A validated genome-wide association study in 2 dairy cattle breeds for milk production and fertility traits using variable length haplotypes

Genome-wide association studies (GWAS) were used to discover genomic regions explaining variation in dairy production and fertility traits. Associations were detected with either single nucleotide polymorphism (SNP) markers or haplotypes of SNP alleles. An across-breed validation strategy was used to narrow the genomic interval containing causative mutations. There were 39,048 SNP tested in a discovery population of 780 Holstein sires and validated in 386 Holsteins and 364 Jersey sires. Previously identified mutations affecting milk production traits were confirmed. In addition, several novel regions were identified, including a putative quantitative trait loci for fertility on chromosome 18 that was detected only using haplotypes greater than 3 SNP long. It was found that the precision of quantitative trait loci mapping increased with haplotype length as did the number of validated haplotypes discovered, especially across breed. Promising candidate genes have been identified in several of the validated regions.     

Reliability of genomic evaluations in Holstein-Friesians using haplotypes based on the BovineHD BeadChip

The objectives of this study were to make subsets of high-density (HD) loci based on localized haplotype clusters, without loss of genomic information, to reduce computing time compared with the use of all HD loci and to investigate the effect on the reliability of the direct genomic value (DGV) when using this HD subset based on localized haplotype clusters in the genomic evaluation for Holstein-Friesians. The DNA was isolated from semen samples of 548 bulls (key ancestors) of the EuroGenomics Consortium, a collaboration between 4 European dairy cattle breeding organizations and scientific partners. These bulls were genotyped with the BovineHD BeadChip [~777,000 (777K) single nucleotide polymorphisms (SNP); Illumina Inc., San Diego, CA] and used to impute all 30,483 Holstein-Friesians from the BovineSNP50 BeadChip [~50,000 (50K) SNP; Illumina Inc.] to HD, using the BEAGLE software package. The final data set consisted of 30,483 animals and 603,145 SNP. For each locus, localized haplotype clusters (i.e., edges of the fitted graph model) identifications were obtained from BEAGLE. Three subsets [38,000 (38K), 116,000 (116K), and 322,000 (322K) loci] were made based on deleting obsolete loci (i.e., loci that do not give extra information compared with the neighboring loci). A fourth data set was based on 38K SNP, which is currently used for routine genomic evaluation at the Cattle Improvement Cooperative (CRV, Arnhem, the Netherlands). A validation study using the HD loci subsets based on localized haplotype clusters was performed for 9 traits (production, conformation, and functional traits). Error of imputation from 50K to HD averaged 0.78%. Three thresholds (0.17, 0.05, and 0.008%) were used for the identification of obsolete HD loci based on localized haplotype clusters to obtain a desired number of HD loci (38K, 116K, and 322K). On average, 46% (using threshold 0.008%) to 93% (using threshold 0.17%) of HD loci were eliminated. The computing time was about 9 d for 38K loci, 15.5 d for 116K loci, 21 d for 322K loci, and 7.5 d for 38K SNP. The increase in reliability of DGV compared with pedigree-based estimated breeding values for kilograms of protein was similar for 322K and 116K loci (30.7%), but was 1.5 to 2% higher compared with 38K loci and 38K SNP. Averaged over 9 traits, subset 116K loci resulted in a higher increase in reliability compared with 38K loci and 38K SNP. Eliminating obsolete loci enormously decreased the amount of data to be analyzed for genomic evaluations. The more HD loci used in a genomic evaluation, the higher the increase in reliability of DGV. It is possible to increase the reliability of DGV by 1 to 2% compared with the SNP currently used for routine genomic evaluation.     

有Mate-Pairs的个体单体型MSR问题的参数化算法

个体单体型MSR(minimum SNP removal)问题是指如何利用个体的基因测序片断数据去掉最少的SNP(single-nucleotide polymorphisms)位点,以确定该个体单体型的计算问题.对此问题,Bafna等人提出了时间复杂度为O(2^kn²m)的算法,其中,m为DNA片断总数,n为SNP位点总数,k为片断中洞(片断中的空值位点)的个数.由于一个Mate-Pair片段中洞的个数可以达到100,因此,在片段数据中有Mate-Pair的情况下,Bafna的算法通常是不可行的.根据片段数据的特点提出了一个时间复杂度为O((n-1)(k₁-1)k₂2^2h+(k₁+1)^2h+nk₂+mk₁)的新算法,其中,k₁为一个片断覆盖的最大SNP位点数(不大于n),k₂为覆盖同一SNP位点的片段的最大数(通常不大于19),h为覆盖同一SNP位点且在该位点取空值的片断的最大数(不大于k₂).该算法的时间复杂度与片断中洞的个数的最大值k没有直接的关系,在有Mate-Pair片断数据的情况下仍然能够有效地进行计算,具有良好的可扩展性和较高的实用价值.     

一种快速精确的个体单体型重建算法

在最少错误更正模型的基础上,提出一种重建单体型的启发式算法 H-MEC。按照单体型的单核苷酸多态性(SNP)位点顺序依次构建算法步骤,根据某SNP位点取值将覆盖该SNP位点的片段划分为2个集合,利用包含片段数较多集合中的片段进行重建。使用HapMap计划发布的CEPH样本中的60个个体,在1号染色体的单体型上进行实验。结果表明,H-MEC算法在各种参数设置下,能获得较Fast Hare算法和DGS算法更高的单体型重建率。此外,该算法在重建长单体型时也具有较高的执行效率。     

A Monte Carlo approach for estimation of haplotype probabilities in half-sib families

The objective of this work was to propose an algorithm (HAPROB) to estimate haplotype probabilities for genotyped members of half-sib families for which parents lacked genotypic information. The algorithm had 2 basic steps. First, a Monte Carlo-based approach was used to estimate haplotype probabilities for sires conditional upon offspring genotypes and population allelic frequencies, and then offspring-haplotype probabilities were estimated conditional upon sire probabilities and population frequencies. The 2 steps were alternated iteratively until estimates of population frequencies were essentially unchanged. Simulation was used to evaluate effects of the number of Monte Carlo cycles on the accuracy of the reconstructed haplotypes. Fifty thousand cycles was found to be sufficient for the haplotype configurations considered. Accuracy of the algorithm was compared with that obtained by the public domain SIMWALK2 software. Predictions of the most likely haplotype configurations are produced by SIM-WALK2, but no estimates of probability are given. The accuracy of the current approach was comparable to that obtained from SIMWALK2. The proportions of times that haplotypes were reconstructed correctly were 87.0 and 92.4% (sires and offspring) for HAPROB vs. 87.5 and 91.5% for SIMWALK2. Effects of family size on accuracy of reconstruction were examined. Accuracy of reconstruction was only about 4% for sires with 2 offspring, but accuracy among the offspring themselves was 65%. Accuracy increased quickly as family size increased and reached 100% for sires with 30 offspring. Maximum accuracy for offspring was about 96%. Estimates of haplotype probabilities produced can be used in regression analyses to estimate effects of haplotypes on quantitative phenotypes.     

最大节约原则下单倍型推导问题的实用算法

在疾病的易感基因研究和药物反应实验中,常常需要知道单倍型,而不仅仅是基因型数据.但是直接通过生物学实验手段来测定单倍型在时间和成本上消耗过大,所以在实验室里往往仅测得基因型,而通过一些计算手段来推导出单倍型.不同于Clark著名的单倍型推导模型,Gusfield和Wang等人提出了一种通过基因型样本推导单倍型的新模型.这种模型试图按照最大节约原则去寻找可以解释基因型样本的最小单倍型集合.这种基于节约原则的模型克服了Clark模型的一些缺陷.提出了节约原则模型的一个多项式时间的贪心算法以及一种把贪心策略和分支限界策略集合在统一框架下的复合算法.相对于Wang原来提出的分支限界完全算法,贪心的近似算法运行快得多,而且同时保持了比较准确的推导结果.新的复合算法也是一种完全算法.实验结果表明,与原来的分支限界算法相比,复合算法可以极大地提高运行效率以及可应用的实例规模.     

Genomic breeding value estimation using genetic markers, inferred ancestral haplotypes, and the genomic relationship matrix

With the introduction of new single nucleotide polymorphism (SNP) chips of various densities, more and more genotype data sets will include animals genotyped for only a subset of the SNP. Imputation techniques based on unobserved ancestral haplotypes may be used to infer missing genotypes. These ancestral haplotypes may also be used in the genomic prediction model, instead of using the SNP. This may increase the reliability of predictions because the ancestral haplotype may capture more linkage disequilibrium with quantitative trait loci than SNP. The aim of this paper was to study whether using unobserved ancestral haplotypes in a genomic prediction model would provide more reliable genomic predictions than using SNP, and to determine how many loci in the genomic prediction model would be redundant. Genotypes of 8,960 bulls and cows for 39,557 SNP were analyzed with a hidden Markov model to associate each individual at each locus to 2 ancestral haplotypes. The number of ancestral haplotypes per locus was fixed at 10, 15, or 20. Subsequently, a validation study was performed in which the phenotypes of 3,251 progeny-tested bulls for 16 traits were used in a genomic prediction model to predict the estimated breeding values of at least 753 validation bulls. The squared correlation between genomic prediction and deregressed daughter performance estimated breeding value, when averaged across traits, was slightly higher when 15 or 20 ancestral haplotypes per locus were used in the prediction model instead of the SNP genotypes, whereas the prediction model using a genomic relationship matrix gave the lowest squared correlations. The number of redundant loci [i.e., loci that had less than 18 jumps (0.1%) from one ancestral haplotype to another ancestral haplotype at the next locus], was 18,793 (48%), which means that only 20,764 loci would need to be included in the genomic prediction model. This provides opportunities for greatly decreasing computer requirements of genomic evaluations with very large numbers of markers.     

重建二倍体个体单体型的改进环基算法

HapCompass算法是求解最少带权边删除模型(the minimum weighted edge removal, MWER)的有效启发式方法,该算法采用删除权值绝对值最小的边的方式消除冲突环基,当同时存在多条权值绝对值最小的边时,HapCompass随机选择删除边,导致求解方案的不确定性,降低重建效果。针对该问题,提出IHapCompass算法,改进去边规则,利用(00)/(11)和(01)/(10)分型的片段支持差异数与总片段数之间的比值来确定删除边,对随机取值问题做出有效限定。此外,IHapCompass以单体型中0/1取值的概率为图中孤立点赋值,明确孤立点取值。采用真实单体型数据进行测试,结果表明,IHapCompass算法在各种参数设置下,均能获得较算法HapCompass、DGS和Fast Hare更高的单体型重建率,具有较高的执行效率。该算法为求解二倍体个体单体型重建问题提供一定的参考。