Modeling X-Linked Ancestral Origins in Multiparental Populations

The models for the mosaic structure of an individual's genome from multiparental populations have been developed primarily for autosomes, whereas X chromosomes receive very little attention. In this paper, we extend our previous approach to model ancestral origin processes along two X chromosomes in a mapping population, which is necessary for developing hidden Markov models in the reconstruction of ancestry blocks for X-linked quantitative trait locus mapping. The model accounts for the joint recombination pattern, the asymmetry between maternally and paternally derived X chromosomes, and the finiteness of population size. The model can be applied to various mapping populations such as the advanced intercross lines (AIL), the Collaborative Cross (CC), the heterogeneous stock (HS), the Diversity Outcross (DO), and the Drosophila synthetic population resource (DSPR). We further derive the map expansion, density (per Morgan) of recombination breakpoints, in advanced intercross populations with L inbred founders under the limit of an infinitely large population size. The analytic results show that for X chromosomes the genetic map expands linearly at a rate (per generation) of two-thirds times 1 - 10/(9L) for the AIL, and at a rate of two-thirds times 1 - 1/L for the DO and the HS, whereas for autosomes the map expands at a rate of 1 - 1/L for the AIL, the DO, and the HS.