Accounting for female space sharing in St. Kilda Soay sheep (Ovis aries) results in little change in heritability estimates

When estimating heritability in free-living populations, it is common practice to account for common environment effects, because of their potential to generate phenotypic covariance among relatives thereby biasing heritability estimates. In quantitative genetic studies of natural populations, however, philopatry, which results in relatives being clustered in space, is rarely accounted for. The two studies that have been carried out so far suggest absolute declines in heritability estimates of up to 43% when accounting for space sharing by relatives. However, due to methodological limitations these estimates may not be representative. We used data from the St. Kilda Soay sheep population to estimate heritabilities with and without accounting for space sharing for five traits for which there is evidence for additive genetic variance (birthweight, birth date, lamb August weight, and female post-mortem jaw and metacarpal length). We accounted for space sharing by related females by separately incorporating spatial autocorrelation, and a home range similarity matrix. Although these terms accounted for up to 18% of the variance in these traits, heritability estimates were only reduced by up to 7%. Our results suggest that the bias caused by not accounting for space sharing may be lower than previously thought. This suggests that philopatry does not inevitably lead to a large bias if space sharing by relatives is not accounted for. We hope our work stimulates researchers to model shared space when relatives in their study population share space, as doing so will enable us to better understand when bias may be of particular concern.