The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon

Abstract

Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions–intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx−for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one’s efforts to understand an organism’s behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function.