Age-dependent traits: a new statistical model to separate within- and between-individual effects.

Evolutionary questions regarding aging address patterns of within-individual change in traits during a lifetime. However, most studies report associations between age and, for example, reproduction based on cross-sectional comparisons, which may be confounded with progressive changes in phenotypic population composition. Unbiased estimation of patterns of age-dependent reproduction (or other traits) requires disentanglement of within-individual change (improvement, senescence) and between-individual change (selective appearance and disappearance). We introduce a new statistical model that allows patterns of variance and covariance to differ between levels of aggregation. Our approach is simpler than alternative methods and can quantify the relative contributions of within- and between-individual changes in one framework. We illustrate our model using data on a long-lived bird species, the oystercatcher (Haematopus ostralegus). We show that for different reproductive traits (timing of breeding and egg size), either within-individual improvement or selective appearance can result in a positive association between age and reproductive traits at the population level. Potential applications of our methodology are manifold because within- and between-individual patterns are likely to differ in many biological situations.