Pedigree-free animal models: the relatedness matrix reloaded

Francesca D Frentiu Sonya M Clegg John Chittock Terry Burke Mark W Blows Ian P.F Owens 0 Department of Animal and Plant Sciences, University of Sheffield , Sheffield S10 2TN, UK 1 Department of Ecology and Evolutionary Biology, University of California , Irvine, CA 92697, USA 2 School of Integrative Biology, University of Queensland , St Lucia, Queensland 4072 , Australia 3 NERC Centre for Population Biology, Imperial College London , Silwood Park, Ascot, Berkshire SL5 7PY, UK Receive free email alerts when new articles cite this article - sign up in the box at the top right-hand corner of the article or click here References Email alerting service To subscribe to Proc. R. Soc. B go to: http://rspb.royalsocietypublishing.org/subscriptions Pedigree-free animal models: the relatedness matrix reloaded 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 variancecovariance matrices (G ) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritlands 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. 1. INTRODUCTION The application of animal models to wild populations promises to revolutionize our understanding of evolutionary genetics in natural environments (Kruuk 2004). This is because animal models, in their broadest sense, are simply individual-based mixed models that use a known pedigree to estimate relatedness among individuals and thereby estimate a range of quantitative genetic parameters (Lynch & Walsh 1998). The key reason that animal models offer such promise for the study of wild populations is that this approach can use a natural pedigree to extract quantitative genetic information under natural conditions. In contrast, most quantitative genetic techniques require breeding experiments and are consequently largely restricted to laboratory or * Author and address for correspondence: Division of Biology, Imperial College London, Silwood Park, Ascot, Berkshire SL5 7PY, UK (). Electronic supplementary material is available at http://dx.doi.org/10. 1098/rspb.2007.1032 or via http://journals.royalsociety.org. One contribution of 18 to a Special Issue Evolutionary dynamics of wild populations. agricultural studies ( Falconer & Mackay 1996). Animal models have now been applied to a number of populations to tackle questions as diverse as the heritability of fitness (Kruuk et al. 2000), evolutionary stasis (Merila et al. 2001; Kruuk et al. 2002), sexual selection and coloration (Hadfield & Owens 2006; Hadfield et al. 2006, 2007), condition dependence (Gleeson et al. 2005), parental care (MacColl & Hatchwell 2003), the genetic consequences of harvesting (Coltman et al. 2003) and the evolutionary response to climate change (Brommer et al. 2005). Such widespread interest in the animal model approach has, however, led to the realization that the need for a known pedigree is itself a limitation. It is no coincidence that most studies to date using the animal model concern populations that have been the subject of long-term projects (Kruuk et al. 2000, 2001, 2002; Merila & Sheldon 2000; Merila et al. 2001; Coltman et al. 2003; Garant et al. 2004, 2005; McCleery et al. 2004; Charmantier et al. 2006a,b). The need for long-term information on individual patterns of mating and reproduction limits the range and type of populations where an animal model can be used. One way potentially to overcome this limitation is to use molecular marker data F. D. Frentiu et al. Pedigree-free animal models to estimate the genetic relationships among individuals in a population and then use the resulting relatedness matrix, instead of a known pedigree, to construct the animal model (Lynch & Walsh 1998; Garant & Kruuk 2005; Rodrguez-Ramilo et al. 2007). This approach could allow the animal model framework to be extended to any population for which it was possible to obtain reliable estimates of relatedness based on molecular marker data (Moore & Kukuk 2002), which would greatly expand the range of potential applications if the approach proved to be robust. Such an approach has yet to be fully implemented in any population, however. The overall aim of this study was therefore to test whether animal models can indeed be based on estimates of relatedness derived entirely from molecular marker data. The idea of estimating quantitative genetic parameters using relatedness estimates derived from molecular marker data has been explored by a number of workers (Mousseau et al. 1998; Thomas & Hill 2000; Thomas et al. 2000; Thomas 2005) and, in particular, has been developed by Ritland (1996, 2000a,b; Ritland & Ritland 1996). Although Ritlands method is conceptually similar to the pedigree-free animal models that we discuss here, there are key differences between the two. The most important of these is that Ritlands method is based on regressing pairwise estimates of phenotypic similarity on pairwise estimates of genetic relatedness (Ritland 1996). Limitations of this approach include difficulties in estimating significance due to non-independence of relatedness estimates and that method of moments relatedness measures do not provide estimates that are internally consistent across the entire population. In contrast, the pedigre (...truncated)