The evolution of labile traits in sex- and age-structured populations.

Many quantitative traits are labile (e.g. somatic growth rate, reproductive timing and investment), varying over the life cycle as a result of behavioural adaptation, developmental processes and plastic responses to the environment. At the population level, selection can alter the distribution of such traits across age classes and among generations. Despite a growing body of theoretical research exploring the evolutionary dynamics of labile traits, a data-driven framework for incorporating such traits into demographic models has not yet been developed. Integral projection models (IPMs) are increasingly being used to understand the interplay between changes in labile characters, life histories and population dynamics. One limitation of the IPM approach is that it relies on phenotypic associations between parents and offspring traits to capture inheritance. However, it is well-established that many different processes may drive these associations, and currently, no clear consensus has emerged on how to model micro-evolutionary dynamics in an IPM framework. We show how to embed quantitative genetic models of inheritance of labile traits into age-structured, two-sex models that resemble standard IPMs. Commonly used statistical tools such as GLMs and their mixed model counterparts can then be used for model parameterization. We illustrate the methodology through development of a simple model of egg-laying date evolution, parameterized using data from a population of Great tits (Parus major). We demonstrate how our framework can be used to project the joint dynamics of species' traits and population density. We then develop a simple extension of the age-structured Price equation (ASPE) for two-sex populations, and apply this to examine the age-specific contributions of different processes to change in the mean phenotype and breeding value. The data-driven framework we outline here has the potential to facilitate greater insight into the nature of selection and its consequences in settings where focal traits vary over the lifetime through ontogeny, behavioural adaptation and phenotypic plasticity, as well as providing a potential bridge between theoretical and empirical studies of labile trait variation.