Modelling collective movement across scales : from cells to wildebeest

Collective movements are ubiquitous in biological systems, occurring at all scales; from the sub-organismal movements of groups of cells, to the far-ranging movements of bird flocks and herds of large herbivores. Movement patterns at these vastly different scales often exhibit surprisingly similar patterns, suggesting that mathematically similar mechanisms may drive collective movements across many systems. The aims of this study were three-fold. First, to develop mechanistic movement models capable of producing the observed wealth of spatial patterns. Second, to tailor statistical inference approaches to these models that are capable of identifying drivers of collective movement that could be applied to a wide range of study systems. Third, to validate the approaches by fitting the mechanistic models to data from diverse biological systems. These study systems included two small-scale in vitro cellular systems, involving movement of groups of human melanoma cells and Dictyostelium discoideum (slime mould) cells, and a third much larger-scale system, involving wildebeest in the Serengeti ecosystem. I developed a series of mechanistic movement models, based on advection-diffusion partial differential equations and integro-differential equations, that describe changes in the spatio-temporal distribution of the study population as a consequence of various movement drivers, including environmental gradients, environmental depletion, social behaviour, and spatial and temporal heterogeneity in the response of the individuals to these drivers. I also developed a number of approaches to statistical inference (comprising both parameter estimation and model comparison) for these models that ranged from frequentist, to pseudo-Bayesian, to fully Bayesian. These inference approaches also varied in whether they required numerical solutions of the models, or whether the need for numerical solutions was bypassed by using gradient matching methods. The inference methods were specifically designed to be effective in the face of the many difficulties presented by advection-diffusion models, particularly high computational costs and instabilities in numerical model solutions, which have previously prevented these models from being fitted to data. It was also necessary for these inference methods to be able to cope with data of different qualities; the cellular data provided accurate information on the locations of all individuals through time, while the wildebeest data consisted of coarse ordinal abundance categories on a spatial grid at monthly intervals. By applying the developed models and inference methods to data from each study system, I drew a number of conclusions about the mechanisms driving movement in these systems. In all three systems, for example, there was evidence of a saturating response to an environmental gradient in a resource or chemical attractant that the individuals could deplete locally. I also found evidence of temporal dependence in the movement parameters for all systems. This indicates that the simplifying assumption that behaviour is constant, which has been made by many previous studies that have modelled movement, is unlikely to be justified. Differences between the systems were also demonstrated, such as overcrowding affecting the movements of melanoma and wildebeest, but not Dictyostelium, and wildebeest having a much greater range of perception than cells, and thus being able to respond to environmental conditions tens of kilometres away. The toolbox of methods developed in this thesis could be applied to increase understanding of the mechanisms underlying collective movement in a wide range of systems. In their current form, these methods are capable of producing very close matches between models and data for our simple cell systems, and also produce a relatively good model fit in the more complex wildebeest system, where there is, however, still some room for improvement. While more work is required to make the models generalisable to all taxa, particularly through the addition of memory-driven movement, inter-individual differences in behaviour, and more complex social dynamics, the advection-diffusion modelling framework is flexible enough for these additional behaviours to be incorporated in the future. A greater understanding of what drives collective movements in different systems could allow management of these movements to prevent the collapse of important migrations, control pest species, or prevent the spread of cancer.