The probability that the tract length is greater than km, where m is the mean conversion tract length and k is a positive integer, becomes negligible as k grows.
We show that modeling overlapping gene conversions is crucial for improving the joint estimation of the gene conversion rate and the mean conversion tract length.
We believe that this aspect of our model is crucial in making the joint estimation of the gene conversion rate and the mean conversion tract length feasible.
In this article, we devise algorithms to incorporate overlapping gene conversions into the PAC model and show that this modification dramatically improves the estimation of the gene conversion rate and the mean conversion tract length.
We show that this simplification frequently leads to gross errors in the estimation of the gene conversion rate and the mean conversion tract length, when all three parameters are being estimated.
In particular, for a given population SNP dataset, the joint estimation of the crossover rate, the gene conversion rate and the mean conversion tract length is widely viewed as a very difficult problem.
We can see that estimates of γ can be substantial although the true value is 0. When the mean conversion tract length becomes longer (e.g., 2000 bp, 8000 bp), we observe multiple peaks in the joint posterior distribution.
In all simulations, we used θ = 1.0/kb for mutation rate and λ=0.5 kb for the mean conversion tract length, both of which being relevant to humans [see Ptak et al. (2004) and Frisse et al. (2001), respectively].
In their article, Gay et al. did not try to estimate the mean conversion tract length, but always fixed it to some reasonable value (actually, the true value in the case of simulation study).
Given our lack of knowledge of the mean conversion tract length in the human genome, the simulations (using the HI994 model) were repeated with this parameter varied within the range of 100 600 bp.
