Indeterminate growth is selected by a trade-off between high fecundity and risk avoidance in stochastic environments

 We developed a stage-structured model to describe optimal energy allocation among growth, reproduction, and survival. Our model includes stochastic fluctuations in survival rate at age 0 but constant survival rate at older ages. Many mammals and birds cease to grow after maturity (i.e., determinate growth), whereas organisms in a number of other taxa grow beyond maturation (i.e., indeterminate growth). We discuss the conditions under which each of the following strategies is optimal: (I) semelparity, (II) iteroparity with determinate growth, and (III) iteroparity with indeterminate growth. Our model demonstrates that iteroparity with indeterminate growth is selected for when a nonlinear relationship exists between weight and energy production; this strategy is also often selected for in stochastic environments, even with a linear relationship between weight and energy production. The optimal strategy in stochastic environments is to maximize the long-term population growth rate, which does not correspond with maximization of total fecundity. The optimal life history is determined by a balance between spreading a risk and increasing the number of offspring. Our model suggests that optimal life history strategy depends on the magnitude of environmental fluctuations, the advantage of investing in growth, the cost of survival, and the nonlinearity between weight and energy production. Received: February 20, 2002 / Accepted: September 20, 2002 Acknowledgments We thank Drs. Y. Matsumiya, K. Morita, K. Shirakihara, and Y. Watanabe for encouragement and helpful advice. We also thank the responsible editor and anonymous reviewers for helpful comments. This work was supported by a Japan Society for the Promotion of Science grant to H.M. Correspondence to:Y. Katsukawa