Narrow-sense heritability
Physiological data on survival, bleaching, and growth (Quigley et al., 2020) were combined with pedigree information (Supplementary Table 1) to calculate narrow-sense heritability estimates for each trait at 27.5°C and 31°C. Relatedness between individual juveniles (sibships and family groups) are calculated from the pedigree input as a random effect. Narrow-sense heritability estimates (h2) were derived from additive genetic variance calculated from the ‘animal model’ (Kruuk, 2004) using the package ‘MCMCglmm’ (Hadfield, 2010), in which the coefficient of relatedness between individual juveniles is parameterized as a random effect. The ‘animal model’ is a type of specialized mixed-effect model that calculates narrow-sense heritability by parameterizing relatedness between measured individuals using random effects (Kruuk, 2004). Hence, this analysis calculates the relative contribution of genetic and environmental influence on phenotypic variance of each trait (Wilson et al., 2010). This analysis builds upon that performed in Quigley et al., 2020 by: 1) using the underlying physiological data and 2) extending the mixed effects models used in that study that parameterized the influence of population of origin (WW, WC, CW) and parental cross (WW1, WW2, WW3, WC, CW) on survival, growth, and bleaching. Three Symbiodiniaceae strains were used for inoculation of juveniles. For clarity, heritability estimates for only Cladocopium , the punitively principal symbiont of Acropora spathulata on the GBR (sensu van Oppen, Palstra, Piquet, & Miller, 2001), is presented in the main results and the additional strains in the Supplementary Information.
Models of h2 of juvenile survival at both temperatures were run with time as a fixed factor, pedigree and individual as random factors, using binary logistic regression (categorical distribution), 150 × 106 iterations, 0.1% burn-in of total iterations and at multiple thinning levels of 7500 (27.5°C:Symbiodinium tridacnidorum , Cladocopium goreaui , andDurusdinium trenchii , 31°C: C. goreaui and D. trenchii ) or 37,500 (31°C: S. tridacnidorum ). Models of h2 of juvenile bleaching and growth at both temperatures were run using 1.5 × 106 iterations, a thinning level of 1,500 and a burn-in of 10% of the total iterations. Fixed and random factors were parameterized in the survival models with a Gaussian distribution.
A non-informative flat prior specification was used, following an inverse gamma distribution (Wilson et al., 2010). Assumptions of chain mixing, normality of posterior distributions and autocorrelation were met. The posterior heritability was calculated by dividing the model variance attributed to relatedness by the sum of additive and residual variance. Given differences in iterations and thinning levels across models, a scaling factor (x’ = x – xmin/xmax – xmin) was applied to the posterior distributions of each trait using the “rescale” function in the ‘plottrix’ package (Lemon, 2006) to visualize each heritability estimate equally to ease interpretation. Specifically, each posterior was re-scaled to the minimum (y = 0.00598) and maximum (y = 57.42421) y-density values for the S. tridacnidorum treatment at 31°C.