Effects of telomere length on survival
The effect of nestling TL on short- and long-term survival was analyzed using two different approaches: First, we analyzed the effect of TL on first-year survival (i.e. before removal of artificially selected individuals) using generalized mixed effects linear models (lme4package) with a binomial error distribution and a logit link function (logistic regression) using the bobyqa optimizer from the ‘minca’ package throughout to improve model convergence (Bates et al., 2014). Birds that were never observed after the season in which they were born (effectively after end of January when field work recommenced the year after they were born) were considered to be dead. Thus, mortality and emigration have the same effect on the local population. The house sparrows show strong site fidelity and generally do not display adult dispersal (Anderson, 2006; Pärn et al., 2009), such that any emigrants do not return to the natal population. We used AICc to compare 26 candidate models including TL, tarsus length, non-linear effects of TL and tarsus length (TL2 and tarsus length2), the NAO_30 index, and an interaction term between tarsus length and population identity, and between TL and population identity, respectively, as explanatory variables. Population identity and sex were included as fixed factors, and brood identity and year were included as random intercepts in all models.
Second, to test the effect of fledgling TL on survival throughout the life of individuals we used multivariate Cox proportional hazards regression to estimate hazard ratios (HR) relative to the baseline sample mean mortality within each strata of all predictor variables. HR is defined as the relative risk of death occurring at a given interval of time compared to the total population (Cox, 1972). Thus, a HR>1 indicates an increased mortality given an increase in the trait. 26 candidate models were constructed using thesurvival package (Therneau, 2015) including TL, tarsus length, non-linear effects of TL and tarsus length, the NAO_30 index, and interaction terms between population identity and tarsus length or TL, respectively. Sex and population identity were included as fixed factors in all models, which were then compared using AICc. Individuals that were removed during the artificial selection were right-censored and the last observation of an individual was used as an estimate of the (minimum) lifespan measured in number of days since hatching. This procedure appropriately accounts for the right-censoring caused by the artificial removal of individuals, but underestimates absolute survival probabilities, as recapture rates were not accounted for in this approach. However, since both populations were carefully monitored each year, we can assume that >90% of the individuals that were present in the study populations were recorded from year to year (Kvalnes et al., 2017), and that the total observation interval correlates with lifespan. No other birds were censored as observations continued until 2012; two years after the last record of any sampled individual (in 2010). The proportional hazards assumption was tested using the correlation between scaled Schoenfeld residuals and time. We accounted for possible non-independence of broods by including brood identity as random factor (cluster).