Differences among species arebased on morphological (size and allocation patterns)rather than on physiological differences. All plantssharing the same morphology and germinating atthe same time define a cohort of individuals. Treescompete for light and water, with shorter trees beingshaded by taller trees and soil water is depletedthrough cumulative transpiration. Competition forwater is asymmetrical with trees with a higher rootdensity experiencing a higher water supply. We use thesimulator to explore general patterns that may emergeat different levels of biological organization. First weexplore how the leaf-level tradeoff between carbongain and water loss expresses at the whole-plant-leveland the influence of allocation strategy on plant perfor-mance along a water availability gradient. Secondly,we ask whether plant competitive mechanisms maychange along annual rainfall and rainfall frequencygradients and, in particular whether shifts from com-petitive to positive interactions are observed. Third,we investigate how stand structure and compositionare modified by changes in the rainfall regime anddisturbances. Specifically, we investigate how annualrainfall and rainfall stochasticity influence standingcrop and coexistence of species differing in theirallocation strategy. Finally, we propose a generalanalytical framework to describe stand dynamics inl .

2

sedm ver-l terc od or-t soilw , ast ility,w ighti wtha nsa iona log-

Fig. 1. Diagram of model flows. Light competition is asymmetricwith trees of a given height (hj) being shaded by taller individuals(hi > hj). Soil moisture is determined as the balance of water inputs(rainfall) and outputs (tree transpiration, drainage and soil evapo-ration). Trees with larger root systems have a larger water supply.Water demand and supply for each individual tree are adjusted thor-ough a physiological model which maximizes carbon tree growthwhile prevents the tree from reaching the cavitation threshold.

ical big-leaf model. Light at a given height is com-puted through a light extinction model (Beerıs Law).Water availability is estimated through a soil water bal-ance model, which considers both climatic conditionsand the cumulative effects of transpiration by individ-ual trees. All model state variables are updated at anhourly scale. Trees of the same height receive the sameradiation and soil moisture is assumed to be homo-geneously distributed in the stand. We do not includeexplicitly spatial heterogeneity (neither vertical or hor-izontal) nor neighbourhood competitive effects, thus,the results from this model are only valid in the contextof stand-level processes and cannot be extrapolated toheterogeneous forest landscapes.

2.1. Individual tree growth, carbon allocation andmortality

Tree growth and mortality are based on a physio-logical model that describes carbon and water balanceindividually for each tree. The environment is charac-terized by air temperature, dew point, radiation, andfrequency and intensity of storm events. The physio-logical model is a big-leaf approximation that predictshourly values of carbon assimilation, transpiration, leaftemperature and stomatal conductance (see Appendix

ight and water-limited size-structured populations

. The forest stand model

The simulator is a size-structured individual-baodel that describes the temporal dynamics of o

apping tree cohorts structured by light and waompetition (Fig. 1). It results from coupling of twifferent models: a model of tree growth and m

ality, and a resource dynamics model (light andater availability). Both models are interconnected

ree performance is a function of resource availabhich depends in turn on tree transpiration and l

nterception by canopy trees. Individual tree grond mortality are functions of both climatic conditiond light and water availability. Carbon assimilatnd transpiration are described through a physio


for details;Zavala, 2004). The soil–plant–atmospherecontinuum is represented by a simplified water poten-tial circuit in which tree canopy, stem and root systemare represented by a single resistance (Sellers et al.,1995). A system of four non-linear equations and fiveunknowns is derived based on assumptions of equilib-rium in canopy latent heat fluxes and energy, carbonand plant water balances. To solve the system, we useBall et al. (1987)equation, which links stomatal con-ductance to carbon assimilation rates. In this equation,however, the parametergF that determines the levelof conductance attained for a given assimilation rate isunknown. To estimategF over the course of the droughtwe use a negative feedback algorithm via leaf waterpotential that ensures the plant performs a strategy oflong-term carbon gain optimization and avoidance ofmortality. This algorithm (seeZavala, 2004) has beenshown to result in realistic gas exchange rates dur-ing the dry period (Tenhunen et al., 1990; Sala andTenhunen, 1996).

Individuals start as seedlings and undergo continu-ous vegetative growth. The plant allocates carbon tofour different compartments: shoot, stem, roots andreproduction. Growth for each allocation compart-ment is evaluated at an hourly scale after discount-ing maintenance respiration from carbon gain. Shootallocation is described by leaf area per unit groundarea (LAI). Physiological canopy conductance per unitground area is estimated as the product of mean leafconductance per unit LAI (equivalent to the paral-l ,1 forw ner rootr m ofi epr itivea is-t ateL omc oca-t ;T uc-t ro-d y bye on-s thes

Tree mortality can result both from exogenous (e.g.,disturbances) or endogenous causes: water stress ornegative carbon balance. Plant water stress is evalu-ated through the parametergF, which integrates plantendogenous processes that can induce stomatal clo-sure in response to drought. Specifically, “plant waterstress” (PWS) is estimated through the number ofdays in whichgF reached its minimum value. TheparametergF is computed through a negative feed-back via leaf water potential, therefore its minimumvalue is reached when leaf water potential approachesthe cavitation threshold. Tree probability of mortalityas a result of drought stress is described as a logis-tic function of PWS. Trees also die when their inte-grated annual carbon balance is negative. Exogenousmortality rate is a free parameter, which allows usto simulate the effect of changes in the disturbanceregime.

2.2. Resource dynamics and tree interactions

Light competition is asymmetric with taller treesshading shorter trees. It decreases exponentiallythroughout the canopy at a rate that depends on LAIof taller trees (Tilman, 1988). Soil water dynamics ismodelled through a discrete time water bucket modelwith water inputs taking place in a fixed instant of theday (evening). Daily variation is described through anstochastic model with rainfall events being Poisson dis-tributed and rainfall depth following an exponentialdS pira-t sup-p al reesa id-u anda ur-p ax-i red( teds untf ateru igh-b iona soilm soilp

el sum of individual leaves’ conductance,Woodward986). Trees differ in their competitive advantageater according to their differential allocation to fi

oot density. A larger investment decreases soil–esistance, which is estimated as the parallel sundividual fine roots conductance. Allocation to deoots (serial resistance) that would confer competdvantage in soils with a vertical gradient in soil mo

ure availability is not considered here. We estimAI, stem height and diameter and root density frarbon concentration in shoot, stem and root allion through allometric equations (Woodward, 1986ilman, 1988). Once the plant has reached reprod

ive age a fraction of carbon is allocated to repuction. The number of seeds produced annuallach individual tree is a function of seed size (ctant in this study) and are dispersed uniformly intand.

istribution (Rodrıguez-Iturbe et al., 1990; Appendix).oil water reserves are depleted by tree trans

ion, soil evaporation and drainage. Tree waterly is variable across individuals with trees with

arger root surface being able to tap more water. Tdjust their transpirational demand to their indival water supply as to maximize carbon uptakevoid mortality during the dry season. For this posegF is iteratively adjusted as to result in the m

mal growth rates for which plant survival is ensuZavala, 2004). Demand and water supply are adjusimultaneously for all trees so we do not accoor competitive strategies associated with faster wptake after storm events. Neither we consider neourhood nor vertical effects in water competitnd assume that both individual root systems andoisture are evenly distributed throughout therofile.


2.3. Model solution and simulations performed

To evaluate plant performance in relation to LAIandR:S ratio we estimated annual net carbon assim-ilation and mortality for a range of trees differing intheir LAI andR:S growing under two water availabil-ity environments: dry (400 mm annual rainfall) andhumid (1200 mm annual rainfall). Stem and reproduc-tive allocations were fixed and plants were consideredto grow in isolation (no competitive interactions). Wealso explored the existence of an optimal LAI andR:S allocation along the rainfall gradient by graduallyincreasing LAI or R:S until the benefit of increas-ing LAI or R:S with respect to annual carbon gainapproached to zero.

To evaluate plants responses to combined gradientsin light and water availability and to explore shifts inplant interactions from competition to facilitation, weexplored plant performance along two axes of vari-ation. The first axis is a water availability gradientdefined by four environments: 400 and 1200 mm ofannual rainfall combined with a high and a low stormfrequency. The second axis is a continuous variationin light suppression estimated as percentage of pho-tosynthetic available radiation (PAR) at full sunlight.Two possible cases were considered: (1) radiation waschanged as an independent factor (e.g., seedling influ-enced by changes in understory radiation), and (2)we explicitly simulated neighbour competition thusreduced radiation was inevitable associated with lowers e.g.,j ndr

andc bil-i ingt ands an am asa ailyp ofri s ins es( m)a n-d ctiono ndi-

Fig. 2. Temporal variation in daily rainfall inputs (mm) and soilwater content (fraction of one) dynamics in the stochastic soil waterbalance model.

tions among species differing in their root to shootallocation strategy we performed more than one hun-dred runs along different combinations of rainfall anddisturbance regimes.

A complete account of model equations and parame-ters are given, respectively, in Appendix and inTable 1.Structural and functional parameters hydraulic resis-tance (Rs), leaf area index (LAI), Root to shoot (R/S),cavitation threshold (Ψc) and light extinction coeffi-cient (α) were set to describe standard values for atypical Mediterranean sclerophyll (Quercus ilex L.)(Jones, 1992). Monthly and hourly values of photo-synthetic available radiation, air temperature and dewpoint for this location were obtained by interpolatingthe 6-h ISLSPC global climate database for a locationin Northeastern Iberian Peninsula, 42◦N–1◦W (Sellerset al., 1995). The stochastic rainfall model was param-eterized to reproduce local rainfall patterns. Prior toeach simulation the model was iterated one hundredtimes to prevent soil moisture content being dependenton initial conditions.

oil moisture because of increased transpiration (uvenile influenced by both lower soil moisture aadiation).

To investigate how stand production, dynamicsomposition change along gradients of water availaty we performed several runs with individuals sharhe same allocation pattern and both deterministictochastic environments. By deterministic, we meodel in which daily precipitation input is estimatedconstant fraction, while in the stochastic regime drecipitation is given by a probability distributionainfall frequency and intensity (Fig. 2, Appendix). Wenvestigated the existence of equilibrium solutiontanding crop for three different precipitation regimxeric, 200 mm; dry, 400 mm and humid, 1200 mnd evaluated its stability from different initial coitions and perturbations, such as biomass extrar episodic droughts. To evaluate coexistence co


Table 1Main parameter values used in the simulations

Sub-model Parameter Value Units Source

Stomatal conductance Do 0.010 mol mol−1 Leuning (1995)Cuticular transpiration (bo) 0.020 mol m−2 s−1

Plant and stand structure Hydraulic resistance (Rs) 15× 106 MPa s m−1 Jones (1992)Leaf area index (LAI) 1.0Root to shoot ratio (R/S) 1.0Cavitation threshold (Ψc) −2.5 MPaLight extinction coefficient (β) 0.0045 Tilman (1988)Height (h)/biomass (B) allometry h = 4× 2500B0.5

Soil water balance Soil depth (Zr) 400 mm Rodrıguez-Iturbe et al. (1990)Saturated hydraulic conductance (Ks) 400 mm day−1

Drainage constant (c) 4.0Soil type curve (k1) −0.04Soil type curve (k2) 1.5Soil porosity (n) 0.425

2.4. General analytical framework

Even under computing intensive simulations onlya small number of parameter combinations can beexplored. Also understanding the causes of modelbehaviour can be cumbersome: e.g., mechanisms lead-ing to stable coexistence among species, identificationof switches from competitive to positive interactionsor the influence of rainfall frequency gradients on den-sity dependence processes. In this section, we proposea general multi-species model of a size-structured treepopulation, which takes into account the effects of com-petition for light and water. We justify the constructionof this general framework to show evidence of conver-gence between forest simulators and analytical models,and leave analytical qualitative and numerical analysis(e.g., as inAngulo and Lopez-Marcos, 2002) for furtherstudies.

The framework introduced is a multi-species size-structured model describing tree growth, mortalityand recruitment (sensuLischke, 2001). The resourcedynamics model (light and soil water availability)included in the simulator will be implicitly taken intoaccount in the general form of functions describinggrowth, mortality and recruitment rates. Both indepen-dent variables size (x) and time (t) are considered tobe continuous. The size variablex represents, follow-ing Kohyama (1992), the dbh (trunk diameter of breastheight). LetNi (t, x) (i = 1, . . ., p) be the populationdensity of trees of speciesi in the stand with respect to

dbh, i.e.,∫ x2x1Ni(t, x) dx represents the number of trees

of speciesi in the stand with dbhx ∈ [x1, x2] at timet.We choose a weighted cumulative basal area of taller

trees as the light index to express the shading effect and,therefore, asymmetric light competition. We supposedifferent ratio height/dbh for each species, denotingαi

the one corresponding to speciesi. This index forx-sized trees of speciesi is defined by,

IiL(t, x) =p∑j=1

βj

(∫ ∞

x(αi/αj)

π

4s2Nj(t, s) ds

)

and measures the basal area of all the trees, of anyspecies that are taller than trees of speciesi with dbhequal tox. Coefficientsβj represent the differences inlight suppression due to trees of the same height ofdifferent species.

We also define a water index through weighted totalbasal area to reflect competition for water, which ischosen to be the following assuming that water uptakeis proportional to root surface and, therefore, to basalarea:

IW(t) =p∑i=1

γi

(∫ ∞

x0

π

4s2Ni(t, s) ds

)

where coefficientsγ i represent possible differencesamong species in the ratio basal area to root surface.The sizex0 is the minimum dbh for a seedling to beconsidered a new recruited individual.


The changes in size distribution depend on the ratesof size growth, mortality and recruitment.

The speciesi growth rate:

Gi(t, x) = gi(x, IiL(t, x), IW(t))

depends on the individual sizex, the size and speciesspecific light index and the water index. In general,gi(u, v,w) can be described as an unimodal function onvariableu reflecting that, under the same environmentalconditions, growth rate increases to attain its maximumat a certain size and then decreases to cero; with respecttov, gi(u, v,w) is a decreasing function due to the neg-ative effect on the growth rate produced by the lightindex which is a measure of shading; finally the depen-dence on variablev is difficult to be generally specifiedbecause, as argued in the introduction, an increase inglobal density could have either positive or negativeeffects on water availability in a Mediterranean climatedepending on annual rainfall and rainfall frequencygradients.

Mortality rate for speciesi, Mi(t, x), must take intoaccount exogenous and endogenous causes as well asrelative size differences. Thus, we propose a generalmortality rate depending on size and light and waterindexes:

Mi(t, x) = mi(x, IiL(t, x), IW(t))

Recruitment rate for speciesi, Ri(t), is consideredt thiss duc-t hi ons , untilt ralf

R

w ri-a onr ei

fora -m s(

Balance law

∂Ni

∂t+ ∂[gi(x, IiL(t, x), IW(t))Ni]

∂x

= −mi(x, IiL(t, x), IW(t))Ni, (t > 0, x > x0)

Birth law

gi(x0, IiL(t, x0), IW(t))Ni(t, x0)

= ri(IiL(t, x0), IW(t))

∫ ∞

xir

π

4s2Ni(t, s) ds, (t > 0)

Initial dbh distribution

Ni(0, x) = φi(x), (x > x0)

Particular cases of this model has been discussedby Kohyama (1991, 1992)where no water competitionnor interspecific differences in allometry are consid-ered.Calsina and Saldana (1997)performed an ana-lytical study (asymptotic behaviour of the solutions)of the particular case for which growth, mortality andrecruitment rates of a single species depend on a lin-ear combination of resource availability but it is size-independent. Similar non-local terms as the one used inour model have been developed and applied byAnguloand Lopez-Marcos (1999, 2000, 2002)to solve numer-ically monospecific size-structured population models.

3. Results

3p

othm iesa nter-c s insD t inh ila-t adT ualr m)a erer eds ol-

o be proportional to the basal area of trees ofpecies which have reached the minimum reproion age,air, with a proportionality coefficient whicncludes the effects of light and water competitioneed germination and seedling establishment (e.g.he minimum sizex0 is attained). So a proposed geneorm for the recruitment rate is:

i(t) = ri(IiL(t, x0), IW(t))

∫ ∞

xir

π

4s2Ni(t, s) ds,

hereri(u, v) is a decreasing function on both vables, andxir is the dbh at the minimum reproductiate, i.e.,xir = x(air) with x(t) being the solution of thnitial value problem dx/dt = Gi(t, x), x(0) =x0.

The model based upon the classical modelstate-structured population, seeMetz and Diek

ann (1986)and de Roos (1997), reads as followi = 1, . . ., p):

.1. Resource allocation and whole-planterformance

Leaf area index (LAI) had a strong effect on bortality and annual carbon gain. A larger LAI impllarger photosynthetic apparatus and larger light ieption but also higher water loss and reductiontomatal conductance (see reduction ingF in Fig. 3).iminishing payoffs in terms of carbon gain resulyperbolic increments of annual net carbon assim

ion per unit of ground with respect to LAI and inecrease of net assimilation per unit of leaf (Fig. 3).his effect was found both in a dry (400 mm annainfall) and in a humid site (annual rainfall 1200 mlthough differences among the two climates wather small. Plant probability of mortality increasharply with respect to LAI in both environments f


Fig. 3. Variation in plant net carbon assimilation per unit of leaf(solid line, left axis), per unit of ground (dashed line, left axis) andin the parametergF (dotted solid line, right axis). Results apply to asingleQuercus ilex individual.

lowing a logistic function (Fig. 4). The risk of mortalitystarted to increase after LAI values around 1.5 in dryand 2.0 in humid environments. For values larger than2.5 the probability of mortality approached 1.0 and 0.69in dry and humid environments, respectively.

Root to shoot allocation (R:S) had also a relativelylarger impact on mortality than on annual net carbonassimilation (Fig. 5). Plant mortality increased afterR:S allocations around 1 and 0.5 in dry and mesic sites,respectively increasing according a logistic function.ForR:S values around 0.5 plant probability of mortalityin mesic sites was close to zero, reaching 0.7 in xericsites. Optimal leaf area index increased linearly withincreasing values of annual precipitation (Fig. 6) withvalues around 1 in sites receiving less than 400 mmand reaching up to 2.5 when annual rainfall exceeded1000 mm. Optimal root to shoot allocation decreasedalong the rainfall gradient to reach a minimum of 0.25at localities receiving annually more than 1000 mm andreached its maximum value around 200 mm (Fig. 6).

3.2. Shade effects, plant interactions and standstructure and dynamics

Plant water stress was strongly modified by lightsuppression, annual rainfall and frequency of rainfallevents (Fig. 7). In humid climates plant water stressreached 27 and 18 days under low and high rainfallfrequencies regimes, respectively. A threshold respondwas observed for a reduction of 70%, which resultedi Ase e dry

Fig. 4. Effects of increasing LAI (leaf area index) on plant annualnet carbon assimilation (left-handed axis, solid line) and plant proba-bility of mortality (right-handed axis, dashed lines) for dry (400 mmannual rainfall, upper figure) and humid (1200 mm annual rainfall,lower figure) environments (R/S = 0.5). Results apply to an isolatedQuercus ilex individual.

than in the humid climate (Fig. 7). Unlike the humidclimate, water stress was significantly lower in the lowthan in the high frequency rainfall regime. Also thedecrease in stress resulting from light suppression washyperbolic (as opposed to logistic). These trends canalso be documented through the variability in the riskof mortality with respect to light, which also showed adramatic effect (Fig. 8). In the drier climate (400 mmof annual rainfall) and low rainfall frequency, prob-ability of mortality reduced with shade according toa logistic function with maximum values around 0.75under full sunlight, down to 0 for a shade reductionof 0.65. A high rainfall frequency resulted in higherplant mortality across the light suppression gradient.In moister climates (1200 mm) shade reduced mortal-ity both under high and low frequency rainfall regimes.The risk of mortality was more elevated in the highfrequency regime where it remained close to one anddecreased sharply for light suppression values lower

n dramatic improvement of plant water status.xpected plant water stress was much higher in th


Fig. 5. Effects of increasingR/S (root to shoot) allocation on plantannual net carbon assimilation (left-handed axis, solid line) and plantprobability of mortality (right-handed axis, dashed lines) for dry(400 mm annual rainfall, upper figure) and humid (1200 mm annualrainfall, lower figure) environments (LAI = 1). Results apply to asingleQuercus ilex individual.

than 0.72. Probability of mortality was lower for thelow frequency treatment, reaching maximum values atfull sunlight, to decrease smoothly afterwards follow-ing a logistic function. Water competition intensifiedconsiderably plant probability of mortality by pushingthe whole curve to the left and the plant becoming moresensitive to radiation (data not shown).

Rainfall regime had a dramatic impact. Standbiomass followed cyclic dynamics without reachingan equilibrium and with cycle amplitude decreasingwith annual precipitation. Standing crop was highlyresilient to initial conditions, disturbances and episodicdroughts. Rainfall stochasticity had a major influenceon stand biomass by increasing considerably stand pro-duction. For the range of climatic conditions exploredwe did not observe coexistence among species dif-fering in theirR:S allocation. Along the precipitationgradient “rooty” species excluded leafy species in thelower dry end of the gradient while “leafy” specieseliminated “rooty” ones in the long run in mesic andhumid sites (Fig. 9). We did not observe a coexis-

Fig. 6. Predicted optimalR/S (root to shoot) allocation (upper figure)and LAI (lower figure) along a rainfall gradient. Results apply to anisolatedQuercus ilex individual.

tence region for intermediate rainfall values but rathera threshold response with shifting dominance of onephenotype over the other. These simulations howeveronly included a few combinations of model parameters.

4. Discussion

4.1. Resources and biomass invested by plants

According to the classical tradeoff between above-and below-ground resource uptake (Tilman, 1988) a


Fig. 7. Plant water stress at the two extremes of an annual rainfallgradient: humid Mediterranean (1200 mm, lower figure) and semi-arid (400 mm, upper figure). The vertical axis shows number of daysin which plant stress reaches critical values. The horizontal axisindicates the percentage of light reduction. The two lines indicaterespectively low (solid lines) and high (dashed lines) rainfall frequen-cies (LAI = 1,R/S = 0.5). Results apply to aQuercus ilex individualwithin a forest stand.

Fig. 8. Effects of rainfall regime and light suppression on plant prob-ability of mortality (LAI = 1,R/S = 0.5). The horizontal axis indicatesthe percentage of light reduction. Two annual rainfall regimes arecontrasted: 400 mm (upper figure) and 1200 mm (lower figure). Tworainfall frequencies are shown: low frequency (solid line) and highfrequency (dashed line).

Fig. 9. Outcome of competition among “rooty” (dashed line) anda “leafy” (solid line) allocation strategies in arid (upper graph),Mediterranean (middle graph) and temperate environments (lowergraph). Simulations are performed in a 1000 m2 plot and with a dis-turbance rate of 10% of annual biomass removal. Simulation andresults apply to a stand of interacting individual trees.

larger allocation to photosynthetic apparatus results inhigher rates of light interception while a larger invest-ment in roots increases below-ground resources uptakerates. Our results imply however that tradeoffs associ-ated with light and water competition express acrossfunctional levels in a qualitatively different mannerthan tradeoffs associated with nutrient competition.Water use in Mediterranean sclerophylls seems gov-erned by a series of mechanisms that operate hierar-chical to maximize long-term carbon gain and escape


summer mortality (Rambal, 1993; Tenhunen et al.,1990; Sala and Tenhunen, 1996). At the leaf levelstomatal adjustments allow the plant to perform a sub-optimal strategy in which leaves optimize water useefficiency under rapidly changing atmospheric con-ditions and a fixed level of soil potential. As wateravailability changes, whole plant carbon gain and wateruse optimization requires that the plant reaches a newfunctional equilibrium in which daily patterns of waterexpenditure are readjusted in terms of soil water avail-ability (Rambal, 1993; Zavala, 2004). Plants with alarger photosynthetic apparatus experience higher tran-spiration rates and deplete water in the soil at a fasterrate than plants with a relatively lower leaf invest-ment. Thus, plant carbon gain per unit of ground areaincreases but so does transpiration per unit ground area.This increase in transpiration translates into longerperiods of stomatal closure. Thus, the payoff of LAIinvestment diminishes, explaining why the relationshipbetween assimilation rate per unit of ground and LAIfollow a hyperbolic relationship as opposed to linear.Moreover, the risk of mortality increases with LAI at afaster rate than plant growth suggesting that the ener-getic leaf-level constrain between carbon acquisitionand water loss expresses as a tradeoff between growthand survival at the plant-level (Cowan, 1982).

A number of experimental studies have shown thatplant optimal allocation may result from a compromiseamong selective forces acting in opposite directions(Tilman, 1988). A high shoot allocation will have ap n-m tivec on-m leafa ctiona byd tial.S ayp lityr di-t reasewA ner taS n).T t tos late.

This disagreement is often the result of lumping inthe same pool roots devoted to structural support andstorage with fine roots which are seemingly linked toresource uptake (Canham et al., 1999; Zavala et al.,2000). Therefore our theoretical results suggest thatroot storage/ support components must be separatedfrom fine root biomass in order to effectively testfor allocational tradeoffs associated with shade anddrought tolerance.

4.2. Shifts in plant interactions alongenvironmental gradient and species coexistence

Our results suggest that under a Mediterranean cli-mate plant interactions can be qualitatively differentthan those observed in temperate forests where lightand nutrients are the main limiting resources (Tilman,1988; Smith and Huston, 1989; Pacala et al., 1996).According to classical plant competition theory anincrease in population size will result in poorer perfor-mance of new recruiting individuals because of reducedlight and nutrient availability. As predicted by ourmodel; however, in a Mediterranean climate detrimen-tal effects of canopy cover (mainly increased light andwater competition) can be offset by the benefits. Thus,neighbouring individuals may facilitate rather than dif-ficult the establishment and growth of new individuals(Callaway, 1992; Maestre et al., 2003). A number ofprocesses haven been shown to ameliorate water stressor to improve resource availability under plant cover( tesc hatc car-b ls ,1 eri dom-i opyi -b esn on(a ta u-t ow( i-r ugha etion

ositive effect on survivorship in light limited enviroents where mortality is mainly the result of a nega

arbon balance. In contrast, water-limited envirents the benefits of shoot allocation (e.g., specificrea) do not compensate the costs of root constrund maintenance. More likely mortality inducedrought results from a collapse in water poteneedlings grown under well watered regimes merform worse during the summer (higher mortaates) than plants grown under water limiting conions because they develop larger shoots that incater losses and mortality (van den Driessche, 1991).ccording to our model predictions allocation to fi

oots can improve plant survivorship (seeCanham el., 1999for temperate forest tree species andVillar-alvador et al., 2000for a Mediterranean evergreehere is some conflicting evidence on how roohoot allocation and drought tolerance interre

seeFig. 10). Irradiance in Mediterranean climaan be very intense resulting in photoinhibition tan increase the risk of mortality and decreaseon gain (Valladares and Pearcy, 1997). Thus, partiahade can facilitate seedling survival (Rey Benayas998). Also water availability can be relatively larg

n the shade than in the open because of the prenant role of soil evaporation with respect to cannterception and tree transpiration (Joffre and Ramal, 1993). Other positive effects of neighbouring treot included in our model include wind protectiWilson and Agnew, 1992), hydraulic lift (Richardsnd Caldwell, 1987), herbivore protection (Castro el., 2002), canopy interception and patchy distrib

ion of soil moisture or nutrients through stem flSchlesinger et al., 1996). Finally, shade can have indect positive effects on seedling performance thro

reduction in herbaceous cover and water depl


Fig. 10. Positive (+) and negative (−) effects of a competing established individual on a seedling during the establishment process. Radiationattenuation by the canopy decreases photosynthesis rates but also ameliorates negative radiation effects. Canopy interception and tree transpirationare major negative effects which decrease soil water available for the seedling. Hydraulic lift, wind and temperature oscillation protection, stemflow and a reduction in soil evaporation tend to improve seedling water status and soil water availability. Also indirect effects through reductionof herbaceous cover have been reported.

rates (Maestre et al., 2004). In agreement with previousempirical studies, the net outcome of plant interac-tions can change along environmental spatial (slopeaspect,Gomez-Aparicio et al., 2004, edaphic,Pugnaireet al., 2004) or temporal gradients associated with theavailability of water (Tielborger and Kadmon, 2000;Kitzberger et al., 2000). Unlike previous simpler graph-ical models (Holmgren et al., 1997) our model providesboth an unifying explanation for the variety of cases inwhich the sign of plant to plant interactions in Mediter-ranean environments can shift, and for the first time amechanistic description that can be linked to data fromcurrent empirical studies.

According to our model the outcome of the interac-tion among two species does not lead to stable coex-istence but rather to dominance of the best competitorfor each environmental condition. A number of studies(e.g.,Hacker and Gaines, 1997) have suggested thatpositive interactions can enhance diversity by creatingnew opportunities for some species. In contrast for therange of simulations performed we did not find evi-dence of light and water-partitioning strategies leadingto stable coexistence as described in light and nutri-ent limited ecosystems. This can be due to the factthat we did explore only a portion of the possibleparameter combinations that can emerge in a complexsimulator highlighting the importance of formulating

or aggregating analytically tractable models. Neverthe-less coexistence in spatial models is often the result ofpartitioning of spatial heterogeneity with each speciesbecoming dominant in a given part of the gradient butwithout long-term coexistence within resource patches(Pacala and Tilman, 1994). Also previous analyticalstudies of stand dynamics under water-limited con-ditions show the existence of multiple stable states(changes between founder control and competitiveexclusion driven by shifts from facilitation to com-petition), and absence of stable coexistence (Zavala,1999).

4.3. Perspectives on scaling ecological processesin Mediterranean forests

The structure and physiognomy of Mediterraneanvegetation is strongly linked to moisture patterns(Miller, 1981). Stand production is very variable fromsite to site depending on slope aspect and other topo-graphic variables, which influence plant water balance.Also gradients in water availability modify commu-nity physiognomy by inducing changes in above- orbelow-ground biomass. In previous studies (Specht,1981; Woodward, 1986), leaf area index is estimatedthrough an optimization process in which it is iter-atively adjusted to maintaining soil water potential


beyond wilting point. However, community level opti-mization processes are not supported by evolution-ary theory and identification of the rules from whichcollective behaviour emerges from individual levelinteractions (the unit of natural selection) is required(Maynard Smith, 1982).

Maximization of water use efficiency (Cowan andFarquhar, 1977) may be a valid strategy for establishedindividuals of tree species that can have good access tosoil water. For this species, carbon gain maximizationmay be achieved by operating at the safety limitsimposed by cavitation and embolism risk. Implemen-tation of such a strategy in a model of Mediterraneangas exchange simulator resulted in realistic water usepatterns (Zavala, 2004) and it is also in agreement withempirical studies of hydraulic performance (Tyreeand Sperry, 1989). In contrast, water use efficiencymaximization is not likely to be selected in competitiveenvironments where saving water is of little use. Bothconservative and wasteful water use strategies havebeen reported in Mediterranean chaparral species(Miller, 1981). Also, in addition to stomatal controlplant phenology (Heilmeier et al., 2002) or resourcetemporal partitioning (Chesson, 1983) may be morerelevant for explaining niche differentiation in thesecommunities.

The scaling of physiological processes directlyfrom the leaf to the stand or to the ecosystem (“GreenSlime models”) may be of little relevance to ecologicalsystems in which demographic processes interactd tationd relye mitt ,1 dn 8;M fulfi s atw ofm llyi ana-l uesi ema phe-nR st sibleg

Acknowledgements

MAZ was supported by grant REN2002-04041-C02-02/ GLO and REN2000-745, CICYT, Ministeriode Ciencia y Tecnologıa (M.C.y T.), Spain. We alsoacknowledge research networks GLOBIMED (CICYT,M.C. y T.) and REDBOME (Junta de Andalucıa) forpromoting stimulating discussions on Mediterraneanforest ecology. Gianluca Biondi and Noemi Gizzi fromPolitecnico di Milano assisted with program imple-mentation and figure elaboration at several stages ofthis work. Comments from Jose M. Rey Benayas, PedroVillar and two anonymous reviewers improved earlierversion of the ms.

Appendix A. Whole-tree physiological model

Tree growth is based on a big-leaf model (seeZavala,2004for details) described by a system of non-linearequations that simulates the following variables: leaftemperature (Tl ), leaf water potential (ψl ), leaf latentheat flux (ϕE), leaf conductance (gs) and plant net car-bon assimilation (An). To estimateTl we assume thatnet canopy energy balance equals the rate of storage,which is considered negligible in relation to the otherterms in the energy balance (Jones, 1992). Net sensi-ble heat loss from the leaf (C) is proportional to thedifference between leaf and air temperature (Tl − Ta),air heat capacity (Cp) and the parameterga, whichd ,1 ratei eri eenl -t hyll(t enta ntr yerc to thela andrm

pli-fi .,

isturbances, history and chance to shape vegeynamics. Mechanistic theories developed so farither on simple analytical or heuristic models that o

oo many critical biological details (Holmgren et al.997; Smith and Huston, 1989) or on size-structureumerical models (Shugart, 1984; Tilman, 198ouillot et al., 2001). Simulation studies are a use

rst approximation to explore the main processeork in any ecosystem but a full understandingodel dynamical behaviour in relation to biologica

nterpretable mechanisms is best achieved throughytical models. Advances in aaggregation techniqn which collective properties of the modelled systre described as emergent properties of biologicalomena at lower levels of organization (e.g.,Auger andoussarie, 1994; Moorcroft et al., 2001) suggest

hat scaling of ecological processes may be a feaoal.

escribes plants boundary layer conductance (Jones992). Transpiration rates are assumed to equilib

nstantaneously with incoming water flux. The forms driven by the difference in water potential betweaves and roots (ψL −ψc) divided by hydraulic resisance to water flow from the soil to leaves mesopRs) (Rambal, 1993). Leaf transpiration (E) is propor-ional toDl (vapour mole fraction difference betwehe leaf and the air), and to leaf conductance (Jarvisnd McNaughton, 1986). We assume a fully turbuleegime in which the series sum of plant boundary laonductance and canopy conductance convergeatter. Plant net carbon assimilation (An) is computeds the difference between gross assimilation rateespiratory losses (both due to CO2 production andaintenance of woody structures).Gross assimilation rate is estimated with a sim

ed version of a photosynthesis model (Farquhar et al


1980) in which leaf photosynthesis is described as aminimum of two potential capacities limited respec-tively by radiation (Je) and Rubisco (Jc) (Collatz etal., 1991; Foley et al., 1996). The light limited rate ofphotosynthesis (Je) is given as:

Je = αPARCi − γ

Ci + 2γ(A.1)

where PAR is flux of photosynthetically active photonsabsorbed by the leaf,α is the intrinsic quantum effi-ciency for CO2 uptake in C3 plants,Ci is CO2 concen-tration in the intercellular air spaces of the leaf andγ isgross photosynthesis compensation point. The param-eterγ is estimated as half the ratio of the atmosphericoxygen concentration [O2] andχ (the ratio of kineticparameters describing the partitioning of enzyme activ-ity to carboxylase or oxygenase function). The Rubiscolimited rate of photosynthesis is estimated as:

Jc = Vm(Ci − γ)

Ci +Kc(1 + [O2]/Ko)(A.2)

whereVm is Rubisco maximum capacity to performthe carboxylase function andKc and Ko are theMichaelis–Menten constants for CO2 and O2, respec-tively. Concentration in the intercellular air spaces ofthe leaf (Ci) is estimated iteratively through the follow-ing equation:

Ci = Ca − An(1.6ga + 1.4gs) (A.3)

wd

e er

R

w entd ),C andr refKc hiusf rv dis-c

fiveu r

equation relatinggs to other state variables. We usea BWB-type of model in which the parameter thatcontrols stomatal conductance for a given net CO2assimilation rate (gF), is unknown for water limitingconditions (Ball et al., 1987). We use the formulationdeveloped byLeuning (1995), stated as:

gs = gFAn

(cs − γ)(1 + (Dl/Do))+ bo (A.5)

where cs is CO2 concentration at the leaf surface(approximately equal toca under fully turbulentregime),Dl is the water vapour mole fraction differ-ence between the leaf and the airDo is a referencevalue expressed in the same units thanDl andbo is leafcuticular conductance.

A.1. Stochastic soil water balance

Soil water balance dynamics is described by adiscrete-time version ofRodrıguez-Iturbe et al., 1990stochastic model, coupled to the whole-plant modelthrough transpiration:

�st = st+1 − st

=(

1

nZr

)[Pt − Et (st) − Tt(st) −Dt(st)]

(A.6)

wherest+1 andst are relative soil moisture in two con-sd tiona umes

V

n

t ives

s

nt( ith

hereCa atmospheric CO2 concentration.Respiratory leaf CO2 production (Rd) was assume

qual to 0.015Vm (Farquhar et al., 1980). Maintenancespiration for woody structures (Rwood) is given by:

wood = βwoodCwoodf (Ta) (A.4)

hereβwood is a maintenance respiration coefficiefined at 15 C◦ (0.20 year−1 for fine root biomasswood describes carbon invested in stem, branches

oots, andf(Ta) is the Arrenhius ambient temperatuunction. The kinetic parameters of the model:χ, Kc,o, Vm and respiratory leaf CO2 production (Rd) alsohange with temperature according to the Arrenunction (seeFoley et al., 1996for exact parametealues). Net leaf assimilation rate is obtained afterounting leaf and wood maintenance respiration.

The resulting system of four equations andnknowns (ϕE, ψl , Tl , gs and An) requires anothe

ecutive hours,Zr is soil depth, andPt, T(st) andD(st)escribe respectively daily precipitation, transpirand drainage. Soil volume is estimated as the volum of air, water and mineral components,

s = Va + Vw + Vm (A.7)

Soil porosity is estimated as:

= Va + Vm

Vs(A.8)

It follows that soil volumetric water content (θ) ishe ratio of water volume to soil volume and relatoil moisture becomes,

= Vw

Va + Vm= θ

n(A.9)

Water inputs (Pt) take place daily at a fixed instaevening) with rainfall events Poisson distributed w


rate τ (average number of day between two succes-sive rainfall arrivals). The probability of a storm eventwithin t days is given by:

P(t) = 1 − e−t/τ (A.10)

Every storm event is characterized by a certain depthor magnitude (r), described by an exponential distribu-tion:

fr(r) = αe−α r (A.11)

wherefr is the probability distribution of rainfall eventsof r intensity, andα is a parameter linked with meandepth. For simplicity canopy interception and evapora-tion are not considered.

Soil evaporation,Et(st), is estimated from poten-tial transpiration (PT) and corrected by an exponentialMichaelis–Menten function of soil moisture:

PT = ηδR

ϕ(δ+ j)(A.12)

where δ is the rate of change of saturation vapourpressure with temperature,ϕ is the latent heat ofwater vaporization,j is the psychometric constant,Ris canopy net heat gain estimated from PAR andη is aparameter that describesR attenuation throughout thecanopy as:

η = e−β LAI (A.13)

w ont (seeR

eb turea ughc

-ri werf teds

D

w ons tial

and relative soil moisture content follows a power law:

ψs = k1(n s)−k2 (A.15)

wheren is soil porosity andk1 and k2 are constantslinked to soil-type (see parameter values inRodrıguez-Iturbe et al., 1990andRambal, 1993).

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