QUANTITATIVE PREDICTIONS OF DELAYED MATURITY.

What are the selective pressures that have driven the evolution of delayed maturity? K-selection (selection operating at high population densities) has been suggested as an explanation, but it does not fit all the data (Wilbur et al., 1974; Stearns, 1977) and it oversimplifies (Whittaker and Goodman, 1979). In a declining population, the rate of decrease is minimized when age at maturity is maximized (Hamilton, 1966; Mertz, 1971), but that explanation is probably not general, for such populations have an increased probability of extinction. Four other hypotheses, which we regard as more plausible, have been suggested: a delay in maturity results (a) in a gain in fecundity (Tinkle, 1969; Gadgil and Bossert, 1970; Tinkle et al., 1970; Wiley, 1974; Schaffer and Elson, 1975; Bell, 1977), (b) in an improvement in the juvenile survival of the offspring produced (Wiley, 1974; Hirshfield and Tinkle, 1977), (c) in a reduction in the cost of reproduction and an increase in adult survival rates (Schaffer, 1972; Wittenberger, 1979), or (d) in increased fitness in the face of unpredictable, catastrophic larval mortality, where the delay comes in the egg stage (Livdahl, 1979). These hypotheses are not mutually exclusive; all four could shape the life-history of some organism. We have built optimality models in which reproduction and survival depend on the age at maturity of the organism. To keep the models tractable, we assumed that we could deal with a population as though it were a set of asexually reproducing, haploid clones, with each clone endowed with a different life-history. The optimization procedure tells us which clone will win the intraspecific competition for numerical dominance in future generations. To do this, we have assumed that the population is in stable age distribution, and that the definition of fitness is the rate at which a new allele grows in the population, where that allele affects age at maturity, survival, and fecundity. Thus the unit of selection in these models is the gene, not the individual or the population, but because we conceive the population as a set of haploid clones, the gene is effectively equivalent to the individual. For those who are uncomfortable with this simplification, we note that this analysis holds for the marginal effect of a gene substitution on phenotypes in a haploid, asexual population (cf. Charlesworth and Williamson, 1975). We also note that a clone can be growing exponentially in a stationary population. In these models, clones grow exponentially at a rate implied by the particular age at maturity and survivorship and fecundity schedules with which they are endowed. Thus the technical definition of fitness is the Malthusian parameter (Fisher, 1930), with neither frequency-dependence nor density-dependence, but we denote it as r-the intrinsic rate of increase of a clone. Our models assume either the fecundity-gain hypothesis (a), the quality-ofyoung hypothesis (b), or both. We have found that either fecundity-gain or quality-of-young assumptions can yield predictions of a considerable delay in maturity when r is maximized. Moreover, when we used published data to predict optimal ages at maturity on the assumption that one, the other, or both effects were at work, the predictions were surprisingly good.