A novel Markov chain monte carlo approach for constructing accurate meiotic maps

Abstract

Mapping markers from linkage data continues to be a task performed in many genetic epidemiological studies. Data collected in a study may be used to refine published map estimates and a study may use markers that do not appear in any published map. Furthermore, inaccuracies in meiotic maps can seriously bias linkage findings. To make best use of the available marker information, multilocus linkage analyses are performed. However, two computational issues greatly limit the number of markers currently mapped jointly; the number of candidate marker orders increases exponentially with marker number and computing exact multilocus likelihoods on general pedigrees is computationally demanding. In this article, a new Markov chain Monte Carlo (MCMC) approach that solves both these computational problems is presented. The MCMC approach allows many markers to be mapped jointly, using data observed on general pedigrees with unobserved individuals. The performance of the new mapping procedure is demonstrated through the analysis of simulated and real data. The MCMC procedure performs extremely well, even when there are millions of candidate orders, and gives results superior to those of CRI-MAP.

Figure 1.

The estimated posterior probabilities of a marker order from the Bayesian analysis of data sets (A) 8-F, (B) 8-M, (C) 1-F, and (D) 1-M. The numbers are distances measuring the discrepancy between the sample order and the simulated marker order. For clarity, results are shown only from the analysis of the first 50 replicates. The simulated marker order has a distance of 0.

Figure 2.

The marker order with the highest estimated posterior probability is converted into a distance and plotted against replicate number for data sets (A) 8-F, (B) 8-M, (C) 1-F, and (D) 1-M. Also, the marker order (converted into a distance) with the largest maximized likelihood obtained via CRI-MAP is plotted against replicate number. For clarity, results are shown only for the first 50 replicates. x, a result obtained using the MCMC procedure; *, a result obtained using CRI-MAP. The simulated marker order has a distance of 0.

Figure A1.

The proposal mechanism for generating a new marker order and set of recombination fractions. A block of markers (M₂, M₃, and M₆) is moved to a new position, resulting in a new marker order and set of recombination fractions. (A) The marker block is moved to the left of marker M₁. (B) The marker block is moved between markers M₅ and M₄. Marker locations are denoted by vertical lines. For the proposed state, a solid horizontal line denotes a chromosomal distance that does not differ from the current state, and a cross-hatched horizontal line denotes a chromosomal distance that is sampled from a uniform distribution.