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).