Estimating phenotypic selection in age-structured populations by removing transient fluctuations.

An extension of the selection differential in the Robertson-Price equation for the mean phenotype in an age-structured population is provided. Temporal changes in the mean phenotype caused by transient fluctuations in the age-distribution and variation in mean phenotype among age classes, which can mistakenly be interpreted as selection, will disappear if reproductive value weighting is applied. Changes in any weighted mean phenotype in an age-structured population may be decomposed into between- and within-age class components. Using reproductive value weighting the between-age class component becomes pure noise, generated by previous genetic drift or fluctuating selection. This component, which we call transient quasi-selection, can therefore be omitted when estimating age-specific selection on fecundity or viability within age classes. The final response can be computed at the time of selection, but can not be observed until lifetime reproduction is realized unless the heritability is one. The generality of these results is illustrated further by our derivation of the selection differential for the continuous time age-structured model with general age-dependent weights. A simple simulation example as well as estimation of selection components in a house sparrow population illustrates the applicability of the theory to analyze selection on the mean phenotype in fluctuating age-structured populations.