A diffusion-based theory of organism dispersal in heterogeneous populations

We develop a general theory of organism movement in heterogeneous populations that can explain the leptokurtic movement distributions commonly measured in nature. We describe population heterogeneity in a state-structured framework, employing advection-diffusion as the fundamental movement process of individuals occupying different movement states. Our general analysis shows that population heterogeneity in movement behavior can be defined as the existence of different movement states and among-individual variability in the time individuals spend in these states. A presentation of moment-based metrics of movement illustrates the role of these attributes in general dispersal processes. We also present a special case of the general theory: a model population composed of individuals occupying one of two movement states with linear transitions, or exchange, between the two states. This two-state "exchange model" can be viewed as a correlated random walk and provides a generalization of the telegraph equation. By exploiting the main result of our general analysis, we characterize the exchange model by deriving moment-based metrics of its movement process and identifying an analytical representation of the model's time-dependent solution. Our results provide general and specific theoretical explanations for empirical patterns in organism movement; the results also provide conceptual and analytical bases for extending diffusion-based dispersal theory in several directions, thereby facilitating mechanistic links between individual behavior and spatial population dynamics.