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Selection for Optimal Life Histories: The Effects of Age Structure

William M. Schaffer
Ecology
Vol. 55, No. 2 (Mar., 1974), pp. 291-303
Published by: Wiley on behalf of the Ecological Society of America
DOI: 10.2307/1935217
Stable URL: http://www.jstor.org/stable/1935217
Page Count: 13
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Selection for Optimal Life Histories: The Effects of Age Structure
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Abstract

The theory of optimal reproductive strategies has traditionally been studied in two ways: formal analysis of simple models that neglect the effects of age structure, and computer studies of complex life histories. Each of these approaches has disadvantages. The consequences of simple models sometimes dependmore on the nature of the simplifying assumptions than on the biological issues in question. On the other hand, computer simulations are only as general as the examples considered. The present study seeks to extend the formal analysis of optimal life histories to complex cases. I show that an optimal life history maximizes for each age class the expected fecundity at that age plus the sum of all future expected parameters. This result enables us to determine, at least inthe case of a three-stage life history, the manner in which the optimal reproductive effort at each age depends on the efforts made at the other ages, and thus, the coevolution of the various age-specific efforts. Three cases are distinguished: (1) If fertility and post-breeding survival and growth are concave functions of reproductive effort (i.e., have second derivatives that areeverywhere negative) there is a single set of age-specific reproductive rates towhich the system evolves regardless of initial conditions. This set of reproductive rates corresponds to an iteroparous life history (repeated breeding at different ages). (2) On the other hand, if fertility and subsequent growth and survival are convex functions of effort (positive second derivatives), semelparity (a single, herculean reproductive effort, followed by death) will most often evolve. However, an alternative, iteroparous life history sometimes exists, although stability considerations suggest that it may be transitory. (3)More realistic fertility and growth survival functions can generate alternative reproductive strategies that are stable since each represents a local maximum infitness. Often one of these alternatives corresponds to semelparity, the second to repeated reproduction. In such cases, the evolutionary outcome depends on initial conditions. This suggests that related species, with similar ecologies, may have very different life histories, the differences resulting from historical accidents that have trapped each on a different adaptive peak. The Salmonid genera, Salmo and Oncorhynchus, are suggested as possible examples.

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