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Ecology, 87(2), 2006, pp. 504–517q 2006 by the Ecological Society of America

A STRUCTURAL EQUATION MODEL TO INTEGRATE CHANGES INFUNCTIONAL STRATEGIES DURING OLD-FIELD SUCCESSION

DENIS VILE,1,2,3 BILL SHIPLEY,2 AND ERIC GARNIER1

1Centre d’Ecologie Fonctionnelle et Evolutive (U.M.R. 5175), Centre National de la Recherche Scientifique, 1919,Route de Mende, 34293 Montpellier Cedex 5, France

2Departement de Biologie, Universite de Sherbrooke, Sherbrooke, Quebec, Canada J1K2R1

Abstract. From a functional perspective, changes in abundance, and ultimately speciesreplacement, during succession are a consequence of integrated suites of traits conferringdifferent relative ecological advantages as the environment changes over time. Here weuse structural equations to model the interspecific relationships between these integratedfunctional traits using 34 herbaceous species from a Mediterranean old-field successionand thus quantify the notion of a plant strategy. We measured plant traits related to plantvegetative and reproductive size, leaf functioning, reproductive phenology, seed mass, andproduction on 15 individuals per species monitored during one growing season. The re-sulting structural equation model successfully accounts for the pattern of trait covariationduring the first 45 years post-abandonment using just two forcing variables: time since siteabandonment and seed mass; no association between time since field abandonment andseed mass was observed over these herbaceous stages of secondary succession. All otherpredicted traits values are determined by these two variables and the cause–effect linkagebetween them. Adding pre-reproductive vegetative mass as a third forcing variable notice-ably increased the predictive power of the model. Increasing the time after abandonmentfavors species with increasing life span and pre-reproductive biomass and decreasing spe-cific leaf area. Allometric coefficients relating vegetative and reproductive components ofplant size were in accordance with allometry theory. The model confirmed the trade-offbetween seed mass and seed number. Maximum plant height and seed mass were majordeterminants of reproductive phenology. Our results show that beyond verbal conceptu-alization, plant ecological strategies can be quantified and modeled.

Key words: allometry; path analysis; phenology; plant size; reproductive allocation; secondarysuccession; seed mass; seed production; structural equation modeling.

INTRODUCTION

The concept of a plant ecological strategy sensuGrime (1979, 2001) involves suites of many plant traitsthat are embedded in a web of direct and indirect causalrelationships that vary in relation to environmental con-ditions. The existence of integrated covariations inplant traits defining species-level adaptive strategies isgaining recognition (e.g., Grime et al. 1988, 1997, Wes-toby et al. 2002, Ackerly 2004, Dıaz et al. 2004). How-ever, as Stearns (1976) has pointed out, it is much easierto propose theories of adaptive specialization than totest them, and strong tests require explicit hypothesesand quantitative predictions. An explicit hypothesis(model) of a plant strategy must therefore specify howthe various traits are structured within the nexus ofinterdependences and/or independences and how se-lection by the external environment generates the ob-served patterns of phenotypic correlation. Here, thisconcept of plant strategy will be addressed at the spe-cies level in the context of secondary succession.

Manuscript received 25 May 2005; revised 29 July 2005; ac-cepted 3 August 2005. Corresponding Editor: R. J. Mitchell.

3 E-mail: denis.vile@cefe.cnrs.fr

Secondary succession is the temporal pattern of veg-etation change that occurs after a disturbance event hasaltered or destroyed a preexisting plant community(Clements 1916). Although species replacement overtime necessarily implies changes in suites of traits, abasic assumption of functional ecology is that speciesreplacement occurs because different suites of traitsconfer different relative ecological advantages as theenvironment changes (Grime 1979, 2001, Tilman1988). The manner in which the collection of planttraits changes during secondary succession in old fieldsand how the plant traits interact as a coordinated systemare the main issues dealt with in this study. In otherwords, can a ‘‘plant strategy’’ be quantified and mod-eled? In this paper, we address these questions for bothvegetative and reproductive traits of established adultplants, measured on a set of 34 herbaceous speciesfound in a Mediterranean old-field succession follow-ing vineyard abandonment.

When the focus is on the identification of suites ofinterrelated traits underlying axes of variation of eco-logical strategies (e.g., Westoby et al. 2002) classicalmultivariate analyses (e.g., principal component anal-ysis [PCA]) may be sufficient (e.g., Grime et al. 1997,

February 2006 505MODELING FUNCTIONAL STRATEGIES

FIG. 1. The hypothetical structural equation model. ‘‘Successional index’’ and ‘‘plant size’’ are two latent (conceptual)variables. One-headed arrows represent causal relationships, and double-headed arrows (e.g., between time since field aban-donment and mean individual seed mass) represent free correlations. Residual error variables (ei), which represent effects ofunexplained causes, are shown.

Ackerly 2004, Dıaz et al. 2004). However, althoughPCA can detect trait covariations, it cannot be used todetect whether there is a particular structural organi-zation among variables. To do so, structural equationmodeling (SEM) techniques provide an attractive so-lution. Structural equation modeling is used to test thefit of data to a priori causal hypotheses about the func-tioning of a system (Grace and Pugesek 1997, seeGough and Grace 1999, Shipley 2000). These hypoth-eses are represented as graphical path models. Here wefirst describe the empirical patterns of functional traitcovariation using principal component analysis. Sec-ond, we impose a theoretical structure relating the di-rect and indirect relationships between these traits and

successional age, and we test this model using struc-tural equation modeling.

The hypothesized structural equation model

The structure of the hypothesized relationshipsamong the variables under study is shown in Fig. 1.The first driving variable is the time since the last majordisturbance, i.e., time since field abandonment (fieldage). This variable tracks the suite of environmentalchanges following abandonment, which are representedhere as a latent, i.e., unmeasured, conceptual variable(successional index). This successional index is a com-plex gradient of correlated directional changes in thephysical environment over time: the intensity and fre-

506 DENIS VILE ET AL. Ecology, Vol. 87, No. 2

quency of disturbance decreases (Grime 1979, 2001,Sousa 1984), the amount of light reaching the soil de-creases (Grime 1979, 2001, Tilman 1990, Bazzaz1996), the proportion of nutrients available in the soiland the rate of litter decomposition decrease (Odum1969, Inouye et al. 1987, Garnier et al. 2004), and therelative amount of nutrients sequestered in living bio-mass increases (Huston and Smith 1987, Aerts andChapin 2000). These environmental constraints mayinfluence plant colonization and persistence and thusaffect the suites of species traits present in the differentstages of succession and therefore act as filters sensuKeddy (1992).

The model posits that this successional index drivesa decrease in specific leaf area (SLA). Wright et al.(2004) have shown a strong trade-off between physi-ological leaf traits related to high metabolic rate (pho-tosynthesis and respiration) and leaf life span and thatthis spectrum of traits is strongly correlated with SLA.These traits all reflect an ecological trade-off betweenresource acquisition and nutrient retention (Wright etal. 2004). Furthermore, a number of studies (e.g., El-berse and Berendse 1993, Berendse 1994, Aerts andChapin 2000) have shown a progressive shift fromtraits related to rapid nutrient uptake and cycling (cor-related with SLA) to traits related to nutrient retentionwith decreasing available soil nutrient supply.

Persistence in the highly disturbed environment atthe start of secondary succession requires the abilityto reproduce rapidly following germination. The suc-cessional index therefore determines the probabilitythat a species found at a given field age will be a pe-rennial or an annual (life span). Since interspecificcompetition is partly determined by plant size (Grime1979, 2001, Tilman 1988), and since competition isexpected to increase during secondary succession asthe intensity of large-scale disturbances decreases andbiomass accumulates, we expect pre-reproductive veg-etative size to increase as a function of the successionalindex. Pre-reproductive vegetative mass is then hy-pothesized to be the main cause of plant size differ-ences between species at seed maturation. We modelplant size at seed maturation as a latent variable mea-sured by four allometrically related components mea-sured at the same time (maximum plant height and leaf,stem, and reproductive mass), and interpreted coeffi-cients in the light of allometry theory (West et al.1999). We also hypothesized that reproductive massfor a given vegetative mass (i.e., reproductive alloca-tion) is dependent upon life span. This relationship isexpected to be negative since, as the intensity of dis-turbances (and the need for rapid reproduction beforedeath) decreases and the intensity of interspecific com-petition (and the need for greater plant size) increases,long-lived species should be favored (Wilson andThompson 1989). Thus, the relationship between suc-cessional index and reproductive mass is influenced bychanges in both life span and plant size.

Disturbances create opportunities for establishmentand recruitment of seedlings; these depend on the quan-tity and quality of propagules produced, which is gov-erned by a trade-off between the number and mass ofseeds produced. The number of seeds produced perplant is determined both by the absolute reproductivebiomass per plant and by the mean seed mass 1 ac-cessory costs (e.g., Shipley and Dion 1992, Aarssenand Jordan 2001, Henery and Westoby 2001). If ac-cessory costs are proportional to seed mass then theslope of the log-linear relationship between seed num-ber per unit reproductive biomass and seed mass isexpected to be 21. In the model, seed number dependsjointly on reproductive mass and seed mass. Althoughseed mass has been found to increase during secondarysuccessions (Baker 1972, Salisbury 1974, Fenner1987), a causal link has not been established; we there-fore allowed seed mass and field age to be freely cor-related (double-headed arrow). Reproductive phenol-ogy of the species is assumed to vary as successionproceeds (Swaine and Whitmore 1988, Kahmen andPoschlod 2004). The model predicts that the date offlowering and the date of seed maturation are subjectto differential filtering depending on successional in-dex. This suggests a successional variation in time forseeds to mature. A causal link between date of flow-ering and date of seed maturation was set since thesevariables are ordered in time. We hypothesized thatflowering date is also related to plant size and to seedmass. A negative relationship may link seed mass andflowering date since the development of big seeds mayrequire longer time and small wind-dispersed seedsneed to be released at sufficient height, which requiresthe production of a stalk and thus tends to delay flow-ering.

METHODS

Study area

We selected eight old fields in southern France(438519 N, 38569 E, 100–160 m above sea level) in asubhumid Mediterranean climate (Daget 1977). Theywere located within a 4 3 4 km area, on soils of similartexture and physico-chemical properties (brown cal-careous or calcic cambisol [FAO 1974]: pH [H2O] be-tween 8.1 and 8.6). These fields, previously cultivatedas vineyards, were abandoned 5–45 years previous toour study, after removal of the vines. Herbaceous spe-cies were dominant in all plots. None of the fields haveexperienced any major disturbance since their aban-donment. Further details are given in Garnier et al.(2004).

Selected species

We studied 34 herbaceous species consisting of 18annuals, two biennials, and 14 perennials (Table 1 andAppendix A), whose individual biomass represented atleast 80% of the maximum standing biomass of the

February 2006 507MODELING FUNCTIONAL STRATEGIES

TABLE 1. Species studied, abbreviation used, their botanical family and life span, and fieldage.

Species Abbreviation Family Life span Field age

Arenaria serpyllifolia As Caryophyllaceae A 3Avena barbata Ab Poaceae A 3Bromus madritensis Bm Poaceae A 3Convolvulus arvensis Cr Convolvulaceae P 3Conyza canadensis Cc Asteraceae A 3Conyza sumatrensis Cs Asteraceae A 3Crepis foetida Cf Asteraceae A 3Erodium ciconium Ec Geraniaceae A 3Geranium rotundifolium Gr Geraniaceae A 3Medicago lupulina Ml Fabaceae A 3Medicago minima Mm Fabaceae A 3Veronica persica Vp Scrophulariaceae A 3Vicia hybrida Vh Fabaceae A 3Vicia sativa Vs Fabaceae A 3

Calamintha nepeta Cn Lamiaceae P 10Cynodon dactylon Cd Poaceae P 10Dactylis glomerata Dg Poaceae P 10Daucus carota Dc Apiaceae B 10Dipsacus fullonum Df Dipsacaceae B 10Lolium multiflorum Lm Poaceae A 10Orlaya grandiflora Og Apiaceae A 10Picris hieracioides Ph Asteraceae P 10Sanguisorba minor Sm Rosaceae P 10Torilis japonica Tj Apiaceae A 10Tordylium maximum Tm Apiaceae A 10Trifolium angustifolium Ta Fabaceae A 10

Agrimonia eupatoria Ae Rosaceae P 25Aristolochia rotunda Ar Aristolochiaceae P 25Brachypodium phoenicoides Bp Poaceae P 25Bromus erectus Be Poaceae P 25Centaurea aspera Ca Asteraceae P 25Inula conyza Ic Asteraceae P 25Rubia peregrina Rp Rubiaceae P 25Sedum sediforme Ss Crassulaceae P 25

Notes: Nomenclature follows Tutin et al. (1993). Key to life-span abbreviations: A, annual,B, biennial, P, perennial. Field age, the time since field abandonment, is the median age (inyears) of old fields in which species most commonly occur. The study was conducted in southernFrance.

plant community present in each field. Based on theirabundance in these fields (Garnier et al. 2004) as wellas on knowledge about their usual position in FrenchMediterranean old-field successions (Braun-Blanquetet al. 1952, Escarre et al. 1983; M. Debussche, personalcommunication), these species were assigned to a spe-cific age of the successional sere (Table 1). These cor-respond to the early (0–6 yr; median 5 3 yr), inter-mediate (7–15 yr; median 5 10 yr), and advanced (15–45 yr; median 5 25 yr) stages of succession followingvineyard abandonment.

Measurements

For each species, 15 individuals were chosen at ran-dom in one of the eight fields and tagged. During thegrowing season of 2002, each individual was monitoredat 1–6 different dates depending on species, until thebeginning of seed maturation. At this time the above-ground parts of each plant were harvested. Becausesome species show indeterminate growth forms, someplants were harvested before all seeds had been pro-duced. In this case, plants were harvested once the first

seeds began to be dispersed, even if some reproductiveparts were not totally mature, in order to minimize theloss of reproductive material. This introduces an errorin the estimation of reproductive mass which is ex-plicitly included in the modeling procedure. At eachmonitoring period, including the final harvest, non-destructive estimates of vegetative (e.g., stem length,leaf number, or height) and reproductive (inflorescence,flower, fruit number, length) size were made. In addi-tion, maximum plant height (Hmax), including repro-ductive structures, was determined. Simultaneously, weperformed 1–4 destructive harvests, depending on spe-cies, of six randomly selected supplementary individ-uals per species. Aboveground parts of plants from thesequential intermediate harvests and the final harvestwere separated into the following groups: stems, greenand senescent leaves, and reproductive structures (in-cluding stalks, flowers, fruits, and seeds). Dry mass ofeach of these compartments was obtained by oven dry-ing for at least 48 h at 608C. Pre-reproductive vege-tative mass (Vm1), excluding any reproductive struc-tures, was determined from the first date of recording

508 DENIS VILE ET AL. Ecology, Vol. 87, No. 2

either by estimating vegetative biomass at the first re-cording based on nondestructive measures or by usingthe first harvest of supplementary individuals (see Ap-pendix B). Plant size at seed maturation was obtainedfrom the mass components of plant size at the time ofseed maturation; dry mass of the stems (Stm) andleaves (Lm) was determined separately, whereas re-productive structures were pooled together to estimatethe total reproductive mass (Rm).

The water-saturated specific leaf area (SLA) of eachspecies, defined as the ratio of leaf projected area todry mass, was determined following the standardizedprocedure described by Garnier et al. (2001). Most val-ues were obtained from measurements taken in May2000, with some additional data collected in the springof 2003 and 2004.

In the rare cases where all the seeds had reachedmaturity and none of the seeds had been disseminated,we counted the total seed number (Sn) produced perindividual during the growing season. Seeds were ex-tracted manually. In all other cases, seed productionwas estimated by the mean number of mature seedsproduced per infructescence multiplied by the numberof infructescences produced per individual. Mean in-dividual seed mass (Sm) was assessed by weightingfive groups of 10 seeds per species, except for Conyzacanadensis and C. sumatrensis, for which three andfour groups of 30 seeds were used, respectively.

For each species, the date of flowering was recordedwhen approximately 50% of the plants in the popula-tion displayed mature flowers. The date of seed mat-uration was the date at which approximately 50% ofthe plants in the population bore mature fruits. Thisdate corresponds mostly to the final harvest date of themonitored individuals.

Table 2 gives the complete list of the traits includedin the analyses.

Data analyses

Data were transformed (Table 2) as necessary toachieve linearity of the bivariate relationships and nor-mal distribution of the residuals. Those transformationsalso helped to satisfy the assumption of univariate aswell as multivariate normality. To characterize the mul-tivariate pattern of correlations, a principal componentanalysis (PCA) was performed on transformed data.Bivariate correlations completed this analysis.

Given the structural equation model (SEM, Fig. 1),it is possible to derive the predicted covariance betweenthe variables (Shipley 2000). Structural equation mod-eling then allows assessment of the degree of fit be-tween the observed and expected covariance structures,which is expressed as a goodness-of-fit chi-square sta-tistic. Assuming that the environment changes in a con-sistent way over time, and since our estimates of timesince field abandonment include error, we fixed the pathcoefficient from field age to successional index to onebut allowed for a nonzero error variance for field age.

This allows the latent successional index to be mea-sured in years following abandonment. The structuralmodels were estimated with the MPLUS program (Mu-then and Muthen 1998, 2003). The statistics of good-ness-of-fit usually used are asymptotically distributedas chi-squares under the assumption of multivariatenormality. Since our models include some dichotomousvariables (life span), the proper estimation techniqueis therefore a weighted (generalized) least squares anal-ysis (Muthen and Muthen 1998, 2003), which gener-alizes to probit regression in this case. The path co-efficients leading to a dichotomous variable are thenexpressed as probit regression coefficients and predictthe probability that a species will take a given value.The fit of the predicted covariance matrix to the samplecovariance matrix was evaluated using a robust cor-rection for means (WLSM) to take into account thenonnormal nature introduced by the dichotomous var-iable (Muthen and Muthen 1998, 2003), and MonteCarlo methods (Shipley 2000) were used to obtain theprobability values given the asymptotic nature of thischi-square statistic. A significant goodness-of-fit chi-square statistic indicates that the model does not fit thedata. Once a model has not been rejected and consid-ered as biologically and ecologically plausible, param-eter estimates can be used to study direct as well asindirect effects. Parameter estimates are tested for sig-nificance using z statistics. Two other indices of fit(comparative fit index [CFI] and root mean square errorof approximation [RMSEA]), which are often used inSEM, are reported to assess closeness of fit. Good mod-els have a RMSEA , 0.05 and a CFI . 0.95.

Rather than concentrating solely on the relationshipsbetween the variables (i.e., the covariances), we useda mean and covariance structure analysis (MEAN-STRUCTURE in the analysis command in MPLUS) tosimultaneously obtain parameter estimates and the in-tercepts of the relationships. This method allowed usto obtain the predicted means of the latent variables.The path coefficients as well as the intercepts were thenused to obtain prediction equations.

In order to visually assess the ability of the structuralequations to predict the pattern of covariation betweenthe endogenous variables (all variables with an arrowpointing to them) in the model, a principal componentanalysis was first performed on the complete set ofobserved values of all endogenous and exogenous var-iables (variables having no causal parent). The pre-dicted values were then used as additional observations(thus not included in calculations) in a PCA to compareobserved and predicted values of the endogenous traitson the first two PCA axes. Observed and predictedcoordinates on the first factors of the PCA were com-pared in linear regression analyses.

RESULTS

Bivariate relationships and principalcomponent analysis

Pearson correlations coefficients, variances and co-variances between pairs of variables, after transfor-

February 2006 509MODELING FUNCTIONAL STRATEGIES

TABLE 2. Definition of abbreviations, units, transformations, and range value (untransformed) of the variables.

Abbreviation Definition Units Transformation Range

Field age time since field abandonment yr 3, 10 or 25Life span life span (0 5 annual or biennial, 1 5 perennial) 0 or 1

Vegetative traitsVm1 vegetative mass at first recording (see Appendix B) g log 0.07–9Stm stem mass at first seed dispersal g log 0.04–13Lm leaf mass at first seed dispersal g log 0.02–11.4SLA specific leaf area m2/kg 5–39

Reproductive traitsHmax maximum (reproductive) height cm square root 8.8–130Rm reproductive mass at first seed dispersal g log 0.017–10.04Sn no. seeds produced per individual per year log 2–36 000Sm mean individual seed mass mg log 0.041–71.4

PhenologyFlowdate flowering date of ;50% of plants in the population day of year 59–220Smatdate date of seed maturation of ;50% of plants in the population day of year 110–296

Note: All masses are dry masses.

mation, and their corresponding significance levels aregiven in Table 3. Appendix C provides a scatterplotmatrix of the variables.

The first, second, and third axes represent 45%, 20%,and 15%, respectively, of the variation in the data ofthe principal component analysis computed with all theobserved variables (Fig. 2); loadings of each variableon these three axes are given in Table 4. Exclusion oflife span, which is binary, did not change the inter-pretation of the axes (not shown). All size-related var-iables are highly correlated (see also Table 3) and con-tribute, along with the date of flowering and of seedmaturation, to most of the first factor variance. Thefirst factor is therefore essentially an axis of increasingplant size and later flowering and seed maturation. Thenumber of seeds produced per plant (Sn) contributessignificantly to the second axis loading (Table 4), asdo field age and life span. Although the mean seedmass (Sm) loads most strongly onto the third factor(Table 4), Sn and Sm appear negatively correlated inthe first plane (Table 3). The second axis thus contrastsshort-lived species with high reproductive biomass thatproduce many small seeds in early succession with spe-cies from later succession that have longer life spanand produce bigger but less numerous seeds. In addi-tion, specific leaf area (SLA), although not very wellrepresented in the first plane, was significantly and neg-atively correlated to the components of plant size andlate phenology (Table 3; Fig. 2a). Specific leaf areawas negatively correlated to field age but almost or-thogonal to the axis formed by Sn, Rm, and Sm. Fig.2b represents the projection of the species on the firsttwo axes. The species form relatively homogeneousgroups according to successional index, along withtheir life span. Inside each group, a transverse gradientis clearly marked from small species producing rela-tively bigger seeds and flowering early in the season(e.g., Bromus madritensis, Medicago minima) to largerspecies producing numerous smaller seeds, flowering

and maturating their seeds late (e.g., Conyza sp., Inulaconyza, Dipsacus fullonum).

The SEM models

The first hypothesized model (Fig. 1) provided agood fit to the data (chi-square 5 50.43, df 5 48, P 50.378, CFI 5 0.983, RMSEA 5 0.039). However, thefree covariance between seed mass and field age (P 50.514) and the paths from the latent successional indexto date of flowering (P 5 0.130) and date of seed mat-uration (P 5 0.309) and from the latent plant size toflowering date (P 5 0.092) were not significantly dif-ferent from zero. We therefore modified this model(Fig. 3) by removing these nonsignificant paths andadding a new direct effect from maximum plant heightto flowering date. Due to developmental constraints onpollination or seed dispersal (see Discussion), flower-ing date was expected to be related to height ratherthan to the overall size of the plant. This modifiedmodel (Fig. 3) also provided a very good fit to the data(chi-square 5 43.43, df 5 50, P 5 0.733, CFI 5 1.0,RMSEA , 1024). Although the path from successionalindex to flowering date was still not significantly dif-ferent from zero (P 5 0.130) we kept this path in sub-sequent models and predictions because when flow-ering date was regressed on field age, height, and seedmass, the partial multiple regression coefficient of suc-cessional index was significantly (P , 0.05) differentfrom zero. All the remaining paths were significant.Parameter estimates and their respective standard error(SE) are given in Appendix D.

Allometry

The components of plant size were all significantlycorrelated. To compare the allometric coefficients ob-served in our study with those predicted by allometrytheory we reran the model in Fig. 3 using log-trans-formed values of plant height. The new model provideda comparable fit to the data, and all the paths unrelated

510 DENIS VILE ET AL. Ecology, Vol. 87, No. 2

TABLE 3. Pearson’s correlations (below diagonal), variances (diagonal; bold type), and covariances (above diagonal; initalics).

Trait Field age Life span Vm1 Stm Lm Hmax

Field age 74.90 3.15 1.86 1.30 1.21 6.73Life span 0.73*** 0.25 0.07 0.05 0.08 0.12Vm1 0.42* 0.25 0.27 0.26 0.27 0.98Stm 0.27 0.18 0.89*** 0.32 0.26 1.04Lm 0.19 0.25 0.70*** 0.62*** 0.54 0.92Hmax 0.35* 0.11 0.86*** 0.83*** 0.56*** 4.90Rm 0.06 20.31† 0.57*** 0.69*** 0.39* 0.61***Sn 20.22 20.33† 0.34† 0.50** 0.01 0.40*Sm 0.20 0.06 0.05 20.11 0.23 20.10SLA 20.60*** 20.42* 20.48** 20.40* 20.19 20.45**Flowdate 0.38* 0.34* 0.63*** 0.61*** 0.21 0.69***Smatdate 0.48** 0.46*** 0.50** 0.55*** 0.14 0.60***

Note: N 5 34 species. See Table 2 for explanations of trait abbreviations.* P , 0.05; ** P , 0.01; *** P , 0.001; † P , 0.10.

to plant height did not differ from Fig. 3. Our modelproduced an estimate of the scaling exponent betweenleaf mass and stem mass of 0.74 6 0.35 (95% CI), i.e.,Lm } Stm0.74. The new path coefficient from plant sizeto height was 0.50 6 0.21 (95% CI), i.e., Hmax } Plantsize0.50, while the path coefficient from plant size toleaf mass was 0.74. The value of the scaling exponentbetween leaf mass and height can thus be derived as0.74/0.50 5 1.47 6 0.61 (95% CI). For the relationshipbetween stem mass (Stm) and height (H), we foundthat Stm } Hmax1/0.5051.9960.59.

Comparison of SEM and PCA

The principal components of the PCA describe thedominant multivariate patterns of covariation betweenthe traits without imposing any structure of cause–ef-fect relationships (Fig. 2). Since no structure is im-posed, no hypotheses concerning this structure can betested. The SEM attempts to describe the same mul-tivariate patterns between traits conditional on a spe-cific ordering of structural relationships that are in-ferred from explicit biological hypotheses. If the SEMsucceeds in both capturing the actual structural con-straints in the empirical data and in providing goodpredictive ability, then the predicted values of each traitfor each species, when projected onto the PCA axes,should closely mirror the actual values.

We obtained the predicted values from the SEM ofeach trait in two ways. First, we used the actual valuesof the exogenous variables (field age and seed mass inFig. 3) to predict values of all other variables given inthe structural equations. Second, we used the two ex-ogenous variables plus vegetative biomass (Vm1) togenerate predicted values of the remaining variables.While the path coefficient between the latent succes-sional index and Vm1 was significant (P 5 0.031), wegenerated this second set of predicted values since therelationship was weak and only explained 30% of var-iation in Vm1 (Fig. 3) and the plant size componentshad a strong loading on the first PCA axis (Table 4;Fig. 2a). In order not to bias our comparison we con-

ducted a second PCA using only the actual values ofthe same variables and plotted the position of eachspecies onto the first two PCA axes. This was doneusing both all the variables excepting field age and seedmass (PCA 2), and field age, seed mass, and Vm1 (PCA3). The loading of each variable on the three first axesof the two corresponding princpal components analysesis given in Table 4 (PCA 2 and PCA 3). We next cal-culated the position of each species on the two PCAaxes using only the predicted values of each trait. Fig.4 plots the actual and predicted position of each specieson the first two PCA axes (Fig. 4a, predictors 5 Fieldage and Sm; Fig. 4b, predictors 5 Field age, Sm, andVm1).

In Fig. 4a, the predicted values deviate from the ob-served ones mainly along the first axis while deviationalong the second axis is generally low. In Fig. 4b thepredicted values are closer to the observed ones alongthe two first axes. This is confirmed when observedPCA scores are regressed on predicted scores. Only22% of the variation in the actual PCA scores of thefirst axis is explained using only two predictors (Fieldage and Sm), while 79% is explained with three pre-dictors (Vm1 added). However, an equivalent amountof variation in the PCA scores of the second (R2 5 0.68and R2 5 0.72, respectively) and the third axes (R2 50.49 and R2 5 0.42) is explained using only two orthree exogenous variables. The loadings for PCA 2 andPCA 3 are almost equivalent to those of PCA 1 (Table4).

DISCUSSION

Interpreting structural equations as plant strategies

Grime (1979:1, 2001:ix) defined a plant strategy asa ‘‘[grouping] of similar or analogous genetic char-acteristics which recur widely among species or pop-ulations and cause them to exhibit similarities in ecol-ogy.’’ However, as pointed out in the introduction, anexplicit hypothesis (model) of a plant strategy mustspecify how the various traits are structured within a

February 2006 511MODELING FUNCTIONAL STRATEGIES

TABLE 3. Extended.

Rm Sn Sm SLA Flowdate Smatdate

0.28 22.02 1.57 238.3 123 19420.09 20.17 0.03 21.54 6.29 10.54

0.17 0.18 0.02 21.82 12.1 12.00.23 0.29 20.06 21.68 12.7 14.30.17 0.01 0.15 21.01 5.77 4.740.79 0.92 20.19 27.31 56.9 60.90.34 0.31 0.04 21.12 5.75 4.490.50** 1.10 20.60 0.61 13.8 13.20.08 20.65*** 0.79 20.54 212.8 215.9

20.26 0.08 20.08 54.6 2127 21480.27 0.36* 20.39* 20.46** 1381 14740.17 0.27 20.39* 20.43** 0.86*** 2133

nexus of interdependences and/or independences andhow selection by the external environment generatesthe observed patterns of phenotypic correlation. In thisstudy we used structural equation modeling to quantifythe notion of an establishment strategy during second-ary succession for herbaceous species. Our model hasjust two forcing (exogenous) variables: time since thelast disturbance and mean individual seed mass. Allother predicted traits values are determined by thesetwo forcing variables and the cause–effect linkages be-tween them. The resulting plant strategy is the set ofdirect and indirect relationships shown and quantifiedin Fig. 3.

The different phenotypic ‘‘solutions’’ allowed bythis strategy are the different predicted phenotypes thatshould occur during the type of secondary successionstudied here. The different phenotypes that are pre-dicted represent the phenotypic ‘‘selections’’ made bythe environment during the succession. The deviationof each species from this predicted phenotype is quan-tified by the error variables in Fig. 3. Multiple causescan be envisaged to explain the deviations from thegeneral strategy, including selective pressures not re-lated to the systematic trend in the environment duringsecondary succession, stochastic variation, or phylo-genetic constraints. For instance, vegetative mass wasonly weakly related to successional index (R2 5 0.30).This, combined with the fact that mean individual seedsize was independent of successional index and thatlifespan was only moderately related to successionalindex (R2 5 0.66), suggests the possibility that recur-ring small-scale disturbances may be a secondary se-lective force. This could explain why the predicted val-ues from the SEM agreed better with the results of thePCA when the actual values of pre-reproductive veg-etative mass were used rather than the predicted values.Nonetheless, this model is mostly consistent with clas-sical strategy theories (MacArthur and Wilson 1967,Odum 1969, Gadgil and Solbrig 1972, Grime 1979)and previous empirical studies (e.g., Bazzaz 1979,Prach et al. 1997). As in any statistical test, the powerto reject an hypothesis depends both on effect sizes andsample size. Despite the fact that our study had more

species than most studies in this field, we still hadrelatively few species in terms of the statistical test.Although our statistical power was sufficient to rejectother preliminary models (not shown), our acceptanceof the present model is only provisional and clearlyrequires further study.

Succession and strategy variation

As expected, life form varied in a consistent manner(Huston and Smith 1987, Pickett et al. 1987a, b; seeEscarre et al. [1983] and Bonet and Pausas [2004] forMediterranean ecosystems). Short-lived species (an-nuals) are found in early stages of succession and areprogressively replaced by species with longer life spans(perennials). According to our model, the probabilityof a species being a perennial in the youngest fields (3yr) is 0.30, reaches 0.50 approximately 10 yr after aban-donment, and reaches 0.88 in the oldest fields (25 yr).Annual and perennial species are however found inmixture in intermediate stages.

In addition, we found that the species that dominatein such intermediate stages exhibit a suite of traits dif-ferent from those that dominate in the earliest and lateststages of succession. This is particularly the case forspecific leaf area and investment in sexual reproduc-tion.

Specific leaf area (SLA) was significantly and neg-atively correlated with field age, vegetative compo-nents of plant size and phenology, but not with repro-ductive mass, seed mass, and seed number. Our modelsuggests that most of these significant correlations arespurious and due to the association between SLA andsuccessional change; fast-growing species with short-lived leaves that both acquire and lose resources rapidlywhen competition is low in early successional stagesare replaced by slow growing ones, investing more inperennial structures allowing greater payback to initialconstruction costs (cf. Weiher et al. 1999, Westoby etal. 2002; see also Gleeson and Tilman 1994, Llambi etal. 2003, Garnier et al. 2004).

The components of plant size were all correlated,reflecting the allometric relationships between the dif-ferent parts of the plants (Niklas 1994; see Allometry).

512 DENIS VILE ET AL. Ecology, Vol. 87, No. 2

FIG. 2. Principal component analysis based on values ofthe variables included in the model in Fig. 1. Only the firsttwo axes, which account for 64% of the total inertia, areshown here. (a) Representation of the variables (see Table 2for abbreviations and Table 4 [PCA 1] for exact loadings ofeach variable). (b) Representation of the 34 species, char-acteristic of early (3 yr; squares), intermediate (10 yr; tri-angles), and advanced (25 yr; circles) successional herba-ceous stages, on which measurement were made (see Table1 for plant name abbreviations).

Pre-reproductive vegetative mass (Vm1) and maximumheight were the only components of plant size that weresignificantly related to time since field abandonment(Table 3) (see also Budowski 1970, Prach et al. 1997),probably as a result of an increase in competition forlight during succession and the selective advantage tobeing taller than neighbors. Trade-offs, such as respi-ration costs due to support structures or hydraulic con-

straints, whose understanding involves the strategies ofthe neighboring competitors, may also influence thispattern (Westoby et al. 2002, Falster and Westoby2003). Particularly when comparing herbaceous spe-cies, vegetative and reproductive height should be dif-ferentiated. Here we dealt with maximum plant heightthat, in herbaceous species, is often reached in the re-productive phase with the development of a floweringstalk. This overtopping strategy not only favors accessto light, but also may be an issue in reproductive bi-ology by enhancing pollination and/or dispersal effi-ciency (Waller 1988, Verbeek and Boasson 1995, Lortieand Aarssen 1999, Soons et al. 2004). Soons et al.(2004) have recently demonstrated that plant height isan important trait controlling seed dispersal in grass-lands. The importance of a tall release height in seeddispersal and high position of flowering structures par-ticipate in the large investment of many grassland plantspecies, especially rosette plants, in stalk length (Baz-zaz et al. 2000).

Seed production depends on the size of the repro-ductive system and the amount of energy invested inreproduction. The number of seeds produced (Sn) isequal to the absolute biomass devoted to reproduction(Rm) divided by mean individual seed mass (Sm) plusaccessory costs per seed, where accessory costs includefruit structures, dispersal structures, and early abortedseeds (Westoby et al. 2002). Controlling for Sm plusaccessory costs, Sn is thus predicted to be directly re-lated to Rm with an allometric slope of 1 (0.99 6 0.36in Fig. 3). Controlling for Rm, Sm is predicted to berelated to Sn with an allometric slope of 21 only ifthere is a proportional biomass allocation to seeds andseed accessory structures; the actual allometric slopein our study was 20.71 6 0.16 (Fig. 3). Therefore,although this estimate is not significantly different from21 (ty532 5 1.81, P 5 0.08), it is possible that specieswith larger seeds have a proportionally greater allo-cation to accessory structures. These results are inagreement with the multiple regression model of Shi-pley and Dion (1992): log(Sn) 5 0.93 log(above groundvegetative biomass) 2 0.78 log(Sm); R2 5 0.72. Neg-ative relationships between seed number (per squaremeter of canopy or per biomass) and seed size (mass)have been previously found (Bazzaz 1979, Aarssen andTaylor 1992, Aarssen and Jordan 2001, Henery andWestoby 2001, Moles and Westoby 2002, Moles et al.2004).

The success of a plant species in a particular envi-ronment greatly depends on the timing of its life historyevents, which may be under biotic as well as abioticselective pressures (e.g., Bishop and Schemske 1998,reviewed by Primack 1985, Rathcke and Lacey 1985,Fenner 1998). Flowering phenology within floras hasalso been suggested to be mostly driven by phyloge-netic constraints (Kochmer and Handel 1986). Thestaggering of timing of flowering and seed maturationfound in our study is consistent with the phenological

February 2006 513MODELING FUNCTIONAL STRATEGIES

TABLE 4. Loading of the variables on the three first axes of three principal component analyses (PCA).

Variable

PCA 1

Factor 1(44%)

Factor 2(20%)

Factor 3(15%)

PCA 2

Factor 1(50%)

Factor 2(19%)

Factor 3(12%)

PCA 3

Factor 1(47%)

Factor 2(21%)

Factor 3(13%)

Field age 20.523 20.705 20.079Life span 20.356 20.780 20.263 20.273 20.849 0.126 20.274 20.848 0.124Vm1 20.913 0.030 0.270 20.925 0.040 0.235Stm 20.905 0.219 0.182 20.931 0.169 0.097 20.917 0.180 0.156Lm 20.574 20.044 0.569 20.599 0.074 0.690 20.550 0.071 0.724Hmax 20.904 0.155 0.131 20.919 0.107 0.035 20.912 0.119 0.096Rm 20.587 0.462 0.442 20.637 0.594 0.106 20.632 0.603 0.180Sn 20.402 0.785 20.270 20.447 0.596 20.516 20.467 0.610 20.485Sm 0.151 20.483 0.772SLA 0.600 0.430 0.023 0.558 0.440 20.075 0.567 0.432 20.128Flowdate 20.806 20.001 20.434 20.790 20.276 20.425 20.818 20.258 20.379Smatdate 20.747 20.128 20.525 20.712 20.403 20.464 20.753 20.385 20.415

Notes: PCA 1 is based on the complete set of variables of the model in Fig. 1 (or Fig. 3). The position of the variablesand the species on the two first axes are shown in Fig. 2. In PCA 2, the two exogenous variables of the model in Fig. 3,time since field abandonment (field age) and mean individual seed mass (Sm), were excluded. The position of the specieson the two first axes is shown in Fig. 4a. In PCA 3, the two preceding variables plus vegetative mass (Vm1) were excluded.The position of the species on the two first axes is shown in Fig. 4b. The percentage of total inertia accounted for by eachaxis appears in parentheses. See Table 2 for explanations of variable abbreviations.

structure of many herbaceous and woody plant com-munities (Bosch et al. 1997, Smith-Ramirez et al. 1998,Ramirez 2002, Osada et al. 2003, Tebar et al. 2004).As predicted, date of flowering and seed maturationtime were highly correlated (r 5 0.86), certainly mostlydue to their time-ordering constraint.

Maximum plant height, seed mass, and, marginally,successional index, seem to constrain flowering date.Successional index has only a marginally significantdirect effect and has a size-mediated indirect effect (seeFig. 3). Kahmen and Poschlod (2004) found a signif-icant increase in flowering date following agriculturalabandonment in a grassland succession, which wasseen as a consequence of the release of grazing con-straints. Maximum plant height appears to be a deter-minant of flowering date; this may be indicative of anovertopping strategy in which high individuals gainadvantage among neighbors. Moreover, if plants pro-ducing flowering stalks need a longer period of growthbefore producing flowers than plants producing flowersnearer to the ground, it is not surprising to observe apositive relationship between maximum plant heightand flowering date.

The negative relationship between seed mass andflowering date is not easy to interpret but is consistentwith a reanalysis of the data set from Debussche et al.(2004), in which we found a highly significant negativerelation between seed mass and start of flowering anda positive relation between seed mass and ripeningtime. Primack (1987) predicted that species with largerfruits should have longer ripening periods and shouldtherefore flower earlier than species with smaller fruits.If the time needed to mature seeds is limiting and iflarger seeds are produced by larger fruits, then a greaterseed mass would result in early flowering (Primack1987). However, since seed mass alone only explains15% of variation in flowering date and since seed mass

was not related to time for seeds to mature (P . 0.2),the predictions of Primack are only weakly supported.However, we cannot exclude the presence of phylo-genetic constraints in the above relationships. For ex-ample, rosette-like Asteraceae produce high floweringstalks, small wind-dispersed seeds, and tend to flowerlater in the season, which is consistent with Kochmerand Handel (1986). Although phenological patterns ina community can also be influenced by climatic vari-ations from year to year (Morales et al. 2005), thepattern reported here appears robust to yearly fluctu-ations: a tight consistency was found in the temporalsequence of flowering between years 2000 and 2002(R2 5 0.85; N 5 18 species; A. Bellmann, unpublisheddata [from 2000] obtained in the same old fields). Amodel in which date of seed maturation had an effecton flowering date was rejected by the data (P , 0.001).

Seed mass has been found to increase with succes-sion (Baker 1972, Salisbury 1974, Fenner 1987), andthis has been explained in part by the relatively greatercapacity of big seeds to face hazards (Leishman et al.2000), in particular shade (reviewed in Poorter andRose 2005), and the requirement for many small seedsto increase the probability of dispersal to new disturbedhabitats. This was not observed in our study; the sameresult has been observed in other studies on herbaceousspecies conducted in old fields in the same climaticregion (Lavorel et al. 1998, 1999; E. Garnier, A. Bell-mann, M.-L. Navas, C. Roumet, and G. Laurent, un-published manuscript).

Allometry

The path coefficients relating plant size componentswere all significant with values close to those predictedby allometry theory (West et al. 1999) and observedin other studies (e.g., Niklas 2003). For instance, En-quist and Niklas (2002) have analytically shown that

514 DENIS VILE ET AL. Ecology, Vol. 87, No. 2

FIG. 3. Structural equation model derived from the model in Fig. 1. Goodness-of-fit statistics are: chi-square 5 43.43,df 5 50, P 5 0.733, comparative fit index (CFI) 5 1.0, root mean square error of approximation (RMSEA) , 1024. Namesand abbreviations of observed variables follow Table 2. Path coefficients between variables are unstandardized partial re-gression coefficients. Arrow widths are proportional to the standardized path coefficient. Intercept values and part of thevariances explained by the model (R2) are given under the variable names. Arrows not originating from a variable representresidual error variables and are the effects of unexplained causes. Note that field age and mean individual seed mass are twoexogenous variables (no arrow pointing to them).

leaf mass is predicted to scale as the 3/4 power of stemmass, i.e., Lm } Stm0.75 while our model produced Lm} Stm0.74. In species with self-supporting stems, Niklas(2003) reported a coefficient of 1.65 6 0.13 (mean 695% CI) for the scaling exponent between leaf massand height, after back transformation of the Model IIcoefficient to least square coefficient; our model pro-duced an estimate of the scaling exponent of 1.47 60.61. We found that Stm } H1.9960.59, while Niklas re-

ported an ordinary least-squares (OLS) scaling expo-nent of 2.49 6 0.13 (95% CI). The scaling exponentsare not significantly different (t test, P . 0.77 and P. 0.40, respectively).

Our model therefore provides support for allometricscaling theory even though our approach is completelyindependent. The deviations may be due to the differentgrowth forms considered in the data sets (mostly woodyspecies with self-supporting stems vs. herbaceous) and

February 2006 515MODELING FUNCTIONAL STRATEGIES

FIG. 4. Two principal component analyses showing ob-served (solid symbols) and predicted (open symbols) valuesfor 34 species characteristic of early (3 yr; squares), inter-mediate (10 yr; triangles), and advanced (25 yr; circles) suc-cessional herbaceous stages. Predicted values were obtainedusing observed values of (a) the two exogenous variables ofthe model in Fig. 3, age since field abandonment (Field age)and mean individual seed mass (Sm); and (b) the two precedingvariables plus vegetative biomass (Vm1). Prediction equationsare derived from the structural equations of the model in Fig.3. Predictors are excluded from analyses, and predicted valuesare treated as supplementary. Loadings of the variables on thethree first axes are given in Table 4, PCA 2 and PCA 3. Thepercentage of total inertia accounted for by each axis is givenin parentheses. Actual and predicted values are linked by a line.

caution should be taken however due to the wide con-fidence intervals on the coefficients.

Reproductive mass was isometrically related to plantsize when statistically controlling for life span. More-

over, controlling for plant size, perennials allocate lessthan annuals in reproductive mass, thus indicating asignificantly higher reproductive allocation, expressedin terms of reproductive mass per unit plant mass, inshort-lived than in long-lived species, and in early suc-cessional species (e.g., Wilson and Thompson 1989).This is in agreement with shifts in allocations in re-sponse to habitat closure (Newell and Tramer 1978,Abrahamson 1979).

In conclusion, our results show that it is possible toexpress the notion of a plant strategy in a form that isquantitative, predictive, and testable. Doing so revealedsurprising links to theoretical work on plant allometryand allows this allometric theory to be embedded inan ecological context. Whether this model holds overa longer successional sequence, during which the traitsof woody species could be influential, remains to betested. Undoubtedly this model could be improved byexplicitly including the physical attributes of the en-vironment and traits related to seedling regeneration.

ACKNOWLEDGMENTS

The authors thank G. Laurent, J.-M. Lalonde, S. Metge, C.Jolibert, and C. Prouzet for field and laboratory assistanceand A. Moles, C. Violle, R. Gros, I. Hummel, X. Morin, E.Kazakou, and J. Thompson for valuable and challenging com-ments on previous versions of the manuscript. This researchwas financially supported by the Natural Sciences and En-gineering Research Council of Canada (NSERC), by a Grad-uate Award of the Universite de Sherbrooke to D. Vile andby the EU ‘‘VISTA’’ (Vulnerability of Ecosystem Services toLand Use Change in Traditional Agricultural Landscapes)program (contract number EVK2-2001-000356). This is apublication from GDR 2574 ‘‘UTILITERRES’’ (CNRS-France).

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APPENDIX A

Mean trait values of the 34 species (Ecological Archives E087-028-A1).

APPENDIX B

Estimation equations for pre-reproductive vegetative biomass (Ecological Archives E087-028-A2).

APPENDIX C

Scatterplots and coefficients of correlation between the traits under study (Ecological Archives E087-028-A3).

APPENDIX D

Unstandardized path coefficients and intercepts of the structural equations (Ecological Archives E087-028-A4).