Can niche‐based distribution models outperform spatial interpolation?

Aim Distribution modelling relates sparse data on species occurrence or abundance to environmental information to predict the population of a species at any point in space. Recently, the importance of spatial autocorrelation in distributions has been recognized. Spatial autocorrelation can be categorized as exogenous (stemming from autocorrelation in the underlying variables) or endogenous (stemming from activities of the organism itself, such as dispersal). Typically, one asks whether spatial models explain additional variability (endogenous) in comparison to a fully specified habitat model. We turned this question around and asked: can habitat models explain additional variation when spatial structure is accounted for in a fully specified spatially explicit model? The aim was to find out to what degree habitat models may be inadvertently capturing spatial structure rather than true explanatory mechanisms. Location We used data from 190 species of the North American Breeding Bird Survey covering the conterminous United States and southern Canada. Methods We built 13 different models on 190 bird species using regression trees. Our habitat‐based models used climate and landcover variables as independent variables. We also used random variables and simulated ranges to validate our results. The two spatially explicit models included only geographical coordinates or a contagion term as independent variables. As another angle on the question of mechanism vs. spatial structure we pitted a model using related bird species as predictors against a model using randomly selected bird species. Results The spatially explicit models outperformed the traditional habitat models and the random predictor species outperformed the related predictor species. In addition, environmental variables produced a substantial R² in predicting artificial ranges. Main conclusions We conclude that many explanatory variables with suitable spatial structure can work well in species distribution models. The predictive power of environmental variables is not necessarily mechanistic, and spatial interpolation can outperform environmental explanatory variables.     

Combining spatial and phylogenetic eigenvector filtering in trait analysis

Aim To analyse the effects of simultaneously using spatial and phylogenetic information in removing spatial autocorrelation of residuals within a multiple regression framework of trait analysis. Location Switzerland, Europe. Methods We used an eigenvector filtering approach to analyse the relationship between spatial distribution of a trait (flowering phenology) and environmental covariates in a multiple regression framework. Eigenvector filters were calculated from ordinations of distance matrices. Distance matrices were either based on pure spatial information, pure phylogenetic information or spatially structured phylogenetic information. In the multiple regression, those filters were selected which best reduced Moran's I coefficient of residual autocorrelation. These were added as covariates to a regression model of environmental variables explaining trait distribution. Results The simultaneous provision of spatial and phylogenetic information was effectively able to remove residual autocorrelation in the analysis. Adding phylogenetic information was superior to adding purely spatial information. Applying filters showed altered results, i.e. different environmental predictors were seen to be significant. Nevertheless, mean annual temperature and calcareous substrate remained the most important predictors to explain the onset of flowering in Switzerland; namely, the warmer the temperature and the more calcareous the substrate, the earlier the onset of flowering. A sequential approach, i.e. first removing the phylogenetic signal from traits and then applying a spatial analysis, did not provide more information or yield less autocorrelation than simple or purely spatial models. Main conclusions The combination of spatial and spatio‐phylogenetic information is recommended in the analysis of trait distribution data in a multiple regression framework. This approach is an efficient means for reducing residual autocorrelation and for testing the robustness of results, including the indication of incomplete parameterizations, and can facilitate ecological interpretation.     

Predicting forest grouse distribution taking account of spatial autocorrelation

Spatially explicit, multi-scale models for predictions of species potential distribution can be useful tools for integrating biodiversity considerations in planning and strategic environmental assessment. In such models, the occurrences of focal species are related to habitat and landscape variables, which in urbanising areas should also include effects of urban disturbances. Moreover, the accuracy of the spatial predictive models may be affected by spatial autocorrelation, which means that a part of the variance is explained by neighbouring values. The aim of this study was to explore the effects of habitat and disturbance patterns on the distribution of two forest grouse species, Tetrao urogallus and Bonasa bonasia, and to detect and model the effects of spatial autocorrelation. The distribution of the two species could be explained in terms of reduction of a main predator, habitat quality, quantity and connectivity, including urban disturbances. The residuals of the initial regressions showed positive spatial autocorrelation that could be quantified by using a spatial probit model. The application of the spatial probit model revealed strongly significant spatial dependencies for both species. Furthermore, the model fit could be increased for T. urogallus by applying this model. The results implied that both species distributions might be affected by both reactions to the underlying land-use pattern, but also by interaction with neighbours. The use of the spatial probit model is a way to incorporate spatial interactions that otherwise cannot be captured by the independent variables.     

The role of biotic interactions in shaping distributions and realised assemblages of species: implications for species distribution modelling

Predicting which species will occur together in the future, and where, remains one of the greatest challenges in ecology, and requires a sound understanding of how the abiotic and biotic environments interact with dispersal processes and history across scales. Biotic interactions and their dynamics influence species' relationships to climate, and this also has important implications for predicting future distributions of species. It is already well accepted that biotic interactions shape species' spatial distributions at local spatial extents, but the role of these interactions beyond local extents (e.g. 10 km² to global extents) are usually dismissed as unimportant. In this review we consolidate evidence for how biotic interactions shape species distributions beyond local extents and review methods for integrating biotic interactions into species distribution modelling tools. Drawing upon evidence from contemporary and palaeoecological studies of individual species ranges, functional groups, and species richness patterns, we show that biotic interactions have clearly left their mark on species distributions and realised assemblages of species across all spatial extents. We demonstrate this with examples from within and across trophic groups. A range of species distribution modelling tools is available to quantify species environmental relationships and predict species occurrence, such as: (i) integrating pairwise dependencies, (ii) using integrative predictors, and (iii) hybridising species distribution models (SDMs) with dynamic models. These methods have typically only been applied to interacting pairs of species at a single time, require a priori ecological knowledge about which species interact, and due to data paucity must assume that biotic interactions are constant in space and time. To better inform the future development of these models across spatial scales, we call for accelerated collection of spatially and temporally explicit species data. Ideally, these data should be sampled to reflect variation in the underlying environment across large spatial extents, and at fine spatial resolution. Simplified ecosystems where there are relatively few interacting species and sometimes a wealth of existing ecosystem monitoring data (e.g. arctic, alpine or island habitats) offer settings where the development of modelling tools that account for biotic interactions may be less difficult than elsewhere.     

Weak climatic associations among British plant distributions

Aim Species distribution models (SDMs) are used to infer niche responses and predict climate change‐induced range shifts. However, their power to distinguish real and chance associations between spatially autocorrelated distribution and environmental data at continental scales has been questioned. Here this is investigated at a regional (10 km) scale by modelling the distributions of 100 plant species native to the UK. Location UK. Methods SDMs fitted using real climate data were compared with those utilizing simulated climate gradients. The simulated gradients preserve the exact values and spatial structure of the real ones, but have no causal relationships with any species and so represent an appropriate null model. SDMs were fitted as generalized linear models (GLMs) or by the Random Forest machine‐learning algorithm and were either non‐spatial or included spatially explicit trend surfaces or autocovariates as predictors. Results Species distributions were significantly but erroneously related to the simulated gradients in 86% of cases (P < 0.05 in likelihood‐ratio tests of GLMs), with the highest error for strongly autocorrelated species and gradients and when species occupied 50% of sites. Even more false effects were found when curvilinear responses were modelled, and this was not adequately mitigated in the spatially explicit models. Non‐spatial SDMs based on simulated climate data suggested that 70–80% of the apparent explanatory power of the real data could be attributable to its spatial structure. Furthermore, the niche component of spatially explicit SDMs did not significantly contribute to model fit in most species. Main conclusions Spatial structure in the climate, rather than functional relationships with species distributions, may account for much of the apparent fit and predictive power of SDMs. Failure to account for this means that the evidence for climatic limitation of species distributions may have been overstated. As such, predicted regional‐ and national‐scale impacts of climate change based on the analysis of static distribution snapshots will require re‐evaluation.     

Analysis of determinants of mammalian species richness in South America using spatial autoregressive models

Classically, hypotheses concerning the distribution of species have been explored by evaluating the relationship between species richness and environmental variables using ordinary least squares (OLS) regression. However, environmental and ecological data generally show spatial autocorrelation, thus violating the assumption of independently distributed errors. When spatial autocorrelation exists, an alternative is to use autoregressive models that assume spatially autocorrelated errors. We examined the relationship between mammalian species richness in South America and environmental variables, thereby evaluating the relative importance of four competing hypotheses to explain mammalian species richness. Additionally, we compared the results of ordinary least squares (OLS) regression and spatial autoregressive models using Conditional and Simultaneous Autoregressive (CAR and SAR, respectively) models. Variables associated with productivity were the most important at determining mammalian species richness at the scale analyzed. Whereas OLS residuals between species richness and environmental variables were strongly autocorrelated, those from autoregressive models showed less spatial autocorrelation, particularly the SAR model, indicating its suitability for these data. Autoregressive models also fit the data better than the OLS model (increasing R² by 5–14%), and the relative importance of the explanatory variables shifted under CAR and SAR models. These analyses underscore the importance of controlling for spatial autocorrelation in biogeographical studies.     

Freshwater biodiversity at regional extent: determinants of macroinvertebrate taxonomic richness in headwater streams

We studied spatial variation of macroinvertebrate species richness in headwater streams at two spatial extents, within and across drainage systems, and assessed the relative importance of three groups of variables (local, landscape and regional) at each extent. We specifically asked whether the same variables proposed to control broad‐scale richness patterns of terrestrial organisms (temperature, topographic variability) are important determinants of species richness also in streams, or whether environmental factors effective at mainly local scales (in‐stream heterogeneity, potential productivity) constrain species richness in local communities. We used forward selection with two stopping criteria to identify the key environmental and spatial variables at each study extent. Eigenvector‐based spatial filtering was applied to evaluate spatial patterns in species richness, and variation partitioning was used to assess the amount of variation in richness attributable to purely environmental and spatial components. A prime regulator of richness variation at the bioregion extent was elevation range (increasing richness with higher topographic variability), whereas hydrological stability and temperature were unimportant. Water chemistry variables, particularly water color, exhibited strong spatially‐structured variation across drainage systems. Local environmental variables explained most of the variation in species richness at the drainage‐system extent, reflecting gradients in total phosphorus and water color (negative effect on richness). The importance of the pure spatial component was strongly region‐dependent, with a peak (60%) in one drainage system, suggesting the presence of unmeasured environmental factors. Our results emphasize the need for spatially‐explicit, regional studies to better understand geographical variation of freshwater biodiversity. Future studies need to relate species richness not only to local factors but also to broad‐scale climatic variables, recognizing the presence of spatially‐structured environmental variation.     

The relative importance of environment, human activity and space in explaining species richness of South African bird orders

Aim To assess the relative importance of environmental (climate, habitat heterogeneity and topography), human (population density, economic prosperity and land transformation) and spatial (autocorrelation) influences, and the interactions between these predictor groups, on species richness patterns of various avifaunal orders. Location South Africa. Methods Generalized linear models were used to determine the amount of variation in species richness, for each order, attributable to each of the different predictor groups. To assess the relationships between species richness and the various predictor groups, a deviance statistic (a measure of goodness of fit for each model) and the percentage deviation explained for the best fitting model were calculated. Results Of the 12 avifaunal orders examined, spatially structured environmental deviance accounted for most of the variation in species richness in 11 orders (averaging 28%), and 50% or more in seven orders. However, orders comprising mostly water birds (Charadriiformes, Anseriformes, Ciconiformes) had a relatively large component of purely spatial deviance compared with spatially structured environmental deviance, and much of this spatial deviance was due to higher‐order spatial effects such as patchiness, as opposed to linear gradients in species richness. Although human activity, in general, offered little explanatory power to species richness patterns, it was an important correlate of spatial variation in species of Charadriiformes and Anseriformes. The species richness of these water birds was positively related to the presence of artificial water bodies. Main conclusions Not all bird orders showed similar trends when assessing, simultaneously, the relative importance of environmental, human and spatial influences in affecting bird species richness patterns. Although spatially structured environmental deviance described most of the variation in bird species richness, the explanatory power of purely spatial deviance, mostly due to nonlinear geographical effects such as patchiness, became more apparent in orders representing water birds. This was especially true for Charadriiformes, where the strong anthropogenic relationship has negative implications for the successful conservation of this group.     

Alternative causes for range limits: a metapopulation perspective

All species have limited distributions at broad geographical scales. At local scales, the distribution of many species is influenced by the interplay of the three factors of habitat availability, local extinctions and colonization dynamics. We use the standard Levins metapopulation model to illustrate how gradients in these three factors can generate species' range limits. We suggest that the three routes to range limits have radically different evolutionary implications. Because the Levins model makes simplifying assumptions about the spatial coupling of local populations, we present numerical studies of spatially explicit metapopulation models that complement the analytical model. The three routes to range limits give rise to distinct spatiotemporal patterns. Range limits in one species can also arise because of environmental gradients impinging upon other species. We briefly discuss a predator–prey example, which illustrates indirect routes to range limits in a metacommunity context.     

Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology

There have been numerous claims in the ecological literature that spatial autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex‐USSR, and Australia. We used richness in 110×110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short‐distance residual spatial autocorrelation in each data set. This distance was used to subsample cells to generate spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual spatial autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short‐distance spatial autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of spatial autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small‐scale patterns for these predictors create weaker and more unstable broad‐scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between spatial and nonspatial regression models should be interpreted with an explicit awareness of spatial scale.     

Partitioning the variation in African vertebrate distributions into environmental and spatial components – exploring the link between ecology and biogeography

There has been a proliferation of studies aimed at predicting the distributions of species from environmental variables despite evidence that spatial interpolation or spatially‐constrained mechanistic models have comparable explanatory power. Moreover, the processes behind environmental and spatial correlations – and their interactions – remain elusive. Here, we examined geographic patterns in the amount of variation explained by environmental correlation and exogenous or endogenous spatial autocorrelation for 4423 terrestrial vertebrate species in Africa using variation partitioning analysis. We also tested the effects of range size and taxonomic class on the relative importance of environmental and spatial correlations, and contrasted empirical patterns to two environmentally‐neutral models to identify potential underlying environmental and spatial mechanisms. Results showed that geographic range size was associated with environmental and spatial variation components in ways that where qualitatively indistinguishable from environmentally‐neutral species with constrained dispersal, suggesting that proportions of variation are due to range cohesiveness rather than other ecological processes. As a consequence, large‐scale patterns of biodiversity should be studied cautiously due to the difficulty of obtaining evidence of causal mechanistic links between species distributions and spatio‐environmental gradients. However, we also uncovered ecologically‐meaningful patterns in the residuals of the relationship between range size and the respective variation components, which differed among vertebrate classes. Moreover, these patterns coincided with contemporary biogeographical regions. This study, therefore, demonstrates that it is possible to extract meaningful environmental and spatial associations that potentially link ecological and biogeographical processes.     

Habitat distribution models,spatial autocorrelation,functional traits and dispersal capacity of alpine plant species

Abstract. We evaluate the potential influence of disturbance on the predictability of alpine plant species distribution from equilibrium‐based habitat distribution models. Firstly, abundance data of 71 plant species were correlated with a comprehensive set of environmental variables using ordinal regression models. Subsequently, the residual spatial autocorrelation (at distances of 40 to 320 m) in these models was explored. The additional amount of variance explained by spatial structuring was compared with a set of functional traits assumed to confer advantages in disturbed or undisturbed habitats. We found significant residual spatial autocorrelation in the habitat models of most of the species that were analysed. The amount of this autocorrelation was positively correlated with the dispersal capacity of the species, levelling off with increasing spatial scale. Both trends indicate that dispersal and colonization processes, whose frequency is enhanced by disturbance, influence the distribution of many alpine plant species. Since habitat distribution models commonly ignore such spatial processes they miss an important driver of local‐ to landscape‐scale plant distribution.     

Environmental and spatial variables influence the composition of frog assemblages in sub-tropical eastern Australia

In community ecology, contrasting theories suggest that the distribution and abundance of species, and thus the composition of assemblages, are influenced by i) environmental gradients, or ii) contagious biotic processes such as predation, competition, dispersal and disease. In the former case, sites with similar environments would tend to support similar assemblages, while in the latter, geographically proximate sites would tend to support more similar assemblages than widely separated sites. I investigated the relative influence of environmental variables and spatial position on the composition of frog assemblages at forest streams in sub-tropical eastern Australia using redundancy analysis (RDA) and partial RDA. Data on the maximum abundance of the frog species at 65 survey sites were transformed such that RDA would yield the Hellinger distance between sites. The following analysis identified 11 environmental variables that explained 45% of the variation in the abundance of species at the survey sites (the species matrix), as a proportion of total variance. The geographic co-ordinates of the survey sites accounted for 12%, while the environmental and spatial variables combined accounted for 47% of the variation in the species matrix. Partial redundancy analysis indicated that of the explained variation, 74% was purely environmental, 5% was purely spatial and 21% was spatial environmental variation. This study is the first to quantify the relative influence of environmental and spatial variables on the composition of amphibian assemblages. It provides support for both the environmental control model and the biotic control model of species' distributions and assemblage composition, although environmental variables appear to have the greater effect at this scale of analysis.     

Testing and interpreting the shared space‐environment fraction in variation partitioning analyses of ecological data

Variation partitioning analyses combined with spatial predictors (Moran's eigenvector maps, MEM) are commonly used in ecology to test the fractions of species abundance variation purely explained by environment and space. However, while these pure fractions can be tested using a classical residuals permutation procedure, no specific method has been developed to test the shared space‐environment fraction (SSEF). Yet, the SSEF is expected to encompass a major driver of community assembly, that is, an induced spatial dependence effect (ISD; i.e. the reflection of a spatially structured habitat filter on a species distribution). A reliable test of this fraction is therefore crucial to properly test the presence of an ISD on ecological data. To bridge the gap, we propose to test the SSEF through spatially‐constrained null models: torus‐translations, and Moran spectral randomisations. We investigated the type I error rate and statistical power of our method based on two real environmental datasets and simulations of tree distributions. Ten types of tree distribution displaying contrasted aggregation properties were simulated, and their abundances were sampled in 153 regularly‐distributed 20 × 20 m quadrats. The SSEF was tested for 1000 simulated tree distributions either unrelated to the environment, or filtered by environmental variables displaying contrasting spatial structures. The method proposed provided a correct type I error rate (< 0.05). The statistical power was high (> 0.9) when abundances were filtered by an environmental variable structured at broad scale. However, the spatial resolution allowed by the sampling design limited the power of the method when using a fine‐scale filtering variable. This highlighted that an ISD can be properly detected providing that the spatial pattern of the filtering process is correctly captured by the sampling design of the study. An R function to apply the SSEF testing method is provided and detailed in a tutorial.     

Disentangling drivers of spatial autocorrelation in species distribution models

Species distribution models (SDMs) are frequently used to understand the influence of site properties on species occurrence. For robust model inference, SDMs need to account for the spatial autocorrelation of virtually all species occurrence data. Current methods do not routinely distinguish between extrinsic and intrinsic drivers of spatial autocorrelation, although these may have different implications for conservation. Here, we present and test a method that disentangles extrinsic and intrinsic drivers of spatial autocorrelation using repeated observations of a species. We focus on unknown habitat characteristics and conspecific interactions as extrinsic and intrinsic drivers, respectively. We model the former with spatially correlated random effects and the latter with an autocovariate, such that the spatially correlated random effects are constant across the repeated observations whereas the autocovariate may change. We tested the performance of our model on virtual species data and applied it to observations of the corncrake Crex crex in the Netherlands. Applying our model to virtual species data revealed that it was well able to distinguish between the two different drivers of spatial autocorrelation, outperforming models with no or a single component for spatial autocorrelation. This finding was independent of the direction of the conspecific interactions (i.e. conspecific attraction versus competitive exclusion). The simulations confirmed that the ability of our model to disentangle both drivers of autocorrelation depends on repeated observations. In the case study, we discovered that the corncrake has a stronger response to habitat characteristics compared to a model that did not include spatially correlated random effects, whereas conspecific interactions appeared to be less important. This implies that future conservation efforts should primarily focus on maximizing habitat availability. Our study shows how to systematically disentangle extrinsic and intrinsic drivers of spatial autocorrelation. The method we propose can help to correctly identify the main drivers of species distributions.     

Temporal variability of ecological niches: a study on intertidal macrobenthic fauna

The determination of temporal niche dynamics under field conditions is an important component of a species’ ecology. Recent developments in niche mapping, and the possibility to account for spatial autocorrelation in species distributions, hold promise for the statistical approach explored here. Using species counts from a landscape‐scale benthic monitoring programme in the western Dutch Wadden Sea during 1997–2005 in combination with sediment characteristics and tidal height as explanatory variables, we statistically derive realised niches for two bivalves, two crustaceans and three polychaetes, encompassing predators, suspension and bottom feeding functional groups. Unsurprisingly, realized niches varied considerably between species. Intraspecific temporal variation was assessed as overlap between the year‐specific niche and the overall mean niche, and this analysis revealed considerable variation between years. The main functional groups represented by these species showed idiosyncratic and wide variability through the study period. There were no strong associations between niche characteristics and mean abundance or body size. Our assessment of intraspecific niche variability has ramifications for species distribution models in general and offers advances from previous methods. 1) By assessing species’ realized niches in the multivariate environmental space, analyses are independent from the relative availability of particular environments. Predicted realized niches present differences between years, rather than annual differences in environmental conditions. 2) Using spatially explicit models to predict species habitat preferences provide more precise and unbiased estimates of species–environment relationships. 3) Current niche models assume constant niches, whereas we illustrate how much these can vary over only a few generations. This emphasizes the potentially limited scope of global change studies with forecasts based on single‐time species distribution snapshots.     

Incorporating spatial autocorrelation may invert observed patterns

Though still often neglected, spatial autocorrelation can be a serious issue in ecology because the presence of spatial autocorrelation may alter the parameter estimates and error probabilities of linear models. Here I re-analysed data from a previous study on the relationship between plant species richness and environmental correlates in Germany. While there was a positive relationship between native plant species richness and an altitudinal gradient when ignoring the presence of spatial autocorrelation, the use of a spatial simultaneous liner error model revealed a negative relationship. This most dramatic effect where the observed pattern was inverted may be explained by the environmental situation in Germany. There the highest altitudes are in the south and the lowlands in the north that result in some locally or regionally inverted patterns of the large-scale environmental gradients from the equator to the north. This study therefore shows the necessity to consider spatial autocorrelation in spatial analyses.     

Relative importance of environment, human activity and spatial situation in determining the distribution of terrestrial mammal diversity in Argentina

Aim The partition of the geographical variation in Argentinian terrestrial mammal species richness (SR) into environmentally, human and spatially induced variation. Location Argentina, using the twenty‐three administrative provinces as the geographical units. Methods We recorded the number of terrestrial mammal species in each Argentinian province, and the number of species belonging to particular groups (Marsupialia, Placentaria, and among the latter, Xenarthra, Carnivora, Ungulates and Rodentia). We performed multiple regressions of each group's SR on environmental, human and spatial variables, to determine the amounts of variation explained by these factors. We then used a variance partitioning procedure to specify which proportion of the variation in SR is explained by each of the three factors exclusively and which proportions are attributable to interactions between factors. Results For marsupials, human activity explains the greatest part of the variation in SR. The purely environmental and purely human influences on all mammal SR explain a similarly high proportion of the variation in SR, whereas the purely spatial influence accounts for a smaller proportion of it. The exclusive interaction between human activity and space is negative in carnivores and rodents. For rodents, the interaction between environment and spatial situation is also negative. In the remaining placental groups, pure spatial autocorrelation explains a small proportion of the variation in SR. Main conclusions Environmental factors explain most of the variation in placental SR, while Marsupials seem to be mainly affected by human activity. However, for edentates, carnivores, and ungulates the pure human influence is more important than the pure spatial and environmental influences. Besides, human activity disrupts the spatial structure caused by the history and population dynamics of rodents and, to a lesser extent, of carnivores. The historical events and population dynamics on the one hand, and the environment on the other, cause rodent SR to vary in divergent directions. In the remaining placental groups the autocorrelation in SR is mainly the result of autocorrelation in the environmental and human variables.     

Evaluating,partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records

Most species data display spatial autocorrelation that can affect ecological niche models (ENMs) accuracy‐statistics, affecting its ability to infer geographic distributions. Here we evaluate whether the spatial autocorrelation underlying species data affects accuracy‐statistics and map the uncertainties due to spatial autocorrelation effects on species range predictions under past and future climate models. As an example, ENMs were fitted to Qualea grandiflora (Vochysiaceae), a widely distributed plant from Brazilian Cerrado. We corrected for spatial autocorrelation in ENMs by selecting sampling sites equidistant in geographical (GEO) and environmental (ENV) spaces. Distributions were modelled using 13 ENMs evaluated by two accuracy‐statistics (TSS and AUC), which were compared with uncorrected ENMs. Null models and the similarity statistics I were used to evaluate the effects of spatial autocorrelation. Moreover, we applied a hierarchical ANOVA to partition and map the uncertainties from the time (across last glacial maximum, pre‐insustrial, and 2080 time periods) and methodological components (ENMs and autocorrelation corrections). The GEO and ENV models had the highest accuracy‐statistics values, although only the ENV model had values higher than expected by chance alone for most of the 13 ENMs. Uncertainties from time component were higher in the core region of the Brazilian Cerrado where Q. grandiflora occurs, whereas methodological components presented higher uncertainties in the extreme northern and southern regions of South America (i.e. outside of Brazilian Cerrado). Our findings show that accounting for autocorrelation in environmental space is more efficient than doing so in geographical space. Methodological uncertainties were concentrated in outside the core region of Q. grandiflora's habitat. Conversely, uncertainty due to time component in the Brazilian Cerrado reveals that ENMs were able to capture climate change effects on Q. grandiflora distributions.