Bani-Fatemi A, Graff A, Zai C, Strauss J, De Luca V. 2016. GWAS analysis of suicide attempt in Schizophrenia: Main genetic effect and interaction with early life trauma. Neuroscience Letters, 622, 102–106.

Bolger M, Lohse M, Usadel B. 2014. Trimmomatic: A flexible trimmer for Illumina sequence data. Bioinformatics, 30, 2114–2120.

Borchers N, Reinsch N, Kalm E. 2004. The number of ribs and vertebrae in a Pietrain cross: variation, heritability and effects on performance traits. Joural of Animal Breeding and Genetics, 121, 392–403.

Browning L, Browning R. 2009. A unified approach to genotype imputation and haplotype-phase inference for large data sets of trios and unrelated individuals. The American Journal of Human Genetics, 84, 210–223.

Browning L, Browning R. 2016. Genotype imputation with millions of reference samples. The American Journal of Human Genetics, 98, 116–126.

Burgos C, Latorre P, Altarriba J, Carrodeguas A, Varona L, Buesa L. 2015. Allelic frequencies of NR6A1 and VRTN, two genes that affect vertebrae number in diverse pig breeds: A study of the effects of the VRTN insertion on phenotypic traits of a Duroc×Landrace-Large White cross. Meat Science, 100, 150–155.

Chang C C, Chow C C, Tellier L C, Vattikuti S, Purcell S M, Lee J J. 2015. Second-generation PLINK: Rising to the challenge of larger and richer datasets. Gigascience, 4, 7.

Chang M, He L, Cai L. 2018. An overview of genome-wide association studies. Methods Molecular Biology, 1754, 97–108.

Chen H, Wang C, Conomos M P, Stilp A M, Li Z, Sofer T, Szpiro A A, Chen W, Brehm J M, Celedón J C, Redline S, Papanicolaou G J, Thornton T A, Laurie C C, Rice K, Lin X H. 2016. Control for population structure and relatedness for binary traits in genetic association studies via logistic mixed models. The American Journal of Human Genetics, 98, 653–666.

Chen Y, Ma B, Wang X, Zha X, Sheng C, Yang P, Qu S. 2021. Potential functions of the bmp family in bone, obesity, and glucose metabolism. Journal of Diabetes Research, 2021, 6707464.

Cingolani P, Platts A, Wang le L, Coon M, Nguyen T, Wang L, Land S J, Lu X, Ruden D M. 2012. A program for annotating and predicting the effects of single nucleotide polymorphisms, SnpEff: SNPs in the genome of Drosophila melanogaster strain w1118; iso-2; iso-3. Fly, 6, 80–92.

Daetwyler H, Capitan A, Pausch H, Stothard P, van Binsbergen R, Brøndum F, Liao X, Djari A, Rodriguez S, Grohs C, Esquerré D, Bouchez O, Rossignol M, Klopp C, Rocha D, Fritz S, Eggen A, Bowman P, Coote D, Chamberlain A, et al. 2014. Whole-genome sequencing of 234 bulls facilitates mapping of monogenic and complex traits in cattle. Nature Genetics, 46, 858–865.

Davies W, Flint J, Myers S, Mott R. 2016. Rapid genotype imputation from sequence without reference panels. Nature Genetics, 48, 965–969.

Donaldson L, Lambe R, Maltin A, Knott S, Bunger L. 2013.Between-and within-breed variations of spine characteristics in sheep. Journal of Animal Science, 91, 995–1004.

Duan Y, Zhang H, Zhang Z, Gao J, Yang J, Wu Z, Fan Y, Xing Y, Li L, Xiao S, Hou Y, Ren J, Huang L. 2018. Vrtn is required for the development of thoracic vertebrae in mammals. International Journal of Biological Sciences, 14, 667–681.

Fan Y, Xing Y, Zhang Z, Ai H, Ouyang Z, Ouyang J, Yang M, Li P, Chen Y, Gao J, Li L, Huang L, Ren J. 2013. A further look at porcine chromosome 7 reveals VRTN variants associated with vertebral number in Chinese and Western pigs. PLoS ONE, 8, e62534.

Fraser R S, Lumsden J S, Lillie B N. 2018. Identification of polymorphisms in the bovine collagenous lectins and their association with infectious diseases in cattle. Immunogenetics, 70, 533–546.

Frey J L, Li Z, Ellis J M, Zhang Q, Farber C R, Aja S, Wolfgang M J, Clemens T L, Riddle R C. 2015. Wnt-Lrp5 signaling regulates fatty acid metabolism in the osteoblast. Molecular and Cellular Biology, 35, 1979–1991.

Gong Y, Slee R, Fukai N, Rawadi G, Roman-Roman S, Reginato A, Wang H, Cundy T, Glorieux F, Lev D, Zacharin M, Oexle K, Marcelino J, Suwairi W, Heeger S, Sabatakos G, Apte S, Adkins W, Allgrove J, Arslan-Kirchner M, et al. 2001. LDL receptor-related protein 5 (LRP5) affects bone accrual and eye development. Cell, 107, 513–523.

Hayes B. 2013. Overview of statistical methods for genome-wide association studies (GWAS). Methods in Molecular Biology, 1019, 149–169.

He X, Cheng R, Huang C, Takahashi Y, Yang Y, Benyajati S, Chen Y, Zhang X A, Ma J X. 2020. A novel role of LRP5 in tubulointerstitial fibrosis through activating TGF-β/Smad signaling. Signal Transduction and Targeted Therapy, 5, 45.

Hikasa H, Sokol S Y. 2013. Wnt signaling in vertebrate axis specification. Cold Spring Harbor Perspectives in Biology, 5, a007955.

Hirose K, Mikawa S, Okumura N, Noguchi G, Fukawa K, Kanaya N, Mikawa A, Arakawa A, Ito T, Hayashi Y, Tachibana F, Awata T. 2013. Association of swine vertnin (VRTN) gene with production traits in Duroc pigs improved using a closed nucleus breeding system. Journal of Animal Science, 84, 213–221.

Hsu Y H, Kiel D P. 2012. Clinical review: Genome-wide association studies of skeletal phenotypes: What we have learned and where we are headed. The Journal of Clinical Endocrinology & Metabolism, 97, E1958–E1977.

Jamdar N, Ema N. 1982. A note on the vertebral formula of the donkey. British Veterinary Journal, 138, 209–211.

Jena N, Martín-Seisdedos C, McCue P, Croce C M. 1997. BMP7 null mutation in mice: Developmental defects in skeleton, kidney, and eye. Experimental Cell Research, 230, 28–37.

Kang K S, Robling A G. 2015. New insights into Wnt-Lrp5/6-β-catenin signaling in mechanotransduction. Frontiers in Endocrinology, 5, 246.

Kato M, Patel M S, Levasseur R, Lobov I, Chang B H J, Glass D A I, Hartmann C, Li L, Hwang T H, Brayton C F, Lang R A, Karsenty G, Chan L. 2002. Cbfa 1-independent decrease in osteoblast proliferation, osteopenia, and persistent embryonic eye vascularization in mice deficient in Lrp5, a Wnt coreceptor. Journal of Cell Biology, 157, 303–314.

King B, Roberts C. 1960. Carcass length in the bacon pig; its association with vertebrae numbers and prediction from radiographs of the young pig. Animal Production, 2, 59–65.

Lavery K, Hawley S, Swain P, Rooney R, Falb D, Alaoui-Ismaili M H. 2009. New insights into BMP-7 mediated osteoblastic differentiation of primary human mesenchymal stem cells. Bone, 45, 27–41.

Levasseur R, Kato M, Patel M S, Chan L, Karsenty G. 2001. Low bone mass, low body weight and abnormal eye vascularization in mice deficient in Lrp5, the gene mutated in human osteoporosis pseudoglioma syndrome (OPS). Journal of Bone and Mineral Research, 16, S152.

Levasseur R, Lacombe D, de Vernejoul M C. 2005. LRP5 mutations in osteoporosis-pseudoglioma syndrome and high-bone-mass disorders. Joint Bone Spine, 72, 207–214.

Li C, Li M, Li X, Ni W, Xu Y, Yao R, Wei B, Zhang M, Li H, Zhao Y, Liu L, Ullah Y, Jiang Y, Hu S. 2019. Whole-genome resequencing reveals loci associated with thoracic vertebrae number in sheep. Frontier Genetics, 10, 674.

Li H, Durbin R. 2009. Fast and accurate short read alignment with Burrows-Wheeler transform. Bioinformatics, 25, 1754–1760.

Li H, Handsaker B, Wysoker A, Fennell T, Ruan J, Homer N, Marth G, Abecasis G, Durbin R, 1000 Genome Project Data Processing Subgroup. 2009. The sequence alignment/Map format and SAMtools. Bioinformatics, 25, 2078–2079.

Lin J, Zheng Z, Liu J, Yang G, Leng L, Wang H, Qiu G, Wu Z. 2021. Lrp5-mediated lipid uptake modulates osteogenic differentiation of bone marrow mesenchymal stromal cells. Frontiers in Cell and Developmental Biology, 9, 766815.

Little R, Carulli J, Del Mastro R, Dupuis J, Osborne M, Folz C, Manning S, Swain P, Zhao S, Eustace B, Lappe M, Spitzer L, Zweier S, Braunschweiger K, Benchekroun Y, Hu X, Adair R, Chee L, FitzGerald M, Tulig C, et al. 2002. A mutation in the LDL receptor-related protein 5 gene results in the autosomal dominant high-bone-mass trait. The American Journal of Human Genetics, 70, 11–19.

Liu S, Huang S, Chen F, Zhao L, Yuan Y, Francis S S, Fang L, Li Z, Lin L, Liu R, Zhang Y, Xu H, Li S, Zhou Y, Davies R W, Liu Q, Walters R G, Lin K, Ju J, Korneliussen T, et al. 2018. Genomic analyses from non-invasive prenatal testing reveal genetic associations, patterns of viral infections, and Chinese population history. Cell, 175, 347–359.

Liu Z, Gao Q, Wang T, Chai W, Zhan Y, Akhtar F, Zhang Z, Li Y, Shi X, Wang C. 2022. Multi-thoracolumbar variations and NR6A1 gene polymorphisms potentially associated with body size and carcass traits of Dezhou donkey. Animals, 12, 1349.

Lyons K M, Hogan B L, Robertson E J. 1995. Colocalization of BMP7 and BMP2 RNAs suggests that these factors cooperatively mediate tissue interactions during murine development. Mechanisms of Development, 50, 71–83.

Mikawa S, Morozumi T, Shimanuki S, Hayashi T, Uenishi H, Domukai M, Okumura N, Awata T. 2007. Fine mapping of a swine quantitative trait locus for number of vertebrae and analysis of an orphan nuclear receptor, germ cell nuclear factor (NR6A1). Genome Research, 17, 586–593.

Mikawa S, Sato S, Nii M, Morozumi T, Yoshioka G, Imaeda N, Yamaguchi T, Hayashi T, Awata T. 2011. Identification of a second gene associated with variation in vertebral number in domestic pigs. BMC Genetics, 12, 5.

Nicod J, Davies R, Cai N, Hassett C, Goodstadt L, Cosgrove C, Yee B, Lionikaite V, McIntyre R, Remme C, Lodder E, Gregory J, Hough T, Joynson R, Phelps H, Nell B, Rowe C, Wood J, Walling A, Bopp N. 2016. Genome-wide association of multiple complex traits in outbred mice by ultra-low-coverage sequencing. Nature Genetics, 48, 912–918.

Niu N, Wang H, Shi G, Liu X, Liu H, Liu Q, Yang M, Wang L, Zhang L. 2021. Genome scanning reveals novel candidate genes for vertebral and teat number in the Beijing Black pig. Animal Genetics, 52, 734–738.

Okonechnikov K, Conesa A, García-Alcalde F. 2016. Qualimap 2: Advanced multi-sample quality control for high-throughput sequencing data. Bioinformatics, 32, 292–294.

Parr B A, Mcmahon A P. 1995. Dorsalizing signal Wnt-7a required for normal polarity of D-V and A-P axes of mouse limb. Nature, 374, 350–353.

Price L, Patterson J, Plenge M, Weinblatt E, Shadick A, Reich D. 2006. Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics, 38, 904–909.

Rohrer G A, Nonneman D J, Wiedmann R T, Schneider J F. 2015. A study of vertebra number in pigs confirms the association of vertnin and reveals additional QTL. BMC Genetics, 16, 129.

Sisson S, Grossman J. 1953. The Anatomy of Domestic Animals. 4th ed. W.B.Saunders, Philadelphia. p. 28.

Stecher R M. 1962. Anatomical variations of the spine in the horse. Journal of Mammalogy, 43, 205–219.

Stock K, Reents R. 2013. Genomic selection: Status in different species and challenges for breeding. Reproduction in Domestic Animals, 48, 2–10.

Teng J, Zhao C, Wang D, Chen Z, Tang H, Li J, Mei C, Yang Z, Ning C, Zhang Q. 2022. Assessment of the performance of different imputation methods for low-coverage sequencing in Holstein cattle. Journal of Dairy Science, 105, 3355–3366.

VanRaden P M. 2008. Efficient methods to compute genomic predictions. Journal of Dairy Science, 91, 4414–4423.

Wang C, Li H, Guo Y, Huang J, Sun Y, Min J, Wang J, Fang X, Zhao Z, Wang S, Zhang Y, Liu Q, Jiang Q, Wang X, Guo Y, Yang C, Wang Y, Tian F, Zhuang G, Fan Y, et al. 2020. Donkey genomes provide new insights into domestication and selection for coat color. Nature Communications, 11, 6014.

Wang Y, Venkatesh A, Xu J, Xu M, Williams J, Smallwood P M, James A, Nathans J. 2022. The WNT7A/WNT7B/GPR124/RECK signaling module plays an essential role in mammalian limb development. Development, 149, dev200340.

Xu G, Ding Z, Shi H. 2019. The mechanism of miR-889 regulates osteogenesis in human bone marrow mesenchymal stem cells. Journal of Orthopaedic Surgery Research, 14, 366.

Xu G Y, Qiu Y, Mao H J. 2014. Common polymorphism in the LRP5 gene may increase the risk of bone fracture and osteoporosis. Biomed Research International, 2014, 290531.

Yadav V K, Arantes H P, Barros E R, Lazaretti-Castro M, Ducy P. 2010. Genetic analysis of Lrp5 function in osteoblast progenitors. Calcified Tissue International, 86, 382–388.

Yang J, Wen Y, Yong L, Feng Z, Ke M, Gao X, An D. 2015. Correlation analysis for beef performance and multi-vertebra properties of Jinchuan yak. Journal of Domestic Animal Ecology, 36, 26–30. (in Chinese)

Yang L, Li Q, Zhang J, Li P, An P, Wang C, Hu P, Zou X, Dou X, Zhu L. 2021. WNT7A promotes the osteogenic differentiation of human mesenchymal stem cells. International Journal of Molecular Medicine, 47, 94.

Yang R, Guo X, Zhu D, Tan C, Bian C, Ren J, Huang Z, Zhao Y, Cai G, Liu D, Wu Z, Wang Y, Li N, Hu X. 2021. Accelerated deciphering of the genetic architecture of agricultural economic traits in pigs using a low-coverage whole-genome sequencing strategy. GigaScience, 10, giab048.

Zhang L C, Yue J W, Pu L, Wang L G, Liu X, Liang J, Yan H, Zhao K B, Li N, Shi H B, Zhang Y B, Wang L X. 2016. Genome-wide study refines the quantitative trait locus for number of ribs in a Large White×Minzhu intercross pig population and reveals a new candidate gene. Molecular Genetics and Genomics, 291, 1885–1890.

Zhang W, Li W, Liu G, Gu L, Ye K, Zhang Y, Li W, Jiang D, Wang Z, Fang M. 2021. Evaluation for the effect of low coverage sequencing on genomic selection in large yellow croaker. Aquaculture, 534, 736323.

Zhou X, Stephens M. 2012. Genome-wide efficient mixed-model analysis for association studies. Nature Genetics, 44, 821–824.

Zimmerli D, Borrelli C, Jauregi-Miguel A, Söderholm S, Brütsch S, Doumpas N, Reichmuth J, Murphy-Seiler F, Aguet M, Basler K, Moor A E, Cantù C. 2020. TBX3 acts as tissue-specific component of the Wnt/β-catenin transcriptional complex. eLife, 9, e58123.