Technical Report No. 2000-5 : Erlang Renewal Models for Genetic Recombination (AU-CAS-MathStats)

Closed form expressions for multilocus probabilities are given for the crossover process when it is a renewal process with the distance between crossovers modeled by a Erlang distribution. Closed form expressions are also given for the multilocus probabilities for the chiasma process on the four strand bundle under the same model of recombination for single gamete and for tetrad data. These expressions yield explicit formulas for the map functions, coincidence functions and distributions of the identity- by-descent process for a class of models that incorporate interference. The alternating renewal models used may be of interest in other fields, e.g. telecommunication networks and queues, where they can be used to model the busy/non-busy state of a system with buffers.