A unified approach to joint modeling of multiple quantitative and qualitative traits in gene mapping

Using graph theory, we present a theoretical basis for mapping oligogenes in the joint presence of multiple phenotypic measurements of both quantitative and qualitative types. Various statistical models proposed earlier for several traits of solely single type are special cases of the unified approach given here. Our emphasis is on the generality of the framework, without specifying explicit assumptions about a sampling design. When information about environmental factors potentially affecting the traits is available, it can be incorporated into the genetic model. We adopt the Bayesian inferential machinery due to its firm theoretical basis and its capability of handling uncertain quantities; such as unobserved model parameters, missing marker data, and even different putative genetic models, probabilistically within a single framework. It is shown here that biological hypotheses about single gene affecting simultaneously multiple traits (pleiotropy) can be intuitively imposed as parameter constraints, leading to pleiotropic models for which posterior probabilities can be calculated. Outline of the possible implementation of the Bayesian method is described using the general reversible-jump Markov chain Monte Carlo algorithm. Some future challenges and extensions are also discussed.