Theoretical description of chromosome architecture after multiple back-crossing

This paper provides a theoretical description of the chromosome architecture resulting from a given number of generations in a back-cross. It is worth considering chromosome architecture as being dependent on a marked point process, whose properties themselves depend on the crossing-over model used. The resulting architecture is presented here for two different models, one without interference, the other with complete interference. Exact distributions, with easy-to-compute formulae, are derived for quantities of interest, as the lengths of donor or receiver fragments, for any chromosome length and for both crossing-over models. Examples are presented to illustrate the use of these distributions in introgression programs.