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Why species are found where they are is a central question in biogeography. The most widely used tool for understanding the controls on distribution is species distribution modelling. Species distribution modelling is now a well-established method in both the theoretical and applied ecological literature. In this special issue we examine the current state of the art in species distribution modelling and explore avenues for including more biological processes in such models. In particular we focus on physiological, demographic, dispersal, competitive and ecological-modulation processes. This overview highlights opportunities for new species distribution model concepts and developments, as well as a statistical agenda for implementing such models.

Within the field of species distribution modelling an apparent dichotomy exists between process-based and correlative approaches, where the processes are explicit in the former and implicit in the latter. However, these intuitive distinctions can become blurred when comparing species distribution modelling approaches in more detail. In this review article, we contrast the extremes of the correlative–process spectrum of species distribution models with respect to core assumptions, model building and selection strategies, validation, uncertainties, common errors and the questions they are most suited to answer. The extremes of such approaches differ clearly in many aspects, such as model building approaches, parameter estimation strategies and transferability. However, they also share strengths and weaknesses. We show that claims of one approach being intrinsically superior to the other are misguided and that they ignore the process–correlation continuum as well as the domains of questions that each approach is addressing. Nonetheless, the application of process-based approaches to species distribution modelling lags far behind more correlative (process-implicit) methods and more research is required to explore their potential benefits. Critical issues for the employment of species distribution modelling approaches are given, together with a guideline for appropriate usage. We close with challenges for future development of process-explicit species distribution models and how they may complement current approaches to study species distributions.

Aim Biotic interactions – within guilds or across trophic levels – have widely been ignored in species distribution models (SDMs). This synthesis outlines the development of ‘species interaction distribution models’ (SIDMs), which aim to incorporate multispecies interactions at large spatial extents using interaction matrices. Location Local to global. Methods We review recent approaches for extending classical SDMs to incorporate biotic interactions, and identify some methodological and conceptual limitations. To illustrate possible directions for conceptual advancement we explore three principal ways of modelling multispecies interactions using interaction matrices: simple qualitative linkages between species, quantitative interaction coefficients reflecting interaction strengths, and interactions mediated by interaction currencies. We explain methodological advancements for static interaction data and multispecies time series, and outline methods to reduce complexity when modelling multispecies interactions. Results Classical SDMs ignore biotic interactions and recent SDM extensions only include the unidirectional influence of one or a few species. However, novel methods using error matrices in multivariate regression models allow interactions between multiple species to be modelled explicitly with spatial co-occurrence data. If time series are available, multivariate versions of population dynamic models can be applied that account for the effects and relative importance of species interactions and environmental drivers. These methods need to be extended by incorporating the non-stationarity in interaction coefficients across space and time, and are challenged by the limited empirical knowledge on spatio-temporal variation in the existence and strength of species interactions. Model complexity may be reduced by: (1) using prior ecological knowledge to set a subset of interaction coefficients to zero, (2) modelling guilds and functional groups rather than individual species, and (3) modelling interaction currencies and species’ effect and response traits. Main conclusions There is great potential for developing novel approaches that incorporate multispecies interactions into the projection of species distributions and community structure at large spatial extents. Progress can be made by: (1) developing statistical models with interaction matrices for multispecies co-occurrence datasets across large-scale environmental gradients, (2) testing the potential and limitations of methods for complexity reduction, and (3) sampling and monitoring comprehensive spatio-temporal data on biotic interactions in multispecies communities.

Aim Species frequency data have been widely used in nature conservation to aid management decisions. To determine species frequencies, information on habitat occurrence is important: a species with a low frequency is not necessarily rare if it occupies all suitable habitats. Often, information on habitat distribution is available for small geographic areas only. We aim to predict grid-based habitat occurrence from grid-based plant species distribution data in a meso-scale analysis. Location The study was carried out over two spatial extents: Germany and Bavaria. Methods Two simple models were set up to examine the number of characteristic plant species needed per grid cell to predict the occurrence of four selected habitats (species data from FlorKart, http://www.floraweb.de). Both models were calibrated in Bavaria using available information on habitat distribution, validated for other federal states, and applied to Germany. First, a spatially explicit regression model (generalized linear model (GLM) with assumed binomial error distribution of response variable) was obtained. Second, a spatially independent optimization model was derived that estimated species numbers without using spatial information on habitat distribution. Finally, an additional uncalibrated model was derived that calculated the frequencies of 24 habitats. It was validated using NATURA2000 habitat maps.

In a recent article (Dormann et al., 2012, Journal of Biogeography, 39, 2119–2131), we compared different approaches to species distribution modelling and depicted modelling approaches along an axis from purely ‘correlative’ to ‘forward process-based’ models. In their correspondence, Kriticos et al. (2013, Journal of Biogeography, doi:10.1111/j.1365-2699.2012.02791.x) challenge this view, claiming that our continuum representation neglects differences among models and does not consider the ability of fitted process-based models to combine the advantages of both process-based and correlative modelling approaches. Here we clarify that the continuum view resulted from recognition of the manifold differences between models. We also reinforce the point that the current trend towards combining different modelling approaches may lead not only to the desired combination of the advantages but also to the accumulation of the disadvantages of those approaches. This point has not been made sufficiently clear previously.