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Statistical models use observations of animals to make inferences about the abundance and distribution of species. However, the spatial distribution of animals is a complex function of many factors, including landscape and environmental features, and intra- and interspecific interactions. Modelling approaches often have to make significant simplifying assumptions about these factors, which can result in poor model performance and inaccurate predictions.\ud Here, we explore the implications of complex spatial structure for modelling the abundance of the Serengeti wildebeest, a gregarious migratory species. The social behaviour of wildebeest leads to a highly aggregated distribution, and we examine the consequences of omitting this spatial complexity when modelling species abundance. To account for this distribution, we introduce a multi-latent framework that uses two random fields to capture the clustered distribution of wildebeest.\ud Our results show that simplifying assumptions that are often made in spatial models can dramatically impair performance. However, by allowing for mixtures of spatial models accurate predictions can be made. Furthermore, there can be a non-monotonic relationship between model complexity and model performance; complex, flexible models that rely on unfounded assumptions can potentially make highly inaccurate predictions, whereas simpler more traditional approaches involve fewer assumptions and are less sensitive to these issues.\ud We demonstrate how to develop flexible spatial models that can accommodate the complex processes driving animal distributions. Our findings highlight the importance of robust model checking protocols, and we illustrate how realistic assumptions can be incorporated into models using random fields.

Collective behavior is characterized by the emergence of large-scale phenomena from local interactions. It is found in many\ud contexts, including political movements, fads and fashions, and animal grouping. In this paper, we aim to elucidate the mechanisms that\ud underlie observed collective behavior by developing a novel mathematical framework based on equation-free modelling procedures and\ud Gaussian process regression. This allows us to circumvent the possible lack of formal mathematical links between scales and instead use\ud statistical emulation to learn an empirical Fokker-Planck equation. Our approach advances our ability to understand how complex systems\ud function at both the individual and collective level when a formal mathematical description of macroscale dynamics is unavailable.

Individual-based models are used in a variety of scientific domains to study systems composed of multiple agents that interact\ud with one another and lead to complex emergent dynamics at the macroscale. A standard approach in the analysis of these systems is\ud to specify the microscale interaction rules in a simulation model, run simulations, and then qualitatively compare outputs to empirical\ud observations. Recently, more robust methods for inference for these types of models have been introduced, notably approximate Bayesian\ud computation, however major challenges remain due to the computational cost of simulations and the nonlinear nature of many complex\ud systems. Here, we compare two methods of approximate inference in a classic individual-based model of group dynamics with well-studied\ud nonlinear macroscale behaviour; we employ a Gaussian process accelerated ABC method with an approximated likelihood and with a\ud synthetic likelihood. We compare the accuracy of results when re-inferring parameters using a measure of macro-scale disorder (the\ud order parameter) as a summary statistic. Our findings reveal that for a canonical simple model of animal collective movement, parameter\ud inference is accurate and computationally efficient, even when the model is poised at the critical transition between order and disorder.

Understanding animal movement is an important challenge in ecology, with improvement in tagging technology permitting the collection of data on an increasingly wide range of species. Consequently, methodologies for statistical analysis of such data has received considerable attention in recent years. Discrete-time random walks are the foundation of the movement data models. The advantages of the discrete-time movement models are that they are intuitive and easily implemented, however the specification of the discretization step is often problematic and must be done in advance. Misspecification of the discretization step might lead to a model mismatch and thus\ud choosing an appropriate test statistic to capture the model mismatch is essential.

Pathogen spillover from wildlife to domestic animals and humans, and the reverse, has caused significant epidemics and pandemics worldwide. Although pathogen emergence has been linked to anthropogenic land conversion, a general framework to disentangle underlying processes is lacking. We develop a multi-host model for pathogen transmission between species inhabiting intact and converted habitat. Interspecies contacts and host populations vary with the proportion of land converted; enabling us to quantify infection risk across a changing landscape. In a range of scenarios, the highest spillover risk occurs at intermediate levels of habitat loss, whereas the largest, but rarest, epidemics occur at extremes of land conversion. This framework provides insights into the mechanisms driving disease emergence and spillover during land conversion. The finding that the risk of spillover is highest at intermediate levels of habitat loss provides important guidance for conservation and public health policy.

Information; Tables S1-S4; Figures S1-S5

Appendix A. R-N phase diagrams for single site breeding migration model. (PDF 203 kb)