Stable Population Structure and Reproductive Value for Populations with Complex Life Cycles

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Abstract
Classical demographic theory was developed to describe age—classified populations, in which knowledge of an individual's age accurately specifies its demographic state. In many species (e.g., plants, insects, fish) individuals of the same age may be in very different states; classical theory is inappropriate for such populations. In this paper, I present general formulae for the stable stage distribution (the analogue of the stable age distribution of classical demography) and the stage—specific reproductive value distribution for populations with arbitrarily complex life histories. The results are obtained by use of z—transforms of a simple graphical representation of the life cycle. They yield literal formulae, which can be used to draw qualitative conclusions about the general properties of the life history. They will also provide quantitative results if numerical values for the parameters are available. Since the selective pressures on life history traits can be expressed simply in terms of the stable stage distribution and reproductive value, these results render complex life cycles amenable to evolutionary analysis. The reproductive value formulae can sometimes be used to calculate optimal schedules of stage—specific reproductive effort.

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