Variation explained in mixed-model association mapping

Genomic mapping of complex traits across species demands integrating genetics and statistics. In particular, because it is easily interpreted, the R(2) statistic is commonly used in quantitative trait locus (QTL) mapping studies to measure the proportion of phenotypic variation explained by molecular markers. Mixed models with random polygenic effects have been used in complex trait dissection in different species. However, unlike fixed linear regression models, linear mixed models have no well-established R(2) statistic for assessing goodness-of-fit and prediction power. Our objectives were to assess the performance of several R(2)-like statistics for a linear mixed model in association mapping and to identify any such statistic that measures model-data agreement and provides an intuitive indication of QTL effect. Our results showed that the likelihood-ratio-based R(2) (R(LR)(2)) satisfies several critical requirements proposed for the R(2)-like statistic. As R(LR)(2) reduces to the regular R(2) for fixed models without random effects other than residual, it provides a general measure for the effect of QTL in mixed-model association mapping. Moreover, we found that R(LR)(2) can help explain the overlap between overall population structure modeled as fixed effects and relative kinship modeled though random effects. As both approaches are derived from molecular marker information and are not mutually exclusive, comparing R(LR)(2) values from different models provides a logical bridge between statistical analysis and underlying genetics of complex traits.