Optimal allocation of resources explains interspecific life-history patterns in animals with indeterminate growth

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Abstract
In a previous paper it was suggested that interspecific allometries of physiological (respiration, assimilation and production rates) as well as life-history (age and size at maturity, life expectancy) parameters are by-products of body-size optimization in animals with determinate growth. Here the analysis is extended to animals with indeterminate growth, such as fish or reptiles. In a seasonal environment it is optimal to grow after maturation, and increasingly more resources should be devoted to reproduction year after year. This leads to growth curves that closely resemble Bertalanffy's curves characterized by growth constant k and asymptotic length l$_{\infty}$. Sets of parameters describing mortality and productivity were generated with a random number generator. Then the schedule of growth was calculated for each `species' obtained, under the assumption of optimal allocation of resources. Interspecific comparisons in a set of such species resemble the empirical patterns discovered by Beverton & Holt and discussed extensively by Charnov: mortality rate and growth constant k are positively related, length at maturity and asymptotic length l$_{\infty}$ are positively correlated, and k and l$_{\infty}$ are negatively correlated. Data for fish and reptiles match these predictions.