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Population dynamics in a stirred, not mixed, ocean. Kendall, Bruce *,1, Siegel, David1, Costello, Christopher1, Gaines, Stephen1, Hilborn, Ray2, Warner, Robert1, Winters, Kraig3, 1 University of California, Santa Barbara, Santa Barbara, CA2 University of Washington, Seattle, WA3 University of California, San Diego, La Jolla, CA ABSTRACT- Most spatially explicit models of species that have large numbers of dispersers (such as seeds or planktonic larvae) assume that each individual disperser's trajectory is independent, such that diffusion models can be used to define the dispersal kernel. However, turbulent motion of the dispersal medium leads to violation of the independence assumption at sufficiently small space and time scales. In the ocean, these scales are a few kilometers and a few days, such that dispersers that are released from nearby sites at about the same time will have strongly correlated trajectories. Thus, if one individual disperses from site A to site B, it is likely that many other individuals have made that same journey. Likewise, it is possible that no individuals at all travel from A to B. This means that the realized dispersal kernel is highly stochastic, with the probability that individuals disperse from A to B being determined by factors such as distance, oceanographic conditions, and time spent in the plankton, and with a successful dispersal event representing a potentially large cohort of settlers. This creates a "spiky" dispersal kernel that not only creates spatio-temporal stochasticity in population abundance, but can change the overall dynamics of the population. For example, when the stochastic spatial variation is combined with density dependence in production or recruitment, the resultant nonlinear averaging reduces the overall mean recruitment rate. The nonlinear averaging also creates stock-recruitment relationships (or a lack thereof) that are very different from what would be seen in a mixed medium. Understanding and incorporating the non-mixing characteristics of the ocean are essential for effectively managing fisheries for which larval dispersal is planktonic. Key words: Spatial models, Population dynamics, Fisheries models, Stochastic recruitment |
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