All methods of statistical gene mapping by means of linkage and/or linkage disequilibrium use, in one way or another, the information on polymorphic phenotypesÂ-typically, the genotypes at one or several polymorphic marker lociÂ-to trace the inheritance of any specific chromosomal position through the available pedigree data. In variance-component (VC) linkage analysis, this transmission pattern is captured by an identity-by-descent (IBD) matrix, which contains the estimated proportions of alleles shared at a particular genomic location for all pairs of pedigree members. Normally, the observed marker locus genotypes provide only partial information about the meiotic transmissions of a given point on a chromosome, such that many different inheritance patterns are compatible with the observed marker locus genotypes. For reasons of computational simplicity, it is currently standard, though likely sub-optimal, practice in VC-based linkage analysis to form a weighted average of IBD sharing over all admissible segregation patterns, with the probability of each possible transmission pattern used for weighting. The resulting estimated IBD matrix is part of the variance-covariance matrix used to compute the likelihood on the data under an assumed multivariate normal distribution [1] or a multivariate *t* distribution [2].

The IBD matrix may be estimated from the genotype information at single marker loci, one locus at a time. Alternatively, the genotypes observed at several linked marker loci may be used jointly to infer the transmission pattern in the data set. Because the genotypes at a single marker locus are almost never fully informative, and because the joint use of several marker loci generally allows more information on the point-wise transmission pattern to be extracted, the "multi-point" approach is often preferred to the "two-point" approach. This is especially true for VC-based linkage analysis where, in contrast to penetrance-model-based linkage analysis, single-marker and multi-marker analyses are equally robust to misspecification of the trait phenotype-trait locus genotype relationship, for reasons explained by Göring and Terwilliger [3]. It should be kept in mind, however, that a multi-marker approach is not penalty-free even for VC-based linkage analysis, because multi-marker analysis is generally less robust to errors in pedigree structure and marker information [e.g., [4, 5]].

A key problem with multi-marker analysis is its computational burden. The Elston-Stewart algorithm [6] allows likelihood computations on large pedigrees but only for a single marker locus or a small number of loci at most, and the Lander-Green algorithm [7] makes possible the joint analysis of many loci but only on pedigrees of moderate size. Several approximate approaches have been developed to overcome these limitations. Markov chain Monte Carlo (MCMC) methods [e.g., [8, 9]] extend the feasibility of linkage analysis with regards to the complexity of a pedigree that can be handled while leaving it intact, and to the number of loci that can be analyzed jointly, by sampling from the permissible inheritance patterns. However, even these approaches can require long computation times. Furthermore, it is typically not clear how closely the obtained information on chromosomal transmissions approximates the information from an exact analysis. An alternative concept to approximating exact multi-locus analysis is sometimes referred to as multiple two-point analysis. The idea behind this approach is to combine the computational simplicity of single-marker analysis and the increased power of multi-marker analysis. In VC-based linkage analysis, this is achieved by first computing exact single-marker IBD matrices for all linked marker loci individually and by then combining these IBD matrices into an approximate multi-marker IBD matrix for a given chromosomal location [10, 11].

Here, we describe an empirical power comparison between VC-based linkage analysis using single-marker (two-point) analysis, approximate multi-marker analysis using a multiple two-point approach, and approximate multi-marker analysis using a multipoint MCMC approach, to quantify the relative gain in power by increasing the computational complexity of IBD matrix estimation.