Mathematical models for red squirrel conservation
Abstract
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.