Bifurcations and chaos in ecology: lynx returns revisited

Abstract

One of the most popular data sets in ecology, that of lynx fur returns, is analysed in order to look for evidence for a bifurcation process. This bifurcation seems to be present from the observation of sudden shifts in the amplitude of oscillations of the lynx time series. Schaffer first proposed the possibility for such a bifurcation in 1985, and suggested that a possible source for the qualitative change of lynx’s fluctuations was an increased trapping effort, which eventually lead to high‐amplitude, chaotic dynamics. By studying the available information from the Hudson Bay Company records, we have found evidence for such an increased trapping pressure that (i) rapidly rose close to the shift from low‐amplitude to large‐amplitude fluctuations around 1820, and (ii) decreased around 1910, when there is another shift again to damped small oscillations. Although an increase in the top‐predator mortality in a three‐species food web typically leads to simpler dynamics and eventual predator extinction, here we show that a recent model involving a minimum bound in the lynx population, due to the presence of alternative prey in the lynx diet, consistently supports the presence of a bifurcation phenomenon.