Four patterns occur in growth and mortality parameters across species of fish. Three of these relations, Mxm = 1.65, M = 1.50K, and L(xm) = 0.66Linf where M is natural mortality, xm is age at maturity, L(xm) is length at maturity, and Linf is asymptotic length, were previously shown to result from optimization of the age at maturity. In this study the fourth relation, that between asymptotic size and the growth coefficient, Linf = CK-h, was obtained from a bioenergetic growth equation. A numerical value of h = 0.33 was predicted, and this agrees with the observed value. The relation between the growth coefficient K and size Linf results from the limited amount of assimilated food that must be used both for growth and body functions, and the body functions are a function of body size. The four Beverton and Holt invariants, together with the net reproductive rate, relate many life history parameters to a metabolic parameter and mortality.
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