Mean free-path length theory of predator–prey interactions: Application to juvenile salmon migration |
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| Institution: | 1. School of Aquatic and Fishery Sciences, University of Washington, Box 358218, Seattle, WA 98195, USA;2. Northwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, 2725 Montlake Blvd. East Seattle, WA 98112, USA;1. School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;2. CREST, Japan Science and Technology Agency, 4-8-1 Honcho, Kawaguchi, Saitama 332-0012, Japan;1. Centre for Ecology and Conservation, College of Life & Environmental Sciences, University of Exeter, Cornwall Campus, Penryn TR10 9EZ, UK;2. Ascension Island Government Conservation Department, Georgetown, Ascension Island, South Atlantic, ASCN 1ZZ, UK;3. Ascension Island Turtle Group, Georgetown, Ascension Island, South Atlantic, UK;4. Environment and Sustainability Institute, College of Life & Environmental Sciences, University of Exeter, Cornwall Campus, Penryn TR10 9EZ, UK;1. Fisheries and Oceans Canada, Arctic and Aquatic Research Division, Freshwater Institute, 501 University Crescent, Winnipeg, Manitoba, R3T-2N6, Canada;2. College of Fisheries and Ocean Sciences, Department of Fisheries, University of Alaska, Fairbanks, P.O. Box 757220, Fairbanks, AK, 99775-7220, USA;3. Fisheries and Oceans Canada, P.O. Box 1871, Inuvik, Northwest Territories, X0E 0T0, Canada;1. Department of Life Science, Tunghai University, Taichung, Taiwan;2. Center for Tropical Ecology and Biodiversity, Tunghai University, Taichung, Taiwan |
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| Abstract: | Ecological theory traditionally describes predator–prey interactions in terms of a law of mass action in which the prey mortality rate depends on the density of predators and prey. This simplifying assumption makes population-based models more tractable but ignores potentially important behaviors that characterize predator–prey dynamics. Here, we expand traditional predator–prey models by incorporating directed and random movements of both predators and prey. The model is based on theory originally developed to predict collision rates of molecules. The temporal and spatial dimensions of predators–prey encounters are determined by defining movement rules and the predator's field of vision. These biologically meaningful parameters can accommodate a broad range of behaviors within an analytically tractable framework suitable for population-based models. We apply the model to prey (juvenile salmon) migrating through a field of predators (piscivores) and find that traditional predator–prey models were not adequate to describe observations. Model parameters estimated from the survival of juvenile chinook salmon migrating through the Snake River in the northwestern United States are similar to estimates derived from independent approaches and data. For this system, we conclude that survival depends more on travel distance than travel time or migration velocity. |
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