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The movement of fish in watersheds is frequently inhibited by human-made migration barriers such as dams or culverts. The resulting lack of connectivity of spatial subpopulations is often cited as a cause for observed population decline. We formulate a matrix model for a spatially distributed fish population in a watershed, and we investigate how location and other characteristics of a single movement barrier impact the asymptotic growth rate of the population. We find that while population growth rate often decreases with the introduction of a movement obstacle, it may also increase due to a ‘retention effect’. Furthermore, obstacle mortality greatly affects population growth rate. In practice, different connectivity indices are used to predict population effects of migration barriers, but the relation of these indices to population growth rates in demographic models is often unclear. When comparing our results with the dentritic connectivity index, we see that the index captures neither the retention effect nor the influences of obstacle mortality. We argue that structural indices cannot entirely replace more detailed demographic models to understand questions of persistence and extinction. We advocate the development of novel functional indices and characteristics.

Connectivity, passability and heterogeneity interact to determine fish population persistence in river networks