Seasonality and extinction in chaotic metapopulations

A body of recent work has used coupled logistic maps to show that these model metapopulations show a decrease in global extinction rate in the chaotic region of model behaviour. In fact, many of the main ecological candidates for low-dimensional chaos are continuous-time host-parasite and predator-prey systems, driven by strong seasonal ‘forcing’ of one or more population parameters. This paper, therefore, explores the relation between seasonal forcing and metapopulation extinction for such systems. We base the analysis on extensive simulations of a stochastic metapopulation model for measles, based on a standard compartmental model, tracking the density of susceptible, exposed, infectious and recovered individuals (the SEIR model). The results show that, by contrast with coupled logistic maps, the increased seasonality which causes chaos maintains or increases levels of global extinction of infection, by increasing the synchrony of sub-population epidemics. The model also illustrates that the population interaction (here between susceptible and infective hosts) has a significant effect on patterns of synchrony and extinction.