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.