Eco-Evolutionary Feedback in Host--Pathogen Spatial Dynamics

TL;DR

This paper investigates how spatial heterogeneity influences host-pathogen dynamics, revealing limitations of traditional models and proposing new methods to understand the evolution and spread of pathogens in spatially structured ecosystems.

Contribution

It introduces a novel simulation approach for spatial host-pathogen systems, demonstrating the failure of standard approximation methods and proposing new measures for invasion dynamics.

Findings

Standard mean field approximation fails in spatial contexts.

Pathogen invasiveness can be temporary, not leading to long-term persistence.

Spatial heterogeneity significantly alters evolutionary outcomes.

Abstract

Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change our understanding of evolutionary dynamics, as the same organism in different places can have different expected evolutionary outcomes. Since organism origins and fates are both determined locally, we must consider heterogeneity explicitly to determine its effects. We use simulations of spatially extended host--pathogen and predator--prey ecosystems to reveal the limitations of standard mathematical treatments of spatial heterogeneity. Our model ecosystem generates heterogeneity dynamically; an adaptive network of hosts on which pathogens are transmitted arises as an emergent phenomenon. The structure and dynamics of this network differ in significant ways from those of related models studied in the adaptive-network field. We use a new technique, organism swapping, to test the efficacy of both simple approximations and more elaborate moment-closure methods, and a new measure to reveal the timescale dependence of invasive-strain behavior. Our results demonstrate the failure not only of the most straightforward ("mean field") approximation, which smooths over heterogeneity entirely, but also of the standard correction ("pair approximation") to the mean field treatment. In spatial contexts, invasive pathogen varieties can prosper initially but perish in the medium term, implying that the concepts of reproductive fitness and the Evolutionary Stable Strategy have to be modified for such systems.