Zero‐inflated spatio‐temporal models for disease mapping

In this paper, our aim is to analyze geographical and temporal variability of disease incidence when spatio‐temporal count data have excess zeros. To that end, we consider random effects in zero‐inflated Poisson models to investigate geographical and temporal patterns of disease incidence. Spatio‐temporal models that employ conditionally autoregressive smoothing across the spatial dimension and B‐spline smoothing over the temporal dimension are proposed. The analysis of these complex models is computationally difficult from the frequentist perspective. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning method provides a frequentist approach to mixed models that is also computationally convenient. We propose to use data cloning, which yields to maximum likelihood estimation, to conduct frequentist analysis of zero‐inflated spatio‐temporal modeling of disease incidence. One of the advantages of the data cloning approach is that the prediction and corresponding standard errors (or prediction intervals) of smoothing disease incidence over space and time is easily obtained. We illustrate our approach using a real dataset of monthly children asthma visits to hospital in the province of Manitoba, Canada, during the period April 2006 to March 2010. Performance of our approach is also evaluated through a simulation study.     

Statistical Modeling of Observational Data With Spatial Dependencies

Abstract I provide a brief introduction to the concept of spatial autocorrelation and its incorporation into regression-type models. Spatial autocorrelation occurs when the response variable is correlated with itself at other locations in the region of interest. The autocorrelation usually takes a specific form where observations close in space are more correlated than those farther apart, and the rate of decay of the correlation is a function of the distance separating 2 locations. I present 2 commonly used models: 1) geostatistical modeling in which data are collected at points in the study region and 2) conditional autoregression (lattice) models in which data are aggregated over small nonoverlapping sub-areas of the study region. I also describe incorporation of explanatory covariates, such as habitat or physico-chemical attributes. I emphasize frequentist methods, but I briefly describe Bayesian approaches. I also provide some advantages, such as obtaining correct standard errors for estimators, and disadvantages, such as requirements for larger sample sizes, of incorporating spatial autocorrelation into the modeling effort. This information can aid researchers in designing and analyzing models of the relationships between species distributions and habitat. As a result, more informative models can be developed which further aid in management of wildlife.     

A hybrid omnibus test for generalized semiparametric single‐index models with high‐dimensional covariate sets

Numerous statistical methods have been developed for analyzing high‐dimensional data. These methods often focus on variable selection approaches but are limited for the purpose of testing with high‐dimensional data. They are often required to have explicit‐likelihood functions. In this article, we propose a “hybrid omnibus test” for high‐dicmensional data testing purpose with much weaker requirements. Our hybrid omnibus test is developed under a semiparametric framework where a likelihood function is no longer necessary. Our test is a version of a frequentist‐Bayesian hybrid score‐type test for a generalized partially linear single‐index model, which has a link function being a function of a set of variables through a generalized partially linear single index. We propose an efficient score based on estimating equations, define local tests, and then construct our hybrid omnibus test using local tests. We compare our approach with an empirical‐likelihood ratio test and Bayesian inference based on Bayes factors, using simulation studies. Our simulation results suggest that our approach outperforms the others, in terms of type I error, power, and computational cost in both the low‐ and high‐dimensional cases. The advantage of our approach is demonstrated by applying it to genetic pathway data for type II diabetes mellitus.     

Widespread evidence for incipient ecological speciation: a meta‐analysis of isolation‐by‐ecology

Ecologically mediated selection has increasingly become recognised as an important driver of speciation. The correlation between neutral genetic differentiation and environmental or phenotypic divergence among populations, to which we collectively refer to as isolation‐by‐ecology (IBE), is an indicator of ecological speciation. In a meta‐analysis framework, we determined the strength and commonality of IBE in nature. On the basis of 106 studies, we calculated a mean effect size of IBE with and without controlling for spatial autocorrelation among populations. Effect sizes were 0.34 (95% CI 0.24–0.42) and 0.26 (95% CI 0.13–0.37), respectively, indicating that an average of 5% of the neutral genetic differentiation among populations was explained purely by ecological contrast. Importantly, spatial autocorrelation reduced IBE correlations for environmental variables, but not for phenotypes. Through simulation, we showed how the influence of isolation‐by‐distance and spatial autocorrelation of ecological variables can result in false positives or underestimated correlations if not accounted for in the IBE model. Collectively, this meta‐analysis showed that ecologically induced genetic divergence is pervasive across time‐scales and taxa, and largely independent of the choice of molecular marker. We discuss the importance of these results in the context of adaptation and ecological speciation and suggest future research avenues.     

The effect of sex‐biased dispersal on opposite‐sexed spatial genetic structure and inbreeding risk

Natal sex‐biased dispersal has long been thought to reduce the risk of inbreeding by spatially separating opposite‐sexed kin. Yet, comprehensive and quantitative evaluations of this hypothesis are lacking. In this study, we quantified the effectiveness of sex‐biased dispersal as an inbreeding avoidance strategy by combining spatially explicit simulations and empirical data. We quantified the extent of kin clustering by measuring the degree of spatial autocorrelation among opposite‐sexed individuals (FM structure). This allowed us to systematically explore how the extent of sex‐biased dispersal, generational overlap, and mate searching distance, influenced both kin clustering, and the resulting inbreeding in the absence of complementary inbreeding avoidance strategies. Simulations revealed that when sex‐biased dispersal was limited, positive FM genetic structure developed quickly and increased as the mate searching distance decreased or as generational overlap increased. Interestingly, complete long‐range sex‐biased dispersal did not prevent the development of FM genetic structure when generations overlapped. We found a very strong correlation between FM genetic structure and both F_IS under random mating, and pedigree‐based measures of inbreeding. Thus, we show that the detection of FM genetic structure can be a strong indicator of inbreeding risk. Empirical data for two species with different life history strategies yielded patterns congruent with our simulations. Our study illustrates a new application of spatial genetic autocorrelation analysis that offers a framework for quantifying the risk of inbreeding that is easily extendable to other species. Furthermore, our findings provide other researchers with a context for interpreting observed patterns of opposite‐sexed spatial genetic structure.     

Repeatability for Gaussian and non‐Gaussian data: a practical guide for biologists

Repeatability (more precisely the common measure of repeatability, the intra‐class correlation coefficient, ICC) is an important index for quantifying the accuracy of measurements and the constancy of phenotypes. It is the proportion of phenotypic variation that can be attributed to between‐subject (or between‐group) variation. As a consequence, the non‐repeatable fraction of phenotypic variation is the sum of measurement error and phenotypic flexibility. There are several ways to estimate repeatability for Gaussian data, but there are no formal agreements on how repeatability should be calculated for non‐Gaussian data (e.g. binary, proportion and count data). In addition to point estimates, appropriate uncertainty estimates (standard errors and confidence intervals) and statistical significance for repeatability estimates are required regardless of the types of data. We review the methods for calculating repeatability and the associated statistics for Gaussian and non‐Gaussian data. For Gaussian data, we present three common approaches for estimating repeatability: correlation‐based, analysis of variance (ANOVA)‐based and linear mixed‐effects model (LMM)‐based methods, while for non‐Gaussian data, we focus on generalised linear mixed‐effects models (GLMM) that allow the estimation of repeatability on the original and on the underlying latent scale. We also address a number of methods for calculating standard errors, confidence intervals and statistical significance; the most accurate and recommended methods are parametric bootstrapping, randomisation tests and Bayesian approaches. We advocate the use of LMM‐ and GLMM‐based approaches mainly because of the ease with which confounding variables can be controlled for. Furthermore, we compare two types of repeatability (ordinary repeatability and extrapolated repeatability) in relation to narrow‐sense heritability. This review serves as a collection of guidelines and recommendations for biologists to calculate repeatability and heritability from both Gaussian and non‐Gaussian data.     

Host plant associations and geography interact to shape diversification in a specialist insect herbivore

Disentangling the processes underlying geographic and environmental patterns of biodiversity challenges biologists as such patterns emerge from eco‐evolutionary processes confounded by spatial autocorrelation among sample units. The herbivorous insect, Belonocnema treatae (Hymenoptera: Cynipidae), exhibits regional specialization on three plant species whose geographic distributions range from sympatry through allopatry across the southern United States. Using range‐wide sampling spanning the geographic ranges of the three host plants and genotyping‐by‐sequencing of 1,217 individuals, we tested whether this insect herbivore exhibited host plant‐associated genomic differentiation while controlling for spatial autocorrelation among the 58 sample sites. Population genomic structure based on 40,699 SNPs was evaluated using the hierarchical Bayesian model entropy to assign individuals to genetic clusters and estimate admixture proportions. To control for spatial autocorrelation, distance‐based Moran's eigenvector mapping was used to construct regression variables summarizing spatial structure inherent among sample sites. Distance‐based redundancy analysis (dbRDA) incorporating the spatial variables was then applied to partition host plant‐associated differentiation (HAD) from spatial autocorrelation. By combining entropy and dbRDA to analyse SNP data, we unveiled a complex mosaic of highly structured differentiation within and among gall‐former populations finding evidence that geography, HAD and spatial autocorrelation all play significant roles in explaining patterns of genomic differentiation in B. treatae. While dbRDA confirmed host association as a significant predictor of patterns of genomic variation, spatial autocorrelation among sites explained the largest proportion of variation. Our results demonstrate the value of combining dbRDA with hierarchical structural analyses to partition spatial/environmental patterns of genomic variation.     

Should ecologists prefer model‐ over distance‐based multivariate methods?

Ecological data sets often record the abundance of species, together with a set of explanatory variables. Multivariate statistical methods are optimal to analyze such data and are thus frequently used in ecology for exploration, visualization, and inference. Most approaches are based on pairwise distance matrices instead of the sites‐by‐species matrix, which stands in stark contrast to univariate statistics, where data models, assuming specific distributions, are the norm. However, through advances in statistical theory and computational power, models for multivariate data have gained traction. Systematic simulation‐based performance evaluations of these methods are important as guides for practitioners but still lacking. Here, we compare two model‐based methods, multivariate generalized linear models (MvGLMs) and constrained quadratic ordination (CQO), with two distance‐based methods, distance‐based redundancy analysis (dbRDA) and canonical correspondence analysis (CCA). We studied the performance of the methods to discriminate between causal variables and noise variables for 190 simulated data sets covering different sample sizes and data distributions. MvGLM and dbRDA differentiated accurately between causal and noise variables. The former had the lowest false‐positive rate (0.008), while the latter had the lowest false‐negative rate (0.027). CQO and CCA had the highest false‐negative rate (0.291) and false‐positive rate (0.256), respectively, where these error rates were typically high for data sets with linear responses. Our study shows that both model‐ and distance‐based methods have their place in the ecologist's statistical toolbox. MvGLM and dbRDA are reliable for analyzing species–environment relations, whereas both CQO and CCA exhibited considerable flaws, especially with linear environmental gradients.     

Bayesian data analysis in population ecology: motivations,methods, and benefits

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.     

Age,sex and beauty: methodological dependence of age‐ and sex‐dichromatism in the great tit Parus major

Carotenoid‐based colour expression is frequently involved in sexual dichromatism, particularly in bird plumage, suggesting a role in sexual selection. Despite much work on expression of the carotenoid‐based ventral plumage coloration of the great tit (Parus major), which represents a popular model in evolution and ecology, a consensus on even the most basic demographic patterns of variation (e.g. age and sex differences) is lacking. This may reflect the use of variable methods for analysing colour variation, although what is not clear, either in this case or in general, is the extent to which these alternative methods are equally effective at describing age‐ and sex‐related dichromatism. Using data obtained over 4 years from a large sample of free‐ranging great tits, we examined how colour‐scoring methodology influences estimates of age‐ and sex‐related dichromatism. We compare: (1) principal components analysis‐derived scores; (2) tristimulus colour variables; (3) a visual model‐independent, carotenoid‐focussed colour score; and (4) two colour scoring methods based on avian visual models, examining how they assess colour variation with respect to age and sex to determine how methodology may influence results. We demonstrate clear age‐ and sex‐dependent expression of this colour trait, both in our own data and in meta‐analyses of results from great tit populations across Europe, and discuss the merits of the various colour scores, which yield very different estimates of the extent of age‐ and sex‐dependent dichromatism. We show variation is likely to be visible to conspecifics and propose a novel, visual model‐derived scoring system for describing variation in carotenoid‐based colour patches, where the perceived signal is divided into independent chromatic and achromatic components, in line with current understanding of visual perception. The present study highlights the impact of colour‐scoring methodology and shows that, as novel measures continue to be developed, researchers should consider carefully how they quantify colour expression. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 777–796.     

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate‐mediated range shifts

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad‐scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment‐only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment‐only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.     

Model‐based integration of observed and expert‐based information for assessing the geographic and environmental distribution of freshwater species

Freshwater ecosystems harbor specialized and vulnerable biodiversity, and the prediction of potential impacts of freshwater biodiversity to environmental change requires knowledge of the geographic and environmental distribution of taxa. To date, however, such quantitative information about freshwater species distributions remains limited. Major impediments include heterogeneity in available species occurrence data, varying detectability of species in their aquatic environment, scarcity of contiguous freshwater‐specific predictors, and methods that support addressing these issues in a single framework. Here we demonstrate the use of a hierarchical Bayesian modeling (HBM) framework that combines disparate species occurrence information with newly‐developed 1 km freshwater‐specific predictors, to account for imperfect species detection and make fine‐grain (1 km) estimates of distributions in freshwater organisms. The approach integrates a Bernoulli suitability and a Binomial observability process into a hierarchical zero‐inflated Binomial model. The suitability process includes point presence observations, records of site visits, 1 km environmental predictors and expert‐derived species range maps integrated with a distance‐decay function along the within‐stream distance as covariates. The observability process uses repeated observations to estimate a probability of observation given that the species was present. The HBM accounts for the spatial autocorrelation in species habitat suitability projections using an intrinsic Gaussian conditional autoregressive model. We used this framework for three fish species native to different regions and habitats in North America. Model comparison shows that HBMs significantly outperformed non‐spatial GLMs in terms of AUC and TSS scores, and that expert information when appropriately included in the model can provide an important refinement. Such ancillary species information and an integrative, hierarchical Bayesian modeling framework can therefore be used to advance fine‐grain habitat suitability predictions and range size estimates in the freshwater realm. Our approach is extendable in terms of data availability and generality and can be used on other freshwater organisms and regions.     

On Distance‐Based Permutation Tests for Between‐Group Comparisons

Summary Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo‐F tests arising from a distance‐based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.     

Decomposing the heterogeneity of species distributions into multiple scales: a hierarchical framework for large‐scale count surveys

We introduce a novel spatially explicit framework for decomposing species distributions into multiple scales from count data. These kinds of data are usually positively skewed, have non‐normal distributions and are spatially autocorrelated. To analyse such data, we propose a hierarchical model that takes into account the observation process and explicitly deals with spatial autocorrelation. The latent variable is the product of a positive trend representing the non‐constant mean of the species distribution and of a stationary positive spatial field representing the variance of the spatial density of the species distribution. Then, the different scales of emergent structures of the distribution of the population in space are modelled from the latent density of the species distribution using multi‐scale variogram models. Multi‐scale kriging is used to map the spatial patterns previously identified by the multi‐scale models. We show how our framework yields robust and precise estimates of the relevant scales both for spatial count data simulated from well‐defined models, and in a real case‐study based on seabird count data (the common guillemot Uria aalge) provided by large‐scale aerial surveys of the Bay of Biscay (France) performed over a winter. Our stochastic simulation study provides guidelines on the expected uncertainties of the scales estimates. Our results indicate that the spatial structure of the common guillemot can be modelled as a three‐level hierarchical system composed of a very broad‐scale pattern (～ 200 km) with a stable location over time that might be environmentally controlled, a broad‐scale pattern (～ 50 km) with a variable shape and location, that might be related to shifts in prey distribution, and a fine‐scale pattern (～ 10 km) with a rather stable shape and location, that might be controlled by behavioural processes. Our framework enables the development of robust, scale‐dependent hypotheses regarding the potential ecological processes that control species distributions.     

Evolution of dispersal polymorphism and local adaptation of dispersal distance in spatially structured landscapes

Many organisms show polymorphism in dispersal distance strategies. This variation is particularly ecological relevant if it encompasses a functional separation of short‐ (SDD) and long‐distance dispersal (LDD). It remains, however, an open question whether both parts of the dispersal kernel are similarly affected by landscape related selection pressures. We implemented an individual‐based model to analyze the evolution of dispersal traits in fractal landscapes that vary in the proportion of habitat and its spatial configuration. Individuals are parthenogenetic with dispersal distance determined by two alleles on each individual's genome: one allele coding for the probability of global dispersal and one allele coding for the variance σ of a Gaussian local dispersal with mean value zero. Simulations show that mean distances of local dispersal and the probability of global dispersal, increase with increasing habitat availability, but that changes in the habitat's spatial autocorrelation impose opposing selective pressure: local dispersal distances decrease and global dispersal probabilities increase with decreasing spatial autocorrelation of the available habitat. Local adaptation of local dispersal distance emerges in landscapes with less than 70% of clumped habitat. These results demonstrate that long and short distance dispersal evolve separately according to different properties of the landscape. The landscape structure may consequently largely affect the evolution of dispersal distance strategies and the level of dispersal polymorphism.     

An integrated modeling approach to estimating Gunnison sage‐grouse population dynamics: combining index and demographic data

Evaluation of population dynamics for rare and declining species is often limited to data that are sparse and/or of poor quality. Frequently, the best data available for rare bird species are based on large‐scale, population count data. These data are commonly based on sampling methods that lack consistent sampling effort, do not account for detectability, and are complicated by observer bias. For some species, short‐term studies of demographic rates have been conducted as well, but the data from such studies are typically analyzed separately. To utilize the strengths and minimize the weaknesses of these two data types, we developed a novel Bayesian integrated model that links population count data and population demographic data through population growth rate (λ) for Gunnison sage‐grouse (Centrocercus minimus). The long‐term population index data available for Gunnison sage‐grouse are annual (years 1953–2012) male lek counts. An intensive demographic study was also conducted from years 2005 to 2010. We were able to reduce the variability in expected population growth rates across time, while correcting for potential small sample size bias in the demographic data. We found the population of Gunnison sage‐grouse to be variable and slightly declining over the past 16 years.     

Methods to account for spatial autocorrelation in the analysis of species distributional data: a review

Species distributional or trait data based on range map (extent‐of‐occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.     

Dispersal constraints and fine‐scale spatial genetic structure in two earthworm species

The limited dispersal ability of earthworms is expected to result in marked genetic isolation by distance and remarkable spatial patterns of genetic variation. To test this hypothesis, we investigated, using microsatellite loci, the spatial genetic structure of two earthworm species, Allolobophora chlorotica and Aporrectodea icterica, in two plots of less than 1 ha where a total of 282 individuals were collected. We used spatial autocorrelation statistics, partial Mantel tests of isolation‐by‐distance (IBD) and isolation‐by‐resistance (IBR), and Bayesian test of clustering to explore recent patterns involved in the observed genetic structure. For A. icterica, a low signal of genetic structure was detected, which may be explained by an important dispersal capacity and/or by the low polymorphism of the microsatellite loci. For A. chlorotica, a weak, but significant, pattern of IBD associated with positive autocorrelation was observed in one of the plots. In the other plot, which had been recently ploughed, two genetically differentiated clusters were identified. These results suggest a spatial neighbourhood structure in A. chlorotica, with neighbour individuals that tend to be more genetically similar to one another, and also highlight that habitat perturbation as a result of human activities may deeply alter the genetic structure of earthworm species, even at a very small scale. © 2015 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114 , 335–347.     

Community versus single‐species distribution models for British plants

Aim Species distribution models are increasingly used to predict the impacts of global change on whole ecological communities by modelling the individualistic niche responses of large numbers of species. However, it is not clear whether this single‐species ensemble approach is preferable to community‐wide strategies that represent interspecific associations or shared responses to environmental gradients. Here, we test the performance of two multi‐species modelling approaches against equivalent single‐species models. Location Great Britain. Methods Single‐ and multi‐species distribution models were fitted for 701 native British plant species at a 10‐km grid scale. Two machine learning methods were used – classification and regression trees (CARTs) and artificial neural networks (ANNs). The single‐species versions are widely used in ecology but their multivariate extensions are less well known and have not previously been evaluated against one another. We compared their abilities to predict species distributions, community compositions and species richness in an independent geographical region reserved from model‐fitting. Results The single‐ and multi‐species models performed similarly, although the community models gave slightly poorer predictive accuracy by all measures. However, from the point of view of the whole community they were much simpler than the array of single‐species models, involving orders of magnitude fewer parameters. Multi‐species approaches also left greater residual spatial autocorrelation than the individualistic models and, contrary to expectation, were relatively less accurate for rarer species. However, the fitted multi‐species response curves had lower tendency for pronounced discontinuities that are unlikely to be a feature of realized niche responses. Main conclusions Although community distribution models were slightly less accurate than single‐species models, they offered a highly simplified way of modelling spatial patterns in British plant diversity. Moreover, an advantage of the multi‐species approach was that the modelling of shared environmental responses resolved more realistic response curves. However, there was a slight tendency for community models to predict rare species less accurately, which is potentially disadvantageous for conservation applications. We conclude that multi‐species distribution models may have potential for understanding and predicting the structure of ecological communities, but were slightly inferior to single‐species ensembles for our data.     

Exploring the effects of spatial autocorrelation when identifying key drivers of wildlife crop‐raiding

Few universal trends in spatial patterns of wildlife crop‐raiding have been found. Variations in wildlife ecology and movements, and human spatial use have been identified as causes of this apparent unpredictability. However, varying spatial patterns of spatial autocorrelation (SA) in human–wildlife conflict (HWC) data could also contribute. We explicitly explore the effects of SA on wildlife crop‐raiding data in order to facilitate the design of future HWC studies. We conducted a comparative survey of raided and nonraided fields to determine key drivers of crop‐raiding. Data were subsampled at different spatial scales to select independent raiding data points. The model derived from all data was fitted to subsample data sets. Model parameters from these models were compared to determine the effect of SA. Most methods used to account for SA in data attempt to correct for the change in P‐values; yet, by subsampling data at broader spatial scales, we identified changes in regression estimates. We consequently advocate reporting both model parameters across a range of spatial scales to help biological interpretation. Patterns of SA vary spatially in our crop‐raiding data. Spatial distribution of fields should therefore be considered when choosing the spatial scale for analyses of HWC studies. Robust key drivers of elephant crop‐raiding included raiding history of a field and distance of field to a main elephant pathway. Understanding spatial patterns and determining reliable socio‐ecological drivers of wildlife crop‐raiding is paramount for designing mitigation and land‐use planning strategies to reduce HWC. Spatial patterns of HWC are complex, determined by multiple factors acting at more than one scale; therefore, studies need to be designed with an understanding of the effects of SA. Our methods are accessible to a variety of practitioners to assess the effects of SA, thereby improving the reliability of conservation management actions.