Age‐Dependent Traits: A New Statistical Model to Separate Within‐ and Between‐Individual Effects

Abstract

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.

Survival costs of reproduction vary with age in North American red squirrels

“…when taking individual heterogeneity into account or not). Moreover, including the age at last reproduction, to take into account the selective disappearance of low-quality individuals (as suggested in Van de Pol & Verhulst 2006), did not affect our results (results not presented). This indicates that, in contrast to large herbivores ( Nussey et al 2008), the variation in individual quality and viability selection is not a major issue in our red squirrel population.…”

“…A variety of genetic, maternal and environmental factors can lead to variation among individuals within a population. For example, in the Kluane red squirrel population, it has been shown that the individual traits vary with territory quality (LaMontagne 2007), year of birth (Descamps et al 2008b) or characteristics of the mothers (McAdam et al 2002;Descamps et al 2008a) Such individual heterogeneity has to be accounted for when studying trade-offs and/or age-specific change in the life-history traits ( Vaupel & Yashin 1985;Cam et al 2002;Van de Pol & Verhulst 2006;Nussey et al 2008).…”

“…negative relationships) are expected (see Cam et al (1998) and Weladji et al (2008) for examples). Such positive covariations do not mean that trade-offs do not exist but rather that individual heterogeneity in quality is pronounced enough to mask any trade-off ( Van Noordwijk & de Jong 1986). In addition, individual heterogeneity in quality within a population can affect viability (sensu Fisher 1930), resulting in an increasing proportion of high-quality individuals with above average survival and/or reproduction in older age classes.…”

Climate change and the risks associated with delayed breeding in a tropical wild bird population

“…To determine if variation seen in the timing of breeding within the population was owing to differences between individuals or owing to within-individual responses to frequency of rainfall, a methodology known as 'within-subject centring' was used [27,28]. Hence, a second model was constructed with two new predictor variables derived to describe the between-subject variance (b b ) and within-subject variance (b w ).…”

The influence of weather conditions during gestation on life histories in a wild Arctic ungulate

“…We included an interaction between ROS utero and both age and its square to determine whether reproductive senescence differed in relation to early-life environment. Age at last observation was also included as fixed effect term to control to for selective disappearance (the non-random departure from the dataset of individuals as age increase) so that age effect reflected an unbiased estimate of within-individual change [52]. Age at last observation was retained in the model independent of its statistical significance.…”