Mathematical models for red squirrel conservation

In this thesis we develop mathematical models to understand the process of ecological invasion when the invading species also carries a disease that is harmful to the native species. In particular we focus on a key case study system of the invasion of grey squirrels and replacement of red squirrels in the UK, in which the shared disease, squirrelpox, has been suggested as a key driver of the rapid expansion of grey squirrels. Our initial study focused on examining the viability of red squirrels in the stronghold forests of Kidland and Uswayford in Northumberland. These are commercially managed forests that Forestry Commission England manage to improve red squirrel population viability. Through close collaboration with the Forestry Commission, we developed a mathematical model that could test squirrel population viability for a range of felling and replanting strategies. Our findings have been used to direct the forest design plans that will be implemented in these forests. Our second study used spatial, stochastic modelling techniques to model the replacement of red squirrels and subsequent control of grey squirrels on the Isle of Anglesey. Our findings indicated that the replacement of red squirrels by grey squirrels on the island was largely driven by competitive interactions. However, on a local level squirrelpox epidemics could occur and lead to mortality in red squirrel populations. Our model was also fitted to data on the control and eradication of grey squirrels and reintroduction of red squirrels that took place on the Isle of Anglesey between 1998-2013. Our fitted model was then used to examine the best conservation strategies to protect the red squirrels on Anglesey. Our final study compared key findings on the process of disease-mediated invasion in deterministic and stochastic model frameworks. The deterministic frameworks predict that a wave of disease can spread through a native population in advance of a wave of replacement of the invading species. A stochastic representation of this system indicated that this wave of disease in advance of the wave of replacement may not occur if the disease is too virulent to the native species. However, if the disease is supported by the invading species, it will still mediate the invasion at the interface between the native and invading species where local epidemic disease outbreaks can occur. In general this thesis shows that mathematical models are powerful tools for the conservation management of native species under threat from invasion