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Persistence metrics for a river population in a two-dimensional benthic-drift model

1 Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA
2 School of Mathematical and Statistical Sciences, Southwest University, Chongqing 400715, China
3 School of Mathematical and Statistical Sciences, Hubei University of Science and Technology, Xianning 437100, China
4 Department of Civil and Environmental Engineering, University of Alberta Edmonton, AB, T6G 1H9, Canada
5 Center for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
6 Department of Biological Sciences, University of Alberta, Edmonton, AB, T6G 2E9, Canada

Special Issues: Applied and Industrial Mathematics in Canada and Worldwide

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.
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Keywords benthic-drift population model; next generation operator; persistence; net reproductive rate; River2D

Citation: Yu Jin, Qihua Huang, Julia Blackburn, Mark A. Lewis. Persistence metrics for a river population in a two-dimensional benthic-drift model. AIMS Mathematics, 2019, 4(6): 1768-1795. doi: 10.3934/math.2019.6.1768


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