The effect of sample size on the accuracy of species distribution models: considering both presences and pseudo‐absences or background sites

Most high‐performing species distribution modelling techniques require both presences, and either absences or pseudo‐absences or background points. In this paper, we explore the effect of sample size, towards developing improved strategies for modelling. We generated 1800 virtual species with three levels of prevalence using ten modelling techniques, while varying the number of training presences (NTP) and the number of random points (NRP representing pseudo‐absences or background sites). For five of the ten modelling techniques we built two versions of models: one with an equal total weight (ETW) setting where the total weight for pseudo‐absence is equivalent to the total weight for presence, and another with an unequal total weight (UTW) setting where the total weight for pseudo‐absence is not required to be equal to the total weight for presence. We compared two strategies for NRP: a small multiplier strategy (i.e. setting NRP at a few times as large as NTP), and a large number strategy (i.e. using numerous random points). We produced ensemble models (by averaging the predictions from 30 models built with the same set of training presences and different sets of random points in equivalent numbers) for three NTP magnitudes and two NRP strategies. We found that model accuracy altered as NRP increased with four distinct patterns of performance: increasing, decreasing, arch‐shaped and horizontal. In most cases ETW improved model performance. Ensemble models had higher accuracy than the corresponding single models, and this improvement was pronounced when NTP was low. We conclude that a large NRP is not always an appropriate strategy. The best choice for NRP will depend on the modelling techniques used, species prevalence and NTP. We recommend building ensemble models instead of single models, using the small multiplier strategy for NRP with ETW, especially when only a small number of species presence records are available.     

Identifying priority areas for conservation of spadefoot toad,Pelobates fuscus insubricus using a maximum entropy approach

In this study, we used a maximum entropy (MaxEnt) approach to model the distribution of the rare European amphibian Pelobates fuscus insubricus, with the final goal of identifying suitable areas for its conservation. We generated the model starting from a dataset of all locations where this species’ presence was confirmed for the region of piedmont in 2004–2010, which consisted of only 15 occurrence records. To verify the working hypothesis that population survival is higher in areas where Maxent identifies higher distribution probability values, we used suitability indexes generated by the model to compare the “historical” (before 1980) and “recent” (1980–1996) distributions of P. f. insubricus populations in the piedmont region. The average area-under-the-curve value (0.878, s = 0.075) of the Maxent model proved significantly informative. Using the Bonferroni confidence interval, we demonstrated that surviving populations occupy geographic areas characterized by significantly higher potential suitability (p < 0.05), and we selected areas accordingly. We therefore conclude that, in our case study, modelling the distribution of rare species may represent a useful strategy to select areas where these species are likely to persist. To further evaluate this approach, we suggest testing it on the study of other rare species.     

Linking local ecological knowledge and habitat modelling to predict absolute species abundance on large scales

Assessing the spatial structure of abundance of a species is a basic requirement to carry out adequate conservation strategies. However, existing attempts to predict species abundance, particularly in absolute units and on large scales, are scarce and have led to weak results. In this work we present a scheme to obtain, in an affordable way, a predictive model of absolute animal abundance on large scales based on the modelling of data obtained from local ecological knowledge (LEK) and its calibration. To exemplify this scheme, we build and validate a predictive absolute abundance model of the endangered terrestrial tortoise Testudo graeca in Southeast Iberian Peninsula. For that purpose, we collected distribution and relative abundance data of T. graeca using a low cost methodology, such as LEK, by means of interviewing shepherds. The information from LEK was employed to build a predictive habitat-based model of relative abundance. The relative abundance model was transformed into an absolute abundance model by means of calibration with a classical absolute abundance sampling method such as distance sampling. The obtained absolute abundance model predicted the observed absolute abundances values well in independent locations when compared with other works (R ² = 36%) and thus can offer a cost-effective predictive ability. Our results show that reliable habitat-based predictive maps of absolute species abundance on regional scales can be obtained starting from low cost sampling methods of relative abundance, such as LEK, and its calibration.     

Improving species distribution models using biotic interactions: a case study of parasites,pollinators and plants

Biotic interactions have been considered as an important factor to be included in species distribution modelling, but little is known about how different types of interaction or different strategies for modelling affect model performance. This study compares different methods for including interspecific interactions in distribution models for bees, their brood parasites, and the plants they pollinate. Host–parasite interactions among bumble bees (genus Bombus: generalist pollinators and brood parasites) and specialist plant–pollinator interactions between Centris bees and Krameria flowers were used as case studies. We used 7 different modelling algorithms available in the BIOMOD R package. For Bombus, the inclusion of interacting species distributions generally increased model predictive accuracy. The improvement was better when the interacting species was included with its raw distribution rather than with its modeled suitability. However, incorporating the distributions of non‐interacting species sometimes resulted in similarly increased model accuracy despite their being no significance of any interaction for the distribution. For the Centris‐Krameria system the best strategy for modelling biotic interactions was to include the interacting species model‐predicted values. However, the results were less consistent than those for Bombus species, and most models including biotic interactions showed no significant improvement over abiotic models. Our results are consistent with previous studies showing that biotic interactions can be important in structuring species distributions at regional scales. However, correlations between species distributions are not necessarily indicative of interactions. Therefore, choosing the correct biotic information, based on biological and ecological knowledge, is critical to improve the accuracy of species distribution models and forecast distribution change.     

Inference is bliss: Simulation for power estimation for an observational study of a cholera outbreak intervention

BackgroundThe evaluation of ring vaccination and other outbreak-containment interventions during severe and rapidly-evolving epidemics presents a challenge for the choice of a feasible study design, and subsequently, for the estimation of statistical power. To support a future evaluation of a case-area targeted intervention against cholera, we have proposed a prospective observational study design to estimate the association between the strength of implementation of this intervention across several small outbreaks (occurring within geographically delineated clusters around primary and secondary cases named ‘rings’) and its effectiveness (defined as a reduction in cholera incidence). We describe here a strategy combining mathematical modelling and simulation to estimate power for a prospective observational study.Methodology and principal findingsThe strategy combines stochastic modelling of transmission and the direct and indirect effects of the intervention in a set of rings, with a simulation of the study analysis on the model results. We found that targeting 80 to 100 rings was required to achieve power ≥80%, using a basic reproduction number of 2.0 and a dispersion coefficient of 1.0–1.5.ConclusionsThis power estimation strategy is feasible to implement for observational study designs which aim to evaluate outbreak containment for other pathogens in geographically or socially defined rings.     

Testing Three Species Distribution Modelling Strategies to Define Fish Assemblage Reference Conditions for Stream Bioassessment and Related Applications

Species distribution models are widely used for stream bioassessment, estimating changes in habitat suitability and identifying conservation priorities. We tested the accuracy of three modelling strategies (single species ensemble, multi-species response and community classification models) to predict fish assemblages at reference stream segments in coastal subtropical Australia. We aimed to evaluate each modelling strategy for consistency of predictor variable selection; determine which strategy is most suitable for stream bioassessment using fish indicators; and appraise which strategies best match other stream management applications. Five models, one single species ensemble, two multi-species response and two community classification models, were calibrated using fish species presence-absence data from 103 reference sites. Models were evaluated for generality and transferability through space and time using four external reference site datasets. Elevation and catchment slope were consistently identified as key correlates of fish assemblage composition among models. The community classification models had high omission error rates and contributed fewer taxa to the ‘expected’ component of the taxonomic completeness (O/E₅₀) index than the other strategies. This potentially decreases the model sensitivity for site impact assessment. The ensemble model accurately and precisely modelled O/E₅₀ for the training data, but produced biased predictions for the external datasets. The multi-species response models afforded relatively high accuracy and precision coupled with low bias across external datasets and had lower taxa omission rates than the community classification models. They inherently included rare, but predictable species while excluding species that were poorly modelled among all strategies. We suggest that the multi-species response modelling strategy is most suited to bioassessment using freshwater fish assemblages in our study area. At the species level, the ensemble model exhibited high sensitivity without reductions in specificity, relative to the other models. We suggest that this strategy is well suited to other non-bioassessment stream management applications, e.g., identifying priority areas for species conservation.     

Extended statistical approaches to modelling spatial pattern in biodiversity in northeast New South Wales. I. Species-level modelling

Statistical modelling of biological survey data in relation to remotely mapped environmental variables is a powerful technique for making more effective use of sparse data in regional conservation planning. Application of such modelling to planning in the northeast New South Wales (NSW) region of Australia represents one of the most extensive and longest running case studies of this approach anywhere in the world. Since the early 1980s, statistical modelling has been used to extrapolate distributions of over 2300 species of plants and animals, and a wide variety of higher-level communities and assemblages. These modelled distributions have played a pivotal role in a series of major land-use planning processes, culminating in extensive additions to the region's protected area system. This paper provides an overview of the analytical methodology used to model distributions of individual species in northeast NSW, including approaches to: (1) developing a basic integrated statistical and geographical information system (GIS) framework to facilitate automated fitting and extrapolation of species models; (2) extending this basic approach to incorporate consideration of spatial autocorrelation, land-cover mapping and expert knowledge; and (3) evaluating the performance of species modelling, both in terms of predictive accuracy and in terms of the effectiveness with which such models function as general surrogates for biodiversity.     

SESAM – a new framework integrating macroecological and species distribution models for predicting spatio‐temporal patterns of species assemblages

Two different approaches currently prevail for predicting spatial patterns of species assemblages. The first approach (macroecological modelling, MEM) focuses directly on realized properties of species assemblages, whereas the second approach (stacked species distribution modelling, S‐SDM) starts with constituent species to approximate the properties of assemblages. Here, we propose to unify the two approaches in a single ‘spatially explicit species assemblage modelling’ (SESAM) framework. This framework uses relevant designations of initial species source pools for modelling, macroecological variables, and ecological assembly rules to constrain predictions of the richness and composition of species assemblages obtained by stacking predictions of individual species distributions. We believe that such a framework could prove useful in many theoretical and applied disciplines of ecology and evolution, both for improving our basic understanding of species assembly across spatio‐temporal scales and for anticipating expected consequences of local, regional or global environmental changes. In this paper, we propose such a framework and call for further developments and testing across a broad range of community types in a variety of environments.     

A complex mode of aggressive mimicry in a scale-eating cichlid fish

Aggressive mimicry is an adaptive tactic of parasitic or predatory species that closely resemble inoffensive models in order to increase fitness via predatory gains. Although similarity of distantly related species is often intuitively implicated with mimicry, the exact mechanisms and evolutionary causes remain elusive in many cases. Here, we report a complex aggressive mimicry strategy in Plecodus straeleni, a scale-eating cichlid fish from Lake Tanganyika, which imitates two other cichlid species. Employing targeted sequencing on ingested scales, we show that P. straeleni does not preferentially parasitize its models but—contrary to prevailing assumptions—targets a variety of co-occurring dissimilar looking fish species. Combined with tests for visual resemblance and visual modelling from a prey perspective, our results suggest that complex interactions among different cichlid species are involved in this mimicry system.     

Giants invading the tropics: the oriental vessel fern, Angiopteris evecta (Marattiaceae)

The Oriental vessel fern, Angiopteris evecta (G.Forst.) Hoffm. (Marattiaceae), has its native range in the South Pacific. This species has been introduced into other localities since the 18th century and is now listed as an invasive species in several regions (Jamaica, Hawaii and Costa Rica). The purpose of our study is (1) to trace the distributional history of the species, and (2) to model its potential future range based on climatic conditions. The native range and the history of introduction are based on the existing literature and on 158 specimens from 15 herbaria, together with field observations. As there are taxonomic problems surrounding A. evecta, we limited our analysis to samples from the Pacific, most closely resembling the type from Tahiti. We modelled the potential range using GARP species distribution modelling with basic climatic variables, elevation, and location in relation to the coast. Analysis of past records shows that the species is able to colonise new ecosystems with relative ease. The modelling reveals that the species could be cultivated over a much wider range than where it currently is grown. The escape of cultivated plants into nature is probably due to distance from natural areas and is limited by local ecological factors, such as soil conditions or competitors. The predicted distribution in Asia and Madagascar is similar to the native distribution of the entire genus Angiopteris. It can therefore be assumed that most Angiopteris species have similar climatic preferences, and the absence of A. evecta in this predicted region may be due to dispersal limitation. In the Americas there is no native Angiopteris, but our climatic model predicts a vast potential habitat in tropical America; an invasion of A. evecta should be anticipated here in localities where the species is cultivated. Vessel ferns are known to alter the natural environment, which may reduce local biodiversity. Since A. evecta is not yet widely cultivated, it is advisable to restrict the trade and spread of the species and to discourage its cultivation as an ornamental. The global climate data available for modelling is however not detailed enough to predict the spread of A. evecta on a local or regional scale.     

Spatial scale,topography and thermoregulatory behaviour interact when modelling species’ thermal niches

The spatial scale at which climate and species’ occupancy data are gathered, and the resolution at which ecological models are run, can strongly influence predictions of species performance and distributions. Running model simulations at coarse rather than fine spatial resolutions, for example, can determine if a model accurately predicts the distribution of a species. The impacts of spatial scale on a model's accuracy are particularly pronounced across mountainous terrain. Understanding how these discrepancies arise requires a modelling approach in which the underlying processes that determine a species’ distribution are explicitly described. Here we use a process‐based model to explore how spatial resolution, topography and behaviour alter predictions of a species thermal niche, which in turn constrains its survival and geographic distribution. The model incorporates biophysical equations to predict the operative temperature (T_e), thermal‐dependent performance and survival of a typical insect, with a complex life‐cycle, in its microclimate. We run this model with geographic data from a mountainous terrain in South Africa using climate data at three spatial resolutions. We also explore how behavioural thermoregulation affects predictions of a species performance and survival by allowing the animal to select the optimum thermal location within each coarse‐grid cell. At the regional level, coarse‐resolution models predicted lower T_e at low elevations and higher T_e at high elevations than models run at fine‐resolutions. These differences were more prominent on steep, north‐facing slopes. The discrepancies in T_e in turn affected estimates of the species thermal niche. The modelling framework revealed how spatial resolution and topography influence predictions of species distribution models, including the potential impacts of climate change. These systematic biases must be accounted for when interpreting the outputs of future modelling studies, particularly when species distributions are predicted to shift from uniform to topographically heterogeneous landscapes.     

Accounting for uncertainty in colonisation times: a novel approach to modelling the spatio‐temporal dynamics of alien invasions using distribution data

A novel, yet generic, Bayesian approach to parameter inference in a stochastic, spatio‐temporal model of dispersal and colonisation is developed and applied to the invasion of a region by an alien plant species. The method requires species distribution data from multiple time points, and accounts for temporal uncertainty in colonisation times inherent in such data. Covariates, such as climate parameters, altitude and land use, which capture variation in the suitability of sites for plant colonisation, are easily incorporated into the model. The method assumes no local extinction of occupied sites and thus is primarily applicable to modelling distribution data at relatively coarse spatial resolutions of plant species whose range is expanding over time. The implementation of the model and inference algorithm are illustrated through application to British floristic atlas data for the widespread alien Heracleum mantegazzianum (giant hogweed) assessed at a 10 × 10 km resolution in 1970 and 2000. We infer key characteristics of this species, predict its future spread, and use the resulting fitted model to inform a simulation‐based assessment of the methodology. Simulated distribution data are used to validate the inference algorithm. Our results suggest that the accuracy of inference is not sensitive to the number of distribution time points, requiring only that there are at least two points in time when distributions are mapped. We demonstrate the utility of the modelling approach by making future forecasts and historic hindcasts of the distribution of giant hogweed in Great Britain. Giant hogweed is one of the worst alien plants in Britain and has rapidly increased its range since 1970, yet we highlight that a further 20% of land area remains susceptible to colonisation by this species. We use the robustness of this case study to discuss the potential for modelling distribution data for other species and at different spatial scales.     

Assessing the accuracy of species distribution models to predict amphibian species richness patterns

1. Evaluating the distribution of species richness where biodiversity is high but has been insufficiently sampled is not an easy task. Species distribution modelling has become a useful approach for predicting their ranges, based on the relationships between species records and environmental variables. Overlapping predictions of individual distributions could be a useful strategy for obtaining estimates of species richness and composition in a region, but these estimates should be evaluated using a proper validation process, which compares the predicted richness values and composition with accurate data from independent sources. 2. In this study, we propose a simple approach to estimate model performance for several distributional predictions generated simultaneously. This approach is particularly suitable when species distribution modelling techniques that require only presence data are used. 3. The individual distributions for the 370 known amphibian species of Mexico were predicted using maxent to model data on their known presence (66,113 presence-only records). Distributions were subsequently overlapped to obtain a prediction of species richness. Accuracy was assessed by comparing the overall species richness values predicted for the region with observed and predicted values from 118 well-surveyed sites, each with an area of c. 100 km(2), which were identified using species accumulation curves and nonparametric estimators. 4. The derived models revealed a remarkable heterogeneity of species richness across the country, provided information about species composition per site and allowed us to obtain a measure of the spatial distribution of prediction errors. Examining the magnitude and location of model inaccuracies, as well as separately assessing errors of both commission and omission, highlights the inaccuracy of the predictions of species distribution models and the need to provide measures of uncertainty along with the model results. 5. The combination of a species distribution modelling method like maxent and species richness estimators offers a useful tool for identifying when the overall pattern provided by all model predictions might be representing the geographical patterns of species richness and composition, regardless of the particular quality or accuracy of the predictions for each individual species.     

The role of functional traits in species distributions revealed through a hierarchical model

Quantifying how functional traits relate to environmental gradients provides insight into mechanisms governing species distributions. Here, we bring together the fields of species distribution modelling and functional trait ecology with hierarchical modelling by explicitly incorporating traits into a multi‐species distribution model. We combined traits from the leaf‐height‐seed strategy scheme (specific leaf area (SLA), plant height and seed mass) with a distribution model for 20 eucalypt taxa in Victoria, Australia. The key insight of this approach is how traits modulate species responses to environmental gradients. The strongest link was between SLA and percent rock cover (species with low SLA had positive responses to rockiness, whereas high SLA species responded negatively to rockiness). We found evidence for complex yet potentially important interactions. For instance, the probability of species occurrence increased with rainfall and solar radiation on average yet the response varied depending on species height and SLA. Tall species were predicted to increase with rainfall and solar radiation across the range of SLA values (tall species with low SLA were especially sensitive to rainfall). Short species responded positively to rainfall and solar radiation only if they had low SLA. This framework readily accounts for interactions between combinations of traits and environmental variables unlike multi‐step approaches. Further application of this concept will contribute to a generalized mechanistic understanding of how traits influence species distributions along environmental gradients, with implications for understanding the response of species to global change.     

Stochastic modelling of prey depletion processes

The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this approach has the drawbacks of assuming continuous population variables and of being deterministic. We propose a general approach to stochastic modelling based on the concept of functional response for a prey depletion process with a constant number of predators. Our model could involve any kind of functional response, and permits a likelihood-based approach to statistical modelling and stable computation using matrix exponentials. To illustrate the method we use the Holling-Juliano functional response and compare the outcomes of our model with a deterministic counterpart considered by Schenk and Bacher [2002. Functional response of a generalist insect predator to one of its prey species in the field. Journal of Animal Ecology 71 (3), 524-531], who observed the depletion of Cassida rubiginosa due to its exclusive predator, Polistes dominulus. The predation was found to be Holling type III, reflecting the ability of the predator to regulate its prey. Our approach corroborates this result, but suggests that the prey depletion census should have been performed more often, and that predation features were significantly different between the two years for which data are available.     

Ecological genomics meets community‐level modelling of biodiversity: mapping the genomic landscape of current and future environmental adaptation

Local adaptation is a central feature of most species occupying spatially heterogeneous environments, and may factor critically in responses to environmental change. However, most efforts to model the response of species to climate change ignore intraspecific variation due to local adaptation. Here, we present a new perspective on spatial modelling of organism–environment relationships that combines genomic data and community‐level modelling to develop scenarios regarding the geographic distribution of genomic variation in response to environmental change. Rather than modelling species within communities, we use these techniques to model large numbers of loci across genomes. Using balsam poplar (Populus balsamifera) as a case study, we demonstrate how our framework can accommodate nonlinear responses of loci to environmental gradients. We identify a threshold response to temperature in the circadian clock gene GIGANTEA‐5 (GI5), suggesting that this gene has experienced strong local adaptation to temperature. We also demonstrate how these methods can map ecological adaptation from genomic data, including the identification of predicted differences in the genetic composition of populations under current and future climates. Community‐level modelling of genomic variation represents an important advance in landscape genomics and spatial modelling of biodiversity that moves beyond species‐level assessments of climate change vulnerability.     

Predicting the spread of Aedes albopictus in Australia under current and future climates: Multiple approaches and datasets to incorporate potential evolutionary divergence

When predicting the potential and future invasive range of a species, there is a growing appreciation that insights about factors limiting distributions can be provided by using multiple modelling approaches and by incorporating information from different parts of a species range. Here we apply this strategy to build on previous CLIMEX models to predict the invasion potential of Aedes albopictus, the Asian tiger mosquito, in mainland Australia. A combination of CLIMEX and MAXENT modelling indicated that the mosquito was expected to become widespread along the eastern seaboard and extend into northern Tasmania, but to remain restricted to the coastal fringe, a pattern which is not expected to shift much under climate change. However, a recent expansion of A. albopictus in North America points to evolutionary changes affecting the distribution of this species; when the North American range is included in models, A. albopictus is predicted to become much more widespread and extend inland and into Western Australia. These patterns highlight the potential impact of evolution on species distributions arising from multiple introductions or in situ evolution. By considering future climate scenarios, we demonstrate that there is likely to be a persistent public health threat associated with invasion by this species.     

A data-integration approach to correct sampling bias in species distribution models using multiple datasets of breeding birds in the Swiss Alps

It is essential to accurately model species distributions and biodiversity in response to many ecological and conservation challenges. The primary means of reliable decision-making on conservation priority are the data on the distributions and abundance of species. However, finding data that is accurate and reliable for predicting species distribution could be challenging. Data could come from different sources, with different designs, coverage, and potential sampling biases. In this study, we examined the emerging methods of modelling species distribution that integrate data from multiple sources such as systematic or standardized and casual or occasional surveys. We applied two modelling approaches, “data-pooling” and “ model-based data integration” that each involves combining various datasets to measure environmental interactions and clarify the distribution of species. Our paper demonstrates a reliable data integration workflow that includes gathering information on model-based data integration, creating a sub-model of each dataset independently, and finally, combining it into a single final model. We have shown that this is a more reliable way of developing a model than a data pooling strategy that combines multiple data sources to fit a single model. Moreover, data integration approaches could improve the poor predictive performance of systematic small datasets, through model-based data integration techniques that enhance the predictive accuracy of Species Distribution Models. We also identified, consistent with previous research, that machine learning algorithms are the most accurate techniques to predict bird species distribution in our heterogeneous study area in the western Swiss Alps. In particular, tree-dependent ensembles of Random Forest (RF) contribute to a better understanding of the interactions between species and the environment.     

Species Invasiveness in Biological Invasions: A Modelling Approach

The study of invasiveness, the traits that enable a species to invade a habitat, and invasibility, the habitat characteristics that determine its susceptibility to the establishment and spread of an invasive species, provide a useful conceptual framework to formulate the biological invasion problem in a modelling context. Another important aspect is the complex interaction emerging among the invader species, the noninvader species already present in the habitat, and the habitat itself. Following a modelling approach to the biological invasion problem, we present a spatially explicit cellular automaton model (Interacting Multiple Cellular Automata (IMCA)). We use field parameters from the invader Gleditsia triacanthos and the native Lithraea ternifolia in montane forests of central Argentina as a case study to compare outputs and performance of different models. We use field parameters from another invader, Ligustrum lucidum, and the native Fagara coco from the same system to run the cellular automaton model. We compare model predictions with invasion values from aerial photographs. We discuss in detail the importance of factors affecting species invasiveness, and give some insights into habitat invasibility and the role of interactions between them. Finally, we discuss the relevance of mathematical modelling for studying and predicting biological invasions. The IMCA model provided a suitable context for integrating invasiveness, invasibility, and the interactions. In the invasion system studied, the presence of an invader's juvenile bank not only accelerated the rate of invasion but was essential to ensure invasion. Using the IMCA model, we were able to determine that not only adult survival but particularly longevity of the native species influenced the spread velocity of the invader, at least when a juvenile bank is present. Other factors determining velocity of invasion detected by the IMCA model were seed dispersal distance and age of reproductive maturity. We derived relationships between species' adult survival, fecundity and longevity of both theoretical and applied relevance for biological invasions. Invasion velocities calculated from the aerial photographs agreed well with predictions of the IMCA model.     

A stratified approach for modeling the distribution of a threatened ant species in the Swiss National Park

We present models predicting the potential distribution of a threatened ant species, Formica exsecta Nyl., in the Swiss National Park (SNP). Data to fit the models have been collected according to a random-stratified design with an equal number of replicates per stratum. The basic aim of such a sampling strategy is to allow the formal testing of biological hypotheses about those factors most likely to account for the distribution of the modeled species. The stratifying factors used in this study were: vegetation, slope angle and slope aspect, the latter two being used as surrogates of solar radiation, considered one of the basic requirements of F. exsecta. Results show that, although the basic stratifying predictors account for more than 50% of the deviance, the incorporation of additional non-spatially explicit predictors into the model, as measured in the field, allows for an increased model performance (up to nearly 75%). However, this was not corroborated by permutation tests. Implementation on a national scale was made for one model only, due to the difficulty of obtaining similar predictors on this scale. The resulting map on the national scale suggests that the species might once have had a broader distribution in Switzerland. Reasons for its particular abundance within the SNP might possibly be related to habitat fragmentation and vegetation transformation outside the SNP boundaries.