A Class The Counting Interval Mapping Of Quantitative Trait

The variation of many quantitative traits in human, plants, or animals can beattributed to genetic e?ects. Quantitative traits locus (QTL) mapping, which mapsloci in the genome that a?ect a quantitative trait, is of important scientific andeconomic value. In recent years, the method of interval mapping is widely used forthe genetic mapping of QTL. Recently, one of the most important challenges facingmodern biology is to understand the genetic mechanisms underlying the adapta-tion of biological traits to environmental factors and use this knowledge to predictthe response of biological structure, organization, and function to changing environ-ments. When grown in di?erent environments, an organism may show a range ofphenotypes. Such a capacity of the organism to alter its phenotypes in response tochanging environment, defined as phenotypic plasticity. This is genetic diversity viagenotype-by-environment interactions.In this article, we consider the estimation problem of QTL parameters thatcontrol the phenotypic plasticity in di?erent environments. We apply a multivariatePoisson model to deal with a kind of count trait, because the phenotype is measuredin counts. An EM algorithm is implemented to obtain the simultaneous computationof maximum likelihood estimates (MLEs) of both QTL positions and the Poissonparameters, which can potentially improve the precision of the estimates. Our modelca also be used to test some hypotheses proposed to explain phenotypic plasticity-di?erent expression of a QTL in di?erent environments. Simulation studies show theadvantages of this algorithm for estimating QTL positions and the Poisson param-eters over existing method. At the same time, our simulation results of hypothetictests show that the approaches we proposed have the correct type I error rates andmuch more powerful.