Offspring Size and Number: A Life History Model Linking Effort Per Offspring and Total Effort

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Abstract
We develop an extension of Schaffer''s (1972) model for a simple life history with constant annual adult and juvenile survival rates. In contrast with previous models, we distinguish betweeen total effort and effort per offspring. We assume that offspring production is the product of the juvenile survival rate and brood size, that the juvenile survival rate is a function of effort per offspring, and that brood size is a function of effort per offspring and total effort. We further assume that the adult survival rate is a function of total effort and that optimal combinations of effort per offspring and total effort are those resulting in the highest population growth rate. Optimal effort per offspring depends only on the minimal effort per offspring and the rate at which the juvenile survival rate increases with increasing effort per offspring. Optimal total effort depends on effort per offspring, the ratio between the realized juvenile survival rate and the maximal adult survival rate, and the threshold at which increasing total effort leads to sharp declines in the adult survival rate. The model and its predictions justify the inclusion of effort per offspring and total effort in descriptions of life history tactics and facilitate the formulation and testing of more-precise life history hypotheses. We suggest several experiments. The model predicts that the rate of increase in optimal total effort with increasing brood size decreases as brood size increases. The relative numbers on which optimal total effort and effort per offspring depend suggest that current variability in effort per offspring should be less than variability in total effort.