Evolution of adult size depends on genetic variance in growth trajectories: a comment on analyses of evolutionary dynamics using integral projection models

1. Integral projection models (IPMs) are an extension of stage-structured population models to continuous classes or traits, such as body size. Recent studies have used age-structured IPMs to investigate the relative contributions of evolutionary versus demographic responses of quantitative traits to environmental change. However, I argue here that evolutionary responses are likely to be underestimated by this approach, because it does not fully capture how phenotypic differences between individuals and genotypes accumulate along life, and are transmitted across generations. 2. Trait transitions upon survival and reproduction are treated in IPMs by two classes of functions. First, an 'inheritance' function relates the trait of a newborn to that of its adult parent, on the time-scale of a reproductive event. Secondly, growth functions relate the traits of surviving individuals between successive ages. This differs from the quantitative genetic approach, where parent-offspring resemblance is generally quantified for age-specific trait values, and on the time-scale of a generation. More importantly, it is unclear to what extent age-structured IPMs account for the fact that phenotypic and genetic variances of adult size are largely caused by differential growth among individuals and genotypes in multicellular organisms. 3. I use simple simulations of growth trajectories to ask what the transition functions from IPMs can tell us about the contribution of genetic evolution to phenotypic change. These simulations illustrate that a flat inheritance function is perfectly compatible with substantial response to selection in adults. They further show that the growth functions from IPMs may obscure genetic differences in body size that accumulate along life owing to genetic variation in growth trajectories. 4. IPMs are a powerful tool for investigating age-dependent components of phenotypic selection, and the demographic consequences of plastic responses that act through environmental effects on growth. But using age-structured IPMs to project evolutionary dynamics requires combining them with measurements of age-specific additive genetic variances and cross-age additive genetic covariances, to accurately describe the accumulation of phenotypic differences across ages, and their transmission across generations.