A random model approach to mapping quantitative trait loci for complex binary traits in outbred populations

Mapping quantitative trait loci (QTL) for complex binary traits is more cha llenging than for normally distributed traits due to the nonlinear relation ship between the observed phenotype and unobservable genetic effects, espec ially when the mapping population contains multiple outbred families. Becau se the number of alleles of a QTL depends on the number of founders in an o utbred population, it is more appropriate to treat the effect of each allel e as a random variable so that a single variance rather than individual all elic effects is estimated and tested. Such a method is called the random mo del approach. In this study, we develop the random model approach of QTL ma pping for binary traits in outbred populations. An EM-algorithm with a Fish er-scoring algorithm embedded in each E-step is adopted here to estimate th e genetic variances. A simple Monte Carlo integration technique is used her e to calculate the likelihood-ratio test statistic. For the first time we s how that QTL of complex binary traits in an outbred population can be scann ed along a chromosome for their positions, estimated for their explained va riances, and tested for their statistical significance. Application of the method is illustrated using a set of simulated data.