Individual fitness and phenotypic selection in age‐structured populations with constant growth rates

Abstract

Powerful multiple regression-based approaches are commonly used to measure the strength of phenotypic selection, which is the statistical association between individual fitness and trait values. Age structure and overlapping generations complicate determinations of individual fitness, contributing to the popularity of alternative methods for measuring natural selection that do not depend upon such measures. The application of regression-based techniques for measuring selection in these situations requires a demographically appropriate, conceptually sound, and observable measure of individual fitness. It has been suggested that Fisher’s reproductive value applied to an individual at its birth is such a definition. Here I offer support for this assertion by showing that multiple regression applied to this measure and vital rates (age-specific survival and fertility rates) yields the same selection gradients for vital rates as those inferred from Hamilton’s classical results. I discuss how multiple regressions, applied to individual reproductive value at birth, can be used efficiently to estimate measures of phenotypic selection that are problematic for sensitivity analyses. These include nonlinear selection, components of the opportunity for selection, and multi-level selection.

Evolution of maternal effect senescence

“…Pð1Þ is mean neonatal survival, and generation time T is the mean age of new mothers in the population P yexpð−ryÞlðyÞmðyÞ (2). Multiplying by generation time rescales Hamilton's sensitivities from time units to generations (34,36); this scale fits best with the quantitative genetic models developed here. Thus, for any vital rate expressed at age x D in the presence of interactors of age x I , the bivariate response to DGEs and IGEs over one generation is…”

“…Here we consider a demographic model with discrete time units. When populations are at a steady state with respect to age structure, these can be identified by partial regression coefficients estimated by conventional multiple regression approaches (27), provided that the relative fitness of individuals is defined as w i = P expð−rxÞl i ðxÞm i ðxÞ (33,34), where the summation continues to the last possible age of reproduction (34,35), l i ðxÞm i ðxÞ is the individual's reproductive output at age x, and r is the population's Malthusian growth rate (35).…”

The influence of birth date via body mass on individual fitness in a long‐lived mammal

“…For a large population living in a constant environment, the sum of the reproductive values over all individuals is proportional to the exponential growth rate r (i.e., Malthusian growth rate) of the population irrespective of its age distribution (Fisher 1930, Engen et al 2009). Moreover, assuming that the population growth rate is constant, reproductive value at birth measures individual fitness (Moorad 2014). Moreover, assuming that the population growth rate is constant, reproductive value at birth measures individual fitness (Moorad 2014).…”

“…For instance, environmental conditions at birth influence both early survival and growth (Landete-Castillejos et al 2001, Beauplet et al 2005, but also adult life history traits such as body mass (roe deer, Capreolus capreolus [Pettorelli et al 2002]), and lifetime reproductive success (red deer [Kruuk et al 1999 (Re´ale et al 2003, Sheldon et al 2003, the young of these early-born females should therefore also have high early survival, so that early-born females should achieve higher fitness than late-born females. While such relationships are often assumed in studies using laying (or birth) date as a proxy of female quality (Sydeman and Eddy 1995, Catry et al 1999, Blums et al 2005, very few studies have explicitly investigated the relationship between reproductive timing and individual fitness, defined here as the individual reproductive value early in life (Moorad 2014; also see Methods for a justification of this measure). While such relationships are often assumed in studies using laying (or birth) date as a proxy of female quality (Sydeman and Eddy 1995, Catry et al 1999, Blums et al 2005, very few studies have explicitly investigated the relationship between reproductive timing and individual fitness, defined here as the individual reproductive value early in life (Moorad 2014; also see Methods for a justification of this measure).…”

Estimating Phenotypic Selection in Age-Structured Populations by Removing Transient Fluctuations

“…Although the Robertson–Price equation is exact, its interpretation in studies of selection in natural populations is complicated by the fact that an individual's contribution to future generations is determined by its production of offspring at different life stages (Brommer et al. ; Moorad , ; Sæther et al. ).…”