This article develops a new evolutionary model for life histories by combining a new production-growth model with some general, yet specific, constraints on reproductive allocation, and by allowing natural selection to adjust the age of first breeding and the metabolic/productive capacity of cells. The optimal life histories correctly predict the numeric value of dimensionless numbers that combine maturation age (size), mortality, and reproductive allocation. The life-history prediction also yields a new lifetime growth model for body mass under indeterminate growth and predicts that the fastest growth rate will be near the size at first reproduction. Table 1 is a glossary of terms, whereas Appendix A is a brief overview of the optimization...