Abstract:
Time series of rapid phenotypic change have recently been documented in age-structured populations living in the wild. Researchers are often interested in identifying the processes responsible for such change. Although there is well developed demographic theory to explain time series of population size, equivalent theory does not exist for the mean values of phenotypic traits in structured populations. We derive an equation to exactly decompose change in the mean value of a phenotypic trait into contributions from fluctuations in the demographic structure, and age-specific viability selection, fertility selection, growth and reversion and differences between offspring and parental trait values. We calculate these contributions to fluctuations in mean birth weight in a well characterized population of red deer. Over the > 30 years of the study mean birth weight has not significantly changed. Stasis has occurred because positive viability selection for an increase in birth weight is countered by transmission bias. Our derivation demonstrates that this is only one of many ways in which equilibria in the mean value of a phenotypic trait can be maintained. The age-structured Price equation we derive and apply has the potential to provide considerable insight into the processes generating now frequently reported cases of rapid phenotypic change.