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1 Department of Statistics, University of Florida, Gainesville, FL, USA
2 Department of Anatomy and Neurobiology, Washington University School of Medicine, St. Louis, MO, USA
* To whom correspondence should be addressed. E-mail: rwu{at}stat.ufl.edu.
Most organisms display remarkable differences in morphological, anatomical and developmental features between the two sexes. It has been recognized that these sex-dependent differences are controlled by an array of specific genetic factors, mediated through various environmental stimuli. In this article, we present a unifying statistical model for mapping quantitative trait loci (QTL) that are responsible for sexual differences in growth trajectories during ontogenetic development. This model is derived within the maximum likelihood context, incorporated by sex stimulated differentiation in growth form that is described by mathematical functions. A typical structural model is implemented to approximate time-dependent covariance matrices for longitudinal traits. This model allows for a number of biologically meaningful hypothesis tests regarding the effects of QTL on overall growth trajectories or particular stages of development. It is in particular powerful to test whether and how the genetic effect of QTL are expressed differently in different sexual backgrounds. Our model has been employed to map QTL affecting body mass growth trajectories in both male and female mice of an F2population derived from the Large (LG/J) and Small (SM/J) mouse strains. We detected four growth QTL on chromosomes 6, 7, 11 and 15, two of which trigger different effects on growth curves between the two sexes. All the four QTL display significant genotype-sex interaction effects on the timing of maximal growth rate in the ontogenetic growth of mice. The implications of our model for studying the genetic architecture of growth trajectories and its extensions to some more general situations are discussed.
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