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Dynamical consequences of harvest in discrete age-structured population models

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Abstract.

The role of harvest in discrete age-structured one-population models has been explored. Considering a few age classes only, together with the overcompensatory Ricker recruitment function, we show that harvest acts as a weak destabilizing effect in case of small values of the year-to-year survival probability P and as a strong stabilizing effect whenever the survival probability approaches unity. In the latter case, assuming n=2 age classes, we find that harvest may transfer a population from the chaotic regime to a state where the equilibrium point (x1*, x2*) becomes stable. However, as the number of age classes increases (which acts as a stabilizing effect in non-exploited models), we find that harvest acts more and more destabilizing, in fact, when the number of age classes has been increased to n=10, our finding is that in case of large values of the survival probabilities, harvest may transfer a population from a state where the equilibrium is stable to the chaotic regime, thus exactly the opposite of what was found in case of n=2. On the other hand, if we replace the Ricker relation with the generalized Beverton and Holt recruitment function with abruptness parameter larger than 2, several of the conclusions derived above are changed. For example, when n is large and the survival probabilities exceed a certain threshold, the equilibrium will always be stable.

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  1. Harstad College, Havnegata 5, 9480, Harstad, Norway

    Arild Wikan

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  1. Arild Wikan
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Revised version: 18 September 2003

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Wikan, A. Dynamical consequences of harvest in discrete age-structured population models . J. Math. Biol. 49, 35–55 (2004). https://doi.org/10.1007/s00285-003-0251-5

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