Performance of different SNP panels for parentage testing in two East Asian cattle breeds

The International Society for Animal Genetics (ISAG) proposed a panel of single nucleotide polymorphisms (SNPs) for parentage testing in cattle (a core panel of 100 SNPs and an additional list of 100 SNPs). However, markers specific to East Asian taurine cattle breeds were not included, and no information is available as to whether the ISAG panel performs adequately for these breeds. We tested ISAG's core (100 SNP) and full (200 SNP) panels on two East Asian taurine breeds: the Korean Hanwoo and the Japanese Wagyu, the latter from the Australian herd. Even though the power of exclusion was high at 0.99 for both ISAG panels, the core panel performed poorly with 3.01% false‐positive assignments in the Hanwoo population and 3.57% in the Wagyu. The full ISAG panel identified all sire–offspring relations correctly in both populations with 0.02% of relations wrongly excluded in the Hanwoo population. Based on these results, we created and tested two population‐specific marker panels: one for the Wagyu population, which showed no false‐positive assignments with either 100 or 200 SNPs, and a second panel for the Hanwoo, which still had some false‐positive assignments with 100 SNPs but no false positives using 200 SNPs. In conclusion, for parentage assignment in East Asian cattle breeds, only the full ISAG panel is adequate for parentage testing. If fewer markers should be used, it is advisable to use population‐specific markers rather than the ISAG panel.     

Single nucleotide polymorphisms for DNA typing in the domestic horse

Genetic markers are important resources for individual identification and parentage assessment. Although short tandem repeats (STRs) have been the traditional DNA marker, technological advances have led to single nucleotide polymorphisms (SNPs) becoming an attractive alternative. SNPs can be highly multiplexed and automatically scored, which allows for easier standardization and sharing among laboratories. Equine parentage is currently assessed using STRs. We obtained a publicly available SNP dataset of 729 horses representing 32 diverse breeds. A proposed set of 101 SNPs was analyzed for DNA typing suitability. The overall minor allele frequency of the panel was 0.376 (range 0.304–0.419), with per breed probability of identities ranging from 5.6 × 10^?35 to 1.86 × 10^?42. When one parent was available, exclusion probabilities ranged from 0.9998 to 0.999996, although when both parents were available, all breeds had exclusion probabilities greater than 0.9999999. A set of 388 horses from 35 breeds was genotyped to evaluate marker performance on known families. The set included 107 parent–offspring pairs and 101 full trios. No horses shared identical genotypes across all markers, indicating that the selected set was sufficient for individual identification. All pairwise comparisons were classified using ISAG rules, with one or two excluding markers considered an accepted parent–offspring pair, two or three excluding markers considered doubtful and four or more excluding markers rejecting parentage. The panel had an overall accuracy of 99.9% for identifying true parent–offspring pairs. Our developed marker set is both present on current generation SNP chips and can be highly multiplexed in standalone panels and thus is a promising resource for SNP‐based DNA typing.     

SNPs for Parentage Testing and Traceability in Globally Diverse Breeds of Sheep

DNA-based parentage determination accelerates genetic improvement in sheep by increasing pedigree accuracy. Single nucleotide polymorphism (SNP) markers can be used for determining parentage and to provide unique molecular identifiers for tracing sheep products to their source. However, the utility of a particular “parentage SNP” varies by breed depending on its minor allele frequency (MAF) and its sequence context. Our aims were to identify parentage SNPs with exceptional qualities for use in globally diverse breeds and to develop a subset for use in North American sheep. Starting with genotypes from 2,915 sheep and 74 breed groups provided by the International Sheep Genomics Consortium (ISGC), we analyzed 47,693 autosomal SNPs by multiple criteria and selected 163 with desirable properties for parentage testing. On average, each of the 163 SNPs was highly informative (MAF≥0.3) in 48±5 breed groups. Nearby polymorphisms that could otherwise confound genetic testing were identified by whole genome and Sanger sequencing of 166 sheep from 54 breed groups. A genetic test with 109 of the 163 parentage SNPs was developed for matrix-assisted laser desorption/ionization–time-of-flight mass spectrometry. The scoring rates and accuracies for these 109 SNPs were greater than 99% in a panel of North American sheep. In a blinded set of 96 families (sire, dam, and non-identical twin lambs), each parent of every lamb was identified without using the other parent’s genotype. In 74 ISGC breed groups, the median estimates for probability of a coincidental match between two animals (P_I), and the fraction of potential adults excluded from parentage (P_E) were 1.1×10(−39) and 0.999987, respectively, for the 109 SNPs combined. The availability of a well-characterized set of 163 parentage SNPs facilitates the development of high-throughput genetic technologies for implementing accurate and economical parentage testing and traceability in many of the world’s sheep breeds.     

Parentage testing of racing camels (Camelus dromedarius) using microsatellite DNA typing

The camel racing industry would have added value in being able to assign parentage with high certainty. This study was aimed at assessing and applying microsatellite multiplexes to construct a parentage testing system for camels. An efficient system of 17 loci from 700 camel samples was used to construct a database of unrelated adults. Based on this, we estimated measures of polymorphism among the markers. In three multiplex reactions, we detected a total of 224 alleles, with 5–23 alleles/locus (mean = 13.18 ± 6.95 SD) and an average heterozygosity (H_E) of 0.54 (range 0.032–0.905). The total parentage exclusion probability was 0.99999 for excluding a candidate parent from parentage of an arbitrary offspring, given only the genotype of the offspring, and 0.9999 for excluding a candidate parent from parentage of an arbitrary offspring, given the genotype of the offspring and the other parent. We used 15 juveniles for parentage testing, as well as 17 sires (bull camels) and 21 dams (cows). In the case of parentage assignment, the microsatellite panel assigned all 15 offspring parentage with high confidence. Overall, these findings offer a set of microsatellite markers that are easy, simple and highly informative for parentage testing in camels.     

The future of parentage analysis: From microsatellites to SNPs and beyond

Parentage analysis is a cornerstone of molecular ecology that has delivered fundamental insights into behaviour, ecology and evolution. Microsatellite markers have long been the king of parentage, their hypervariable nature conferring sufficient power to correctly assign offspring to parents. However, microsatellite markers have seen a sharp decline in use with the rise of next‐generation sequencing technologies, especially in the study of population genetics and local adaptation. The time is ripe to review the current state of parentage analysis and see how it stands to be affected by the emergence of next‐generation sequencing approaches. We find that single nucleotide polymorphisms (SNPs), the typical next‐generation sequencing marker, remain underutilized in parentage analysis but are gaining momentum, with 58 SNP‐based parentage analyses published thus far. Many of these papers, particularly the earlier ones, compare the power of SNPs and microsatellites in a parentage context. In virtually every case, SNPs are at least as powerful as microsatellite markers. As few as 100–500 SNPs are sufficient to resolve parentage completely in most situations. We also provide an overview of the analytical programs that are commonly used and compatible with SNP data. As the next‐generation parentage enterprise grows, a reliance on likelihood and Bayesian approaches, as opposed to strict exclusion, will become increasingly important. We discuss some of the caveats surrounding the use of next‐generation sequencing data for parentage analysis and conclude that the future is bright for this important realm of molecular ecology.     

Parentage testing in alpacas (Vicugna pacos) using semi-automated fluorescent multiplex PCRs with 10 microsatellite markers

The aim of this study was to assess and apply a microsatellite multiplex system for parentage determination in alpacas. An approach for parentage testing based on 10 microsatellites was evaluated in a population of 329 unrelated alpacas from different geographical zones in Perú. All microsatellite markers, which amplified in two multiplex reactions, were highly polymorphic with a mean of 14.5 alleles per locus (six to 28 alleles per locus) and an average expected heterozygosity ( H _E) of 0.8185 (range of 0.698–0.946). The total parentage exclusion probability was 0.999456 for excluding a candidate parent from parentage of an arbitrary offspring, given only the genotype of the offspring, and 0.999991 for excluding a candidate parent from parentage of an arbitrary offspring, given the genotype of the offspring and the other parent. In a case test of parentage assignment, the microsatellite panel assigned 38 (from 45 cases) offspring parentage to 10 sires with LOD scores ranging from 2.19 × 10⁺¹³ to 1.34 × 10⁺¹⁵ and Δ values ranging from 2.80 × 10⁺¹² to 1.34 × 10⁺¹⁵ with an estimated pedigree error rate of 15.5%. The performance of this multiplex panel of markers suggests that it will be useful in parentage testing of alpacas.     

Population structure and breed composition prediction in a multi-breed sheep population using genome-wide single nucleotide polymorphism genotypes

Knowledge of population structure and breed composition of a population can be advantageous for a number of reasons; these include designing optimal (cross)breeding strategies in order to maximise non-additive genetic effects, maintaining flockbook integrity by authenticating animals being registered and as a quality control measure in the genotyping process. The objectives of the present study were to 1) describe the population structure of 24 sheep breeds, 2) quantify the breed composition of both flockbook-recorded and crossbred animals using single nucleotide polymorphism BLUP (SNP-BLUP), and 3) quantify the accuracy of breed composition prediction from low-density genotype panels containing between 2000 and 6000 SNPs. In total, 9334 autosomal SNPs on 11 144 flockbook-recorded animals and 1172 crossbred animals were used. The population structure of all breeds was characterised by principal component analysis (PCA) as well as the pairwise breed fixation index (F_st). The total number of animals, all of which were purebred, included in the calibration population for SNP-BLUP was 2579 with the number of animals per breed ranging from 9 to 500. The remaining 9559 flockbook-recorded animals, composite breeds and crossbred animals represented the test population; three breeds were excluded from breed composition prediction. The breed composition predicted using SNP-BLUP with 9334 SNPs was considered the gold standard prediction. The pairwise breed F_st ranged from 0.040 (between the Irish Blackface and Scottish Blackface) to 0.282 (between the Border Leicester and Suffolk). Principal component analysis revealed that the Suffolk from Ireland and the Suffolk from New Zealand formed distinct, non-overlapping clusters. In contrast, the Texel from Ireland and that from New Zealand formed integrated, overlapping clusters. Composite animals such as the Belclare clustered close to its founder breeds (i.e., Finn, Galway, Lleyn and Texel). When all 9334 SNPs were used to predict breed composition, an animal that had a majority breed proportion predicted to be ≥0.90 was defined as purebred for the present study. As the panel density decreased, the predicted breed proportion threshold, used to identify animals as purebred, also decreased (≥0.85 with 6000 SNPs to ≥0.60 with 2000 SNPs). In all, results from the study suggest that breed composition for purebred and crossbred animals can be determined with SNP-BLUP using ≥5000 SNPs.     

Validation of microsatellite markers for routine horse parentage testing

A parallel testing of 4803 routine Quarter Horse parentage cases, using 15 loci of blood group and protein polymorphisms (blood typing) and 11 loci of dinucleotide repeat microsatellites (DNA typing), validated DNA markers for horse pedigree verification. For the 26 loci, taken together, the theoretical effectiveness of detecting incorrect parentage was 99·999%, making it extremely unlikely that false parentage would fail to be recognized. The tests identified incorrect parentage assignment for 95 offspring (2% of cases). Despite fewer loci, DNA typing was as effective as blood typing and, in parentage exclusion cases, provided more systems to substantiate the genetic incompatibility. Five offspring presented potential genetic incompatibilities with their parents in only a single microsatellite system, but the parentage exclusions could not be confirmed with discordant results at additional loci. Two of these five incompatibilities could be explained as consequences of a null allele and three as fragment size increases or decreases (putative mutations). Provided that an exclusion assignment was based on at least two systems of genetic incompatibility, such rare genetic events did not lead to false exclusions. Notwithstanding the near 100% effectiveness estimations for either typing panel alone to identify incorrect parentage, this validation test showed an actual effectiveness of 97·3% for blood typing and 98·2% for DNA typing. The DNA-based test, however, may feasibly achieve higher efficacy than reported here by adding selected systems to the parentage test panel.     

A novel polymorphism of the myogenin gene is associated with body measurement traits in native Chinese breeds

Using PCR-SSCP and DNA sequencing technology, we examined the association of single nucleotide polymorphisms (SNPs) in the bovine MyoG gene with body measurement traits in 779 individuals of six native Chinese cattle breeds, namely Luxi, Luxi × Simmental crossbred, Nanyang, Xia'nan, Jiaxian red, and Qinchuan. A novel SNP, T314C, was detected. Allelic frequencies of MyoG-T/C in the six breeds were 0.8308/0.1692, 0.8774/0.1226, 0.8021/0.1979, 0.8209/0.1791, 0.8630/0.1370, 0.8044/0.1956, respectively. Least squares analysis revealed a significant (P < 0.05) association of the MyoG SNP with rump length in four breeds (Luxi, Xia'nan, Jiaxian red, and Qinchuan), with hucklebone width in three breeds (Luxi × Simmental crossbred, Nanyang and Xia'nan), with waist height in two breeds (Luxi × Simmental crossbred and Nanyang) and with body length in the Luxi breed. We conclude that the MyoG SNP has potential as a genetic marker for economically relevant body measurement traits in native Chinese cattle breeds.     

Genomic differentiation between swamp and river buffalo using a cattle high-density single nucleotide polymorphisms panel

Buffalo (Bubalus bubalis) is an important livestock species in many tropical and subtropical regions. In recent decades, the interest in buffalo’s milk have expanded and intensive buffalo farms start to emerge. However, breeding programs and population genetics information for this species is scarce or inexistent. The present study aims to test the suitability of the commercial high-density single nucleotide polymorphisms (SNP) genotyping panel, the Illumina BovineHD BeadChip, to estimate population genetics parameters, pedigree control and identification of common variants in major production candidate genes. From a total of 777 962 SNPs included in the panel, 20 479 were polymorphic in water buffalo at a call rate of 86% and an average expected heterozygosity (H_E) of 0.306. From these, 357 were mapped within or around the flanking regions of several major candidate genes. A principal components analysis identified three different clusters, each representing pure swamp buffalo type, pure river buffalo type and admixed river buffalo. The hybrids between swamp and river buffalo were clearly identified as an intermediary cluster. The suitability of these SNPs data set for parentage and identity testing demonstrated that the combination of just 30 to 50 SNPs were enough to attain high probabilities of parentage exclusion (0.9999) in both types and identity (2.3×10⁻⁵ and 2.0×10⁻⁷) for river and swamp buffalo, respectively. Our analysis confirms the suitability of the BovineHD BeadChip to assess population structure, hybridization and identity of the water buffalo populations.     

The evaluation of the usefulness of pedigree verification-dedicated SNPs for breed assignment in three polish cattle populations

The breed assignment in cattle is one of the issues of molecular genetics which needs further testing and development. Although several statistical approaches have been developed to enable such application, the obtained results strongly depend on specific populations differentiation and power of markers discrimination or their informativeness. Currently, all breeding animals are being tested for parentage with the use of panel of 12 microsatellite markers, which in near future probably will be replaced by about 100 single nucleotide polymorphisms (SNPs). Despite the fact that SNPs are mainly bi-allelic, the multilocus genotypes can reach the level of polymorphism of a panel of microsatellite markers. In this study we attempted to determine the breed of origin of 741 cattle by using 120 SNPs dedicated for parentage testing and included in the BovineSNP50 BeadChip genotyping assay (Illumina). The applied Bayesian and frequency-based methods allowed such differentiation, however, the reliability of the results was not completely satisfying, suggesting that the studied markers are not the best tool for breed assignment.     

Preselection statistics and Random Forest classification identify population informative single nucleotide polymorphisms in cosmopolitan and autochthonous cattle breeds

Commercial single nucleotide polymorphism (SNP) arrays have been recently developed for several species and can be used to identify informative markers to differentiate breeds or populations for several downstream applications. To identify the most discriminating genetic markers among thousands of genotyped SNPs, a few statistical approaches have been proposed. In this work, we compared several methods of SNPs preselection (Delta, F_st and principal component analyses (PCA)) in addition to Random Forest classifications to analyse SNP data from six dairy cattle breeds, including cosmopolitan (Holstein, Brown and Simmental) and autochthonous Italian breeds raised in two different regions and subjected to limited or no breeding programmes (Cinisara, Modicana, raised only in Sicily and Reggiana, raised only in Emilia Romagna). From these classifications, two panels of 96 and 48 SNPs that contain the most discriminant SNPs were created for each preselection method. These panels were evaluated in terms of the ability to discriminate as a whole and breed-by-breed, as well as linkage disequilibrium within each panel. The obtained results showed that for the 48-SNP panel, the error rate increased mainly for autochthonous breeds, probably as a consequence of their admixed origin lower selection pressure and by ascertaining bias in the construction of the SNP chip. The 96-SNP panels were generally more able to discriminate all breeds. The panel derived by PCA-chrom (obtained by a preselection chromosome by chromosome) could identify informative SNPs that were particularly useful for the assignment of minor breeds that reached the lowest value of Out Of Bag error even in the Cinisara, whose value was quite high in all other panels. Moreover, this panel contained also the lowest number of SNPs in linkage disequilibrium. Several selected SNPs are located nearby genes affecting breed-specific phenotypic traits (coat colour and stature) or associated with production traits. In general, our results demonstrated the usefulness of Random Forest in combination to other reduction techniques to identify population informative SNPs.     

Using blocks of linked single nucleotide polymorphisms as highly polymorphic genetic markers for parentage analysis

Single nucleotide polymorphisms (SNPs) are plentiful in most genomes and amenable to high throughput genotyping, but they are not yet popular for parentage or paternity analysis. The markers are bi-allelic, so individually they contain little information about parentage, and in nonmodel organisms the process of identifying large numbers of unlinked SNPs can be daunting. We explore the possibility of using blocks of between three and 26 linked SNPs as highly polymorphic molecular markers for reconstructing male genotypes in polyandrous organisms with moderate (five offspring) to large (25 offspring) clutches of offspring. Haplotypes are inferred for each block of linked SNPs using the programs Haplore and Phase 2.1. Each multi-SNP haplotype is then treated as a separate allele, producing a highly polymorphic, 'microsatellite-like' marker. A simulation study is performed using haplotype frequencies derived from empirical data sets from Drosophila melanogaster and Mus musculus populations. We find that the markers produced are competitive with microsatellite loci in terms of single parent exclusion probabilities, particularly when using six or more linked SNPs to form a haplotype. These markers contain only modest rates of missing data and genotyping or phasing errors and thus should be seriously considered as molecular markers for parentage analysis, particularly when the study is interested in the functional significance of polymorphisms across the genome.     

Detection and characterization of SNPs useful for identity control and parentage testing in major European dairy breeds

We propose the use of single nucleotide polymorphisms (SNPs) instead of polymorphic microsatellite markers for individual identification and parentage control in cattle. To this end, we present an initial set of 37 SNP markers together with a gender-specific SNP for identity control and parentage testing in the Holstein, Fleckvieh and Braunvieh breeds. To obtain suitable SNPs, a total of 91.13 kb of random genomic DNA was screened yielding 531 SNPs. These, and 43 previously identified SNPs, were subjected to the following selection criteria: (1) the frequency of the minor allele must be larger than 0.1 in at least two of the three examined breeds, and (2) markers should not be linked closely. Allele frequencies were estimated by analysing sequencing traces of pooled DNA or by genotyping individual DNA samples. The selected SNP loci were physically mapped by radiation hybrid mapping or by fluorescence in situ hybridization, and tested against the neutral mutation hypothesis. The presented marker set theoretically allows probabilities of identity less than 10(-13) for individual verification and exclusion powers exceeding 99.99% for parentage testing.     

Development,inheritance and evaluation of 55 novel single nucleotide polymorphism markers for parentage assignment in the Pacific oyster (Crassostrea gigas)

Expressed sequence tags (ESTs) are essential to ascertain gene function, but also to identify polymorphic gene-associated single nucleotide polymorphisms (SNPs) (type I markers) suitable for map construction and population analysis in the Pacific oyster (Crassostrea gigas). In this study, a total of 48,769 putative SNPs were detected from 46,171 ESTs of the Pacific oyster. Fifty-five gene-derived SNPs were isolated and characterized by means of high resolution melting analysis. The observed and expected heterozygosities ranged from 0.063–0.563 and 0.091–0.448, with an average of 0.284 and 0.279, respectively. The SNPs were tested on 6 families of C. gigas for examination of inheritance mode of SNPs. One hundred and thirty-two tests of segregation ratios at 48 loci revealed 30 (22 %) significant departures from expected Mendelian ratios, but no null allele was detected. The power of these SNPs in parentage assignment was evaluated, and the real data demonstrated that 17 % of all real offspring were unambiguously assigned parents with 30 SNPs, and 100 % of the offspring were correctly allocated to their parents when 40 or more SNPs were used. The results obtained in this study suggest that gene-derived SNPs will complement the currently available microsatellite markers and may be useful for comparative mapping, marker-assisted selection and evolutionary studies.     

利用全基因组连锁不平衡估计中国荷斯坦牛有效群体大小

有效群体大小是群体遗传学研究的一个重要内容,有助于我们更清楚地了解群体的遗传变异、进化和复杂性状的遗传机制等。随着高密度SNP标记的出现,越来越多的研究利用SNP标记间连锁不平衡估计有效群体大小。文章采集北京地区中国荷斯坦牛2 093个样本,并利用牛SNP芯片(Illumina BovineSNP50,含5 4001 SNPs)进行基因型测定,估计不同世代中国荷斯坦牛的有效群体大小。质量控制标准设定为SNP检出率0.95,最小等位基因频率>0.05,样本检出率0.95,哈代温伯格平衡检验显著性水平P<0.0001。经过质量控制,共1 968个样本和38 796个SNPs用于连锁不平衡分析。文章选取SNP间距0.1、0.2、0.5、1、2、5、10、15(Mb),估计中国荷斯坦牛在4世代之前有效群体大小。结果表明,中国荷斯坦牛的有效群体呈逐代下降趋势,至4世代前,中国荷斯坦牛平均有效群体为45头左右。     

Estimation of genotyping error rate from repeat genotyping,unintentional recaptures and known parent–offspring comparisons in 16 microsatellite loci for brown rockfish (Sebastes auriculatus)

Genotyping errors are present in almost all genetic data and can affect biological conclusions of a study, particularly for studies based on individual identification and parentage. Many statistical approaches can incorporate genotyping errors, but usually need accurate estimates of error rates. Here, we used a new microsatellite data set developed for brown rockfish (Sebastes auriculatus) to estimate genotyping error using three approaches: (i) repeat genotyping 5% of samples, (ii) comparing unintentionally recaptured individuals and (iii) Mendelian inheritance error checking for known parent–offspring pairs. In each data set, we quantified genotyping error rate per allele due to allele drop‐out and false alleles. Genotyping error rate per locus revealed an average overall genotyping error rate by direct count of 0.3%, 1.5% and 1.7% (0.002, 0.007 and 0.008 per allele error rate) from replicate genotypes, known parent–offspring pairs and unintentionally recaptured individuals, respectively. By direct‐count error estimates, the recapture and known parent–offspring data sets revealed an error rate four times greater than estimated using repeat genotypes. There was no evidence of correlation between error rates and locus variability for all three data sets, and errors appeared to occur randomly over loci in the repeat genotypes, but not in recaptures and parent–offspring comparisons. Furthermore, there was no correlation in locus‐specific error rates between any two of the three data sets. Our data suggest that repeat genotyping may underestimate true error rates and may not estimate locus‐specific error rates accurately. We therefore suggest using methods for error estimation that correspond to the overall aim of the study (e.g. known parent–offspring comparisons in parentage studies).     

Impact of Genotype Imputation on the Performance of GBLUP and Bayesian Methods for Genomic Prediction

The aim of this study was to evaluate the impact of genotype imputation on the performance of the GBLUP and Bayesian methods for genomic prediction. A total of 10,309 Holstein bulls were genotyped on the BovineSNP50 BeadChip (50 k). Five low density single nucleotide polymorphism (SNP) panels, containing 6,177, 2,480, 1,536, 768 and 384 SNPs, were simulated from the 50 k panel. A fraction of 0%, 33% and 66% of the animals were randomly selected from the training sets to have low density genotypes which were then imputed into 50 k genotypes. A GBLUP and a Bayesian method were used to predict direct genomic values (DGV) for validation animals using imputed or their actual 50 k genotypes. Traits studied included milk yield, fat percentage, protein percentage and somatic cell score (SCS). Results showed that performance of both GBLUP and Bayesian methods was influenced by imputation errors. For traits affected by a few large QTL, the Bayesian method resulted in greater reductions of accuracy due to imputation errors than GBLUP. Including SNPs with largest effects in the low density panel substantially improved the accuracy of genomic prediction for the Bayesian method. Including genotypes imputed from the 6 k panel achieved almost the same accuracy of genomic prediction as that of using the 50 k panel even when 66% of the training population was genotyped on the 6 k panel. These results justified the application of the 6 k panel for genomic prediction. Imputations from lower density panels were more prone to errors and resulted in lower accuracy of genomic prediction. But for animals that have close relationship to the reference set, genotype imputation may still achieve a relatively high accuracy.