3. Statistical methods
To test for an effect of parental age on chicks’ telomere erosion and telomere measurements at first and second sampling, we used repeated measures mixed models and the R package lmerTest (Kuznetsova, Brockhoff & Christensen, 2017). Chick nested in the respective nest was included as a random effect in our analysis. Models included age groups (young or old) of either mother and foster mother or father and foster father as categorical predictors, to emphasize our study design and questions. Similar models were also run with age as a continuous factor (Table S1). Separate models were run for mother’s and father’s age effect, since the age of parents was strongly correlated and could not be entered in the same models. Both models with and without interaction (Tables 1 and S2) with sampling occasion (first or second) were run. Interval between sampling varied between individuals, but this was not included in these models as it was not related to telomere length (Figure S8, Table S6, p = 0.805). Parental age effect models were run for head size as a dependent variable (Tables S4-S5). In these models, chick age was included as a predictive factor since it correlated significantly with head size. Markov Chain Monte Carlo (MCMC) multivariate generalised linear mixed models where used for assessing the continuous effects of parental age (hatch year) on telomere length and telomere length dynamics. Repeatabilites were calculated using R package rptR (Stoffel et al., 2017). Heritabilities were obtained using one-way ANOVA from the full sib design and (for the models including parental age and treatment effects) using generalised linear mixed models for the repeated measures design (R package MCMCglmm) (Hadfield 2010, de Villemereuil, Morrissey, Nakagawa & Schielzeth, 2018; Kuznetsova & Hadfield, 2010). The models were run for both telomere measurements (first and second) as well as change as a dependent variable. The models included parent nest as random effect and the same fixed effects as the repeated measures mixed model for the effect of telomere length change. Both repeatability and heritability measures are reported together with 95% coefficient intervals (CI). The distribution of the traits was normal or close to normal distribution (Figures S1-S3), accordingly, models were ran with untransformed values. Power analyses were conducted based on Monte Carlo simulations (Green & MacLeod, 2015) (Table S3). The R code for different steps in the statistical analyses is accessible from the supplementary material.