Mathematical models assessing the importance of disease on ecological invasions

Abstract

A general understanding of the role that both shared disease and competition may play in ecological invasions is lacking. We develop a theoretical framework to determine the role of disease, in addition to competition, in invasions. We first investigate the e ect of disease characteristics on the replacement time of a native species by an invader. The outcome is critically dependent on the relative e ects that the disease has on the two species and less dependent on the basic epidemiological characteristics of the interaction. This framework is extended to investigate the e ect of disease on the spatial spread of an invader and indicates that a wave of disease spreads through a native population in advance of the replacement. A probabilistic simulation model is developed to examine the particular example of the replacement of red squirrels by grey squirrels in the United Kingdom. This model is used to examine conservation strategies employed within red squirrel refuges and compared to observations from Sefton Coast Red Squirrel Refuge. Our findings indicate that culling greys may be e ective at protecting red populations from replacement, but none of the conservation strategies currently employed can prevent periodic outbreaks of infection within red squirrel refuges.