Partitioning variance in reproductive success, within years and across lifetimes

Abstract

Variance in reproductive success (, with k = number of offspring) plays a large role in determining the rate of genetic drift and the scope within which selection acts. Various frameworks have been proposed to parse factors that contribute to , but none has focused on age‐specific values of , which indicate the degree to which reproductive skew is overdispersed (compared to the random Poisson expectation) among individuals of the same age and sex. Instead, within‐age effects are generally lumped with residual variance and treated as “noise.” Here, an ANOVA sums‐of‐squares framework is used to partition variance in annual and lifetime reproductive success into between‐group and within‐group components. For annual reproduction, the between‐age effect depends on age‐specific fecundity (bx), but relatively few empirical data are available on the within‐age effect, which depends on ϕx. By defining groups by age‐at‐death rather than age, the same ANOVA framework can be used to partition variance in lifetime reproductive success (LRS) into between‐group and within‐group components. Analytical methods are used to develop null‐model expectations for random contributions to within‐group and between‐group components. For analysis of LRS, random variation in longevity appears as part of the between‐group variance, and effects (if any) of skip breeding and persistent individual differences contribute to the within‐group variance. Simulations are used to show that the methods for variance partitioning are asymptotically unbiased. Practical application is illustrated with empirical data for annual reproduction in American black bears and lifetime reproduction in Dutch great tits. Results show that overdispersed within‐age variance (1) dominates annual in both male and female black bears, (2) is the primary factor that reduces annual effective size to a fraction of the number of adults, and (3) represents most of the opportunity for selection. In contrast, about a quarter of the variance in LRS in great tits can be attributed to random variation in longevity, and most of the rest is due to modest differences in fecundity with age estimated for a single cohort of females. R code is provided that reads generic input files for annual and lifetime reproductive success and allows users to conduct variance partitioning with their own data.