THE EVOLUTION OF LIFE HISTORIES IN SPATIALLY HETEROGENEOUS ENVIRONMENTS - OPTIMAL REACTION NORMS REVISITED

Natural populations live in heterogeneous environments, where habitat variation drives the evolution of phenotypic plasticity. The key feature of population structure addressed in this paper is the net flow of individuals from source (good) to sink (poor) habitats. These movements make it necessary to calculate fitness across the full range of habitats encountered by the population, rather than independently for each habitat. As a consequence, the optimal phenotype in a given habitat not only depends on conditions there but is linked to the performance of individuals in other habitats. We generalize the Euler-Lotka equation to define fitness in a spatially heterogeneous environment in which individuals disperse among habitats as newborn and then stay in a given habitat for life. In this case, maximizing fitness (the rate of increase over all habitats) is equivalent to maximizing the reproductive value of newborn in each habitat but not to maximizing the rate of increase that would result if individuals in each habitat were an isolated population. The new equation can be used to find optimal reaction norms for life history traits, and examples are calculated for age at maturity and clutch size. In contrast to previous results, the optimal reaction norm differs from the line connecting local adaptations of isolated populations each living in only one habitat. Selection pressure is higher in good and frequent habitats than in poor and rare ones. A formula for the relative importance of these two factors allows predictions of the habitat in which the genetic variance about the optimal reaction norm should be smallest.