Population persistence in the face of advection

Many populations live in 'advective' media, such as rivers, where flow is biased in one direction. In these environments, populations face the possibility of extinction by being washed out of the system, even if the net reproductive rate (R) is greater than one. We propose a formal condition for population persistence in advective systems: a population can persist at any location in a homogeneous habitat if and only if it can invade upstream. This leads to a remarkably simple recipe for calculating the minimal value for the net reproductive rate for population persistence. We apply this criterion to discrete-time models of a semelparous population where dispersal is characterized by a mechanistically derived kernel. We demonstrate that persistence depends strongly on the form of the kernel's 'tail', a result consistent with previous literature on the speed of spread of invasions. We apply our theory to models of stream invertebrates with a biphasic life cycle, and relate our results to the 'colonization cycle' hypothesis where bias in downstream drift is offset by upstream bias in adult dispersal. In the absence of bias in adult dispersal, variability in the duration of the larval stage and in oviposition sites have a large effect of the persistence condition. The minimization calculations required in our approach are very straightforward, indicating the feasibility of future applications to life history theory.