Modem Differential Geometrics

This paper describes about the modern differential geometry.@IAC

Comparison of Population-Based Association Study Methods Correcting for Population Stratification

Population stratification can cause spurious associations in population–based association studies. Several statistical methods have been proposed to reduce the impact of population stratification on population–based association studies. We simulated a set of stratified populations based on the real haplotype data from the HapMap ENCODE project, and compared the relative power, type I error rates, accuracy and positive prediction value of four prevailing population–based association study methods: traditional case-control tests, structured association (SA), genomic control (GC) and principal components analysis (PCA) under various population stratification levels. Additionally, we evaluated the effects of sample sizes and frequencies of disease susceptible allele on the performance of the four analytical methods in the presence of population stratification. We found that the performance of PCA was very stable under various scenarios. Our comparison results suggest that SA and PCA have comparable performance, if sufficient ancestral informative markers are used in SA analysis. GC appeared to be strongly conservative in significantly stratified populations. It may be better to apply GC in the stratified populations with low stratification level. Our study intends to provide a practical guideline for researchers to select proper study methods and make appropriate inference of the results in population-based association studies

Quantitative trait locus analysis of hybrid pedigrees: variance-components model, inbreeding parameter, and power

<p>Abstract</p> <p>Background</p> <p>For the last years reliable mapping of quantitative trait loci (QTLs) has become feasible through linkage analysis based on the variance-components method. There are now many approaches to the QTL analysis of various types of crosses within one population (breed) as well as crosses between divergent populations (breeds). However, to analyse a complex pedigree with dominance and inbreeding, when the pedigree's founders have an inter-population (hybrid) origin, it is necessary to develop a high-powered method taking into account these features of the pedigree.</p> <p>Results</p> <p>We offer a universal approach to QTL analysis of complex pedigrees descended from crosses between outbred parental lines with different QTL allele frequencies. This approach improves the established variance-components method due to the consideration of the genetic effect conditioned by inter-population origin and inbreeding of individuals. To estimate model parameters, namely additive and dominant effects, and the allelic frequencies of the QTL analysed, and also to define the QTL positions on a chromosome with respect to genotyped markers, we used the maximum-likelihood method. To detect linkage between the QTL and the markers we propose statistics with a non-central χ²-distribution that provides the possibility to deduce analytical expressions for the power of the method and therefore, to estimate the pedigree's size required for 80% power. The method works for arbitrarily structured pedigrees with dominance and inbreeding.</p> <p>Conclusion</p> <p>Our method uses the phenotypic values and the marker information for each individual of the pedigree under observation as initial data and can be valuable for fine mapping purposes. The power of the method is increased if the QTL effects conditioned by inter-population origin and inbreeding are enhanced. Several improvements can be developed to take into account fixed factors affecting trait formation, such as age and sex.</p

Efficient and Accurate Construction of Genetic Linkage Maps from the Minimum Spanning Tree of a Graph

Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap

Multiple Local and Recent Founder Effects of TGM1 in Spanish Families

<div><h3>Background</h3><p>Mutations in the <em>TGM1</em> gene encoding transglutaminase 1 are a major cause of autosomal recessive congenital ichthyosis. In the Galician (NW Spain) population, three mutations, c.2278C>T, c.1223_1227delACAC and c.984+1G>A, were observed at high frequency, representing ∼46%, ∼21% and ∼13% of all <em>TGM1</em> gene mutations, respectively. Moreover, these mutations were reported only once outside of Galicia, pointing to the existence of historical episodes of local severe genetic drift in this region.</p> <h3>Methodology/Principal Findings</h3><p>In order to determine whether these mutations were inherited from a common ancestor in the Galician population, and to estimate the number of generations since their initial appearance, we carried out a haplotype-based analysis by way of genotyping 21 SNPs within and flanking the <em>TGM1</em> gene and 10 flanking polymorphic microsatellite markers spanning a region of 12 Mb. Two linkage disequilibrium based methods were used to estimate the time to the most recent common ancestor (TMRCA), while a Bayesian-based procedure was used to estimate the age of the two mutations. Haplotype reconstruction from unphased genotypes of all members of the affected pedigrees indicated that all carriers for each of the two mutations harbored the same haplotypes, indicating common ancestry.</p> <h3>Conclusions/Significance</h3><p>In good agreement with the documentation record and the census, both mutations arose between 2,800–2,900 years ago (y.a.), but their TMRCA was in the range 600–1,290 y.a., pointing to the existence of historical bottlenecks in the region followed by population growth. This demographic scenario finds further support on a Bayesian Coalescent Analysis based on <em>TGM1</em> haplotypes that allowed estimating the occurrence of a dramatic reduction of effective population size around 900–4,500 y.a. (95% highest posterior density) followed by exponential growth.</p> </div

Mapping the sex determination locus in the hāpuku (Polyprion oxygeneios) using ddRAD sequencing

Background&nbsp; Hāpuku (Polyprion oxygeneios) is a member of the wreckfish family (Polyprionidae) and is highly regarded as a food fish. Although adults grow relatively slowly, juveniles exhibit low feed conversion ratios and can reach market size in 1&ndash;2 years, makingP. oxygeneiosa strong candidate for aquaculture. However, they can take over 5years to reach sexual maturity in captivity and are not externally sexually dimorphic, complicating many aspects of broodstock management. Understanding the sex determination system ofP. oxygeneiosand developing accurate assays to assign genetic sex will contribute significantly towards its full-scale commercialisation.&nbsp; Results&nbsp; DNA from parents and sexed offspring (n = 57) from a single family of captive bredP. oxygeneioswas used as a template for double digestion Restriction-site Associated DNA (ddRAD) sequencing. Two libraries were constructed usingSbfI&ndash;SphI andSbfI &ndash;NcoI restriction enzyme combinations, respectively. Two runs on an Illumina MiSeq platform generated 70,266,464 raw reads, identifying 19,669 RAD loci. A combined sex linkage map (1367cM) was constructed based on 1575 Single Nucleotide Polymorphism (SNP) markers that resolved into 35 linkage groups. Sex-specific linkage maps were of similar size (1132 and 1168cM for male and female maps respectively). A single major sex-determining locus, found to be heterogametic in males, was mapped to linkage group 14. Several markers were found to be in strong linkage disequilibrium with the sex-determining locus. Allele-specific PCR assays were developed for two of these markers, SphI6331 and SphI8298, and demonstrated to accurately differentiate sex in progeny within the same pedigree. Comparative genomic analyses indicated that many of the linkage groups within theP. oxygeneiosmap share a relatively high degree of homology with those published for the European seabass (Dicentrarchus labrax).&nbsp; Conclusion&nbsp; P. oxygeneioshas an XX/XY sex determination system. Evaluation of allele-specific PCR assays, based on the two SNP markers most closely associated with phenotypic sex, indicates that a simple molecular assay for sexingP. oxygeneiosshould be readily attainable. The high degree of synteny observed withD. labraxshould aid further molecular genetic study and exploitation of hāpuku as a food fish

The Five AhMTP1 Zinc Transporters Undergo Different Evolutionary Fates towards Adaptive Evolution to Zinc Tolerance in Arabidopsis halleri

Gene duplication is a major mechanism facilitating adaptation to changing environments. From recent genomic analyses, the acquisition of zinc hypertolerance and hyperaccumulation characters discriminating Arabidopsis halleri from its zinc sensitive/non-accumulator closest relatives Arabidopsis lyrata and Arabidopsis thaliana was proposed to rely on duplication of genes controlling zinc transport or zinc tolerance. Metal Tolerance Protein 1 (MTP1) is one of these genes. It encodes a Zn2+/H+ antiporter involved in cytoplasmic zinc detoxification and thus in zinc tolerance. MTP1 was proposed to be triplicated in A. halleri, while it is present in single copy in A. thaliana and A. lyrata. Two of the three AhMTP1 paralogues were shown to co-segregate with zinc tolerance in a BC1 progeny from a cross between A. halleri and A. lyrata. In this work, the MTP1 family was characterized at both the genomic and functional levels in A. halleri. Five MTP1 paralogues were found to be present in A. halleri, AhMTP1-A1, -A2, -B, -C, and -D. Interestingly, one of the two newly identified AhMTP1 paralogues was not fixed at least in one A. halleri population. All MTP1s were expressed, but transcript accumulation of the paralogues co-segregating with zinc tolerance in the A. halleri X A. lyrata BC1 progeny was markedly higher than that of the other paralogues. All MTP1s displayed the ability to functionally complement a Saccharomyces cerevisiæ zinc hypersensitive mutant. However, the paralogue showing the least complementation of the yeast mutant phenotype was one of the paralogues co-segregating with zinc tolerance. From our results, the hypothesis that pentaplication of MTP1 could be a major basis of the zinc tolerance character in A. halleri is strongly counter-balanced by the fact that members of the MTP1 family are likely to experience different evolutionary fates, some of which not concurring to increase zinc tolerance

A high density linkage map of the bovine genome

<p>Abstract</p> <p>Background</p> <p>Recent technological advances have made it possible to efficiently genotype large numbers of single nucleotide polymorphisms (SNPs) in livestock species, allowing the production of high-density linkage maps. Such maps can be used for quality control of other SNPs and for fine mapping of quantitative trait loci (QTL) via linkage disequilibrium (LD).</p> <p>Results</p> <p>A high-density bovine linkage map was constructed using three types of markers. The genotypic information was obtained from 294 microsatellites, three milk protein haplotypes and 6769 SNPs. The map was constructed by combining genetic (linkage) and physical information in an iterative mapping process. Markers were mapped to 3,155 unique positions; the 6,924 autosomal markers were mapped to 3,078 unique positions and the 123 non-pseudoautosomal and 19 pseudoautosomal sex chromosome markers were mapped to 62 and 15 unique positions, respectively. The linkage map had a total length of 3,249 cM. For the autosomes the average genetic distance between adjacent markers was 0.449 cM, the genetic distance between unique map positions was 1.01 cM and the average genetic distance (cM) per Mb was 1.25.</p> <p>Conclusion</p> <p>There is a high concordance between the order of the SNPs in our linkage map and their physical positions on the most recent bovine genome sequence assembly (Btau 4.0). The linkage maps provide support for fine mapping projects and LD studies in bovine populations. Additionally, the linkage map may help to resolve positions of unassigned portions of the bovine genome.</p