Global habitat suitability models of terrestrial mammals.

Detailed large-scale information on mammal distribution has often been lacking, hindering conservation efforts. We used the information from the 2009 IUCN Red List of Threatened Species as a baseline for developing habitat suitability models for 5027 out of 5330 known terrestrial mammal species, based on their habitat relationships. We focused on the following environmental variables: land cover, elevation and hydrological features. Models were developed at 300 m resolution and limited to within species' known geographical ranges. A subset of the models was validated using points of known species occurrence. We conducted a global, fine-scale analysis of patterns of species richness. The richness of mammal species estimated by the overlap of their suitable habitat is on average one-third less than that estimated by the overlap of their geographical ranges. The highest absolute difference is found in tropical and subtropical regions in South America, Africa and Southeast Asia that are not covered by dense forest. The proportion of suitable habitat within mammal geographical ranges correlates with the IUCN Red List category to which they have been assigned, decreasing monotonically from Least Concern to Endangered. These results demonstrate the importance of fine-resolution distribution data for the development of global conservation strategies for mammals.

Introduction of snow and geomorphic disturbance variables into predictive models of alpine plant distribution in the Western Swiss Alps

Indirect topographic variables have been used successfully as surrogates for disturbance processes in plant species distribution models (SDM) in mountain environments. However, no SDM studies have directly tested the performance of disturbance variables. In this study, we developed two disturbance variables: a geomorphic index (GEO) and an index of snow redistribution by wind (SNOW). These were developed in order to assess how they improved both the fit and predictive power of presenceabsence SDM based on commonly used topoclimatic (TC) variables for 91 plants in the Western Swiss Alps. The individual contribution of the disturbance variables was compared to TC variables. Maps of models were prepared to spatially test the effect of disturbance variables. On average, disturbance variables significantly improved the fit but not the predictive power of the TC models and their individual contribution was weak (5.6% for GEO and 3.3% for SNOW). However their maximum individual contribution was important (24.7% and 20.7%). Finally, maps including disturbance variables (i) were significantly divergent from TC models in terms of predicted suitable surfaces and connectivity between potential habitats, and (ii) were interpreted as more ecologically relevant. Disturbance variables did not improve the transferability of models at the local scale in a complex mountain system, and the performance and contribution of these variables were highly species-specific. However, improved spatial projections and change in connectivity are important issues when preparing projections under climate change because the future range size of the species will determine the sensitivity to changing conditions.

The branch-site test of positive selection is surprisingly robust but lacks power under synonymous substitution saturation and variation in GC

Positive selection is widely estimated from protein coding sequence alignments by the nonsynonymous-to-synonymous ratio omega. Increasingly elaborate codon models are used in a likelihood framework for this estimation. Although there is widespread concern about the robustness of the estimation of the omega ratio, more efforts are needed to estimate this robustness, especially in the context of complex models. Here, we focused on the branch-site codon model. We investigated its robustness on a large set of simulated data. First, we investigated the impact of sequence divergence. We found evidence of underestimation of the synonymous substitution rate for values as small as 0.5, with a slight increase in false positives for the branch-site test. When dS increases further, underestimation of dS is worse, but false positives decrease. Interestingly, the detection of true positives follows a similar distribution, with a maximum for intermediary values of dS. Thus, high dS is more of a concern for a loss of power (false negatives) than for false positives of the test. Second, we investigated the impact of GC content. We showed that there is no significant difference of false positives between high GC (up to similar to 80%) and low GC (similar to 30%) genes. Moreover, neither shifts of GC content on a specific branch nor major shifts in GC along the gene sequence generate many false positives. Our results confirm that the branch-site is a very conservative test.

Conservation of the Eurasian Lynx (Lynx lynx) in a fragmented landscape - habitat models, dispersal and potential distribution

Abstract: The expansion of a recovering population - whether re-introduced or spontaneously returning - is shaped by (i) biological (intrinsic) factors such as the land tenure system or dispersal, (ii) the distribution and availability of resources (e.g. prey), (iii) habitat and landscape features, and (iv) human attitudes and activities. In order to develop efficient conservation and recovery strategies, we need to understand all these factors and to predict the potential distribution and explore ways to reach it. An increased number of lynx in the north-western Swiss Alps in the nineties lead to a new controversy about the return of this cat. When the large carnivores were given legal protection in many European countries, most organizations and individuals promoting their protection did not foresee the consequences. Management plans describing how to handle conflicts with large predators are needed to find a balance between "overabundance" and extinction. Wildlife and conservation biologists need to evaluate the various threats confronting populations so that adequate management decisions can be taken. I developed a GIS probability model for the lynx, based on habitat information and radio-telemetry data from the Swiss Jura Mountains, in order to predict the potential distribution of the lynx in this mountain range, which is presently only partly occupied by lynx. Three of the 18 variables tested for each square kilometre describing land use, vegetation, and topography, qualified to predict the probability of lynx presence. The resulting map was evaluated with data from dispersing subadult lynx. Young lynx that were not able to establish home ranges in what was identified as good lynx habitat did not survive their first year of independence, whereas the only one that died in good lynx habitat was illegally killed. Radio-telemetry fixes are often used as input data to calibrate habitat models. Radio-telemetry is the only way to gather accurate and unbiased data on habitat use of elusive larger terrestrial mammals. However, it is time consuming and expensive, and can therefore only be applied in limited areas. Habitat models extrapolated over large areas can in turn be problematic, as habitat characteristics and availability may change from one area to the other. I analysed the predictive power of Ecological Niche Factor Analysis (ENFA) in Switzerland with the lynx as focal species. According to my results, the optimal sampling strategy to predict species distribution in an Alpine area lacking available data would be to pool presence cells from contrasted regions (Jura Mountains, Alps), whereas in regions with a low ecological variance (Jura Mountains), only local presence cells should be used for the calibration of the model. Dispersal influences the dynamics and persistence of populations, the distribution and abundance of species, and gives the communities and ecosystems their characteristic texture in space and time. Between 1988 and 2001, the spatio-temporal behaviour of subadult Eurasian lynx in two re-introduced populations in Switzerland was studied, based on 39 juvenile lynx of which 24 were radio-tagged to understand the factors influencing dispersal. Subadults become independent from their mothers at the age of 8-11 months. No sex bias neither in the dispersal rate nor in the distance moved was detected. Lynx are conservative dispersers, compared to bear and wolf, and settled within or close to known lynx occurrences. Dispersal distances reached in the high lynx density population - shorter than those reported in other Eurasian lynx studies - are limited by habitat restriction hindering connections with neighbouring metapopulations. I postulated that high lynx density would lead to an expansion of the population and validated my predictions with data from the north-western Swiss Alps where about 1995 a strong increase in lynx abundance took place. The general hypothesis that high population density will foster the expansion of the population was not confirmed. This has consequences for the re-introduction and recovery of carnivores in a fragmented landscape. To establish a strong source population in one place might not be an optimal strategy. Rather, population nuclei should be founded in several neighbouring patches. Exchange between established neighbouring subpopulations will later on take place, as adult lynx show a higher propensity to cross barriers than subadults. To estimate the potential population size of the lynx in the Jura Mountains and to assess possible corridors between this population and adjacent areas, I adapted a habitat probability model for lynx distribution in the Jura Mountains with new environmental data and extrapolated it over the entire mountain range. The model predicts a breeding population ranging from 74-101 individuals and from 51-79 individuals when continuous habitat patches < 50 km2 are disregarded. The Jura Mountains could once be part of a metapopulation, as potential corridors exist to the adjoining areas (Alps, Vosges Mountains, and Black Forest). Monitoring of the population size, spatial expansion, and the genetic surveillance in the Jura Mountains must be continued, as the status of the population is still critical. ENFA was used to predict the potential distribution of lynx in the Alps. The resulting model divided the Alps into 37 suitable habitat patches ranging from 50 to 18,711 km2, covering a total area of about 93,600 km2. When using the range of lynx densities found in field studies in Switzerland, the Alps could host a population of 961 to 1,827 residents. The results of the cost-distance analysis revealed that all patches were within the reach of dispersing lynx, as the connection costs were in the range of dispersal cost of radio-tagged subadult lynx moving through unfavorable habitat. Thus, the whole Alps could once be considered as a metapopulation. But experience suggests that only few disperser will cross unsuitable areas and barriers. This low migration rate may seldom allow the spontaneous foundation of new populations in unsettled areas. As an alternative to natural dispersal, artificial transfer of individuals across the barriers should be considered. Wildlife biologists can play a crucial role in developing adaptive management experiments to help managers learning by trial. The case of the lynx in Switzerland is a good example of a fruitful cooperation between wildlife biologists, managers, decision makers and politician in an adaptive management process. This cooperation resulted in a Lynx Management Plan which was implemented in 2000 and updated in 2004 to give the cantons directives on how to handle lynx-related problems. This plan was put into practice e.g. in regard to translocation of lynx into unsettled areas. Résumé: L'expansion d'une population en phase de recolonisation, qu'elle soit issue de réintroductions ou d'un retour naturel dépend 1) de facteurs biologiques tels que le système social et le mode de dispersion, 2) de la distribution et la disponibilité des ressources (proies), 3) de l'habitat et des éléments du paysage, 4) de l'acceptation de l'espèce par la population locale et des activités humaines. Afin de pouvoir développer des stratégies efficaces de conservation et de favoriser la recolonisation, chacun de ces facteurs doit être pris en compte. En plus, la distribution potentielle de l'espèce doit pouvoir être déterminée et enfin, toutes les possibilités pour atteindre les objectifs, examinées. La phase de haute densité que la population de lynx a connue dans les années nonante dans le nord-ouest des Alpes suisses a donné lieu à une controverse assez vive. La protection du lynx dans de nombreux pays européens, promue par différentes organisations, a entraîné des conséquences inattendues; ces dernières montrent que tout plan de gestion doit impérativement indiquer des pistes quant à la manière de gérer les conflits, tout en trouvant un équilibre entre l'extinction et la surabondance de l'espèce. Les biologistes de la conservation et de la faune sauvage doivent pour cela évaluer les différents risques encourus par les populations de lynx, afin de pouvoir rapidement prendre les meilleuresmdécisions de gestion. Un modèle d'habitat pour le lynx, basé sur des caractéristiques de l'habitat et des données radio télémétriques collectées dans la chaîne du Jura, a été élaboré afin de prédire la distribution potentielle dans cette région, qui n'est que partiellement occupée par l'espèce. Trois des 18 variables testées, décrivant pour chaque kilomètre carré l'utilisation du sol, la végétation ainsi que la topographie, ont été retenues pour déterminer la probabilité de présence du lynx. La carte qui en résulte a été comparée aux données télémétriques de lynx subadultes en phase de dispersion. Les jeunes qui n'ont pas pu établir leur domaine vital dans l'habitat favorable prédit par le modèle n'ont pas survécu leur première année d'indépendance alors que le seul individu qui est mort dans l'habitat favorable a été braconné. Les données radio-télémétriques sont souvent utilisées pour l'étalonnage de modèles d'habitat. C'est un des seuls moyens à disposition qui permette de récolter des données non biaisées et précises sur l'occupation de l'habitat par des mammifères terrestres aux moeurs discrètes. Mais ces méthodes de- mandent un important investissement en moyens financiers et en temps et peuvent, de ce fait, n'être appliquées qu'à des zones limitées. Les modèles d'habitat sont ainsi souvent extrapolés à de grandes surfaces malgré le risque d'imprécision, qui résulte des variations des caractéristiques et de la disponibilité de l'habitat d'une zone à l'autre. Le pouvoir de prédiction de l'Analyse Ecologique de la Niche (AEN) dans les zones où les données de présence n'ont pas été prises en compte dans le calibrage du modèle a été analysée dans le cas du lynx en Suisse. D'après les résultats obtenus, la meilleure mé- thode pour prédire la distribution du lynx dans une zone alpine dépourvue d'indices de présence est de combiner des données provenant de régions contrastées (Alpes, Jura). Par contre, seules les données sur la présence locale de l'espèce doivent être utilisées pour les zones présentant une faible variance écologique tel que le Jura. La dispersion influence la dynamique et la stabilité des populations, la distribution et l'abondance des espèces et détermine les caractéristiques spatiales et temporelles des communautés vivantes et des écosystèmes. Entre 1988 et 2001, le comportement spatio-temporel de lynx eurasiens subadultes de deux populations réintroduites en Suisse a été étudié, basé sur le suivi de 39 individus juvéniles dont 24 étaient munis d'un collier émetteur, afin de déterminer les facteurs qui influencent la dispersion. Les subadultes se sont séparés de leur mère à l'âge de 8 à 11 mois. Le sexe n'a pas eu d'influence sur le nombre d'individus ayant dispersés et la distance parcourue au cours de la dispersion. Comparé à l'ours et au loup, le lynx reste très modéré dans ses mouvements de dispersion. Tous les individus ayant dispersés se sont établis à proximité ou dans des zones déjà occupées par des lynx. Les distances parcourues lors de la dispersion ont été plus courtes pour la population en phase de haute densité que celles relevées par les autres études de dispersion du lynx eurasien. Les zones d'habitat peu favorables et les barrières qui interrompent la connectivité entre les populations sont les principales entraves aux déplacements, lors de la dispersion. Dans un premier temps, nous avons fait l'hypothèse que les phases de haute densité favorisaient l'expansion des populations. Mais cette hypothèse a été infirmée par les résultats issus du suivi des lynx réalisé dans le nord-ouest des Alpes, où la population connaissait une phase de haute densité depuis 1995. Ce constat est important pour la conservation d'une population de carnivores dans un habitat fragmenté. Ainsi, instaurer une forte population source à un seul endroit n'est pas forcément la stratégie la plus judicieuse. Il est préférable d'établir des noyaux de populations dans des régions voisines où l'habitat est favorable. Des échanges entre des populations avoisinantes pourront avoir lieu par la suite car les lynx adultes sont plus enclins à franchir les barrières qui entravent leurs déplacements que les individus subadultes. Afin d'estimer la taille de la population de lynx dans le Jura et de déterminer les corridors potentiels entre cette région et les zones avoisinantes, un modèle d'habitat a été utilisé, basé sur un nouveau jeu de variables environnementales et extrapolé à l'ensemble du Jura. Le modèle prédit une population reproductrice de 74 à 101 individus et de 51 à 79 individus lorsque les surfaces d'habitat d'un seul tenant de moins de 50 km2 sont soustraites. Comme des corridors potentiels existent effectivement entre le Jura et les régions avoisinantes (Alpes, Vosges, et Forêt Noire), le Jura pourrait faire partie à l'avenir d'une métapopulation, lorsque les zones avoisinantes seront colonisées par l'espèce. La surveillance de la taille de la population, de son expansion spatiale et de sa structure génétique doit être maintenue car le statut de cette population est encore critique. L'AEN a également été utilisée pour prédire l'habitat favorable du lynx dans les Alpes. Le modèle qui en résulte divise les Alpes en 37 sous-unités d'habitat favorable dont la surface varie de 50 à 18'711 km2, pour une superficie totale de 93'600 km2. En utilisant le spectre des densités observées dans les études radio-télémétriques effectuées en Suisse, les Alpes pourraient accueillir une population de lynx résidents variant de 961 à 1'827 individus. Les résultats des analyses de connectivité montrent que les sous-unités d'habitat favorable se situent à des distances telles que le coût de la dispersion pour l'espèce est admissible. L'ensemble des Alpes pourrait donc un jour former une métapopulation. Mais l'expérience montre que très peu d'individus traverseront des habitats peu favorables et des barrières au cours de leur dispersion. Ce faible taux de migration rendra difficile toute nouvelle implantation de populations dans des zones inoccupées. Une solution alternative existe cependant : transférer artificiellement des individus d'une zone à l'autre. Les biologistes spécialistes de la faune sauvage peuvent jouer un rôle important et complémentaire pour les gestionnaires de la faune, en les aidant à mener des expériences de gestion par essai. Le cas du lynx en Suisse est un bel exemple d'une collaboration fructueuse entre biologistes de la faune sauvage, gestionnaires, organes décisionnaires et politiciens. Cette coopération a permis l'élaboration du Concept Lynx Suisse qui est entré en vigueur en 2000 et remis à jour en 2004. Ce plan donne des directives aux cantons pour appréhender la problématique du lynx. Il y a déjà eu des applications concrètes sur le terrain, notamment par des translocations d'individus dans des zones encore inoccupées.

Effects of sample size on the performance of species distribution models

A wide range of modelling algorithms is used by ecologists, conservation practitioners, and others to predict species ranges from point locality data. Unfortunately, the amount of data available is limited for many taxa and regions, making it essential to quantify the sensitivity of these algorithms to sample size. This is the first study to address this need by rigorously evaluating a broad suite of algorithms with independent presence-absence data from multiple species and regions. We evaluated predictions from 12 algorithms for 46 species (from six different regions of the world) at three sample sizes (100, 30, and 10 records). We used data from natural history collections to run the models, and evaluated the quality of model predictions with area under the receiver operating characteristic curve (AUC). With decreasing sample size, model accuracy decreased and variability increased across species and between models. Novel modelling methods that incorporate both interactions between predictor variables and complex response shapes (i.e. GBM, MARS-INT, BRUTO) performed better than most methods at large sample sizes but not at the smallest sample sizes. Other algorithms were much less sensitive to sample size, including an algorithm based on maximum entropy (MAXENT) that had among the best predictive power across all sample sizes. Relative to other algorithms, a distance metric algorithm (DOMAIN) and a genetic algorithm (OM-GARP) had intermediate performance at the largest sample size and among the best performance at the lowest sample size. No algorithm predicted consistently well with small sample size (n < 30) and this should encourage highly conservative use of predictions based on small sample size and restrict their use to exploratory modelling.

What matters for predicting spatial distributions of trees: techniques, data, or species' characteristics?

Data characteristics and species traits are expected to influence the accuracy with which species' distributions can be modeled and predicted. We compare 10 modeling techniques in terms of predictive power and sensitivity to location error, change in map resolution, and sample size, and assess whether some species traits can explain variation in model performance. We focused on 30 native tree species in Switzerland and used presence-only data to model current distribution, which we evaluated against independent presence-absence data. While there are important differences between the predictive performance of modeling methods, the variance in model performance is greater among species than among techniques. Within the range of data perturbations in this study, some extrinsic parameters of data affect model performance more than others: location error and sample size reduced performance of many techniques, whereas grain had little effect on most techniques. No technique can rescue species that are difficult to predict. The predictive power of species-distribution models can partly be predicted from a series of species characteristics and traits based on growth rate, elevational distribution range, and maximum elevation. Slow-growing species or species with narrow and specialized niches tend to be better modeled. The Swiss presence-only tree data produce models that are reliable enough to be useful in planning and management applications.

Accuracy of indirect estimation of power output from uphill performance in cycling.

PURPOSE: To use measurement by cycling power meters (Pmes) to evaluate the accuracy of commonly used models for estimating uphill cycling power (Pest). Experiments were designed to explore the influence of wind speed and steepness of climb on accuracy of Pest. The authors hypothesized that the random error in Pest would be largely influenced by the windy conditions, the bias would be diminished in steeper climbs, and windy conditions would induce larger bias in Pest. METHODS: Sixteen well-trained cyclists performed 15 uphill-cycling trials (range: length 1.3-6.3 km, slope 4.4-10.7%) in a random order. Trials included different riding position in a group (lead or follow) and different wind speeds. Pmes was quantified using a power meter, and Pest was calculated with a methodology used by journalists reporting on the Tour de France. RESULTS: Overall, the difference between Pmes and Pest was -0.95% (95%CI: -10.4%, +8.5%) for all trials and 0.24% (-6.1%, +6.6%) in conditions without wind (<2 m/s). The relationship between percent slope and the error between Pest and Pmes were considered trivial. CONCLUSIONS: Aerodynamic drag (affected by wind velocity and orientation, frontal area, drafting, and speed) is the most confounding factor. The mean estimated values are close to the power-output values measured by power meters, but the random error is between ±6% and ±10%. Moreover, at the power outputs (>400 W) produced by professional riders, this error is likely to be higher. This observation calls into question the validity of releasing individual values without reporting the range of random errors.

Childhood cancer and nuclear power plants in Switzerland: a census-based cohort study.

BACKGROUND: Previous studies on childhood cancer and nuclear power plants (NPPs) produced conflicting results. We used a cohort approach to examine whether residence near NPPs was associated with leukaemia or any childhood cancer in Switzerland. METHODS: We computed person-years at risk for children aged 0-15 years born in Switzerland from 1985 to 2009, based on the Swiss censuses 1990 and 2000 and identified cancer cases from the Swiss Childhood Cancer Registry. We geo-coded place of residence at birth and calculated incidence rate ratios (IRRs) with 95% confidence intervals (CIs) comparing the risk of cancer in children born <5 km, 5-10 km and 10-15 km from the nearest NPP with children born >15 km away, using Poisson regression models. RESULTS: We included 2925 children diagnosed with cancer during 21 117 524 person-years of follow-up; 953 (32.6%) had leukaemia. Eight and 12 children diagnosed with leukaemia at ages 0-4 and 0-15 years, and 18 and 31 children diagnosed with any cancer were born <5 km from a NPP. Compared with children born >15 km away, the IRRs (95% CI) for leukaemia in 0-4 and 0-15 year olds were 1.20 (0.60-2.41) and 1.05 (0.60-1.86), respectively. For any cancer, corresponding IRRs were 0.97 (0.61-1.54) and 0.89 (0.63-1.27). There was no evidence of a dose-response relationship with distance (P > 0.30). Results were similar for residence at diagnosis and at birth, and when adjusted for potential confounders. Results from sensitivity analyses were consistent with main results. CONCLUSIONS: This nationwide cohort study found little evidence of an association between residence near NPPs and the risk of leukaemia or any childhood cancer.

Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.

Biotic interactions boost spatial models of species richness

Biotic interactions are known to affect the composition of species assemblages via several mechanisms, such as competition and facilitation. However, most spatial models of species richness do not explicitly consider inter-specific interactions. Here, we test whether incorporating biotic interactions into high-resolution models alters predictions of species richness as hypothesised. We included key biotic variables (cover of three dominant arctic-alpine plant species) into two methodologically divergent species richness modelling frameworks - stacked species distribution models (SSDM) and macroecological models (MEM) - for three ecologically and evolutionary distinct taxonomic groups (vascular plants, bryophytes and lichens). Predictions from models including biotic interactions were compared to the predictions of models based on climatic and abiotic data only. Including plant-plant interactions consistently and significantly lowered bias in species richness predictions and increased predictive power for independent evaluation data when compared to the conventional climatic and abiotic data based models. Improvements in predictions were constant irrespective of the modelling framework or taxonomic group used. The global biodiversity crisis necessitates accurate predictions of how changes in biotic and abiotic conditions will potentially affect species richness patterns. Here, we demonstrate that models of the spatial distribution of species richness can be improved by incorporating biotic interactions, and thus that these key predictor factors must be accounted for in biodiversity forecasts

Overcoming limitations of modelling rare species by using ensembles of small models

1. Species distribution models (SDMs) have become a standard tool in ecology and applied conservation biology. Modelling rare and threatened species is particularly important for conservation purposes. However, modelling rare species is difficult because the combination of few occurrences and many predictor variables easily leads to model overfitting. A new strategy using ensembles of small models was recently developed in an attempt to overcome this limitation of rare species modelling and has been tested successfully for only a single species so far. Here, we aim to test the approach more comprehensively on a large number of species including a transferability assessment. 2. For each species numerous small (here bivariate) models were calibrated, evaluated and averaged to an ensemble weighted by AUC scores. These 'ensembles of small models' (ESMs) were compared to standard Species Distribution Models (SDMs) using three commonly used modelling techniques (GLM, GBM, Maxent) and their ensemble prediction. We tested 107 rare and under-sampled plant species of conservation concern in Switzerland. 3. We show that ESMs performed significantly better than standard SDMs. The rarer the species, the more pronounced the effects were. ESMs were also superior to standard SDMs and their ensemble when they were independently evaluated using a transferability assessment. 4. By averaging simple small models to an ensemble, ESMs avoid overfitting without losing explanatory power through reducing the number of predictor variables. They further improve the reliability of species distribution models, especially for rare species, and thus help to overcome limitations of modelling rare species.