Bifurcations and chaos in ecology: lynx returns revisited

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 bifu rcation seems to be present from the observation of sudden shifts in the am plitude of oscillations of the lynx time series. Schaffer first proposed th e 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) ra pidly rose close to the shift from low-amplitude to large-amplitude fluctua tions around 1820, and (ii) decreased around 1910, when there is another sh ift again to damped small oscillations. Although an increase in the top-pre dator mortality in a three-species food web typically leads to simpler dyna mics and eventual predator extinction, here we show that a recent model inv olving a minimum bound in the lynx population, due to the presence of alter native prey in the lynx diet, consistently supports the presence of a bifur cation phenomenon.