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.