Variance components models are powerful and flexible tools for extracting genetic information and for mapping genes from quantitative trait data in pedigrees. We extend these models in two directions: multivariate outbred (human) analysis and inbred strain analysis. In the first direction, correlated traits exist, and it is uncertain which trait is primary as in the case of type 2 diabetes where, for example, obesity, impaired glucose tolerance and high cholesterol occur together. Sadly, only univariate or bivariate trait analysis is routinely carried out even when many traits have been measured because of a lack of appropriate software. Creating software is difficult for two mathematical reasons: one, estimating covariance matrices requires satisfying increasingly complicated constraints as the number of traits increases and two, estimating parameters requires maximizing a high-dimensional likelihood surface. By combining factor analysis with the traditional quantitative trait locus (QTL) mapping model and placing it in an efficient quasi-Newton algorithm, our software maps QTL simultaneously for any number of traits while providing information on pleiotropic major genes or polygenes and common environmental determinants with reasonable computation times. In the second direction, together with human studies, animal models of disease and QTL mapping studies are proceeding at a rapid pace. In the arena of inbred strains, cross-specific fixed effects models have been successful in mapping many genes using two strains, although cloning efforts lag far behind. To close the gap, many researchers are exploring multiple strain methods and observing the importance of background genetic variation. We have developed two new QTL mapping models that explicitly model the background genetic variation as a random effect which lead to general covariance expressions that are cross-independent and accomodate any number of strains. This generalization of the traditional QTL mapping model for outbred populations must take into account the peculiar genetic architecture of inbred strains: completely homozygous and genetically identical.
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