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Effective size in management and conservation of subdivided populations
Authors:Tufto Jarle  Hindar Kjetil
Institution:Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway. jarlet@math.ntnu.no
Abstract:A numerical method for computing the eigenvalue variance effective size of a subdivided population connected by any fixed pattern of migration is described. Using specific examples it is shown that total effective size of a subdivided population can become less than the sum of the subpopulation sizes as a result of directionalities in the pattern of migration. For an extension of the model with threshold harvesting and local deterministic logistic population dynamic we consider the problem of maximizing the total harvesting yield with constraints on the total effective size. For some simple source-sink systems and more complicated population structures where subpopulations differ in their degree of isolation, it is shown to be optimal, for a given total effective size, to raise the harvesting thresholds relatively more in small and in isolated populations. Finally, we show how the method applies to populations which are supplemented, either intentionally or unintentionally. It is shown that the total effective size can be reduced by several orders of magnitude if the captive component of a population is much smaller than the wild component, even with symmetric backward migration.
Keywords:Migration  Subdivided population  Effective population size  Harvesting  Escaping farmed salmon  Atlantic salmon
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