Mathematics, Department of


Date of this Version



AIMS Mathematics, 4(6): 1768–1795.


© 2019 the Author(s)

Open access



The study of population persistence in river ecosystems is key for understanding population dynamics, invasions, and instream flow needs. In this paper, we extend theories of persistence measures for population models in one-dimensional rivers to a benthic-drift model in two-dimensional depth- averaged rivers. We define the fundamental niche and the source and sink metric, and establish the net reproductive rate R0 to determine global persistence of a population in a spatially heterogeneous two-dimensional river. We then couple the benthic-drift model into the two-dimensional computational river model, River2D, to study the growth and persistence of a population and its source and sink regions in a river. The theory developed in this study extends existing R0 analysis to spatially heterogeneous two-dimensional models. The River2D program provides a method to analyze the impact of river morphology on population persistence in a realistic river. The theory and program derived here can be applied to species in real rivers.