Heritabilities and genetic correlation of telomere length, tarsus length, and body condition
We used a multivariate Bayesian animal model (Kruuk, 2004; Hadfield, 2019) fitted with Markov chain Monte Carlo (MCMC) to estimate heritability and genetic correlations of early-life TL, age-standardized tarsus length and body condition in the two natural island populations (Hestmannøy and Træna, n =2662) and the two manipulated island populations (Leka & Vega, n =569) that underwent artificial size selection. TL was log10-transformed and all traits were fitted with a Gaussian error distribution using the R package ‘MCMCglmm’ (Hadfield, 2010). Models included sex, fledgling age at sampling, island identity, and inbreeding coefficient (F ) as fixed effects (Wilson, 2008), which were fitted such that different regression slopes were estimated for each trait (Hadfield, 2019). To estimate variance components, random intercepts were included for individual identity (‘animal’, VA ), brood identity (VB ) nested under mother identity, father (VF ) and mother identity (VM ), and birth year (cohort effects,VY ). Parental effects include those influences on offspring TL that are repeatable across the lifetime of the mother or father (Kruuk & Hadfield, 2007), while brood identity accounts for other common environmental effects (McAdam, Garant, & Wilson, 2014). House sparrows are multi-brooded laying up to 3 clutches in a season and may breed in multiple years, with an average of 3.6±1.3 S.D. fledglings per brood in this study. They are socially monogamous, but extra-pair paternity occurs at rates of 14-18 % in wild populations (Ockendon, Griffith, & Burke, 2009; Hsu, Schroeder, Winney, Burke, & Nakagawa, 2014). Using genetic pedigrees, extra-pair paternity can be seen as natural cross-fostering experiments that improve statistical power to separate genetic and environmental variance components (Kruuk & Hadfield, 2007). Random effects were specified with 3x3 covariance matrices to estimate the variances and covariances between the effects for each trait.
We also ran univariate models of TL, tarsus length and body condition including the same fixed and random effects as in the multivariate model (Appendix S2). For comparison with previous studies (e.g. Asghar et al., 2015), we tested whether maternal TL and/or paternal TL predicted offspring TL using two LMMs (parent-offspring regressions, Appendix S2). Furthermore, we included maternal (VDAM ) and paternal (VSIRE ) genetic effects (e.g. Wolf & Wade, 2016) in a multivariate animal model to quantify these effects while accounting for the environmental variances specified above (Appendix S2). To test for sex-specific heritabilities (e.g. Jensen et al., 2003; Olsson et al., 2011), we ran a bivariate animal model of TL in females and males as two different phenotypic traits with a genetic correlation between them (Appendix S2).
We used inverse-Wishart priors for random effects and residual variances in the multivariate model (V=I3 and nu=3, Hadfield, 2019). We re-ran analyses with other relevant priors (parameter expanded) to verify that results were not too sensitive to the choice of prior. The MCMC chain was run for 2,000,000 iterations, sampling every 500 iterations after a burn-in of 5% (100,000 iterations). Mixing and stationarity of the MCMC chain was checked visually and using Heidelberger and Welch’s convergence test (Heidelberger & Welch, 1983) implemented in the ‘coda’ package (Plummer, Best, Cowles, & Vines, 2006). All autocorrelation values were <0.1 and effective sample sizes were >3,000. The narrow-sense heritability was calculated as the posterior mode of the proportion of phenotypic variance explained by additive genetic variance (Wilson et al., 2010):\(h^{2}=\frac{V_{A}}{(V_{A}+{V_{B}+V_{F}+V_{M}+V_{R}+\ V}_{Y})}\), where VR is the residual variance. Estimates are provided as their posterior mode with 95% highest posterior density intervals (HPD). All analyses were performed in R version 3.6.3 (R Core Team, 2020).