R0 or r: A matter of taste?

In the recently published textbooks of life-history evolution (Stearns. 1992; Roff, 1992) it has been cmphasizcd that different fitness measures lcad to ditrcrcnt results even in otherwise identical optimization models. We think that proper fitness measures should always lead to the same results when applied in a proper way. The apparent confusion in the literature stems from two separate problems. In models aiming to find optimal reaction norms for e.g. age of maturity within a heterogeneous population (review in the cited textbooks and Kozlowski, 1993) r and R,, are not equivalent fitness measures. Moreover. they can be used only under rather restrictive assumptions about the variation of individual states. R,, is appropriate when the state of an individual is fixed for its lifetime, while r can be used when the state changes randomly from year to year and the state distribution of parents and their ofTspring is the same (Kawecki and Stearns, 1993; Houston and McNamara. 1992; Kisdi et al., submitted). In these models density-dependence can be ignored as far as the predictions arc concerned with the optimal reaction norm at a fixed density. However, in optimization models aiming to explain dill‘erences between populations, density-dependence must be included and in this case I’ and R,, are equivalent fitness measures. RofT presents a simple example to demonstrate that the effect of the age schedule of mortality on the optimal age of maturity may depend upon the fitness measure adopted and concludes that “the general inferences about how the optimal age of maturity, or any life history trait, should not be made without considerable attention to the assumptions underlying this analysis (pp. 1 X3184)“.