School of Mathematics

Jonathan Sherratt

Jonathan Sherratt abstract

Jonathan Sherratt, Department of Mathematics, Heriott-Watt

Title: How Does Seasonal Forcing Affect Vole Population Cycles?

In many parts of Northern Europe, voles exibit multi-year cycles in abundence. The traditional explanation for population cycles is predation, and this has a long history of study via mathematical models. In Scandinavia it has been suggested that a North-South gradient in the extent of generalist predation modifies the dynamics that result from interactions with weasels (a specialist predator). I will show that this explanation is significantly complicated by the pronounced seasonal forcing in areas such as Scandinavia and Northern UK. I will describe the use of bifurcation theory of forced dynamical systems to study the wide range of oscillatory behaviours that occur in the presence of this seasonal forcing. Recent field experiments suggestthat although predation is the driving force behind vole cycles in Scandinavia, it does not play a controlling factor in Northern UK. An alternative  explanation is suggested by recent  data indicating that the species of grass eaten by voles in Northern UK exhibits a defense response: after herbivory, its leaves regrow with an increased level of silica, which significantly reduces the nutritional benefit of the plant to voles. I will describe a mathematical model based on greenhouse experiments on the response of grass to herbivory, and laboratory data on the effect of dietary silica on voles. In the presence of seasonal forcing, the model predicts population cycles that closely resemble those seen in field data from Northern UK.