On the formulation and analysis of a stage-structured eco-evolutionary model with pulsed disturbances

Abstract

Motivated by the pulsed control and resulting evolution of harmful biological populations, we develop and analyze an ordinary differential equation model of an n-dimensional stage-structured population undergoing periodic disturbances. The eco-evolutionary model couples both ecological dynamics through life cycle information, and evolutionary dynamics of allele frequency changes. Building off prior work in eco-evolutionary models and theory of linear systems, we show that if a resistant allele is present in the population, the population will always approach full resistance. Furthermore, we establish persistence conditions and show that these depend solely on system dynamics at full resistance. Finally, we demonstrate the utility of this model via an application to the Spotted-Winged Drosophila, an invasive species often treated periodically with insecticides. We use a parameterized model to further understand the complexities of relationships between ecological and evolutionary features of a species and its resistance evolution due to pulsed disturbances.