Origin of relation between K and Linf and synthesis of relations among life history parameters

Four patterns occur in growth and mortality parameters across species of fish. Three of these relations, Mx m = 1.65, M = 1.50K, and L(x m ) = 0.66L inf where M is natural mortality, x m is age at maturity, L(x m ) is length at maturity, and L inf 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, L inf = 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 L inf 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.