Pedigree-free animal models: the relatedness matrix reloaded

Abstract

Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.

Figure 1

Performance of four different algorithms in estimating genetic relatedness between individuals: QR (Queller & Goodnight 1989), LR (Lynch & Ritland 1999), W (Wang 2002) and FT (Fernández & Toro 2006). Mean relatedness denoted by circles (full-sibling pairs) or triangles (putatively unrelated pairs). Bars indicate twice the standard error. Full-sibling pairs were inferred from behavioural observations and Colony (Wang 2004a,b). Samples consist of 30 independent pairs of either full siblings or putatively unrelated individuals and are identical for each estimator.

Figure 2

Scree diagrams of eigenvectors for (a) the relatedness matrix used in the Ritland pairwise regression analyses and (b) the relatedness matrix used for the pedigree-free animal model based on the molecular genealogy. The arrow shows the point along the eigenvector axis after which eigenvalues become consistently negative.