Linkage disequilibrium under polysomic inheritance

The influence of genetic drift on linkage disequilibrium in finite populations has been extensively studied in diploids. However, to date the effects of ploidy on LD has not been extensively studied. We here extend the linkage disequilibrium measure D and Burrow’s Δ statistic to include polysomic inheritance, as well as their corresponding squared correlation coefficients r2 and , where the former is for phased genotypes and the latter for unphased genotypes. Weir & Hill’s double non-identity framework is also extended to include polysomic inheritance, and the expressions of double non-identity coefficients are derived under five mating systems. On this basis, the approximated expectations of estimated r2 and at equilibrium state, d2 and δ2, are derived under five mating systems. We assess the behaviors of the estimated r2 and and the influence of the recombination rate on d2 or δ2, simulate the application of estimating effective population size, and evaluate the statistical performance of the method of estimating.

Identifying rare variants for quantitative traits in extreme samples of population via Kullback-Leibler distance

Background The rapid development of sequencing technology and simultaneously the availability of large quantities of sequence data has facilitated the identification of rare variant associated with quantitative traits. However, existing statistical methods depend on certain assumptions and thus lacking uniform power. The present study focuses on mapping rare variant associated with quantitative traits. Results In the present study, we proposed a two-stage strategy to identify rare variant of quantitative traits using phenotype extreme selection design and Kullback-Leibler distance, where the first stage was association analysis and the second stage was fine mapping. We presented a statistic and a linkage disequilibrium measure for the first stage and the second stage, respectively. Theory analysis and simulation study showed that (1) the power of the proposed statistic for association analysis increased with the stringency of the sample selection and was affected slightly by non-causal variants and opposite effect variants, (2) the statistic here achieved higher power than three commonly used methods, and (3) the linkage disequilibrium measure for fine mapping was independent of the frequencies of non-causal variants and simply dependent on the frequencies of causal variants. Conclusions We conclude that the two-stage strategy here can be used effectively to mapping rare variant associated with quantitative traits.

New multilocus linkage disequilibrium measure for tag SNP selection

Numerous approaches have been proposed for selecting an optimal tag single-nucleotide polymorphism (SNP) set. Most of these approaches are based on linkage disequilibrium (LD). Classical LD measures, such as D′ and r2, are frequently used to quantify the relationship between two marker (pairwise) linkage disequilibria. Despite of their successful use in many applications, these measures cannot be used to measure the LD between multiple-marker. These LD measures need information about the frequencies of alleles collected from haplotype dataset. In this study, a cluster algorithm is proposed to cluster SNPs according to multilocus LD measure which is based on information theory. After that, tag SNPs are selected in each cluster optimized by the number of tag SNPs, prediction accuracy and so on. The experimental results show that this new LD measure can be directly applied to genotype dataset collected from the HapMap project, so that it saves the cost of haplotyping. More importantly, the proposed method significantly improves the efficiency and prediction accuracy of tag SNP selection.

Non-random association between electromorphs and inversion chromosomes in finite populations

SUMMARYWith the aim of knowing the probable magnitude of non-random association between inversion chromosomes and electromorphs, both deterministic and stochastic studies are conducted on the evolutionary change of non-random association, which is defined as the difference in the frequency of a given allele between inversion and non-inversion chromosomes. In these studies inversion chromosomes are assumed to be subject to selection but electromorphs are selectively neutral, and recombination is allowed to occur between inversion and non-inversion chromosomes with a low frequency. The deterministic study has shown that in a variety of selective schemes for inversion chromosomes the non-random association decays at a rate equal to the recombination value in every generation. Thus, if the recombination value is of the order of 10−5 ˜ 10−4, it would take a long time for the non-random association to disappear. Furthermore, the stochastic study has indicated that random genetic drift generates non-random association of inversions and electromorphs in finite populations and the standard error of non-random association often becomes larger than the mean. In addition to these problems the time required for the electromorph frequencies in the inversion and noninversion chromosomes to become equal in a finite population and the probability that the population of inversion chromosomes remains monomorphic for the allele which existed in the initial inversion introduced are studied. Considering all these quantities, it is concluded that data on the non-random association between electromorphs and inversions are not very informative for the study of the maintenance of protein polymorphism. It is also indicated that in the study of association between electromorphs and inversion chromosomes non-random association or Yule's coefficient of association has a better property than the usual linkage disequilibrium measure or correlation coefficient. Implications of this study on some experimental observations are discussed.

A STUDY OF LINKAGE DISEQUILIBRIUM IN BRITISH POPULATIONS OF DROSOPHILA SUBOBSCURA

ABSTRACT Data have been obtained concerning the genetic content of samples of O chromosomes from three British populations, and J chromosomes from one population, of Drosophila subobscura. Some improvements to the genetic map of the O and J chromosomes have been made. Allele frequencies at the loci studied do not show much geographical variation, except where associations with geographically varying gene arrangements distort the picture. Striking nonrandom associations between alleles at three enzyme loci and closely linked O chromosome gene arrangements are present. Some historical explanation for these associations cannot at present be ruled out, but it is clear that a very high degree of genetic differentiation must exist between different gene arrangements in this species. There is no convincing direct evidence for linkage disequilibrium between pairs of enzyme loci, although there is a significant association between close linkage and a high value of the linkage disequilibrium measure. This suggests that there may be disequilibria between closely linked enzyme loci that are too small to be individually detectable. These results are in broad agreement with those reported by workers on other Drosophila species. At present there appears to be no evidence to support the concept that selection is sufficiently strong at individual enzyme loci to produce a high degree of nonrandom associations. (FRANKLIN and LEWONTIN 1970).