Optimal life histories: a generalisation of the Perran-FrobeniusTheorem

Abstract State dependent optimal life history strategies are analysed using a matrix population model. For a given life history strategy the Perron-Frobenius eigenvalue of the population projection matrix gives the stable rate of increase of that population. An optimal strategy maximises this rate of increase. This paper presents a characterisation of the optimal life history strategy using the optimality operator of dynamic programming. This characterisation allows one to verify that a given strategy is indeed optimal. An iterative procedure for calculating the optimal life history strategy is also given. This is a robust and very general procedure which can be used to find the optimal strategy for complex life cycles. The previously derived relation between maximum reproductive value and discounted maximum future expected reward is easily obtained from the general approach used.

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