A Note on Species Richness and the Variance of Epidemic Severity

TL;DR

This paper investigates how increasing species diversity in ecological communities reduces both the average and variance of epidemic severity, using an idealized multi-species SIR model to clarify the dilution and variance reduction effects.

Contribution

It introduces a quantitative analysis of variance in epidemic severity within a multi-species community, highlighting differences between density- and frequency-dependent transmission models.

Findings

Variance of community R_0 decreases with species richness.

Variance reduction effect is consistent across transmission types.

Provides a framework for future research on variance effects in disease dynamics.

Abstract

The commonly observed negative correlation between the number of species in an ecological community and disease risk, typically referred to as "the dilution effect", has received a substantial amount of attention over the past decade. Attempts to test this relationship experimentally have revealed that, in addition to the mean disease risk decreasing with species number, so too does the variance of disease risk. This is referred to as the "variance reduction effect", and has received relatively little attention in the disease-diversity literature. Here, we set out to clarify and quantify some of these relationships in an idealized model of a randomly assembled multi-species community undergoing an epidemic. We specifically investigate the variance of the community disease reproductive ratio, a multi-species extension of the basic reproductive ratio R_0, for a family of random-parameter meta-community SIR models, and show how the variance of community $R_0$ varies depending on whether transmission is density or frequency-dependent. We finally outline areas of further research on how changes in variance affect transmission dynamics in other systems.