Stochastic spatial models of plant diseases
David H. Brown
TL;DR
The work develops and applies stochastic, spatially explicit frameworks to plant–pathogen dynamics, showing how local structure reshapes invasion thresholds, persistence, and coevolution beyond classical mean-field predictions. Using pair approximation and moment-closure techniques with a separation-of-timescales approach, it yields three focused studies: a nonlethal disease altering competitive hierarchies, a spatially resolved analysis of epidemic thresholds in a SIR point process, and an ESS-based exploration of resistance evolution when hosts share a pathogen with a superior competitor. The results reveal that spatial clustering can enable coexistence, create complex spatiotemporal patterns, and drive directionally dependent evolution of resistance, with implications for understanding natural plant communities and managing disease dynamics. The analyses also highlight both the power and limitations of closure-based methods in capturing early-epidemic structure and the need for systems-specific validation.
Abstract
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of timescales argument to determine the effects of spatial clustering on threshold structure. By computing the spatial structure early in an invasion, I find explicit corrections to mean field theory. In the first chapter, I present a lattice model of a disease that is not directly lethal to its host, but affects its ability to compete with neighbors. I use a type of pair approximation to determine conditions for invasions and coexistence. In the second chapter, I study a basic SIR epidemic point process in continuous space. I implement a multiplicative moment closure scheme to compute the threshold transmission rate as a function of spatial parameters. In the final chapter, I model the evolution of pathogen resistance when two plant species share a pathogen. Evolution may lead to non--resistance by a host that finds the disease to be a useful weapon. I use a lattice model with the ordinary pair approximation assumption to study phenotypic evolution via repeated invasions by novel strains.