University of Georgia Athens, Georgia, United States
Abstract: Predicting geographical spread over heterogeneous landscapes is an important problem in ecology, epidemiology, and demography. Examples include spatial transmission of infectious diseases related to the movement of hosts, vector transfer of non-native species from one spatial unit to another that facilitates invasion into novel habitats, and migration of species that can be tracked by monitoring gene flow over space. Understanding what drives spread is needed to anticipate how invasions will unfold and to appropriately allocate management efforts. Past efforts have successfully used "gravity models" to represent the pairwise connections between patches of different size or quality. However, I argue that traditional gravity models are over-specified. The goal of this study was to develop a general framework for modeling pairwise spatial interactions that include gravity models as a special case, but allows for other, possibly mechanistically derived formulas, to represent the redistribution of an expanding population over a landscape.
To understand the space of possible models, I present a conceptual and modular model of movement in which the process of migration occurs from a source to a destination via a relocation function in a discrete spatially extended system (i.e., a metapopulation). Next, I develop a menu of source, relocation, and destination functions. Linking this migration model to a local model of stochastic establishment provides a statistical framework that can be used for a variety of quantitative tasks, including parameter estimation, statistical inference, model selection, probabilistic forecasting, and scenario analysis. We then applied the framework to data from the 10th outbreak of Ebola in the Democratic Republic of the Congo. We quantify the effects of road and river networks for movement, international boundaries, and armed conflicts on spatial spread and containment. We show that information obtained early in the epidemic process significantly constrains the potential trajectories of the epidemic, highlighting the need for early detection and rapid response to such events. In conclusion, this work suggests that a multi-scale approach may be necessary for modeling the spread of epidemics and colonizing species and that such an approach can generate actionable information even when fitted to the limited data available early in the invasion process.
