EQUILIBRIUM MODELING OF ALPINE PLANT DISTRIBUTION : HOW ...

EQUILIBRIUM MODELING OF ALPINE PLANT DISTRIBUTION : HOW FAR CAN WE GO ? Antoine Guisan & Jean-Paul Theurillat Abstract. Predictive distribution modeling of species and communities has gained much importance in recent years. In this paper, generalized linear models (GLM) are implemented in a Geographical Information System to mimic the spatial distribution of alpine and subalpine species’ habitat and diversity in the study area of Belalp (Aletsch region, Wallis, Swiss Alps). Quantitative predictors used to quantify environmental requirements of species are: annual mean temperature, slope angle, topographic position, solar radiation, snow cover indices and the three spectral bands of a color infrared aerial photograph, as well as disjunctive classes of qualitative substrate-related predictors. Presence-absence logistic GLM are adjusted for 63 species. Percent ground cover measured on an ordinal scale is additionally modeled using a special case of GLM for 26 species with significant variation of abundance in the field. Both ordinal abundance and presence/absence at each spatial location are successfully modeled for some species, as shown by quantitative evaluation using an independent data set. Finally, species richness (SR) is modeled by (i) using a Poisson GLM and (ii) summing up single species predictions by presence/absence models. Successful models are finally used to mimic potential impact of climatic change on plant distribution and diversity. Results from these scenarios suggest (i) an overall trend toward a reduction of suitable habitat for alpine species and (ii) two different responses for the distribution of SR, namely: (a) a serious shift of the optimal SR elevation belt upward in elevation or (b) the SR optimal belt shifting only slightly upward in elevation, accompanied by a parallel spatial spread out of high SR patches at these elevations. Limitations of both species and diversity models are discussed and some suggestions for future research are proposed. Key-words: Species distribution, generalized linear model, logistic regression, ordinal abundance, species richness, remote sensing, geographical information system, climate change, impact scenarios, Swiss Alps. Nomenclature: Aeschimann & Heitz (1996)

1

Introduction

One of the on-going debates in ecology has been to ascertain whether or not natural systems are in equilibrium with their direct environment (e.g. BAZZAZ 1996). Vegetation was classified early on by using the fundamental environmental parameters which determine a particular type of equilibrium, or climax. Climatic climax is e.g. reached when climate is the key determinant, whereas edaphic climax occurs when soil parameters are the driving factors (e.g. MUELLERDOMBOIS & ELLENBERG 1974). One question frequently raised is to know if climatic climax vegetation is truly in equilibrium with climate. Scale and time resolution are two parameters that need to be determined as a prelude to any such discussion, as a phenomenon that can be seen as stationary on a given temporal scale would be perceived to be in permanent evolution when studied over a longer time scale (GRAHAM & GRIME 1990, THEURILLAT et al. 1998). As a basic postulate, however, a relative equilibrium can be assumed for a given period of time and for a given level of variation. As a result, one can only describe a relationship between species or communities and their environment (e.g. climate) in this limited time frame, which can give rise to such problems as: (i) analyzing data sets which integrate observations that have been sampled over a very long period of time, thus possibly implying that different equilibria have been reached for each successive phase (BUCKLEY 1982), and (ii) considering possible alternative equilibria, depending on the sequence of arrival of the various species (ROUGHGARDEN 1989, DRAKE 1991). Predictive modeling of species and communities distribution (see e.g. GUISAN et al. 1998, 1999; ZIMMERMANN & KIENAST 1999; or GUISAN & ZIMMERMANN (in press) for a review) is one field of ecology which relies entirely on the postulate of such an environmental (pseudo-)equilibrium between the biotic entities and the physical characteristics of their environment. For this reason, it has sometimes been subject to criticism (e.g. WOODWARD & BEERLING 1997). A central argument against such static models is the missing time dimension. Dynamic modeling of vegetation succession is often cited as an alternative which is not constrained in this way, although it is recognized that it can have certain limitations such as the lack of spatial dimension (LISCHKE et al. 1998, GUISAN & ZIMMERMANN in press) or drawbacks in parameterization (LOEHLE 1998). Another criticism is that it is difficult to include competition and other biotic interactions in these models in a controlled way. In fact, these interactions are intrinsically, but indirectly, integrated into the models, by modifying the fundamental responses of species (i.e. physiological) into more empirical responses (defining the realized niche; see AUSTIN et al. 1990, BAZZAZ 1996). It can be argued that some dynamic models incorporate such biotic relationships in a more realistic way. However, both approaches suffer the same limitations when predictions have to be made for future environmental conditions under which all present species’ relationships may have changed. This is borne out by many palaeoecological investigations describing responses of species in the past as individualistic and concluding that if climate changes significantly, the species composition of communities will probably be rather different from those described today (e.g. HUNTLEY 1991, THEURILLAT et al. 1998). Despite all these criticisms, static modeling has taken on much importance in recent years (see GUISAN & ZIMMERMANN, in press). Some applications of these models, and their projections, have proved very useful when discussed in the correct ecological context and when the main limitations to modeling are identified prior to the modeling itself. For instance, recent papers show the strength of static modeling for testing biogeographic hypotheses (e.g. BIRKS 1996, MOURELL & EZCURRA 1996, LEATHWICK 1998), for exploring possible response of species (LISCHKE et al. 1998, GUISAN & THEURILLAT in rev.) or communities (BRZEZIECKI et al. 1995, KIENAST et al. 1996) to climatic change, or for suggesting new

sampling sites in conservation issues (e.g. for discovering new sites for rare species; GUISAN unpubl.). Furthermore, instead of contrasting them, it would seem to be a more promising procedure to combine static and dynamic models in order to provide spatio-temporal models of plant and animal distribution (see e.g. SOLOMON & LEEMANS 1990). Generalized Linear Modeling (GLMs; MCCULLAGH & NELDER 1983) is one statistical technique which proved especially successful in many previous ecological studies (e.g. NICHOLLS 1989, AUSTIN et al. 1990, AUSTIN 1992, LENIHAN 1993, LEHMANN et al. 1994, BROWN 1994, HEIKKINEN 1996, FRANKLIN 1998, GUISAN et al. 1998, 1999, ZIMMERMANN 1996, ZIMMERMANN & KIENAST 1999). Furthermore, GLMs are fairly easy to implement for many species at once in a Geographical Information System (GIS; GUISAN et al. 1999). Generalized Additive Models (GAMs), through their non-parametric adjustment of response curves (smoothing techniques), are a popular modeling alternative (as used e.g. by YEE & MITCHELL 1991, AUSTIN & MEYERS 1996, BIO et al. 1998, LEHMANN 1998, LEATHWICK 1998), although more difficult to implement in a GIS and to interpret. Thus, they are often used to explore the possible shape of environmental responses (e.g. BROWN 1994, FRANKLIN 1998). Other techniques commonly used in the field of distribution modeling are classification and regression trees (CART; e.g. MOORE et al. 1991, LEES & RITMAN 1991, GUISAN 1997), canonical correspondence analysis (CCA; e.g. HILL 1991, BIRKS 1996, GOTTFRIED et al. 1998, GUISAN et al. 1999), artificial neural networks (ANN; e.g. FITZGERALD & LEES 1992, TAN & SMEINS 1994, LEK et al. 1996), Bayesian classifiers (BC; e.g. SKIDMORE 1989, FISCHER 1990, 1994, ASPINALL 1992, BRZEZIECKI et al. 1993) or environmental envelopes (e.g. BUSBY 1991, CARPENTER et al. 1993, SHAO & HALPIN 1995). Few of these modeling studies have been applied to predict the distribution of species or communities in an alpine landscape, where a high resolution is needed to obtain reliable results (see GUISAN et al. 1998, ZIMMERMANN & KIENAST 1999). However, much has been published about relevant factors with respect to plant ecophysiology and vegetation patterning in an alpine environment (e.g. BILLINGS & MOONEY 1968, LARCHER 1980, OZENDA 1985, CHAPIN & KÖRNER 1995, GUISAN et al. 1995, THEURILLAT et al. 1998, KÖRNER 1999). The first aim of our study was therefore to set up models for the spatial distribution of plant species and species' richness in an alpine landscape, using environmental data at the 25-m resolution of the countrywide Swiss digital elevation model. The second aim was to examine the overall applicability of such equilibrium models for ecological investigations and conservation issues. In particular, in the context of the effect of climate change on mountain ecosystems. We propose answers based on case studies of species and diversity modeling in a small alpine catchment of the Swiss Alps.

2

Methods

Study Area The study area of Belalp is a wide, open, north-south oriented side valley of the Rhone valley, located in the Aletsch region (Valais, Switzerland; figure 1). Elevation ranges between 1867 m and 3554 m. Geology is mainly siliceous (gneiss, granite). The climate is of a subcontinental type and soils are mostly of a podzolic type. The upper subalpine vegetation is mainly dominated by mesophilous heaths, swards, and fens. The alpine vegetation belt ranges from 2300 m to 3000 m and is dominated by low heaths, swards, and snowbed communities. The landscape has been modified by human activity for centuries

through intensive grazing by cattle, sheep and goats, with a resultant lowering of the timberline by several hundred meters. At present grazing is extensive. Species data Two species data sets were used in this study. A data set of 205 points quadrat was used for calibrating the models. It was sampled by visiting every intersection point of a 250 m x 250 m grid overlaying the whole study area. Spatial autocorrelation is avoided (FISCHER 1994) on this sampling scale, which greatly simplifies model calibration. A second data set, consisting of 92 points quadrat sampled randomly on a finer 25 x 25 m grid, was used as a second step to evaluate the models. In the field, sampling points were localized with a GPS navigator, a map accurate to a scale of 1:10’000 and a Thommen altimeter. An exhaustive list of observed plant species was made at each point on a 4 m2 square surface, and a cover abundance value within the square was attributed to each (using the BARKMAN et al. 1964 scale). Abundancedominance values were later re-coded into a simplified cover density measure, on an ordinal scale. The new density scale ranks classes 0 to 5 which correspond respectively to: no cover (0%), 1-5 %, 5-12,5 %, 12,5-25 % and 50-100% ground cover. The 4 m2 size is appropriate for this type of study (GUISAN et al., in prep.), as it is big enough to account for year-to-year spatial species turnover. Several response variables were considered in this study. The density cover was directly modeled as ordinal when species showed a sufficient variation over the set of calibration plots. All observations were also re-coded into presence/absence and modeled as such. Finally, the number of species present in each plot was modeled as Poisson counts and constituted the third type of response. Environmental data Important environmental descriptors for modeling the distribution of alpine species are discussed in earlier work (see e.g. GUISAN 1997, GUISAN et al. 1998). The predictors used in this study originate from four main data sources: (1) existing vector maps (geology, rocky cover, hydrology); (2) 25-m Digital Elevation Model (DEM); (3) temporal series of black and white aerial photographs; and (4) a color infrared aerial photograph. We used annual mean temperature (amt) instead of elevation as it is physiologically more meaningful for plants (GUISAN et al. 1998). Various characteristics of topography were calculated from the DEM: slope angle (slo), slope aspect (transformed into two linear North-South (NS; northness) and East-West (EW; eastness) continuous gradients respectively; nness and eness), and four indices of topographic positions representing a gradient from ridge top to middle slope to valley, and calculated with different moving windows’ radii of respectively 125, 250, 500 and 1000 meters (tp100, tp250, tp500 and tp1000; see GUISAN et al. 1999 for their calculation). Two indices of solar radiation (rad1 and rad2) were obtained from a principal component analysis (PCA; first two axes) on 19 individual daily solar radiation calculations (as used by GUISAN et al. 1998). Two snow cover indices are obtained by combining four aerial photographs taken at regular intervals during 1996 and 1997 and rectified using the DEM (snowi96 and snowi97). Finally, a raster map of the potential permafrost (perm) was modeled using the PERMAKART model (KELLER 1992). The classes of rock cover used were: (i) open vegetation with rocks (usually meadows with isolated, but numerous, rocks), (ii) rock outcrops and (iii) screes (rock1, rock2 and rock3). The three classes of geology of importance for the vegetation in the study area were

respectively amphiboles, historical moraines and Würm moraine (geol1, geol2 and geol3). Map units with none of these categories corresponded to gneiss or granite. The capture, storage and, in some cases, calculation of all predictor layers was done using the ARCINFO® geographical information system (release 7.1.2, Environmental Science Research Institute (ESRI), Redlands, California). Statistical analyses Overall, three types of GLMs (fig. 2) were fitted in this study: (1) Ordinal Proportional Odds (PO) models (fitted by a series of logistic GLMs), as used e.g. by GUISAN et al. (1998), GUISAN & HARRELL (2000) and GUISAN (2000); (2) GLM with Binomial distribution and logistic link, as used by GUISAN et al. (1999); and (3) GLM with Poisson distribution and logarithmic link, as used by GUISAN et al. (in prep.). For mathematical rationales of these models, interested readers should consult the cited references. Ordinal GLMs were used to predict the spatial variation in plant cover density, whereas Binomial GLMs were used to predict species' occurrence (i.e. presence/absence) only. The Poisson GLM was used to mimic the spatial variations in species' richness. As an alternative to the Poisson Species' Richness model (SRP), we also tested to which extent species' richness can be predicted from individual presence/absence predictions, by cumulating the number of presences predicted for each species at each modeled unit (see fig. 2; as similarly carried out by Lehmann and collaborators with fern species in New-Zealand; LEHMANN Pers. Comm.) or Austin with Eucalypt forests in Australia (AUSTIN 1998). Hereafter, this alternative model will be called the Cumulative Species Richness model (SRC). As a first step, GAMs were used to explore the shape of univariate responses, and to detect visually if significant skewness occurred in curvi-linear and unimodal responses. Attempts were then made to reproduce these curves in a parametric form in GLMs. Secondly, a stepwise AIC-based procedure (Akaike Information Criterion; see MCCULLAGH & NELDER 1983) was used to make a rough selection of the predictors that explain a significant amount of deviance. Lastly, models were retained only if all selected predictors had a p-value lower than 0.05 on: (i) the 2-test of deviance reduction and (ii) the t-test of coefficient different from zero. The measure of the fit of the models was expressed as the percentage of explained deviance adjusted by the number of degrees of freedom used (similar to the adjusted-R2 in the case of Least-Square regression; see WEISBERG 1980) and is called the adjusted-D2 hereafter (see GUISAN et al. 1999 for details on its calculation). Model evaluation was performed differently for the three models, in accordance with the types of response. Ordinal predictions were compared to observations using Gamma and dyx, two appropriate measures of agreement for semi-quantitative variables (GONZALEZ & NELSON 1996; see also GUISAN et al. 1998, GUISAN & HARRELL 2000, GUISAN 2000). Predictions from the binomial models were compared to observed presence/absence using the κ statistics (COHEN 1960), an agreement measure to guard against chance performance. Finally, count predictions by the Poisson model were compared to effective species' richness using the non-parametric Spearman’s rank correlation coefficient. The latter was also used to compare predictions by the SRC model to both actual richness and to predictions by the SRP model (thus comparing the two models). All statistical calculations were done using the S-Plus for Windows statistical software (release 4.5; Mathsoft Inc.).

Potential Maps Potential maps were calculated, for each species and for the two species' richness models, from the GLM outputs in the ARCINFO GIS. Each model was implemented by building a single formula where each model coefficient multiplies its related predictor variable. The results of the calculations were obtained to the scale of the linear predictor (LP), so that the inverse of the link function was then necessary to obtain probability values to the scale of the response at every cell of the grid. In the case of the Binomial GLMs, the inverse of the logistic function is [exp(LP) / (1 + LP)]. In the case of the Poisson GLM, the inverse is simply exp(LP). Assessing change in species composition At least four steps had to be taken to make an assessment of change in species composition (fig. 2) . First, a k-means non-hierarchical cluster analysis (HARTIGAN & WONG 1979) was performed on the calibration relevés, to define groups of relevés sharing the same subset of species. Second, a classification tree was fitted to the clusters (as the response variable), by using the individual species observations as the explanatory variables. Third, the same tree was used to predict vegetation clusters at each site using the individual species predictions from the binomial GLM models at the same site. Fourth, the procedure of point three was followed using the predictions made under the three scenarios of climate change instead of those made under the current climate. The adjustment of the classification tree was assessed by comparing observed to fitted clusters in a confusion matrix and calculating the misclassification rate and κ statistics (Cohen 1960). The κ statistics was also used to compare observed clusters to those predicted from individual species models (binomial GLMs). The potential impact of a climatic change on species' composition was also detected in similar confusion matrices, by checking if all clusters would still be predicted under changed climatic conditions. Again, all steps were here done using S-Plus.

3

Results

Presence/absence models Overall results from the binomial models are presented in figure 3. Models' goodness-of-fit, expressed in each case through the adjusted–D2 measure of deviance reduction, ranges between hardly any deviance explained to almost 70 % deviance explained (fig. 3a). Figure 3a additionally shows that κ as measured on the calibration data set correlates very well with the adjusted–D2, although it often takes slightly higher values (up to 0.834). This further suggests that κ is appropriate for an overall evaluation of models with independent held-back data, although it does not include any information on the type of error (commission versus omission) occurring (see FIELDING & BELL 1997, GUISAN 2000). Results from the independent evaluation based on κ range from no agreement at all for some species (down to = 0) to a good agreement for several species (up to = 0.621) on the scale proposed by MONSERUD & LEEMANS (1992), which is similar to the results published by ZIMMERMANN & KIENAST (1999). Values of κ at the evaluation are always lower than or equal to values of κ at the calibration, as shown in figure 3b, with some very great disparities recorded for some species (the most extreme being a calibration κ of 0.7 and an evaluation κ of nearly zero). Most of these differences correspond to species only observed in a very few plots (down to one or two) throughout the evaluation data set, which is illustrated in figure 3c (bottom-left corner of the plot). Overall, however, most species have a similar proportion of occurrence in both data sets

(fig. 3c). Figure 3d provides the frequencies, throughout the models, of the various probabilistic thresholds used to cut the probabilistic predictions into presence/absence. Surprisingly, the threshold histogram is not centered on 0.5 with symmetric tails in each opposite direction (toward 0 and 1), rather all values range between 0.05 and 0.65 with a mean at 0.35 and an asymmetric shape. Models can be ranked according to their evaluation, as done by ZIMMERMANN & KIENAST (1999). In our study, the best presence/absence models overall are those (in order of decreasing evaluation, with calibration/evaluation κ in brackets after the species name) of the species: Deschampsia flexuosa (0.60/0.62), Plantago alpina (0.54/0.60), Gnaphalium supinum (0.73/0.60), Nardus stricta (0.83/0.60), Vaccinium myrtillus (0.53/0.58), Trifolium alpinum (0.70/0.57), Ligusticum mutellina (0.67/0.57), Calluna vulgaris (0.54/0.57), Carex curvula (0.76/0.55), Vaccinium uliginosum subsp. microphylum (0.53/0.54), Leontodon helveticus (0.66/0.52) and Veronica alpina (0.54/0.50). The worst evaluations (no agreement at all) are observed for Cerastium pedunculatum, Cirsium spinosissimum, Luzula alpinopilosa, Ranunculus kuepferi, Sedum montanum and Veronica bellidioides all of which have an evaluation κ of zero and a poor calibration κ. C. pedunculatum is an exception, with a high value of κ at the calibration (0.69), but only one (wrongly predicted) occurrence in the evaluation data set, resulting in its very low evaluation. All other models lie between these extremes (fair to poor evaluation). Figure 4 presents the comparison of the evaluations obtained in this study to those obtained by ZIMMERMANN & KIENAST (1999), for nine species considered in both studies. Results are very similar for five species (Poa alpina, Phleum alpinum subsp. rhaeticum, Anthoxanthum alpinum Löve & Löve, Luzula multiflora), two species (Nardus stricta, Agrostis rupestris) have a difference of about 0.2 units while results diverge completely for Carex sempervirens and Luzula alpino-pilosa. In both studies, Carex curvula is well predicted, Luzula multiflora and Anthoxantum alpinum Löve & Löve have poor agreement between observed and predicted occurrences, and Phleum alpinum subsp. rhaeticum and Poa alpina have very poor to no agreement. Nardus stricta and Carex sempervirens are well predicted by our model, but less so (to much less) by ZIMMERMANN & KIENAST (1999), and conversely Agrostis rupestris and Luzula alpino-pilosa are well predicted by their model and less (to much less) by ours. Selection frequence of the various predictors in the models are given in figure 5. Annual mean temperature is much the most important predictor in this respect, being selected in 95 % of all models. The topographic position calculated with the smallest radius (100 m) is the next most important predictor, followed by the second index of solar radiation. Slope angle, the snow index for 1997, the first index of solar radiation, the snow index for 1996 and the topographic position calculated with the largest radius (1000 m) are then retained in approximately the same proportion of models. The three bands of the aerial color infrared photograph come next, but are selected in less than 15 % of models. All remaining predictors are retained in less than 10 % of all models. Results for the 26 ordinal abundance models are presented in figure 6. The percentage of explained deviance ranges between 15 % and 65 % (fig. 6a, b), an interval similar to binomial presence/absence models. Gamma calculated at the calibration does not provide an agreement measure so well related to the measure of the fit (adjusted-D2; fig. 6a) as dyx does (fig. 6b). Both measures almost always take better values at calibration than at evaluation, and both have a reasonable correlation between calibration and evaluation (fig. 6c and 6d). Just as for binomial models (fig. 5), annual mean temperature is by far the most important predictor in ordinal models, being selected in 92 % of the models (fig. 6e). Topographic position with a radius of 100 m and the snow index for 1997 are two other important predictors in ordinal

models, which are also well retained in binomial models. Overall, however, the ranking of importance of predictors is slightly different between both types of models, the three bands of the infrared photograph being the most important in ordinal models, while snow index for 1996 is most important for binomial models. Potential habitat maps and scenarios Figure 7 provides an example of cartographic probabilistic predictions for the binomial model of Leontodon helveticus, under present (fig. 7a), and future climate (+ 1.5 K, + 3 K and + 4.5 K; fig. 7b, 7c and 7d). Most suitable habitats for this species are predicted to shift upward in elevation, with larger loss of surface as warming increases. Climate change scenarios for some additional species are given in figure 8, which illustrates that various scenarios of change in species distribution can be expected, from a few locally favored species (e.g. Calluna vulgaris and Vaccinium myrtillus) to some dramatic local decline predicted (e.g. Carex curvula, Salix herbacea, Gnaphalium supinum, Ligusticum mutellina). Figure 9 provides an example of cartographic predictions for the ordinal model of Nardus stricta, under present (fig. 9a), and future climates (+ 1.5 K, + 3 K and + 4.5 K; fig. 9b, 9c and 9d respectively). As for L. helveticus in figure 7, the range of potential habitat for this species is predicted to shift upward in elevation, with additional changes predicted in the spatial distribution of those habitats particularly suitable, and able to host higher density cover of the species on the ground. Species richness predictions Figure 10 provides the cartographic predictions of both types of species' richness models: the Poisson GLM (SRP) and Cumulative model (SRC). Predictions by both models are correlated at 95 % (Spearman rank correlation coefficient) on the calibration data set, and at 55 % on the evaluation data set. According to each model, species' richness would respond differently to a warming stress. The SRP model predicts little or no shift upward in elevation but rather a less directional spreading of species' richness hot spots at middle elevation (see GUISAN et al., in prep.). However, the SRC model predicts a shift in SR that would parallel the shifts in species ranges (on which it is based). Species assemblages Figure 11 provides the structure of the classification tree adjusted to predict the eight vegetation clusters, previously calculated by a k-mean cluster analysis, from species occurrences (see figure 1 for the meaning of the different clusters). The number of terminal nodes is 17, the tree has a D2 of 0.97 (proportion of deviance explained) and the misclassification rate is 19 %. κ calculated between fitted and observed cluster values is 0.77. It takes value 0.45 when cluster predictions are made from species presence/absence predicted by the individual binomial models (somewhat similar to the procedure used to fit the cumulative species richness model; see fig. 2), still using the same classification tree model. The classification tree is subdivided into two groups of nodes based on the presence/absence of Arnica montana. The group without A. montana is further divided into two subgroups based on the presence/absence of Ligusticum mutellina. Table 2 compares the fitted or predicted values to the observed vegetation clusters under present climatic conditions (table 2a and 2b), and the predicted to the observed clusters under warmer climatic conditions (fig. 2c to 2e). Results show that all clusters are predicted under present climate, although clusters 6 and 7 have low values of occurrence in the plots where they were observed. Under the low warming scenario (fig. 2c), cluster 6 is no longer predicted for the plots where it used to occur and there

are only few occurrences predicted for clusters 2, 5 and 8. Interestingly, cluster 1 retains a high occurrence where it is observed at present. Under intermediate warming (fig. 2d), cluster 8 is not predicted and clusters 2, 5 and 6 no longer occur in their present positions. In addition, clusters 5 and 6 have low values of occurrence. Under the highest warming scenario clusters 6 and 8 are no longer predicted and, apart from cluster 1, no cluster is predicted where it presently occurs. Clusters 3 and 5 have low values of occurrence.

4

Discussion

This paper illustrates the use of static distribution models (in the sense of GUISAN & ZIMMERMANN, in press) applied to mimic the spatial variation of plant species' occurrence, species' abundance and plant species' richness in an alpine environment. Single species predictions are also combined to predict species' richness in an alternative fashion, and to predict species' assemblages. One possible application of this approach is shown to be the evaluation of climatic change impact at three levels of modeling - species occurrence, abundance and community composition - by changing the input climatic parameters in the models. Several conclusions arise from these various modeling experiences, with additional concerns on model accuracy and model applicability. They are all summarized in the following sections. Presence-absence modeling Sixty out of the sixty-three models integrate annual mean temperature, in its linear and/or quadratic form. Thus, most species appear to have a well defined elevation range, of varying amplitude. As we discussed in GUISAN et al. (1998) for Carex curvula, a cold temperature appears to define the upper limit of species, whereas inter-specific competition is probably responsible for defining the lower limit of species along elevation. This is in accordance with the theory of Brown et al. (1996), that in most ecological gradients, the majority of species appear to find one direction to be physically stressful and the other to be biologically stressful. These authors use it principally for explaining latitudinal gradients of plant distribution, but naturally extend it to similar situations such as to explain plant distribution along elevation gradients. The regular influence of the finest topographic position (100 m; i.e. close to a measure of curvature), retained in almost 40 % of models, mirrors the influence of microtopographic relief (creating several topoclimates; THORNWAITE 1954). Both indices of radiation, both indices of snow cover duration, slope angle and the coarsest topographic position (radius of 1000 m) account for a similar proportion, each of these predictors being selected in 30 ± 3 % of models. These results are coherent with previous findings in alpine ecology, which define solar radiation and snow cover as important variables for alpine landscape modeling (e.g. FISCHER 1990, GUISAN 1997, GOTTFRIED et al. 1998). Both integrate slope aspect, slope angle and micro-topography (GUISAN et al. 1998), although slope angle additionally translates gravitation processes operating with increasing steepness (THEURILLAT et al. 1998, ZIMMERMANN & KIENAST 1999). Thus, slope angle is frequently retained as an additional predictor, whereas slope aspect (decomposed in our case into northness and eastness), which provide a similar environmental information to radiation, is not. The three bands of the color infrared (CIR) aerial photograph are only retained in a reduced number of binomial presence/absence models (about 15 %). This is no surprise since they mainly denote moisture in the environment, as discussed by FRANK & ISARD (1986) and FRANK (1988) who generally used such an infrared aerial photograph to segregate wet from dry vegetation in an alpine landscape. Whereas only very few characteristic wetland species had enough occurrences to be modeled in our study. Hence, these predictors are only used in a

few models, for differentiating wetter from drier habitats, where two environments would otherwise have been defined as similar on the basis of all other predictors. Models’ fit and accuracy are shown to vary considerably, from up to 70 percent of deviance explained down to nearly zero, and associated values in a same range of variation. However, a few models with high value of fit and high value of κ at calibration did not perform well at the evaluation. This can be imputed, for some species (e.g. Cerastium pedunculatum), to their very low number of occurrences in the evaluation data set. For other species, unmapped disturbances (e.g. grazing) or dependence on unmapped environmental variation (e.g. water resurgence) are probably the reason, as previously suggested by a correspondence analysis on all species (GUISAN 1997). In addition, the 25-m resolution digital elevation model may be still too coarse for many species to take into account the effect of fine topography on plant species distribution. Overall however, our findings are comparable to those obtained with North-American plant species in the Spring mountains of Nevada (USA; GUISAN et al. 1999). Ordinal abundance modeling Ordinal models are also shown to provide fairly good predictions, when enough variation in density cover is recorded for the species throughout the total number of sites where it occurred (see also GUISAN & HARRELL 2000; GUISAN 2000). When too few sites have intermediate and/or high values of cover density (i.e. classes higher than 2), fitting an ordinal density model does not prove more efficient than fitting a simple presence/absence model, or the model adjustment fails (e.g. no predictor is selected). As regards the ranking in importance of the various predictors, it differs partly from the ranking found for binomial models. This result was expected as, in the case of ordinal models, additional ecological information is used for fitting the variation in ground cover density, which is not used for fitting simple species occurrences. Annual mean temperature is still the most important predictor. The ranking of the second band of the color infrared aerial photograph in second position shows indirectly the importance of moisture information for modeling the variations in abundance between sites where a species is present, whereas it was shown to be less important for modeling presence/absence only. Topographic positions at the finest (100 m) and coarsest (1000 m) resolution, the first index of radiation and snow cover 1997 rank next and have a similar representation in ordinal and binomial models (around 35-40 % for tp100, around 30 %, for the others, see fig. 6), thus confirming their importance for modeling species' distribution and abundance in an alpine environment. As is the case for binomial models, aspect-related variables, northness and eastness, are poorly represented in ordinal models, due to their correlation with radiation (direct and resource predictors were entered first in the stepwise selection, then the indirect ones). Finally, slope angle seems to lose some importance when abundance is modeled, which would indicate that the variation in abundance of most species does not much depend upon change in steepness. However, one should keep in mind that, although there were 63 binomial models, only 26 ordinal models were adjusted. As a result, the previous percentages might not be fully comparable from one model type to the other, although they provide a good basis for discussion. Species' richness and species' assemblages Both species' richness models were successfully adjusted, as attested by the fairly reasonable correlation values obtained between fitted and observed values on the one hand, and the high correlation obtained between fitted values of both models on the other hand. Using a Poisson distribution assumption proved to be appropriate, in our study, for modeling species' richness (i.e. counts of species; GUISAN et al., in prep.). More surprisingly, summing up individual species' predictions at each pixel was nearly as powerful as modeling the counts directly, when

only the sixty-three species modeled were considered in both approaches. Both approaches predict a belt of maximum species' richness at middle elevation in the study area (around 2200 m), which could be related directly to annual mean temperature, but also indirectly to some particular geomorphological structures more frequent at these elevations (GUISAN et al. in prep.). The eight pre-defined vegetation clusters could be successfully predicted at each calibration site, using 63 species, from both observed species' distribution and predicted species' distribution (table 2). These results suggest that: (1) the Gleasonian theory of individualistic behavior, which considers observed vegetation units as assemblages of species sharing a similar portion of their ecological niche, seems to operate in alpine vegetation where competition between species is reduced due to the stressful environment; and (2) the overall species' modeling effort was good enough to reproduce vegetation richness and composition successfully. Figure 11 shows that only cluster 4 (meso-thermophilous communities of the Nardion alliance) and cluster 6 (meso-thermophilous communities of the Nardion alliance) could be defined with only one node in the classification tree. All other clusters refer to at least two nodes, cluster 3 (communities of the Nardion alliance and transitional communities of the Nardion/Caricion curvulae alliances) being the most spread across the classification tree with four nodes belonging equally to the two main groups, and then cluster 8 (alpine communities of the Caricion curvulae alliance) with three nodes. Model evaluation and cost analysis Much can be said about evaluating presence/absence and ordinal models. However, predictions by the Poisson GLM would seem to be correctly evaluated by the non parametric Spearman rank correlation coefficient and will not therefore be discussed more specifically here. A thorough review of evaluation measures for presence/absence models is given in FIELDING & BELL (1997). For our study, we mainly used κ for comparing model predictions (although each confusion matrix was also cautiously analyzed separately), as also used by ZIMMERMANN & KIENAST (1999), despite some of its drawbacks in evaluating model accuracy, particularly when conservation issues are in focus. We consider κ to be an appropriate measure to compare predictions from a set of models against chance performance predictions. However, we agree entirely with FIELDING & BELL (1997) and other authors, that κ might not be the most appropriate measure when discussing the predicted distribution of a single species in a particular conservation perspective, since it cannot distinguish false negative from false positive rates. As to the evaluation of ordinal models, dyx seems to provide a better evaluation than Gamma in terms of (i) being closer to the goodness-of-fit criterion (i.e. adjusted-D2; fig. 6a), (ii) remaining more constant between calibration and evaluation (fig. 6b), (iii) being less prone to failure in predicting higher ordinal classes (resulting in asymmetric confusion matrices), and (iv) minimizing false negative rate (i.e. omission error type) when predictions are re-coded into presence/absence which, in terms of cost, is expected by such a model. Effectively, we consider that predicting a species when it has not been observed is less serious than not predicting (i.e. omitting) a species when it has been observed. There are two reasons for such differential weighting of omission and commission error types: (1) it is reasonable to think that a species might be overlooked at a site (for many reasons, such as visiting the site at the wrong phenological period), even though it is known to be present, and thus was actually correctly predicted there, whereas the reverse is impossible; (2) even if the species is truly absent from a site, we consider it a better (and easier) approach to minimize false negative errors as a first step and then try to correct false positive errors using additional discriminating factors (i.e. to transform some wrongly predicted presence into absence using additional environmental

filters). Thus, our results show that providing only Gamma or dyx for assessing the accuracy of ordinal abundance models is not enough and one should additionally provide an evaluation of models' ability to predict at least presence/absence correctly (as e.g. measured by κ or any other measure of model adequacy; see FIELDING & BELL 1997). Climate change scenarios Due to the fact that accurate climate change scenarios for alpine regions were not available for our study area, we considered only three very simple temperature warming scenarios (+ 1.5 K, + 3 K, + 4.5 K). In the future, more meaningful ecological impact scenarios can easily be derived from adjusted models, e.g. if predictions of change can be forecast for climatic parameters other than annual mean temperature. Detailed scenarios for all sixty-three species can be found in GUISAN & THEURILLAT (in rev.). Therefore, only the main trends are given in the following discussion. As a consequence of the importance of annual mean temperature in most models, all species (except for Crepis aurea, Phleum alpinum subsp. rhaeticum, Cirsium spinosissiumum) might be affected by climatic change, with varying amplitude in their response as a function of the degree of the change in temperature. With a low scenario (+ 1.5 K), a majority of species would lose suitable habitat, a significant minority of species would gain suitable habitat and a few others would maintain their present extent. This is close to previous assumptions made by KÖRNER (1995), THEURILLAT (1995) and THEURILLAT et al. (1998). With increasing temperature (+ 3 K and + 4.5 K), the proportion of favored species would however severely diminish, as would the proportion of species not affected by climate change. As discussed in more detail in GUISAN & THEURILLAT (in rev.), these models and scenarios only consider the potential distribution of present and future species’ habitat and not the distribution of species themselves. The main limitations to these scenarios are nonetheless the missing factors of: (1) time dimension and associated dynamic processes, (2) biotic interactions, (3) possible inertia and persistence of ecological systems (e.g. alpine soils, plant communities), (4) natural or anthropogenic barriers to dispersal, and (5) the total elevation and distribution extent of the species within the Alps, which might alter the shape of ecological response curves. Due to the latter limitation, a lower definition to prediction had to be drawn on each species' richness scenario map, to indicate the elevation boundary at which other species, not taken into account for building the model, might invade from lower elevations. These scenarios thus provide a first evaluation of the potential impact that the three different levels of climate change might have, but they do not aim to predict accurately where the species would be distributed in such a climatically changed future. Assessing change in species' composition As suggested by several authors (e.g. HUNTLEY 1991), species would certainly respond individually to changes in climate. Thus, it might be more appropriate to model species rather than communities in this context (LISCHKE et al. 1998), although similar but less severe drawbacks do exist with this approach (as stated by ZIMMERMANN & KIENAST 1999). Due to these remaining drawbacks (e.g. change in biotic interactions, barrier to dispersal, inertia, persistence), composition of future species' assemblages cannot be entirely predicted from individual predictions (as also attested by our own results), but an evaluation of the degree of change can be made instead. One way to explore the impact of climate change on species' composition is to predict, at each calibration site, the eight pre-defined vegetation clusters from species' predictions under the three warming scenarios. Under a scenario of “no change” in species composition, all vegetation clusters should still be predicted. Under the lowest climate change scenario (table 2c), most of the meso-thermophilous swards of the Nardion alliance (cluster 6) would probably be replaced by the nearby heath-

swards transitional communities (cluster 4), which would thus be favored. Alpine communities of the Caricion curvulae alliance (cluster 8) would also strongly decrease. They would probably be replaced by transitional sward communities, intermediate between the Nardion and Caricion curvulae alliances (cluster 3) and (cool-)mesophilous swards of the Nardion alliance (cluster 7) which would shift higher in elevation. Subalpine heaths would slightly decrease (cluster 2), and the occurrence of snowbed, moraine and scree communities, as well as mesophilous swards of the Nardion alliance (cluster 5), would not undergo much change. Under intermediate warming (fig. 2d), the alpine meadows of cluster 8 would no longer occur, meso-thermophilous swards of the Nardion alliance (cluster 6) would almost disappear, as would the mesophilous swards of cluster 5, which would decrease much more than in the previous scenario. To a lesser extent, subalpine heaths (cluster 2) might also lose suitable habitats. Meso-thermophilous heath-swards of the Nardion alliance (cluster 4) would cover a similar surface as before, as would, but to a lesser extent, (cool-) mesophilous swards of the same alliance (cluster 7). The strong increase in the prediction of “alpine communities” (cluster 1) is an artefact due to the fact that true high alpine communities or fens have none or very few of the 63 species used in the classification. Therefore, this cluster becomes the default cluster for plant communities which do not pertain to any of the other seven clusters. Under the highest warming scenario, communities of cluster 4 and 7 would still maintain their extent of cover, and there would still be some transitional sward communities (cluster 3) as well as some heaths (cluster 2), but the majority of communities would pertain to other vegetation types (cluster 1). However, predicting new communities is a more difficult task because new species (e.g. from lower elevations) are likely to invade part of the study area. Model limitations and future perspectives By comparing our results to those of ZIMMERMANN & KIENAST (1999) for the nine species commonly modeled (fig. 4), we found a majority of these species to be modeled with similar success, whereas strong discrepancies occurred for a few species, well modeled by one model and not by the other. We see three main causes for these differences, which can also be seen as modeling limitations: (1) the different predictors used in each study, (2) the different resolution (25 m in our case vs. 50 m in their study) and scale used (i.e. a small catchment area vs. several thousands of km2), and (3) too low a number of occurrences for some species in the evaluation data set, observed in one or the other study. The predictors common to both studies are: annual mean temperature, solar radiation and slope angle, although solar radiation was handled differently in the two cases. Additionally, we use several topographic predictors (eastness, northness, topographic position) and spectral information from aerial photographs as surrogates of soil moisture and snow cover duration (and thus of solid precipitation). ZIMMERMANN AND KIENAST (1999) used additional bioclimatic predictors integrating precipitation (continentality and moisture indices) and sum of temperature (growing degreedays). Interestingly, both Carex sempervirens and Nardus stricta models include topographic position, and N. stricta additionally includes the snow cover index for 1997, such ecological information is not available in the study by Zimmermann and Kienast. In turn, Agrostis rupestris and Luzula alpino-pilosa include moisture and degree-days predictors in their model, whereas such related ecological information is only poorly provided in our study (moisture, indirectly in CIR photographs). The different resolution used can influence the result for some species but not for others. Both resolutions would seem too coarse for modeling the distribution of any alpine species, because: (i) these species are often small in size, (ii) their environmental requirements can accordingly be very restricted in space and (iii) their spatial distribution can fluctuate strongly over short distances (to the order of a few meters). It is now possible to reach a resolution of one meter, (with the developments of GIS, photogrammetry and DGPS technologies), the use of which should thus be considered for future studies, as

recently experimented by GOTTFRIED et al. (1998) in Austria. Finally, the problem of having too few occurrences of some species in the evaluation data set can be solved: (1) by increasing the size of the evaluation data set (our ninety-two evaluation plots would now appear rather too few in this respect), and (2) by considering a random-stratified sampling (see e.g. GOEDICKEMEIER et al. 1997, WESSELS et al. 1998, CHERIX et al. 1998) which would attempt to represent every environmental combination – and thus every habitat – in an equivalent manner in the final data set, as suggested by ZIMMERMANN & KIENAST (1999). 5

Conclusion

In conclusion, the following statements can be made: 1. Alpine/subalpine species and communities can be successfully mimicked by static distribution models, as shown by earlier studies (e.g. FISCHER 1990, 1994) and more recently by GUISAN et al. (1998), ZIMMERMANN & KIENAST (1999) and the present study; Generalized Linear Models (GLM) proved to be useful tools in this respect; 2. The best model accuracy of logistic presence/absence models, as measured by κ on an independent data set, is 0.90 for alpine communities (ZIMMERMANN & KIENAST 1999) and 0.62 for alpine species (this paper). Other evaluation measures (see FIELDING & BELL 1997) might be more appropriate in other situations; best evaluation of ordinal models is provided by Somer’s dyx, with a maximum value of 0.79. 3. Best models are usually obtained for dominant species, frequently distributed over both calibration and evaluation data sets; this is especially true for ordinal models; 4. Species richness can be satisfactorily modeled, both with a Poisson GLM model or by superimposing individual species predictions; the Poisson approach seems however more realistic, as it correlates those sites with high species richness to meaningful landscape structures (see also GUISAN et al. in prep.), and thus provides more realistic climate change scenarios; 5. Several possible limitations to this modeling approach and the associated climate change scenarios were evidenced in this study (and by comparing our results to those from another study). In particular, static distribution models can lack one or several of the following properties: (1) time dimension and associated dynamic processes, (2) biotic interactions (and particularly interspecific competition), (3) possible inertia of ecological systems, (4) considering the whole elevation and distribution extent (chorology) of the species, (5) all driving ecological factors in the set of predictors, (6) appropriate study resolution. 6. Directions for future research include improving the spatial resolution of alpine studies (to 1 m or more accurate; as used e.g. by GOTTFRIED et al. 1998), developing systems of models to integrate interspecific competition (as suggested in GUISAN 1997), improving the quality of predictors (making them more physiologically meaningful and more accurately modeled, as discussed by ZIMMERMANN 1996 and ZIMMERMANN & KIENAST 1999), improving the quality of the sampling, e.g. by designing surveys in a more stratified way (as used e.g. in GUISAN et al. 1999).

Acknowledgements This study was carried out within the coordinated project ECOCLINE, as part of the CLEAR integrated project of the Priority Program for the Environment, granted by the Swiss National Science Foundation (SNF; projects 5001-35341, 5001-44604 and 5001-35040). We would like to thank the Conservatoire et Jardin botaniques of the City of Geneva and the Academic

Society of Geneva for additional financial support, and the Swiss Federal Office for Air Space (OFADCA) for providing the aerial photographs. Our next thanks go to the following people for their help on different matters: Dr. F. Keller for the Permafrost modeling , Dr. P. Terrettaz for rectifying the aerial photographs, Dr. F. Kienast for modeling solar radiation predictors and his valuable comments during the study, Dr. A.H. Fielding for providing functions for presence/absence accuracy assessment, Dr. R. Gonzalez for providing the S-Plus function for calculating ordinal agreements, Dr. L.D. Bacon for providing the S-Plus function for calculating κ, Prof. F.E. Harrell for providing his Design library and personal support for adjusting ordinal models. We would additionally like to thank S-Plus Germany (GraS) for providing some facilities with S-Plus. Finally, our sincere thanks go to Dr. N.E. Zimmermann, Dr. F. Kienast, Prof. M. Beniston, Prof. C. Körner, Prof. B. Ammann, Prof. J. Franklin, Prof. G. Grabherr, Dr. D. Gyalistras, Dr. H. Lischke and Dr. H.S. Fisher for their valuable comments at one time or another during the course of this study. Last but not least, our deep thanks go to Julie Warrillow who undertook the linguistic revision of this paper (and many others previously). References Aeschimann, D. & Heitz, C. (1996). Index synonymique de la Flore de Suisse. Centre du Réseau Suisse de Floristique (CRSF), Chambésy, Genève, Switzerland. Aspinall, R. (1992). An inductive modeling procedure based on Bayes' theorem for analysis of pattern in spatial data. - Int. J. Geogr. Inform. Syst. 6(2): 105-121. Austin, M.P. (1998). An ecological perspective on biodiversity investigations: examples from Australian Eucalypt forests. Ann. Missouri Bot. Gard. 85: 2-17 Austin, M.P. (1992). Modelling the environmental niche of plants: implications for plant community response to elevated CO2 levels. - Austral. J. Bot. 40: 615-630. Austin, M.P. & Meyers, J.A. (1996). Current approaches to modelling the environmental niche of eucalypts: implications for management of forest biodiversity. - Forest Ecol. Managem. 85: 95-106. Austin, M.P., Nicholls, A.O. & Margules, C.R. (1990). Measurement of the realized qualitative niche: environmental niches of five Eucalyptus species. - Ecol. Monogr. 60: 161-177. Barkman, J.J., Doing, H. & Segal, S. (1964). Kritische Bemerkungen und Vorschläge zur quantitativen Vegetationsanalyse. - Acta Bot. Neerl. 13: 394-419. Bazzaz, F.A. (1996). Plants in changing environments. - Cambridge University Press, Cambridge. 320 pp. Billings, W.D. & Mooney, H.A. (1968). The ecology of arctic and alpine plants. - Biol. Rev. 43: 481-529. Bio, A.M.F, Alkemade, R. & Barendregt, A. (1998). Determining alternative models for vegetation response analysis: a nonparametric approach. - J. Veg. Sci. 9: 5-16. Birks, H.J.B. (1996). Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora. - Ecography 19: 332-340. Brown, D.G. (1994). Predicting vegetation types at treeline using topography and biophysical disturbance variables. - J. Veg. Sci. 5: 641-656. Brown, J.H., Stevens, G.C. & Kaufman, D.M. (1996). The geographic range: size, shape, boundaries, and internal structure. - Ann. Rev. Ecol. Syst. 27: 597-623. Brzeziecki, B., Kienast, F. & Wildi, O. (1993). A simulated map of the potential natural forest vegetation of Switzerland. - J. Veg. Sci. 4: 499-508. Buckley, R. 1982. The habitat-unit model of Island-Biogeography. - J. Biogeogr. 9: 339-344. BusbyJ.R. (1991). BIOCLIM - A bioclimate analysis and prediction system. - In: C.R. Margules & M.P. Austin, M.P. (eds.): Nature conservation: cost effective biological surveys and data analysis, chapter 10 - CSIRO, Melbourne.

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Woodward, F.I. & Beerling, D.J. (1997). The dynamics of vegetation change : health warnings for equilibrium “ dodo ” models. - Global Ecol. Biogeogr. Letters 6: 413-418. Yee T.W. & Mitchell N.D. (1991). Generalized additive models in plant ecology. - J. Veg. Sci. 2: 587-602. Zimmermann, N.E. (1996). Ein klimasensitives, räumliches Vegetationsmodell für die alpine Stufe der Schweiz. - Diss. Universität Bern. 102 pp. + annexes. Zimmermann, N.E. & Kienast, F. (1999). Predictive mapping of alpine grasslands in Switzerland: species versus community approach. - J. Veg. Sci. 10: 469-482. Authors’addresses: Dr. Antoine Guisan, Swiss Center for Faunal Cartography, Terreaux 14, CH-1032 Neuchâtel, Switzerland. E-mail: [email protected], fax +41 21 683 30 67 Dr. Jean-Paul Theurillat, Fondation J.-M. Aubert, CH-1938 Champex, and Conservatoire et Jardin botaniques, Case postale 60, CH-1292 Chambésy. E-mail : [email protected]

Table captions Table 1 : Cross-tabulation of models qualities between calibration and evaluation. Agreement classes are taken from Monserud & Leemans (1992). N = no agreement, VP = very poor agreement, P = poor, F = fair, G = good, VG = very good. The categories ‘excellent’ (0.85 < < 0.99) and ‘perfect’ ( > 0.99) are not represented here. Numbers in the table relate to the number of species’models. calibration N 0 0 0 0 0 0

evaluation

N VP P F G VG

VP 1 1 1 0 0 0

P 6 5 6 1 0 0

F 0 6 10 4 3 0

G 1 1 8 2 2 0

VG 0 0 0 1 4 0

Table 2 : Confusion matrices from model classifications (i.e. predictions) of vegetation. clusters. Height clusters are first obtained using a k-means non-hierarchical clustering of the vegetation relevés. These clusters are predicted from individual species’ presence/absence using a classification tree (see fig. 11). (a) observed versus fitted vegetation clusters, (b) observed versus predicted from individual GLM species predictions under present climatic conditions, (c) observed versus predicted from individual GLM species predictions under three scenarios of climate change: cc1 = + 1.5 K, cc2 = + 3 K, cc3 = + 4.5 K. Numbers relate to the number of plots.

1 2 3 4 5 6 7 8

1 44 0 1 0 0 0 1 3

2 1 16 0 1 1 1 2 0

3 0 0 22 3 0 2 3 4

4 0 1 0 17 0 1 0 0

5 0 0 0 1 19 2 2 0

6 0 1 0 1 0 6 0 0

(b) predicted 7 0 0 1 0 1 0 9 0

8 1 0 0 1 2 0 1 33

observed

observed

(a) fitted

observed

(c) cc1 1 2 3 4 5 6 7 8

1 25 8 0 3 3 0 9 1

2 5 2 0 1 3 0 0 3

3 6 2 12 4 4 1 3 12

4 1 0 6 8 10 4 2 7

Figure captions

5 1 1 1 0 2 0 0 13

1 2 3 4 5 6 7 8

1 37 0 0 0 0 0 0 3

2 0 11 0 1 0 0 2 0

3 2 0 10 2 1 3 7 2

4 0 3 0 10 2 3 3 1

5 2 1 3 7 11 4 3 2

6 0 0 0 2 0 1 0 1

7 0 3 4 1 3 0 3 0

(d) cc2 6 1 0 0 0 0 0 0 1

7 4 5 5 8 1 7 4 2

8 3 0 0 0 0 0 0 1

1 6 18 12 18 11 9 15 1

2 5 0 0 0 0 1 1 0

3 11 0 3 1 5 0 0 11

4 18 0 2 1 1 0 0 21

5 1 0 0 0 0 0 0 0

8 5 0 7 1 6 1 0 31

(e) cc3 6 4 0 0 0 0 0 0 0

7 1 0 7 4 6 2 2 7

8 0 0 0 0 0 0 0 0

1 14 18 24 24 23 12 18 24

2 7 0 0 0 0 0 0 5

3 6 0 0 0 0 0 0 0

4 13 0 0 0 0 0 0 2

5 2 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0

7 4 0 0 0 0 0 0 9

8 0 0 0 0 0 0 0 0

Fig. 1 : The study area and some of the environmental predictors used to mimic plant and diversity distribution. (a) The situation of the Belalp study area in Switzerland; (b) Elevation isolines and the spatial sampling design of calibration and evaluation plots; (c) Color InfraRed (CIR) aerial photograph; (d) First index of solar radiation; (e) Hydrological network and the distribution of the three classes of geology of ecological interest (amphibole and two types of moraine). Fig. 2: The study design. GLMs with different specifications are chosen to model appropriately the different types of response variables. GLMs with a Binomial probability distribution and a logistic link are used to model presence-absence, Proportional Odds GLMs are used to model ordinal density of species on the ground and a GLM with a Poisson distribution of probabilities and a logarithmic link is used to model species richness (SR). Alternatively, SR is also modeled by summing up individual presence-absence predictions by the 63 binomial species models. Species composition is assessed through clustering and classification tree techniques. All models are finally used to predict potential impact of climate change on the distribution of plant species and diversity, and to assess change in species composition. Fig. 3 : Overall results for the 63 binomial species models: (a) adjusted-D2 measure of the fit versus calibration κ; (b) Calibration versus evaluation κ; (c) Number of presence of a species over the calibration plots versus its number of presence over the evaluation plots; (d) Histogram of calibrated probability thresholds used to cut probabilistic predictions into presence/absence predictions. Fig. 4 : Values of κ calculated between model predictions, made on the independent data set (test data), and observed occurrences for nine species. Comparison between modeling results from Zimmermann & Kienast (1999) and the models presented in this paper. agrrup = Agrostis rupestris, antalp = Anthoxantum alpinum s.l., carcur = Carex curvula, carsem = Carex sempervirens, luzalp = Luzula alpino-pilosa, luzmul = Luzula multiflora, narstr = Nardus stricta, phlalp = Phleum alpinum s.l., poaalp = Poa alpina. Fig. 5: Histogram showing the frequency of selection of all available predictors in the Binomial presence/absence (p/a) models. amt = annual mean temperature; slo = slope angle; nness = Northness (N-S gradient); eness = Eastness (E-W gradient); tp100 to tp1000 = topographic position calculated with radii respectively set at 100, 250, 500 and 1000 m; rad1 and rad2 = the two radiation indices; cir-1 to cir-3 = the three spectral bands of a color infrared aerial photograph; sc96 = snow cover index 1996; sc97 = snow cover index 1997; Fig. 6: Overall results for the 26 ordinal models: (a) adjusted-D2 measure of the fit versus calibration Gamma(G); (b) adjusted-D2 measure of the fit versus calibration dyx; (c) Calibration versus evaluation κ calculated for each species from reducing ordinal predictions into presence/absence, using the species-specific calibrated threshold optimizing Gamma; (d) Calibration versus evaluation κ calculated for each species from reducing ordinal predictions into presence/absence, using the species-specific calibrated threshold optimizing dyx; (e) frequency of selection of all available predictors in the ordinal models; see key to fig. 4 for the description of abbreviations. Fig. 7: An example of a probabilistic cartographic result for the binomial presence/absence model of Leontodon helveticus: (a) present distribution of potential habitat; (b) future distribution under a +1.5K temperature warming scenario and (c) under a + 3K scenario. The camembert graph shows the extent of area which would be respectively classified as 'presence' and as 'absence' under each scenario. The model includes the predictors: AMT, AMT2, RAD2, RAD22, TP1000, SNOWI972. Fig. 8: Climate change scenarios for twelve species, as derived from their respective binomial presence/absence model. Scenarios include a +1.5 K, + 3 K, and + 4.5 K warming. a-d:

meadow species; e-h: snow-bed species; i-l: heath species. Dashed = proportion of pixels with species present; white = proportion of pixels with species absent. Fig. 9: Cartographic prediction of the ground cover density of Nardus stricta, as obtained from the ordinal model of the species. (a) present distribution of potential habitat; (b) future distribution under a +1.5 K temperature warming scenario, (c) under a + 3 K scenario, and (d) under a + 4.5 K scenario. The model includes the predictors: AMT, AMT2, CIR-1, CIR-12, CIR-2, CIR-22. Fig. 10: Species richness (SR) spatial predictions. Cartographic prediction by the Poisson species richness (SRP) model (a-d) and by the Cumulative species richness (SRC) model (e-h). The SRP model (GLM) includes the predictors: AMT, AMT2, SLO, RAD-2, SNOWI-97, CIR-1. The SRC model is obtained by summing presence/absence predictions from 63 individual species models (most common species); (a) present potential distribution predicted by the SRP model; (b) future distribution under a +1.5 K temperature warming scenario, (c) under a + 3 K warming, and (d) under a + 4.5 K warming; (e) present potential distribution predicted by the SRC model; (f) future distribution under a +1.5 K temperature warming scenario, (g) under a + 3 K warming, and (h) under a + 4.5 K warming. Fig. 11: Classification tree used for predicting the eight vegetation clusters from individual species observations and GLM predictions (see also table 1). cluster 1: alpine communities (snowbeds, moraines, screes) of the Salicion herbaceae and the Androsacion alpinae alliances, as well as acidophilous and baso-nitrophilous fens of the Caricion fuscae and Caricion davallianae alliances; cluster 2: subalpine mesophilous and thermophilous heaths of the Rhododendro-Vaccinion, Loiseleurio-Vaccinion and Juniperion nanae alliances; cluster 3: transitional sward communities intermediate between the Nardion and Caricion curvulae alliances; cluster 4: meso-thermophilous heath-swards of the Nardion alliance; cluster 5: mesophilous communities of the Nardion alliance; cluster 6: meso-thermophilous swards of the Nardion alliance; cluster 7: (cool-)mesophilous swards of the Nardion alliance; cluster 8: alpine communities of the Caricion curvulae alliance. (Nomenclature of alliances according to THEURILLAT et al. 1995.)

N W

(c)

E

(a)

S

0

50 Kilometers

(b)

Région d'étude Indice de radiation solaire I 0-3000 mj 3001-6000 mj 6001-9000 mj 9001-12000 mj 12001-15000 mj 15001-18000 mj 18001-21000 mj 21001-24000 mj 24001-27000 mj

(d)

(e) Figure 1 ↑ / Figure 2 ↓

Response

0 1 2 3 4 5

presence / absence

# occ

0

Summing: = counts (# of species)

species richness

species

Climatic Annual Mean Temp. Permafrost Substrate Geology Rock cover

species relevés

comparing

plant communities I

Reclassification: 0 stays 0; > 0 becomes 1

relevés

Primary models (GLM)

Secondary models plant communities II

# occ

abundance

relevés

species

Environmental predictors

1

Topographic Slope Angle Northness Eastness Topographic Position Curvature Solar radiation (2 indices) Spectral Information Color Infrared Aerial photographs (moisture) Black/White aerial photographs (series -> 2 snow indices)

Ordinal distribution Parallel regressions Logistic link functions

clustering analysis

k abundance models (only for species showing sufficient variation in abundance)

species assemblages

Binomial distribution Logistic link function

n p/a models (for all common species n ≥ k)

summing the predictions

Poisson distribution Logarithmic link function

SR model I

SR model II comparing

1

(b)

0,9

1 0,9

0,8

0,8

0,7

0,7

Evaluation Kappa

Calibration Kappa

(a)

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0,2

0,2

0,1

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0 0

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0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

1

Adjusted-D2

70

(d)

12

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8

nr of models

nr of presence - evaluation

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1

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6 4

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probability threshold

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100 120 140 160

nr of presence - calibration

Figure 3 ↑ / Figure 4 ↓

0,8

Kappa Guisan & Theurillat

0,7

narstr

0,6

carcur 0,5 0,4

carsem

luzmul antalp

0,3

agrrup

0,2 0,1

phlalp poaalp

0 0

0,1

0,2

luzalp 0,3

0,4

0,5

0,6

Kappa Zimmermann & Kienast

0,7

0,8

100 90

% selection in p/a models

80 70 60 50 40 30 20 10

tp250

nness

eness

tp500

cir.1

cir.3

cir.2

tp1000

sc96

rad1

sc97

slo

rad2

tp100

amt

0

Figure 5 ↑ / Figure 6 ↓

1

1

(b)

0,9

0,9

0,8

0,8

0,7

0,7

Calibration dyx

Calibration Gamma

(a)

0,6

(e)

0,6 0,5

amt

0,4

cir-2

0,3

0,3

tp100

0,2

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0,1

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0

0

0,5 0,4

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

42

rad1

35

sc97 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Adjusted-D2

92 46

Adjusted-D2

31 31

tp1000 cir-3

27

slo

(c)

1

(d)

0,9

Evaluation Kappa dyx

Evaluation Kappa G

0,8 0,7 0,6 0,5 0,4 0,3 0,2

1

cir-1

0,9

sc96

0,8

rad2

0,7

tp250

0,6

8 4

nness

0,4

eness

0,3

4 0 0

50

100

% of models including the predictor

0,1

0

15 12

tp500

0,5

0,2

0,1

27 23

0

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Calibration Kappa G

Calibration Kappa dyx

Figure 7 ↑ / Figure 8 ↓ (a)

(b)

(c)

Trifolium alpinum

Carex curvula

(d) Nardus stricta

Leontodon helveticus

100%

100%

100%

100%

80%

80%

80%

80%

60%

60%

60%

60%

40%

40%

40%

40%

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present

Present

+1.5K

+ 1.5 K

+3K

+3K

+4.5k

present

+ 4.5 K

Present

(e)

+1.5K

+ 1.5 K

+3K

0%

present

+4.5k

+3K

+ 4.5 K

Present

(f)

Salix herbacea

+1.5K

+ 1.5 K

+3K

+3K

+4.5k

present

+ 4.5 K

Present

(g)

100%

100%

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60%

60%

60%

60%

40%

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40%

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++1.5K 1.5 K

++3K 3K

++4.5k 4.5 K

present Present

(i)

++1.5K 1.5 K

++3K 3K

(j)

Vaccinium myrtillus

+1.5K + 1.5 K

++3K 3K

++4.5k 4.5 K

present Present +1.5K + 1.5 K

(k)

Calluna vulgaris 100%

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++4.5k 4.5 K

present Present

+1.5K + 1.5 K

++3K 3K

++4.5K 4.5 K

+ 4.5 K

+3K +3K

+4.5k + 4.5 K

(l)

80%

++1.5K 1.5 K

+4.5k

Deschampsia flexuosa

R. ferrugineum

100%

present Present

+3K

0%

present Present

++4.5k 4.5 K

+3K

Veronica alpina

100%

present Present

+ 1.5 K

(h)

Ligusticum mutellina

Gnaphalium supinum

+1.5K

0%

present Present

+1.5K + 1.5 K

++3K 3K

++4.5k 4.5 K

present Present

+1.5K + 1.5

K

+3K +3

K

+4.5k + 4.5 K

cover classes

Figure 9

Figure 10

a

p arnmon

a

p

a

p

ligmut

a

pulver

p

a

p

narstr

a

p

a

p

antalp

1

a

p

plaalp

8

a

eupmin

p

a

geumon

2

7

3

7

a 5

a 8

1

8

Figure 11

p selalp

2 p

selalp

3

p

antalp

3

a

p

cambar

p

gnasup

a

p vacmic

p

trialp

a

a

plaalp

3

5

4

6