Non-stationarity and local approaches to modelling the distributions of wildlife

Despite a growing interest in species distribution modelling, relatively little attention has been paid to spatial autocorrelation and non-stationarity. Both spatial autocorrelation (the tendency for adjacent locations to be more similar than distant ones) and non-stationarity (the variation in modelled relationships over space) are likely to be common properties of ecological systems. This paper focuses on non-stationarity and uses two local techniques, geographically weighted regression (GWR) and varying coefficient modelling (VCM), to assess its impact on model predictions. We extend two published studies, one on the presence–absence of calandra larks in Spain and the other on bird species richness in Britain, to compare GWR and VCM with the more usual global generalized linear modelling (GLM) and generalized additive modelling (GAM). For the calandra lark data, GWR and VCM produced better-fitting models than GLM or GAM. VCM in particular gave significantly reduced spatial autocorrelation in the model residuals. GWR showed that individual predictors became stationary at different spatial scales, indicating that distributions are influenced by ecological processes operating over multiple scales. VCM was able to predict occurrence accurately on independent data from the same geographical area as the training data but not beyond, whereas the GAM produced good results on all areas. Individual predictions from the local methods often differed substantially from the global models. For the species richness data, VCM and GWR produced far better predictions than ordinary regression. Our analyses suggest that modellers interpolating data to produce maps for practical actions (e.g. conservation) should consider local methods, whereas they should not be used for extrapolation to new areas. We argue that local methods are complementary to global methods, revealing details of habitat associations and data properties which global methods average out and miss.     

Improving generalized regression analysis for the spatial prediction of forest communities

Aim This study used data from temperate forest communities to assess: (1) five different stepwise selection methods with generalized additive models, (2) the effect of weighting absences to ensure a prevalence of 0.5, (3) the effect of limiting absences beyond the environmental envelope defined by presences, (4) four different methods for incorporating spatial autocorrelation, and (5) the effect of integrating an interaction factor defined by a regression tree on the residuals of an initial environmental model. Location State of Vaud, western Switzerland. Methods Generalized additive models (GAMs) were fitted using the grasp package (generalized regression analysis and spatial predictions, http://www.cscf.ch/grasp ). Results Model selection based on cross‐validation appeared to be the best compromise between model stability and performance (parsimony) among the five methods tested. Weighting absences returned models that perform better than models fitted with the original sample prevalence. This appeared to be mainly due to the impact of very low prevalence values on evaluation statistics. Removing zeroes beyond the range of presences on main environmental gradients changed the set of selected predictors, and potentially their response curve shape. Moreover, removing zeroes slightly improved model performance and stability when compared with the baseline model on the same data set. Incorporating a spatial trend predictor improved model performance and stability significantly. Even better models were obtained when including local spatial autocorrelation. A novel approach to include interactions proved to be an efficient way to account for interactions between all predictors at once. Main conclusions Models and spatial predictions of 18 forest communities were significantly improved by using either: (1) cross‐validation as a model selection method, (2) weighted absences, (3) limited absences, (4) predictors accounting for spatial autocorrelation, or (5) a factor variable accounting for interactions between all predictors. The final choice of model strategy should depend on the nature of the available data and the specific study aims. Statistical evaluation is useful in searching for the best modelling practice. However, one should not neglect to consider the shapes and interpretability of response curves, as well as the resulting spatial predictions in the final assessment.     

Spatial autocorrelation in predictors reduces the impact of positional uncertainty in occurrence data on species distribution modelling

Aim To investigate the impact of positional uncertainty in species occurrences on the predictions of seven commonly used species distribution models (SDMs), and explore its interaction with spatial autocorrelation in predictors. Methods A series of artificial datasets covering 155 scenarios including different combinations of five positional uncertainty scenarios and 31 spatial autocorrelation scenarios were simulated. The level of positional uncertainty was defined by the standard deviation of a normally distributed zero‐mean random variable. Each dataset included two environmental gradients (predictor variables) and one set of species occurrence sample points (response variable). Seven commonly used models were selected to develop SDMs: generalized linear models, generalized additive models, boosted regression trees, multivariate adaptive regression spline, random forests, genetic algorithm for rule‐set production and maximum entropy. A probabilistic approach was employed to model and simulate five levels of error in the species locations. To analyse the propagation of positional uncertainty, Monte Carlo simulation was applied to each scenario for each SDM. The models were evaluated for performance using simulated independent test data with Cohen’s Kappa and the area under the receiver operating characteristic curve. Results Positional uncertainty in species location led to a reduction in prediction accuracy for all SDMs, although the magnitude of the reduction varied between SDMs. In all cases the magnitude of this impact varied according to the degree of spatial autocorrelation in predictors and the levels of positional uncertainty. It was shown that when the range of spatial autocorrelation in the predictors was less than or equal to three times the standard deviation of the positional error, the models were less affected by error and, consequently, had smaller decreases in prediction accuracy. When the range of spatial autocorrelation in predictors was larger than three times the standard deviation of positional error, the prediction accuracy was low for all scenarios. Main conclusions The potential impact of positional uncertainty in species occurrences on the predictions of SDMs can be understood by comparing it with the spatial autocorrelation range in predictor variables.     

Generalized models vs. classification tree analysis: Predicting spatial distributions of plant species at different scales

Abstract. Statistical models of the realized niche of species are increasingly used, but systematic comparisons of alternative methods are still limited. In particular, only few studies have explored the effect of scale in model outputs. In this paper, we investigate the predictive ability of three statistical methods (generalized linear models, generalized additive models and classification tree analysis) using species distribution data at three scales: fine (Catalonia), intermediate (Portugal) and coarse (Europe). Four Mediterranean tree species were modelled for comparison. Variables selected by models were relatively consistent across scales and the predictive accuracy of models varied only slightly. However, there were slight differences in the performance of methods. Classification tree analysis had a lower accuracy than the generalized methods, especially at finer scales. The performance of generalized linear models also increased with scale. At the fine scale GLM with linear terms showed better accuracy than GLM with quadratic and polynomial terms. This is probably because distributions at finer scales represent a linear sub‐sample of entire realized niches of species. In contrast to GLM, the performance of GAM was constant across scales being more data‐oriented. The predictive accuracy of GAM was always at least equal to other techniques, suggesting that this modelling approach is more robust to variations of scale because it can deal with any response shape.     

Modelling the occurrence of threatened plant species in taiga landscapes: methodological and ecological perspectives

Aim Understanding the spatial patterns of species distribution and predicting the occurrence of high biological diversity and rare species are central themes in biogeography and environmental conservation. The aim of this study was to model and scrutinize the relative contributions of climate, topography, geology and land‐cover factors to the distributions of threatened vascular plant species in taiga landscapes in northern Finland. Location North‐east Finland, northern Europe. Methods The study was performed using a data set of 28 plant species and environmental variables at a 25‐ha resolution. Four different stepwise selection algorithms [Akaike information criterion (AIC), Bayesian information criterion (BIC), adaptive backfitting, cross selection] with generalized additive models (GAMs) were fitted to identify the main environmental correlates for species occurrences. The accuracies of the distribution models were evaluated using fourfold cross‐validation based on the area under the curve (AUC) derived from receiver operating characteristic plots. The GAMs were tentatively extrapolated to the whole study area and species occurrence probability maps were produced using GIS techniques. The effect of spatial autocorrelation on the modelling results was also tested by including autocovariate terms in the GAMs. Results According to the AUC values, the model performance varied from fair to excellent. The AIC algorithm provided the highest mean performance (mean AUC = 0.889), whereas the lowest mean AUC (0.851) was obtained from BIC. Most of the variation in the distribution of threatened plant species was related to growing degree days, temperature of the coldest month, water balance, cover of mire and mean elevation. In general, climate was the most powerful explanatory variable group, followed by land cover, topography and geology. Inclusion of the autocovariate only slightly improved the performance of the models and had a minor effect on the importance of the environmental variables. Main conclusions The results confirm that the landscape‐scale distribution patterns of plant species can be modelled well on the basis of environmental parameters. A spatial grid system with several environmental variables derived from remote sensing and GIS data was found to produce useful data sets, which can be employed when predicting species distribution patterns over extensive areas. Landscape‐scale maps showing the predicted occurrences of individual or multiple threatened plant species may provide a useful basis for focusing field surveys and allocating conservation efforts.     

Scaling down distribution maps from atlas data: a test of different approaches with virtual species

Aim Conservation managers are increasingly looking for modelled projections of species distributions to inform management strategies; however, the coarse resolution of available data usually compromises their helpfulness. The aim of this paper is to delineate and test different approaches for converting coarse‐grain occurrence data into high‐resolution predictions, and to clarify the conceptual circumstances affecting the accuracy of downscaled models. Location We used environmental data from a real landscape, southern Africa, and simulated species distributions within this landscape. Methods We built 10 virtual species at a resolution of 5 arcmin, and for each species we simulated atlas range maps at four decreasing resolutions (15, 30, 60, 120 arcmin). We tested the ability of three downscaling strategies to produce high‐resolution predictions using two modelling techniques: generalized linear models and generalized boosted models. We calibrated reference models with high‐resolution data and we compared the relative reduction of predictive performance in the downscaled models by using a null model approach. We also estimated the applicability of downscaling procedures to different situations by using distribution data for Mediterranean reptiles. Results All reference models achieved high performance measures. For all strategies, we observed a reduction of predictive performance proportional to the degree of downscaling. The differences in evaluation indices between reference models and downscaled projections obtained from atlases at 15 and 30 arcmin were never statistically significant. The accuracy of projections scaled down from 60 arcmin largely depended on the combination of approach and algorithm adopted. Projections scaled down from 120 arcmin gave misleading results in all cases. Main conclusions Moderate levels of downscaling allow for reasonably accurate results, regardless of the technique used. The most general effect of scaling down coarse‐grain data is the reduction of model specificity. The models can successfully delineate a species’ environmental association up until a 12‐fold downscaling, although with an increasing approximation that causes the overestimation of true distributions. We suggest appropriate procedures to mitigate the commission error introduced by downscaling at intermediate levels (approximately 12‐fold). Reductions of grain size > 12‐fold are discouraged.     

Updating bird species distribution at large spatial scales: applications of habitat modelling to data from long-term monitoring programs

Mapping of species distributions at large spatial scales has been often based on the representation of gathered observations in a general grid atlas framework. More recently, subsampling and subsequent interpolation or habitat spatial modelling techniques have been incorporated in these projects to allow more detailed species mapping. Here, we explore the usefulness of data from long-term monitoring (LTM) projects, primarily aimed at estimating trends in species abundance and collected at shorter time intervals (usually yearly) than atlas data, to develop predictive habitat models. We modelled habitat occupancy for 99 species using a bird LTM program and evaluated the predictive accuracy of these models using independent data from a contemporary and comprehensive breeding bird atlas project from the same region. Habitat models from LTM data using generalized linear modelling were significant for all the species and generally showed a high predictive power, albeit lower than that from atlas models. Sample size and species range size and niche breadth were the most important factors behind variability in model predictive accuracy, whereas the spatial distribution of sampling units at a given sample size had minor effects. Although predictive accuracy of habitat modelling was strongly species dependent, increases in sample size and, secondarily, a better spatial distribution of sampling units should lead to more powerful predictive distribution models. We suggest that data from LTM programs, now established in a large number of countries, has the potential for being a major source of good quality data suitable for the estimation and regularly update of distributions at large spatial scales for a number of species.     

Effect of species rarity on the accuracy of species distribution models for reptiles and amphibians in southern California

Aim Several studies have found that more accurate predictive models of species’ occurrences can be developed for rarer species; however, one recent study found the relationship between range size and model performance to be an artefact of sample prevalence, that is, the proportion of presence versus absence observations in the data used to train the model. We examined the effect of model type, species rarity class, species’ survey frequency, detectability and manipulated sample prevalence on the accuracy of distribution models developed for 30 reptile and amphibian species. Location Coastal southern California, USA. Methods Classification trees, generalized additive models and generalized linear models were developed using species presence and absence data from 420 locations. Model performance was measured using sensitivity, specificity and the area under the curve (AUC) of the receiver‐operating characteristic (ROC) plot based on twofold cross‐validation, or on bootstrapping. Predictors included climate, terrain, soil and vegetation variables. Species were assigned to rarity classes by experts. The data were sampled to generate subsets with varying ratios of presences and absences to test for the effect of sample prevalence. Join count statistics were used to characterize spatial dependence in the prediction errors. Results Species in classes with higher rarity were more accurately predicted than common species, and this effect was independent of sample prevalence. Although positive spatial autocorrelation remained in the prediction errors, it was weaker than was observed in the species occurrence data. The differences in accuracy among model types were slight. Main conclusions Using a variety of modelling methods, more accurate species distribution models were developed for rarer than for more common species. This was presumably because it is difficult to discriminate suitable from unsuitable habitat for habitat generalists, and not as an artefact of the effect of sample prevalence on model estimation.     

The importance of incorporating imperfect detection in biodiversity assessments: a case study of small mammals in an Australian region

Aim Assessments of biodiversity are an essential requirement of conservation management planning. Species distributional modelling is a popular approach to quantifying biodiversity whereby occurrence data are related to environmental covariates. An important confounding factor that is often overlooked in the development of such models is uncertainty due to imperfect detection. Here, I demonstrate how an analytical approach that accounts for the bias due to imperfect detection can be applied retrospectively to an existing biodiversity survey data set to produce more realistic estimates of species distributions and unbiased covariate relationships. Location Pilbara biogeographic region, Australia. Methods As a component of the Pilbara survey, presence/absence (i.e. undetected) data on small ground‐dwelling mammals were collected. I applied a multiseason occupancy modelling approach to six of the most common species encountered during this survey. Detection and occupancy rates, as well as extinction and colonization probabilities, were determined, and the influence of covariates on these parameters was examined using the multi‐model inference approach. Results Detection probabilities for all six species were considerably lower than 1.0 and varied across time and species. Naïve estimates of occupancy underestimated occupancy rates corrected for species detectability by up to 45%. Seasonal variation in occupancy status was attributed to changes in detection for two of the focal species, while reproductive events explained variation in occupancy in three others. Covariates describing the substrate strongly influenced site occupancy for most of the species modelled. A comparison of the occupancy model with a generalized linear model, assuming perfect detection, showed that the effects of the covariates were underestimated in the latter model. Main conclusions The application of the multiseason occupancy modelling approach to the Pilbara mammal data set demonstrated a powerful framework for examining changes in site occupancy, as well as local colonization and extinction rates of species which are not confounded by variable species detection rates.     

A new method for dealing with residual spatial autocorrelation in species distribution models

Species distribution modelling (SDM) is a widely used tool and has many applications in ecology and conservation biology. Spatial autocorrelation (SAC), a pattern in which observations are related to one another by their geographic distance, is common in georeferenced ecological data. SAC in the residuals of SDMs violates the ‘independent errors’ assumption required to justify the use of statistical models in modelling species’ distributions. The autologistic modelling approach accounts for SAC by including an additional term (the autocovariate) representing the similarity between the value of the response variable at a location and neighbouring locations. However, autologistic models have been found to introduce bias in the estimation of parameters describing the influence of explanatory variables on habitat occupancy. To address this problem we developed an extension to the autologistic approach by calculating the autocovariate on SAC in residuals (the RAC approach). Performance of the new approach was tested on simulated data with a known spatial structure and on strongly autocorrelated mangrove species’ distribution data collected in northern Australia. The RAC approach was implemented as generalized linear models (GLMs) and boosted regression tree (BRT) models. We found that the BRT models with only environmental explanatory variables can account for some SAC, but applying the standard autologistic or RAC approaches further reduced SAC in model residuals and substantially improved model predictive performance. The RAC approach showed stronger inferential performance than the standard autologistic approach, as parameter estimates were more accurate and statistically significant variables were accurately identified. The new RAC approach presented here has the potential to account for spatial autocorrelation while maintaining strong predictive and inferential performance, and can be implemented across a range of modelling approaches.