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Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.

La translocation robertsonienne 1/29, anomalie chromosomique de structure, intervient frequemment comme cause d'infertilite. Nous avons donc voulu connaitre sa frequence en race bovine Blanc Bleu Belge, jusqu'alors non etudiee pour ce facteur. Au sein d'un echantillon de 138 taureaux de race Blanc Bleu Belge, la translocation 1/29 n'a pas pu etre identifiee. Nous pouvons estimer avec 5% de risque d'erreur que la frequence de cette translocation au sein de la population Blanc Bleu Belge doit etre inferieure a 0,69%. Ce resultat trouve une explication dans l'origine de cette race. En effet, le Blanc Bleu Belge est issu d'un melange de races laitieres locales et de la race Shorthorn, lesquelles peuvent etre a priori considerees comme indemnes de la translocation 1/29.

Background Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects. Results The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods. Conclusions The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.

extracts is limited by means of formation of artifacts during PCR. One of these artifacts, the so called allelic-dropout (failure of the amplification of alleles), may result in false-homozygote typing of a sample, if genotyping is based on the analysis of a single amplification product. 30 tooth- and bone samples collected from 17 individuals of three burial sites were investigated in a blind test. Using the polymerase chain reaction (PCR) the two indipendant segregating STR-loci HUMVWA and HUMTH01 were amplified. Corresponding to a mathematical estimation, multiple amplifications of each sample and genelocus were carried out. The results of this genotyping were compared intraindividually. Zusammenfassung: Die Reproduzierbarkeit der Amplifikation von Short-Tandem-Repeats (STRs) aus aDNA Extrakten wird durch Artefaktbildung wahren der PCR begrenzt. Eines dieser Artefakte, das sogenannte allelic-dropout (Ausfall der Amplifikation von Allelen), kann zu falsch-homozygoter Typisierung einer Probe fuhren, wenn die Genotypisierung auf der Auswertung lediglich eines Amplifikationsproduktes beruht. In einem Blindversuch wurden 30 Zahn- und Knochenproben untersucht, die von 17 Skelettindividuen dreier Grabungsorte stammten. Mit Hilfe der Polymerase Chain Reaction (PCR) wurden die beiden unabhangig segregierenden STR-Loci HUMVWA und HUMTH01 amplifiziert. Gemas einer mathematischen Abschatzung wurden mehrfache Amplifikationen und Alleldeterminationen je Probe und Genort durchgefuhrt. Die Ergeb

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