Empirical studies have shown that in teleosts there is a significant correlation between the life history parameters, age at first reproduction, natural mortality, and growth rate. In this paper 1 hypothesize that these correlations are the result of evolutionary adjustments due to the trade-off between reproduction, growth, and survival. A simple and reasonable assumption is that the costs of reproduction are sufficient to cause the ltmt function to decrease. A simple expression relating the age at first reproduction is derived from this assumption. This formula accounts for a statistically significant portion (60.6%) of the variation in age at first reproduction in 30 stocks of fish. To extend the model to predict the distribution of life history parameters across all teleosts, an explicit cost function is incorporated. The model is analyzed with respect to two fitness measures, the expected lifetime fecundity and malthusian parameter, r. In the first case it is shown that the optimal age at maturity, T, depends only on the natural mortality rate (M) and the growth rate (k). In the second case, T is a function of k and the logarithm of a parameter, In C; the latter is a product of egg and larval survival, maximum body length (Lx), and the proportionality coefficient of the fecundity/length function. Difficulties of measuring egg and larval survival make the testing of the latter case difficult for particular species. However, this method provides a simple formula for the computation of r; this is shown generally to be approximately zero, thereby adding strength to the assumptions of the first analysis. The distribution patterns of T on k and M on k are predicted and compared with the observed pattern. In general, the predictions are validated: however, certain combinations of k and ln C are shown to occur very infrequently. The prediction of such "empty" regions of the parameter space remains a challenge for future development of life history theory.
Consistent thermodynamic treatment for a quark-mass density-dependent model
