Study area
All simulations were run at a 100 × 100 m resolution for the entire European Alps, which cover ~200,000 km². Elevations reach 4,810 m above sea level at the highest peak (Mont Blanc, elevational data were obtained from ref. 44). Mean annual temperature ranges from approximately −13 up to 16 °C and annual precipitation sums reach up to ~3,600 mm (climatic conditions were obtained from WorldClim45).
Species data
True presences/absences were derived from complete species lists of 14,040 localized plots covering subalpine and alpine non-forest vegetation of the Alps, compiled from published46 and unpublished data sources. For more information see the supplementary information in ref. 21.
Data on demographic rates as well as dispersal parameters were taken from ref. 21, Supplementary Table 1. Detailed values are provided in Supplementary Table 1.
Environmental variables
Current climate data
Maps of current climatic conditions were generated on the basis of mean, minimum and maximum monthly temperature obtained from WorldClim45 and monthly precipitation sums derived from ref. 47 at a resolutions of 0.5 arcmin and 5 km, respectively. Temperature and precipitation data were downscaled to 100 m as described in ref. 21 and using ordinary kriging with elevation as covariable. As the reference periods of these two datasets do not match (temperature values represent averages for 1950–2000, while precipitation covers 1970–2005) temperature values were adapted using the E-OBS climate grids available online (www.ecad.eu/download/ensembles/download.php). We used these spatially refined temperature and precipitation grids to derive maps of mean annual temperature and mean annual precipitation sum. We chose only two climatic variables to keep models simple and, therefore, interpretation of results more straightforward. In fact, the climatic drivers of population performance and distribution can be more complex48 and vary among species, life history stages and vital rates49. However, as correlations between different descriptors of temperature (such as coldest month or warmest month temperature, Pearson correlation of 0.84) as well as between precipitation variables are high in the European Alps, we chose mean annual temperature and mean annual precipitation sum as they give the most basic description of how climatic conditions change over geographical and elevational gradients.
Future climate data
Monthly time series of mean temperature as well as precipitation sums predicted for the twenty-first century were extracted from the Cordex data portal (http://cordex.org). We chose two IPCC5 scenarios from the RCP families representing mild (RCP 2.6) and severe (RCP 8.5) climate change to consider the uncertainty in the future climate predictions. Both scenarios were generated by Météo-France/Centre National de Recherches Météorologiques using the CNRM-ALADIN53 model, fed by output from the global circulation model CNRM-CM5 (ref. 50). The RCP 2.6 scenario assumes that radiative forcing reaches nearly 3 W m−2 (equal to 490 ppm CO2 equivalent) mid-century and will decrease to 2.6 W m−2 by 2100. In the RCP 8.5 scenario, radiative forcing continues to rise throughout the twenty-first century and reaches >8.5 W m−2 (equal to 1,370 ppm CO2 equivalent) in 210024.
These time series were statistically downscaled (delta method) by (1) calculating differences (deltas) between monthly temperature and precipitation values hindcasted for the current climatic conditions (mean 1970–2005) and forecasted future values at the original spatial resolution of 11′; (2) spatially interpolating these differences to a resolution of 100 × 100 m using cubic splines and (3) adding them to the downscaled current climate data separately for each climatic variable21,36. Subsequently, we calculated running means (averaged over 35 years) for every tenth year (2030, 2040 through to 2080) for each climatic variable and finally derived, on the basis of the monthly data, mean annual temperature and mean annual precipitation sums for these decadal time steps. The application of 35-yr running means ensures that we use the same time interval for parameterization and prediction. Furthermore, for long-lived species such as alpine plants, running means over long time intervals appear most appropriate to characterize climatic niches33.
Soil data
In addition to the climatic data we used a map of the percentage of calcareous substrate within a cell (5′ longitude × 3′ latitude dissolved to 100 m resolution; further referred to as soil) as described in the supplementary information of ref. 21.
Environmental suitability modelling
We parameterized logistic regression models (LRMs) with a logit link function using species presence/absence data as response and the three environmental (two bioclimatic and one soil) variables as predictors. All predictor variables entered the model as second-order polynomials in agreement with the standard unimodal niche concept.
From the models, we also derived a threshold value to use for translating predicted probability of occurrence (as a measure of site suitability) into predicted presence or absence of each species at a site (called occurrence threshold, OT, henceforth). The threshold was defined such that it optimized the true skills statistic (TSS), a measure of predictive accuracy derived from comparing observed and predicted presence–absence maps51.
Genetic model and niche partitioning
Species-specific suitability curves for the annual mean temperature gradient derived from the LRMs were partitioned into suitability curves of ecologically different haplotypes of a species as defined by allelic variation in up to three diploid loci (Extended Data Fig. 6). The number of alleles was varied (n = 1, 2, 3, 5 and 10 alleles) as was the proportion of the entire species’ (temperature) niche covered by each haplotype. Models with more than one locus were run with diallelic loci, as otherwise computational efforts would have increased excessively (for each haplotype the number of seeds, juveniles and adults has to be stored and all seeds have to be distributed separately). Each combination of haplotype number and allelic niche size used in a particular simulation is further referred to as setting. Species-specific suitability curves along the other two dimensions (precipitation and soil) remained unpartitioned to ease interpretation of results. The implications of relaxing this assumption by modelling niche partitioning along different environmental gradients are hard to predict. Outcomes would probably depend on the direction and strength of individual specialization along these gradients, whether they are positively or negatively correlated, as well as on how both temperature and precipitation patterns will be affected by climate change. As a consequence, the patterns we found could be re-enforced, for example when the replacement of cold-adapted haplotypes within the species elevational range is further delayed, for example, because those haplotypes adapted to warmer conditions can cope less well with higher precipitation at higher elevations. Vice versa, maladaptation to the warming temperatures might be attenuated, for example, if temperature increase is paralleled by precipitation decrease and emerging drought stress. If, in this case, haplotypes from lower elevations can better cope with both higher temperatures and less water availability than those of median elevations, they may replace the latter faster at these median elevations and hence shorten the phase of maladaptation.
Allelic effects were assumed to define the temperature optimum additively. Hence, the heterozygotes’ optimum is always exactly between the optima of the two corresponding homozygotes, corresponding to a codominant genetic model. Finally, all haplotypes corresponding to one setting were assumed to have constant (temperature) niche size, defined as a proportion (ω = 50%, 75% and 100%, for one haplotype only 100%) of the entire species’ (temperature) niche. The temperature niche was computed as the difference between the upper and lower temperature values at which the LRM-derived suitability curve predicted a suitability equal to OT (with precipitation and soil set to the respective optima of the species, also derived from the LRMs). To derive the same geographic distribution under current climatic conditions for each setting, the union of the niches of all haplotypes of one set has to approximate the niche of the single-species model (Extended Data Fig. 6). Note, however, that, the aspired equality of niches is impossible, as the niches resulting from a logistic regression with quadratic terms are always elliptic in shape. Therefore, the optima of the two extreme homozygotes (that is, those carrying haplotypes adapted to the coldest or warmest margins of the entire species’ niche) are fixed at: niche limits ± 1/2 × ω × niche size and all other optima are distributed between them at equal distances (Extended Data Fig. 6 gives a schematic illustration). As a consequence, the performance of the extreme haplotypes, both coldest and warmest, is modelled to be somewhat higher towards the cold and warm margins of the temperature niche, respectively, compared with the performance modelled for the species without intraspecific niche partitioning (compare the overlap of the black with the red and blue curves in Extended Data Fig. 6a). However, as haplotype number did not affect modelled range loss (compare Table 1), this marginal mismatch does not apparently impact our results. Homozygotes were ordered from the cold-adapted A1A1 up to the warm-adapted AnAn.
Finally, the suitability curves of the genotypes were assumed to have the same value at their optimum as the species-specific suitability curve at this point (Extended Data Fig. 6).
Artificial landscapes
Artificial landscapes were defined as a raster of 50 × 112 cells (of 100 × 100 m). These rasters were homogeneous with respect to precipitation and soil carbon conditions which were set to the values optimal for each species according to the LRMs. With respect to temperature, by contrast, we implemented a gradient across the raster running from the minimum –9.1 °C to the maximum +3.8 °C temperature for which the LRM predicts values >OT across all six species. Buffering by 1 °C at both limits was done to avoid truncating simulation results. Further 4 °C at the lower limit were added to consider simulated temperature increase (below). The final temperature range represented by the raster ran from −14.1 to +4.8 °C. Temperature increased linearly along this axis by an increment of 0.171 °C per cell, derived from a 20° slope and a temperature decrease of 0.5 °C per 100 m of elevational change. Along the 50-cell breadth of the landscape, temperature values were kept constant. On the basis of these grids, we implemented a moderate and a severe climate change scenario, characterized by temperature increases of 2 and 4 °C, respectively, over 80 yr. Therefore, temperature of each raster cell increased annually by 0.025 and 0.05 °C, respectively.
Simulations of spatiotemporal range dynamics
CATS21 is a spatially and temporarily explicit model operating on a two-dimensional grid (of 100 m mesh size in this case). CATS combines simulations of local species’ demography with species’ distribution models by scaling demographic rates relative to occurrence probabilities (suitabilities) predicted for the respective site or grid cell by the latter. Dispersal among grid cells is modelled as a combination of wind, exozoochoric and endozoochoric (that is, animal dispersal via attachment to the fur or ingestion and defecation, respectively) dispersal of plant seeds. Time proceeds in annual steps. The annually changing occurrence probabilities at each site affect the demography of local populations and hence, eventually, the number of seeds that are produced in each grid cell in the respective year. As a consequence, local populations grow or decrease, become extinct or establish anew and hence the species’ distribution across the whole study area changes as a function of the changing climate.
Demographic modelling
Climate-dependence of local demography was modelled by linking demographic rates (seed persistence, germination, survival, flowering frequency, seed yield and clonal reproduction) and carrying capacity to occurrence probabilities predicted by LRMs by means of sigmoidal functions. Furthermore, all rates were fixed at OT at a value ensuring stable population sizes; for more information see refs. 21,33. Demographic rates were confined by zero and a species-specific maximum value (Supplementary Table 1), which was assumed to be the same for all genotypes of a species. As a corollary, the demographic rates of all genotypes of a species are the same under optimal environmental conditions but their actual values for a particular site in a particular year differ due to different temperature optima of genotypes. In addition, germination, survival and clonal reproduction were modelled as density-dependent processes to account for intraspecific competition between genotypes. In our application, for all density-dependent functions, the species abundance is defined as the sum of all adult individuals in a given cell, regardless of their genotypes. Density dependence is commonly achieved by multiplying rates with (C – N)/C, where N is the species abundance and C is the (site- and genotype-specific) carrying capacity. This correction for density dependence causes the functions to drop to zero when N approximates C. To avoid the subsequent collapse of population sizes, we defined density-dependent rates as (C – N)/C × rate() + N/C × rate(OT), which ensures stable population sizes at densely populated sites occupied by only one genotype. To account for uncertainty in parameters of demographic rates, we assigned each species two value sets representing the upper and lower end of a plausible range of values on the basis of information derived from databases and own measurements (Supplementary Table 1).
The simulations allowed for cross-pollination between genotypes. We used the relative amount of flowers (genotype-specific flowering frequency as defined by the sigmoid curve for the given suitability in the given raster cell for the given year × number of adults of that genotype in the population of that cell) to derive an estimate of the haplotype frequencies in the total pollen produced by the population within a grid cell. For the multiallelic case we allowed for recombination between loci with a recombination rate of 0.1%. These frequencies were set equal to the probability that particular haplotypes are transmitted to each year’s seed yield by pollination. Spatial pollen dispersal was accounted for in the following way: in each cell, 5% of the pollen involved in producing the annual seed yield, was assumed to stem from outside the respective raster cell. The proportions of different haplotypes in this 5% were derived from the overall pollen frequencies in all cells within a 700 m radius around the target cell (following estimates in ref. 52). Subsequently, produced seeds of each genotype were divided into resulting genotypes regarding the adult’s haplotype composition and the haplotype frequencies in the cells’ entire pollen load.
Dispersal modelling
For wind dispersal of plant species we parameterized the analytical WALD kernel53 on the basis of measured seed traits and wind speed data from a meteorological station in the Central Alps of Austria. Exozoochorous and endozoochorous plant kernels were parameterized on the basis of correlated random walk simulations for the most frequent mammal dispersal vector in the study area, the chamois (Rupicapra rupicapra L.). For more details, see ref. 33. To account for uncertainties in species-specific dispersal rates, the proportion of seeds dispersed by the more far-reaching zoochorous kernels was assumed either as high (1–5%) or low (0.1–0.5%), setting upper and lower boundaries of a credible range of the dispersal ability of species.
Simulation set up and simulation initialization
To test for the effects of climate change on genetic diversity in 2080, we ran CATS over the period 2000 to 2080 for each of the six study species across the entire Alps under a full factorial combination of (1) three niche sizes (50%, 75% and 100%); (2) six numbers of haplotypes (equal to two, three, five and ten alleles for one locus and four and eight for the diallelic two- and three-locus models, respectively); (3) three climate scenarios (current climate, RCP 2.6 and RCP 8.5); and (4) two sets of demographic and dispersal parameters. As a ‘control’ we also ran simulations for all climate scenarios and the two demographic and dispersal parameter sets for a setting with one genotype filling the whole niche of the species. To account for stochastic elements in CATS four replications were run for each combination of ‘treatments’.
For simulations in artificial landscapes we used, instead of RCP 2.6 and RCP 8.5, ‘artificial’ climatic scenarios with an assumed warming of 2 and 4 °C, respectively, and no change in precipitation.
All simulation runs were started with homozygotic individuals only. As initial distribution, for each simulation run each cell predicted to be environmentally suitable to the species (that is, occurrence probability of species >OT)—and within the real distribution range of the species28 (not relevant for simulations in artificial landscapes, of course)—was assumed to be occupied by an equal number of adults of each (homozygotic) genotype, with the total sum equal to the carrying capacity of the site. To accommodate this arbitrary within-cell genetic mixture of homozygotes (and missing heterozygotes) to actual local conditions we started simulations of range dynamics with a burn-in phase of 200 yr, run under constant current climatic conditions. To have a smooth transition from the burn-in phase under current climate (corresponding to the climate of the years 1970–2005; see current climate data) to future climate projections (starting with 2030) and to derive annual climate series, climate data were linearly interpolated between these two time intervals.
Statistical analysis
We evaluated the contribution of climate scenario, haplotype number and haplotype niche size to overall species’ range change as well as the change in the frequency of the warm-adapted haplotype by means of linear models. In these models, log(range size in 2080/range size in 2000) and log(percentage of warm-adapted haplotype in 2080/percentage of warm-adapted haplotype in 2000), averaged over the four replicates and the two demographic and dispersal parameter sets, were the response variables. For the analysis of the change of the warm-adapted haplotype simulation settings with 100% niche size were ignored, as in this setting all haplotypes have the same temperature optimum (that is, neutral genetic variation). Approximate normality of residuals was confirmed by visual inspection.
As indicator of the ‘topographic opportunity’ remaining to the species in the real world we calculated the area colonizable at elevations higher than those already occupied at the end of the simulation period. We therefore drew a buffer of 1 km around each cell predicted to be occupied in 2080 and then summed the area within these buffers at a higher elevation than the focal, occupied cell. Overlapping buffer areas were only counted once. This calculation was done for simulations conducted with one full-niche genotype per species only.
Sensitivity analysis
We interpret the simulated relative decrease of warm-adapted haplotypes mainly as an effect of (1) the unrestricted expansion of cold-adapted haplotypes at the leading edge and (2) the resistance of the locally predominating haplotype that becomes increasingly maladapted with progressive climate warming, to recruitment by better-adapted haplotypes from below that are either rare or not present at all initially. However, the results achieved, and our conclusions, may be sensitive to assumptions about particular parameter values. Parameters that control the longevity of adult plants, and indirectly the rate of recruitment of new individuals, as well as those controlling gene flow via pollen (instead of seeds) may be particularly influential in this respect. We additionally ran simulations on artificial landscapes under alternative values of these parameters. In particular, we set the maximum age of plants to 10 yr instead of 100 yr and raised the proportion of locally produced pollen assumed to be transported up to 700 m to 10%. Both of these values are thus probably set to rather extreme levels: a maximum age of 10 yr is much shorter than the 30–50 yr assumed to be the standard age of (non-clonal) alpine plants31; and a cross-pollination rate between cells of 10% is high given that among the most important alpine pollinators only bumblebees are assumed to transport pollen >100 m regularly54,55. We add that we ran these additional simulations only in combination with the demographic species parameters set to high values because a short life span combined with low-level demographic parameters did not allow for stable populations of some species, even under current climatic conditions.
For individual species, adapting plant age and cross-pollination rate between cells (Extended Data Fig. 7), did change the magnitude of loss of the warm-adapted haplotype. Nevertheless, for all of them the warm-adapted haplotype still became rarer when climate warmed and this effect increased with the level of warming. We are confident that our conclusions are qualitatively insensitive to variation of these parameters within a realistic range.
Finally, in the simulations where we assumed a multilocus structure of the temperature niche, the recombination rate may also affect simulation results because it determines the rate by which new haplotypes can emerge. We also tested sensitivity of our simulations to doubling the recombination rate to 0.2%. Again, we found that a higher recombination rate had little qualitative effect on the results. Quantitatively, it resulted in a slightly pronounced relative decrease of the warmth-adapted haplotype in most species (Extended Data Fig. 8).
Reporting Summary
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