Genotype-environment interaction
The interaction term (Iijk) testing for a genotype-environmental interaction for Equation (1) was not significant for our indices of either immune response (F19,42 = 0.86; p = 0.63) or body condition (F19,42 = 0.81, p = 0.69). This showed that chicks from the two sampling sites did not respond differently to nest environments from the other population. Similarly, there were no significant differences between the sites for the phenotypic means of our indices of either immunocompetence (F1,119 = 0.88, p = 0.35) or body condition (F1,119 = 3.28, p = 0.08), or the breeding values of broods for either trait (Immunocompetence F1,39 = 1.85, p = 0.18: Body condition F1,39 = 3.32, p = 0.08; Figure 1). As explained in the Methods section, the marginally non-significant difference between the populations in our index of body condition is not sufficient to cause a spurious correlation between our indices of body condition and immunocompetence. As shown in Figure 1, although one population tends to have slightly higher breeding values for our index of body condition, both populations span almost the full range of values for both traits. Site was not, therefore, considered in the subsequent genetic models.
Genetic covariance
When we based our analyses on comparisons between siblings alone, we detected positive genetic covariance between our indices of immune response and body condition. A plot of the breeding values, based on BLUP methodology, for our indices of immune response and body condition visually demonstrates the positive trend indicating a positive genetic correlation (Fig. 1).
The mixed-model approach detected positive covariances for observational components of covariance y1 and y3 for our indices of both immune response and body condition (Table 1). These components accounted for the majority of additive genetic variation in the design matrix (Table 2), which was relatively free of confounding non-additive and environmental effects. The estimates of additive direct genetic variance for our indices of immune response and body condition were 0.034 ± + 0.016 (p = 0.036) and 0.149 ± + 0.156 (p = 0.342), respectively. Most importantly, however, we detected significant positive genetic covariance (0.053 ± + 0.024, p = 0.030) between our indices of immunocompetence and body condition (Table 3). The estimate of the genetic correlation (rA) between our indices of immune response level and body condition was 0.75 ± + 0.41 (Table 3), suggesting that approximately 56% of the additive genetic variance in body condition can be explained by genetic variation in our index of immune response, which was calculated as square of the genetic correlation [43]. No other causal components were significant in any of the analyses.
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