Optimal maturation age and length versus von Bertalanffy growth coefficient, for five survival rates.

In all four panels, the horizontal axis corresponds to the growth rate k in the non-linear von Bertalanffy growth curve. The vertical axis presents the optimal maturation age on the left two panels (A, C) and the optimal maturation length on the right two panels (B, D), for each value of k. For the top two panels the underlying fitness function is R0; for the bottom two panels the underlying fitness function is r. In each panel, optimal age and size curves are drawn for five values of survival rates s (red: 0.25; orange: 0.50; green: 0.70; blue: 0.80; violet: 0.85). As the annual survival rate increases from s = 0.25 to 0.85, the optimal maturation age and length increase for a given k. In panels A & C, the horizontal black dashed line indicates the age at smolting; the colored points at the peak of the vertical lines indicate the maximum value of optimal maturation ages for a given annual survival s. In panels B and D, the horizontal red dashed line represents the asymptotic length of the von Bertalanffy growth function.