A Markov chain model of coalescence with recombination
A model of sequence evolution is described that includes the recombination rate as a free parameter and which is applied to study the effects of recombination on the sampling properties of DNA sequences. A Markov chain model to derive the exact probability distribution of the number of recombination events for a sample of size two (n=2) in the two-locus case (m=2) was used. This case was amenable to exact analytic results because it involves only nine sites. A similar approach might be used to derive results for other small values of ''m'' and ''n'', but the number of states, and the complexity of the analysis, grow very quickly. For n=2 and m=2 a discrete-time Markov chain was used and a key result is the probability distribution of the number to each state. From this distribution the probability distribution of the number of recombination events in the the history of the sample is derived, and the joint distribution of tree times at two loci. Both of these have implications for statistical properties of DNA sequences. The Markov chain model generalizes to any ''n'' and ''m''; this model is a straightforward and computationally useful tool. The computer program consists of repeating three basic steps: 1. In the current state, determine the probabilities of moving to any other state; 2. Randomly choose the next state; 3. Update the current state. Many interesting properties of DNA sequences, such as those depending on tree times or the number of recombination events, may be studied using simulations of the simpler Markov chain, with no topology information.
scientific article; zbMATH DE number 1092892