Theoretical recombination processes incorporating interference effects

With the acquisition of genetic, physical, and sequence maps, linkage relationships among genes (markers) may be more accurately approached in terms of global models for the distribution of recombination events that take into account interference. There are two principal analytical methods used for ascertaining linkage relationships. The first method, the Haldane-Kosambi differential equation approach, has the limitation that all of its calculations rest on consideration of only three gene markers, where recombination depends only on the physical distance between markers. In this formulation the resulting map function is in general not feasible for use with multiple markers. The second method starts with a model of the crossover process from which recombination values are determined. The best studied global recombination processes are based on sequential (renewal) crossover formation processes, the count-location crossover structure, and crossovers evolving by a cascade mechanism. This paper, containing both review and new results, concentrates on two aspects of recombination structures: (i) classifications and characterizations of multimarker crossover distributions; and (ii) analysis of regular and higher order crossover interference forms. In eucaryotic species, the general impression is that positive interference prevails, while in procaryotic and viral organisms, there may be circumstances of negative interference. We would propose in estimating the crossover formation process a binomial count distribution or any other count distribution satisfying property (a) of Theorem 9.1 and a location distribution fitted by the data. It is also reasonable to try one or more obligate crossover points superimposed on independent Poisson processes determining other crossover points. This latter model also generates a situation of positive interference (Theorem 3.1).