Null models for the Opportunity for Selection

Abstract

Crows Opportunity for Selection (I=variance in relative fitness) is an important albeit controversial eco-evolutionary concept, particularly regarding the most appropriate null model(s). Here we treat this topic in a comprehensive way by considering opportunities for both fertility selection (If) and viability selection (Im) for discrete generations, both seasonal and lifetime reproductive success in age-structured species, and for experimental designs that include either a full or partial life cycle, with complete enumeration or random subsampling. For each scenario, a null model that includes random demographic stochasticity can be constructed that follows Crows initial formulation that I=If+Im. The two components of I are qualitatively different. Whereas an adjusted If ({Delta}If) can be computed that accounts for random demographic stochasticity in offspring number, Im cannot be similarly adjusted in the absence of data on phenotypic traits under viability selection. Including as potential parents some individuals that die before reproductive age produces an overall, zero-inflated-Poisson null model. It is always important to remember that (1) Crows I represents only the opportunity for selection and not selection itself, and (2) the species biology can lead to random stochasticity in offspring number that is either overdispersed or underdispersed compared to the Poisson (Wright-Fisher) expectation.