Invited review: efficient computation strategies in genomic selection

The purpose of this study is review and evaluation of computing methods used in genomic selection for animal breeding. Commonly used models include SNP BLUP with extensions (BayesA, etc), genomic BLUP (GBLUP) and single-step GBLUP (ssGBLUP). These models are applied for genomewide association studies (GWAS), genomic prediction and parameter estimation. Solving methods include finite Cholesky decomposition possibly with a sparse implementation, and iterative Gauss–Seidel (GS) or preconditioned conjugate gradient (PCG), the last two methods possibly with iteration on data. Details are provided that can drastically decrease some computations. For SNP BLUP especially with sampling and large number of SNP, the only choice is GS with iteration on data and adjustment of residuals. If only solutions are required, PCG by iteration on data is a clear choice. A genomic relationship matrix (GRM) has limited dimensionality due to small effective population size, resulting in infinite number of generalized inverses of GRM for large genotyped populations. A specific inverse called APY requires only a small fraction of GRM, is sparse and can be computed and stored at a low cost for millions of animals. With APY inverse and PCG iteration, GBLUP and ssGBLUP can be applied to any population. Both tools can be applied to GWAS. When the system of equations is sparse but contains dense blocks, a recently developed package for sparse Cholesky decomposition and sparse inversion called YAMS has greatly improved performance over packages where such blocks were treated as sparse. With YAMS, GREML and possibly single-step GREML can be applied to populations with >50 000 genotyped animals. From a computational perspective, genomic selection is becoming a mature methodology.     

Assessment of Genetic Heterogeneity in Structured Plant Populations Using Multivariate Whole-Genome Regression Models

Plant breeding populations exhibit varying levels of structure and admixture; these features are likely to induce heterogeneity of marker effects across subpopulations. Traditionally, structure has been dealt with as a potential confounder, and various methods exist to “correct” for population stratification. However, these methods induce a mean correction that does not account for heterogeneity of marker effects. The animal breeding literature offers a few recent studies that consider modeling genetic heterogeneity in multibreed data, using multivariate models. However, these methods have received little attention in plant breeding where population structure can have different forms. In this article we address the problem of analyzing data from heterogeneous plant breeding populations, using three approaches: (a) a model that ignores population structure [A-genome-based best linear unbiased prediction (A-GBLUP)], (b) a stratified (i.e., within-group) analysis (W-GBLUP), and (c) a multivariate approach that uses multigroup data and accounts for heterogeneity (MG-GBLUP). The performance of the three models was assessed on three different data sets: a diversity panel of rice (Oryza sativa), a maize (Zea mays L.) half-sib panel, and a wheat (Triticum aestivum L.) data set that originated from plant breeding programs. The estimated genomic correlations between subpopulations varied from null to moderate, depending on the genetic distance between subpopulations and traits. Our assessment of prediction accuracy features cases where ignoring population structure leads to a parsimonious more powerful model as well as others where the multivariate and stratified approaches have higher predictive power. In general, the multivariate approach appeared slightly more robust than either the A- or the W-GBLUP.     

The Effects of Demography and Long-Term Selection on the Accuracy of Genomic Prediction with Sequence Data

The use of dense SNPs to predict the genetic value of an individual for a complex trait is often referred to as “genomic selection” in livestock and crops, but is also relevant to human genetics to predict, for example, complex genetic disease risk. The accuracy of prediction depends on the strength of linkage disequilibrium (LD) between SNPs and causal mutations. If sequence data were used instead of dense SNPs, accuracy should increase because causal mutations are present, but demographic history and long-term negative selection also influence accuracy. We therefore evaluated genomic prediction, using simulated sequence in two contrasting populations: one reducing from an ancestrally large effective population size (N_e) to a small one, with high LD common in domestic livestock, while the second had a large constant-sized N_e with low LD similar to that in some human or outbred plant populations. There were two scenarios in each population; causal variants were either neutral or under long-term negative selection. For large N_e, sequence data led to a 22% increase in accuracy relative to ∼600K SNP chip data with a Bayesian analysis and a more modest advantage with a BLUP analysis. This advantage increased when causal variants were influenced by negative selection, and accuracy persisted when 10 generations separated reference and validation populations. However, in the reducing N_e population, there was little advantage for sequence even with negative selection. This study demonstrates the joint influence of demography and selection on accuracy of prediction and improves our understanding of how best to exploit sequence for genomic prediction.     

羊驼种群内亲缘关系的研究

应用RAPD技术对羊驼群体进行亲缘关系检测。在所采用的40条随机引物中筛选出10条,优化了RAPD的反应条件,确立了适合于羊驼基因组RAPD分析的最佳反应体系和反应程序。计算出个体间之间的带纹相似系数及遗传距离指数,带纹相似系数位于0.3901~0.7851之间,平均为0.5374;彼此间的遗传距离最小为0.2149,最大为0.6099,平均为0.4626,并绘制出个体间亲缘关系树状聚类图。结果显示羊驼种群内遗传基础广泛,证明其个体间的血缘关系较远,这将有利于羊驼种群的正常生长、发育、繁殖和快速扩群。     

Fluctuations in the Size of Isolated Single-Species Populations and Natural Selection

This paper discusses the basic types of dynamical behavior of populations obtained in discrete models, such as monotonous dynamics, stable limited cycles, and chaotic variations. All these modes are shown to have possibly arisen in the evolution of limited populations under the effect of density-independent selection. This effect together with that of density-dependent non-selective factors has been termed F-selection, which is characterized by independence of relative fitnesses from population density, whereas populations may be ecologically limited; in other words, absolute fitnesses prove to be a function of population size. The characteristic of F-selection is to be not sensitive to changes in population size but to lead to fluctuations, that create conditions for achieving density-dependent selection.     

具有亲缘关系矩阵的混合模型的方差组分迭代估计——应用于计算BLUP的方差比值和遗传参数

论述的是来自非均街资料的混合模型中具有亲缘关系矩阵时利用迭代法估计方差组分问题。这篇文章表明计算程序是可行的,只要能够按照混合模型中固定效应的结构矩阵和Henderson方法3的固定效应的假设条件正确地计算二次型约化平方和,就可获得较为精确的方差组分估计值;而且表明方差初始比值k偏高或偏低,不影响迭代求解的最后结果,这是因为在迭代过程中可以通过结构矩阵x'x和x'x的控制而自行调整。这些方差组分不仅可应用于选种种畜用的BLUP计算,还可用来估计遗传参数。     

普通小麦三个基因组之间的遗传关系及原位杂交分析

以普通小麦（Ｔｒｉｔｉｃｕｍ ａｅｓｔｉｖｕｍＬ．）的３个可能的二倍体供体种（乌拉尔图小麦（Ｔ．ｕｒａｒｔｕＴｈｕｍ．）拟斯卑尔脱山羊草（ＡｅｇｉｌｏｐｓｓｐｅｌｔｏｉｄｅｓＴａｕｓｃｈ）和粗山羊草（Ａｅ．ｔａｕｓｃｈｉｉＣｏｓｓ．）的基因组ＤＮＡ为研究对象,通过它们之间的相互杂交,比较杂交强度以及泳道中带纹的不同,并结合部分ＤＮＡ重复序列在基因组间含量差异的数据,得出结论：Ａ＾ｕ和Ｄ基因组的关系     

Genetic Relationship and Genomic in situ Hybridization Analysis of the Three Genomes in Triticum aestivum

Common wheat ( Triticum　aestivum L.) is an allohexaploid, consisting of three different genomes (Au, B and D ) which are genetically closely related. Genomic DNA of the three possible genome donors, T. urartu Thum., Aegilops speltoides Tausch and Ae. tauschii Coss.,were employed as probes to hybridize with the diploid genomic DNA digested by Eco RⅠand Hin dⅢ respectively. Both the hybridization strength and band patterns among the genomes would be good indicators of genome relationships. Combining distr ibution data of some repetitive DNA sequences cloned from T. urartu in the three genomes, the authors draw a conclusion that Au and D are more closely related to each other than either one to the B genome. Genomic in situ hybridization (GISH) of T. aestivum cv. Chinese Spring with genomic DNA probes of the three diploid progenitors respectively indicated that the three genomes could be discriminated clearly via GISH. The signals on the chromosomes of Au and D genomes were even. However, when Ae. speltoides DNA was used as probe, there were very strong cross hybridization and the signals condensed on some areas of the metaphasic chromosomes. In the interphase nucleus, the chromatin of B genome dispersed on the same region and the signals on the homologous chromosomes distributed symmetrically. Rich repetitive DNA sequences in B genome, especially the tandem repetitives, perhaps take an important role for the formation of the special hybridization pattern. The main difference between B and the other two genomes probably is in the repetitive DNA sequences.     

Five Confidence Intervals of the Closed Population Size in the Capture‐recapture Problem under Inverse Sampling with Replacement

In the capture‐recapture problem for two independent samples, the traditional estimator, calculated as the product of the two sample sizes divided by the number of sampled subjects appearing commonly in both samples, is well known to be a biased estimator of the population size and have no finite variance under direct or binomial sampling. To alleviate these theoretical limitations, the inverse sampling, in which we continue sampling subjects in the second sample until we obtain a desired number of marked subjects who appeared in the first sample, has been proposed elsewhere. In this paper, we consider five interval estimators of the population size, including the most commonly‐used interval estimator using Wald's statistic, the interval estimator using the logarithmic transformation, the interval estimator derived from a quadratic equation developed here, the interval estimator using the χ²‐approximation, and the interval estimator based on the exact negative binomial distribution. To evaluate and compare the finite sample performance of these estimators, we employ Monte Carlo simulation to calculate the coverage probability and the standardized average length of the resulting confidence intervals in a variety of situations. To study the location of these interval estimators, we calculate the non‐coverage probability in the two tails of the confidence intervals. Finally, we briefly discuss the optimal sample size determination for a given precision to minimize the expected total cost. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reconciling Genetic and Demographic Estimators of Effective Population Size in the Anuran Amphibian Bufo Calamita

We used genetic and demographic methods to estimate the variance effective population sizes (N _e) of three populations of natterjack toads Bufo calamita in Britain. This amphibian breeds in temporary pools where survival rates can vary among families. Census population sizes (N) were derived from spawn string counts. Point and coalescent-based maximum likelihood estimates of N _e based on microsatellite allele distributions were similar. N _e/N ratios based on genetic estimates of N _e ranged between 0.02 and 0.20. Mean demographic estimates of N _e were consistently higher (2.7–8.0-fold) than genetic estimates for all three populations when variance in breeding success was evaluated at the point where females no longer influence their progeny. However, discrepancies between genetic and demographic estimators could be removed by using a model that included extra variance in survivorship (above to Poisson expectations) among families. The implications of these results for the estimation of N _e in wild populations are discussed.     

Interval Estimation of the Effective Population Size from Heterozygote‐Excess in SNP Markers

The effective population size N_e is an important parameter in population genetics and conservation biology. In recent years, there has been great interest in the use of molecular markers to estimate N_e. Although the point estimates from molecular markers in general suffer from a low reliability, the use of single nucleotide polymorphism (SNP) markers over a wide range of genome is expected to remarkably improve the reliability. In this study, expressions were derived for interval estimates of N_e from one published method, the heterozygote‐excess method, when it is applied to SNP markers. The conditional variance theory is applied to the derivation of a confidence interval for N_e under random union of gametes, monogamy and polygyny. Stochastic simulation shows that the obtained confidence interval is slightly conservative, but fairly useful for practical applications. The result is illustrated with real data on SNP markers in a pig strain.     

Analysing Population Numbers of the House Sparrow in the Netherlands With a Matrix Model and Suggestions for Conservation Measures

The House Sparrow (Passer domesticus), formerly a common bird species, has shown a rapid decline in Western Europe over recent decades. In The Netherlands, its decline is apparent from 1990 onwards. Many causes for this decline have been suggested that all decrease the vital rates, i.e. survival and reproduction, but their actual impact remains unknown. Although the House Sparrow has been dominant in The Netherlands, data on life history characteristics for this bird species are scarce: data on reproduction are non-existent, and here we first present survival estimates based on live encounters and dead recoveries of marked individuals over the period 1976–2003, 14 years before and 14 years during the decline, reported to the Dutch Ringing Centre. We show that there is an indication that both juvenile and adult survival are lower during the period of decline. Secondly, to be able to analyse the relative impact of changes in the vital rates, we formulated a general matrix model based on a range of survival values between zero and one with a step size of 0.01 (both juvenile and adult yearly survival) and a range of realistic reproduction values (one, three or five fledglings per pair per year). With the matrix model, we calculated the finite rate of population change (λ) and applied elasticity analysis. To diagnose the cause of the decline in the Dutch House Sparrow, we parameterised the model with estimates of survival values before and during the decline and present the resulting λ. With the survival estimates from the declining period, λ < 1 only if reproduction is relatively low. We discuss this result within the light of available literature data on survival in the House Sparrow. Finally, we evaluate which of the suggested causes of population decline should be reversed to mitigate the decline and how this can be achieved.     

Effect of Extra-Pair Paternity on Effective Population Size in a Reintroduced Population of the Endangered Hihi, and Potential for Behavioural Management

We collected genetic and behavioural data on hihi (Notiomysts cincta, an endangered New Zealand bird) after reintroduction to Mokoia Island to assess the effect of extrapair copulation on effective population size (N _e), and investigate the potential for increasing N _e through behavioural management. DNA fingerprinting revealed that 46% of chicks (n = 188) resulted from extra-pair paternity, and 82% of broods (n = 56) had at least one extra-pair chick. Of the extra-pair young, 34%(n = 89) were from unpaired males, and the remainder were from paired males. Variance in reproductive success (VRS) among individuals changed between years, and the relative variance among males and females depended on the sex ratio. VRS increased when measured over longer time scales, the variance in recruits being three times higher than the variance in the number of hatchlings. Extra-pair copulation increased VRS by 150% in 1 year and decreased it by 30% in another year, but this only caused a 4% decrease and 8% increase, respectively, to N _e/N. Although there is potential to manage VRS in this species through behavioural management, a more important factor is adult lifespan, which is the main correlate of lifetime reproductive success as well as the determinant of generation time. The high annual mortality rate in Mokoia hihi (females = 64%, males = 52%) has prevented the population from growing, so the key factors limiting N and N _e/N are the same.     

Inversion Polymorphisms in Populations of Drosophila Melanogaster in the South-West Islands of Japan: Comparisons with the Mainland Populations

Natural populations of D. melanogaster newly collected from the South-West Islands of Japan were examined for the frequencies of inversions, and the results, together with previous data, were compared with those of the mainland populations. The four Common cosmopolitan inversions (2Lt, 2RNS, 3LP, 3RP) were detected from most of the populations with higher frequencies. The three Rare cosmopolitan inversions (3LM, 3RC, 3RMo), three Quasi cosmopolitan inversions (2LA, 3LY, 3RK) and two new Endemic inversions were also found but with lower frequencies. Some of the South-West Island populations still maintained higher levels of inversion polymorphisms compared to the mainland populations, while others lost the polymorphisms to various degrees. The South-West Island populations were characterized by the higher frequency of In(3L)P. The ratios of In(3L)P/In(3R)P in the South-West Islands are significantly higher than those of the mainland populations, suggesting that the In(3L)P is relatively adaptive in the South-West Islands.     

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

The estimation of gametic effects via marker-assisted BLUP requires the inverse of the conditional gametic relationship matrix G. Both gametes of each animal can either be identified (distinguished) by markers or by parental origin. By example, it was shown that the conditional gametic relationship matrix is not unique but depends on the mode of gamete identification. The sum of both gametic effects of each animal – and therefore its estimated breeding value – remains however unaffected. A previously known algorithm for setting up the inverse of G was generalized in order to eliminate the dependencies between columns and rows of G. In the presence of dependencies the rank of G also depends on the mode of gamete identification. A unique transformation of estimates of QTL genotypic effects into QTL gametic effects was proven to be impossible. The properties of both modes of gamete identification in the fields of application are discussed.     

Identification of Double-stranded Genomic DNA Spanning All Chromosomes with Mutated KRAS and p53 DNA in the Serum Exosomes of Patients with Pancreatic Cancer

Exosomes are small vesicles (50–150 nm) of endocytic origin that are released by many different cell types. Exosomes in the tumor microenvironment may play a key role in facilitating cell-cell communication. Exosomes are reported to predominantly contain RNA and proteins. In this study, we investigated whether exosomes from pancreatic cancer cells and serum from patients with pancreatic ductal adenocarcinoma contain genomic DNA. Our results provide evidence that exosomes contain >10-kb fragments of double-stranded genomic DNA. Mutations in KRAS and p53 can be detected using genomic DNA from exosomes derived from pancreatic cancer cell lines and serum from patients with pancreatic cancer. In addition, using whole genome sequencing, we demonstrate that serum exosomes from patients with pancreatic cancer contain genomic DNA spanning all chromosomes. These results indicate that serum-derived exosomes can be used to determine genomic DNA mutations for cancer prediction, treatment, and therapy resistance.     

甲板甲床部分切除联合苯酚烧灼术治疗嵌甲症的临床研究

目的:探讨甲板甲床部分切除联合苯酚烧灼术治疗嵌甲症的临床疗效。方法:选择武汉市中心医院2004年10月至2013年5月收治的115例148趾拇趾嵌甲进行研究。以2004年10月至2007年12月的患者53例(67趾)作为对照组行单纯甲板甲床部分切除术治疗,2008年1月至2013年5月的患者62例(81趾)作为观察组行甲板甲床部分切除联合苯酚烧灼术治疗。对比两组患者的出血、疼痛缓解和康复时间,了解一年后患者复发情况及满意度。结果:148趾手术伤口均一期愈合,观察组病例术后出血时间、疼痛缓解时间(1.85±0.42天、13.25±2.17小时)较对照组(2.69±0.53天、21.54±2.56小时)低,但术后恢复时间(11.32±2.37天)较对照组(8.93±2.06天)长,差异均有统计学意义(P0.05),观察组和对照组的复发率及总体满意率分别为6.15%、12.5%及97.06%、91.07%,两组差异并无统计学意义(P0.05)。结论:甲板甲床部分切除联合苯酚烧灼术治疗嵌甲症与单纯甲板甲床部分切除术的疗效相当,但可显著减少患者痛苦。     

Matrix metalloproteinases regulate mesonephric cell migration in developing XY gonads which correlates with the inhibition of tissue inhibitor of metalloproteinase-3 by Sry

In the mouse, the sex determining gene Sry, on the Y chromosome, controls testis differentiation during embryogenesis. Following Sry expression, indifferent XY gonads increase their size relative to XX gonads and form cord-like structures with the adjacent mesonephros, providing XY gonad somatic cells. This mesonephric cell migration is known to depend on Sry, but the molecular mechanism of mesonephric cell migration remains unknown. In this study, it was shown that cells expressing Sry induced proliferation of mesonephric cells migrating into male gonads, and inhibited expression of the tissue inhibitor of metalloproteinases (TIMP)-3 gene, which is the endogenous inhibitor of matrix metalloproteinases (MMP). In addition, the mesonephric cell migration was blocked by a chemically synthesized inhibitor of MMP in a gonad/mesonephros organ co-culture system with enhanced green fluorescent protein transgenic embryos. The findings indicate that MMP may play a critical role in mesonephric cell migration, and the function of MMP may be regulated by a Sry-TIMP-3 cascade. These findings are an important clue for the elucidation of testicular formation in developing gonads.     

Proteomic Analysis to Examine the Role of Matrix Proteins in a Gouty Tophus from a Patient with Recurrent Gout

To examine the role of matrix proteins in the formation of gouty tophus, we analyzed the crystalline components and matrix proteins in a gouty tophus from a patient with recurrent gout. Micro-area X-ray diffraction analysis and infrared spectroscopy indicated that the tophus was composed of monosodium urate monohydrate. Proteomic analysis identified 134 proteins from the tophus as matrix proteins. Many proteins relevant to inflammation and host defense were identified, and immunoglobulin was detected in all four extracted fractions (KCl, formic acid, guanidine-HCl, and ethylenediaminetetraacetic acid) and from many spots throughout a broad molecular weight range after electrophoresis. It is thought that the process of biological defense including the immunity has occurred in the gouty tophus.