Statistical analyses
To evaluate effects of the parasitic infection and brood manipulation on the nestlings’ telomere length and shortening we built a linear mixed effects model with telomere length as dependent variable (hereafter, telomere model). The following terms were included as fixed effects: age, Carnus presence, brood manipulation, sex, the 4-way interaction among these variables and all lower-order terms. We also included nestling body mass and the 2-way interactions between body mass and age, sex, brood manipulation and Carnus presence. Random effects included year of birth to control for temporal variation, colony to control for spatial variation, foster nest, gel identity to control for between-gel differences, and individual identity to control for repeated measures on the same individual. Individual identity was nested in foster nest (nesting individual identity also in year of birth gave singularity problems, so this random effect was removed). The model was fitted using the R package lme4 1.1-27.1 in R 3.6.3 (R Development Core Team 2020).
Nestling body mass was standardised (mean = 0, SD = 1) by age group to control for the different scale in the mean and standard deviation of mass between day 5 (mean = 42.31 g, SD = 8.03, n = 326) and day 30 nestlings (mean = 229 g, SD = 20.57, n = 326). Standardisation of mass was done separately for nestlings in reduced and enlarged broods to avoid confounding brood size manipulation with nestling mass in the telomere model.
To evaluate whether telomere shortening within individuals was (i) due to consistent parasite effects yearly (within-year effect), (ii) dependent on parasite abundance variation between years (between-year effect), or (iii) both, we followed . The model included ‘averageCarnus ’ (mean proportion of parasite infestation in the population or between-year differences), ‘delta Carnus ’ (deviation of each individuals’ sample from the mean or within-year differences), age, sex, brood manipulation, body mass scaled by age group and the 2-way interaction of each with age as fixed effects, and the same random effects as in the telomere model. A model with ‘averageCarnus ’, Carnus presence, and the same fixed and random effects described in the previous model tested whether the slope of the between- and within-year effects was significantly different.
To evaluate the effects of the parasitic infection and brood manipulation on nestling growth between ages 5 and 30 days we built a linear mixed effects model with mass as dependent variable (hereafter, mass model). We specified age, Carnus presence, brood manipulation, sex and the interaction among them as fixed effects. The random effects were the same as in the telomere model (without gel identity). This model was fitted using the R package blme 1.0-4 , which avoids convergence and singular fit problems by using Bayes modal estimation with an inverse Wishart covariance prior for the random effects .
For all of the above, we present the full model, which incorporated all predictors relevant to our hypotheses. Unless stated otherwise, all predictor variables were mean-centered to improve the interpretability of regression coefficients of main effects when interactions are present in the model . All diagnostics plots were examined to confirm that there were no deviations from model assumptions and variance inflation factors (VIF) were calculated to check for multicollinearity (all variables had VIF < 2.5) before interpreting model estimates. To ensure that the results were not biased by the presence of extremely influential points or unbalanced sample size between groups (i.e. Carnuspresence, see results section for information on parasite prevalence in the models) we used parametric bootstrapping (n = 1,000) to obtain 95% confidence intervals. Results were confirmed for all models, and thus we chose to present β estimates, standard errors and p-values.