Including organism and environmental heterogeneity in kinematic continuum models of collective behaviour with applications to locust foraging and group structure

Abstract

Collective behaviour occurs at all levels of the natural world, from cells joining together to form complex structures, to locusts interacting to form large and destructive plagues. These complex behaviours arise from simple individual and environmental interactions, and thus lend themselves well to mathematical modelling. One simplifying assumption, that of relative homogeneity of organisms, is often applied to keep the mathematics tractable. However, heterogeneity arising due to the internal state of individuals has an impact on these interactions and thus plays a role in group structure and dynamics. In this paper, we introduce a continuum model that accounts for this heterogeneity in the form of a state space that models an organisms internal state and converts this to movement characteristics. Using a variety analytic techniques, we investigate the effect of internal state on aggregation density and aggregation formation behaviour, finding that density and formation is most affected by the ratio of attractive to dispersive interactions. We then apply the model to a concrete example of locust foraging to investigate the effect of food, hunger, and gregarisation on locust group formation and structure. Through numerical simulations we find that the most gregarious and satiated locusts tend to be located towards the centre of locust groups. Conversely, hunger drives locusts towards the edges of the group. Finally, we find that locust group dispersal may be driven in part by hunger. Author SummaryCollective behaviour occurs at all levels of the natural world, from cells joining together to form complex structures, to locusts interacting to form large and destructive plagues. We can modelling these complex behaviours using mathematical models however we often need to rely on simplifying assumptions to keep the mathematics easy enough to analyse. One simplifying assumption that is often employed is assuming that all the modelled organisms are the same (or in one of only a few possible states). However, this is often not the case in nature where the differences between individuals arising due to internal characteristics, such as hunger or age, often affects their behaviour and thus can change group dynamics. In this paper we introduce a mathematical model that is able to capture these differences and apply the newly developed model to locust foraging. We find that hunger tends to drive individuals to the edges of aggregations as well as lowers the maximum possible density. These two results combine to give a possible mechanism for the dispersal of locust groups.