Harvesting in a resource dependent age structured Leslie type population model

Details Harvesting in a resource dependent age structured Leslie type population model Harvesting in a resource dependent age structured Leslie type population model

2005-02-25

arxiv.org/abs/q-bio/0502042v1

Math. Biosciences vol. 189 (2004) 141-151

Biology

Quantitative Biology

Populations and Evolution

26 pages, 4 figures

Scientific paper

We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying capacity of the resources. Under the effect of proportional harvest, we give a sufficient condition for a population to extinguish, and we show that the magnitude of proportional harvest depends on the resources available to the population. We show that the harvesting yield can be periodic, quasi-periodic or chaotic, depending on the dynamics of the harvested population. For populations with large fertility numbers, small harvesting mortality leads to abrupt extinction, but larger harvesting mortality leads to controlled population numbers by avoiding over consumption of resources. Harvesting can be a strategy in order to stabilise periodic or quasi-periodic oscillations in the number of individuals of a population.

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