Phenotype-associated inbreeding biases estimates of inbreeding depression in a wild bird population

Inbreeding depression is usually quantified by regressing individual phenotypic values on inbreeding coefficients, implicitly assuming there is no correlation between an individual's phenotype and the kinship coefficient to its mate. If such an association between parental phenotype and parental kinship exists, and if the trait of interest is heritable, estimates of inbreeding depression can be biased. Here we first derive the expected bias as a function of the covariance between mean parental breeding value and parental kinship. Subsequently, we use simulated data to confirm the existence of this bias, and show that it can be accounted for in a quantitative genetic animal model. Finally, we use long-term individual-based data for white-throated dippers (Cinclus cinclus), a bird species in which inbreeding is relatively common, to obtain an empirical estimate of this bias. We show that during part of the study period, parents of inbred birds had shorter wings than those of outbred birds, and as wing length is heritable, inbred individuals were smaller, independent of any inbreeding effects. This resulted in the overestimation of inbreeding effects. Similarly, during a period when parents of inbred birds had longer wings, we found that inbreeding effects were underestimated. We discuss how such associations may have arisen in this system, and why they are likely to occur in others, too. Overall, we demonstrate how less biased estimates of inbreeding depression can be obtained within a quantitative genetic framework, and suggest that inbreeding and additive genetic effects should be accounted for simultaneously whenever possible.