ORIGIN OF THE RELATION BETWEEN K AND L-INF AND SYNTHESIS OF RELATIONSAMONG 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-mf is asymptotic length, were pre viously shown to result from optimization of the age at maturity. In t his study the fourth relation, that between asymptotic size and the gr owth coefficient, L-inf = CK-h, was obtained from a bioenergetic growt h equation. A numerical value of h = 0.33 was predicted, and this agre es with the observed value. The relation between the growth coefficien t 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 fu nctions are a function of body size. The four Beverton and Holt invari ants, together with the net reproductive rate, relate many life histor y parameters to a metabolic parameter and mortality.