Modelling the spread of Wolbachia in spatially heterogeneous environments.

Penelope A Hancock,H Charles J Godfray

doi:10.1098/rsif.2012.0253

Penelope A Hancock, H Charles J Godfray

Open Access

https://doi.org/10.1098/rsif.2012.0253

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Abstract

The endosymbiont Wolbachia infects a large number of insect species and is capable of rapid spread when introduced into a novel host population. The bacteria spread by manipulating their hosts' reproduction, and their dynamics are influenced by the demographic structure of the host population and patterns of contact between individuals. Reaction–diffusion models of the spatial spread of Wolbachia provide a simple analytical description of their spatial dynamics but do not account for significant details of host population dynamics. We develop a metapopulation model describing the spatial dynamics of Wolbachia in an age-structured host insect population regulated by juvenile density-dependent competition. The model produces similar dynamics to the reaction–diffusion model in the limiting case where the host's habitat quality is spatially homogeneous and Wolbachia has a small effect on host fitness. When habitat quality varies spatially, Wolbachia spread is usually much slower, and the conditions necessary for local invasion are strongly affected by immigration of insects from surrounding regions. Spread is most difficult when variation in habitat quality is spatially correlated. The results show that spatial variation in the density-dependent competition experienced by juvenile host insects can strongly affect the spread of Wolbachia infections, which is important to the use of Wolbachia to control insect vectors of human disease and other pests.

Highlights

It has been estimated that up to 60 per cent of all insect species may be infected with the endosymbiotic bacteria Wolbachia [1]
The equilibrium speed of the travelling wave of Wolbachia infection derived from the reaction– diffusion
The reaction–diffusion model predicts that the speed of spread declines to zero as pÃ approaches 0.5; the metapopulation model indicates that spread stops at lower values of pÃ for weak densitydependence but the limit is above 0.5 for strong density-dependence

Summary

Introduction

It has been estimated that up to 60 per cent of all insect species may be infected with the endosymbiotic bacteria Wolbachia [1]. Wolbachia are vertically transmitted from mothers to offspring, and can spread rapidly when introduced into a novel host population. The bacteria increase in frequency by manipulating their hosts’ reproductive system, often using a mechanism known as cytoplasmic incompatibility (CI) [2,3]. CI causes incompatibility between the sperm of Wolbachia-infected males and the eggs of uninfected females, leading to failure of embryonic development unless the egg carries the bacterium [2,4]. The presence of Wolbachia carrying males reduces the proportion of viable offspring that are uninfected, allowing the bacterium to spread. Wolbachia epidemiology is closely linked to the host’s demography and patterns of contact between individual hosts

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Conclusion