Seasonal Influences on Population Spread and Persistence in Streams: Critical Domain Size

The critical domain size problem determines the size of the region of habitat needed to ensure population persistence. In this paper we address the critical domain size problem for seasonally fluctuating stream environments and determine how large a reach of suitable stream habitat is needed to ensure population persistence of a stream-dwelling species. Two key factors, not typically found in critical domain size problems, are fundamental in determining whether population can persist. These are the unidirectional nature of stream flow and seasonal fluctuations in the stream environment. We characterize the fluctuating environments in terms of seasonal correlations among the flow, transfer rates, diffusion, and settling rates, and we investigate the effect of such correlations on the critical domain size problem. We show how results for the seasonally fluctuating stream can formally be connected to those for autonomous integro-differential equations, through the appropriate weighted averaging methods.