Multivalent tetraploids that include many plant species, such as potato, sugarcane, and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in multivalent tetraploids is challenged by their unique cytogenetic properties, such as double reduction. We develop a statistical method for mapping multivalent tetraploid QTLs by considering these cytogenetic properties. This method is built in the mixture model-based framework and implemented with the EM algorithm. The method allows the simultaneous estimation of QTL positions, QTL effects, the chromosomal pairing factor, and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We used simulated data to examine the statistical properties of the method and validate its utilization. The new method and its software will provide a useful tool for QTL mapping in multivalent tetraploids that undergo double reduction. 1. Introduction Genetic analysis in polyploids has received considerable interest in recent years because of the biological and economic importance [1–3]. Genetic linkage maps constructed from molecular markers have been published for several major polyploids [4–10]. Statistical models for linkage analysis and map construction that consider unique biological properties of polyploids have been developed [11–14]. For bivalent polyploids, Wu et al. [15, 16] incorporated the so-called chromosomal pairing preference [17] into the linkage analysis framework, to increase the biological relevance of linkage mapping models. There have been several statistical models developed to map quantitative trait loci (QTLs) in bivalent polyploids [18, 19]. There is also a group of polyploids, called multivalent polyploids, in which chromosomes pair among more than two homologous copies at meiosis, rather than only two copies as like in bivalent polyploids. The origin of multivalent polyploids is mostly from the duplication of similar genomes and, for this reason, they are called autopolyploids [20, 21]. The consequence of multivalent pairing in autopolyploids is the occurrence of double reduction, that is, two sister chromatids of a chromosome sort into the same gamete [22]. Fisher [23] proposed a conceptual model for characterizing the individual probabilities of 11 different modes of gamete formation for a quadrivalent polyploid in terms of the recombination fraction between two different loci and their double reductions. Wu et al. [24] used Fisher's model to derive the EM algorithm for the
References
[1]
P. S. Soltis and D. E. Soltis, “The role of genetic and genomic attributes in the success of polyploids,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 13, pp. 7051–7057, 2000.
[2]
J. G. Robins, D. Luth, T. A. Campbell et al., “Genetic mapping of biomass production in tetraploid alfalfa,” Crop Science, vol. 47, no. 1, pp. 1–10, 2007.
[3]
M. Stift, C. Berenos, P. Kuperus, and P. H. Van Tienderen, “Segregation models for disomic, tetrasomic and intermediate inheritance in tetraploids: a general procedure applied to rorippa (yellow cress) microsatellite data,” Genetics, vol. 179, no. 4, pp. 2113–2123, 2008.
[4]
J. A. G. da Silva, M. E. Sorrells, W. L. Burnquist, and S. D. Tanksley, “RFLP linkage map and genome analysis of Saccharum spontaneum,” Genome, vol. 36, no. 4, pp. 782–791, 1993.
[5]
R. Ming, S. C. Liu, Y. R. Lin et al., “Detailed alignment of Saccharum and Sorghum chromosomes: comparative organization of closely related diploid and polyploid genomes,” Genetics, vol. 150, no. 4, pp. 1663–1682, 1998.
[6]
R. Ming, S. C. Liu, J. E. Irvine, et al., “Comparative QTL analysis in a complex autopolyploid: candidate genes for determinants of sugar content in sugarcane,” Genome Research, vol. 11, pp. 2075–2084, 2001.
[7]
R. C. Meyer, D. Milbourne, C. A. Hackett, J. E. Bradshaw, J. W. McNichol, and R. Waugh, “Linkage analysis in tetraploid potato and association of markers with quantitative resistance to late blight (Phytophthora infestans),” Molecular and General Genetics, vol. 259, no. 2, pp. 150–160, 1998.
[8]
D. J. Brouwer and T. C. Osborn, “A molecular marker linkage map of tetraploid alfalfa (Medicago sativa L.),” Theoretical and Applied Genetics, vol. 99, no. 7-8, pp. 1194–1200, 1999.
[9]
Z. W. Luo, C. A. Hackett, J. E. Bradshaw, J. W. McNicol, and D. Milbourne, “Construction of a genetic linkage map in tetraploid species using molecular markers,” Genetics, vol. 157, no. 3, pp. 1369–1385, 2001.
[10]
B. Julier, S. Flajoulot, P. Barre et al., “Construction of two genetic linkage maps in cultivated tetraploid alfalfa (Medicago sativa) using microsatellite and AFLP markers,” BMC Plant Biology, vol. 3, article 9, 2003.
[11]
C. A. Hackett, J. E. Bradshaw, R. C. Meyer, J. W. McNicol, D. Milbourne, and R. Waugh, “Linkage analysis in tetraploid species: a simulation study,” Genetical Research, vol. 71, no. 2, pp. 143–154, 1998.
[12]
M. I. Ripol, G. A. Churchill, J. A. G. da Silva, and M. Sorrells, “Statistical aspects of genetic mapping in autopolyploids,” Gene, vol. 235, no. 1-2, pp. 31–41, 1999.
[13]
Z. W. Luo, R. M. Zhang, and M. J. Kearsey, “Theoretical basis for genetic linkage analysis in autotetraploid species,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 18, pp. 7040–7045, 2004.
[14]
Z. W. Luo, ZE. Zhang, L. Leach, R. M. Zhang, J. E. Bradshaw, and M. J. Kearsey, “Constructing genetic linkage maps under a tetrasomic model,” Genetics, vol. 172, no. 4, pp. 2635–2645, 2006.
[15]
R. Wu, C. X. Ma, and G. Casella, “A bivalent polyploid model for linkage analysis in outcrossing tetraploids,” Theoretical Population Biology, vol. 62, no. 2, pp. 129–151, 2002.
[16]
R. Wu, C. X. Ma, and G. Casella, “A mixed polyploid model for linkage analysis in outcrossing tetraploids using a pseudo-test backcross design,” Journal of Computational Biology, vol. 11, no. 4, pp. 562–580, 2004.
[17]
J. Sybenga, “Preferential pairing estimates from multivalent frequencies in tetraploids,” Genome, vol. 37, no. 6, pp. 1045–1055, 1994.
[18]
C. X. Ma, G. Casella, Z. J. Shen, T. C. Osborn, and R. Wu, “A unified framework for mapping quantitative trait loci in bivalent tetraoploids using single-dose restriction fragments: a case study from alfalfa,” Genome Research, vol. 12, no. 12, pp. 1974–1981, 2002.
[19]
R. Wu, C. X. Ma, and G. Casella, “A bivalent polyploid model for mapping quantitative trait loci in outcrossing tetraploids,” Genetics, vol. 166, no. 1, pp. 581–595, 2004.
[20]
J. D. Bever and F. Felber, “The theoretical population genetics of autopolyploidy,” Oxford Surveys in Evolutionary Biology, vol. 8, pp. 185–217, 1992.
[21]
D. V. Butruille and L. S. Boiteux, “Selection-mutation balance in polysomic tetraploids: impact of double reduction and gametophytic selection on the frequency and subchromosomal localization of deleterious mutations,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 12, pp. 6608–6613, 2000.
[22]
C. D. Darlington, “Chromosome behaviour and structural hybridity in the Tradescantiae,” Journal of Genetics, vol. 21, no. 2, pp. 207–286, 1929.
[23]
R. A. Fisher, “The theory of linkage in polysomic inheritance,” Philosophical Transactions of the Royal Society B, vol. 233, pp. 55–87, 1947.
[24]
S. S. Wu, R. Wu, C. X. Ma, Z. B. Zeng, M. C. K. Yang, and G. Casella, “A multivalent pairing model of linkage analysis in autotetraploids,” Genetics, vol. 159, no. 3, pp. 1339–1350, 2001.
[25]
R. Wu and C. X. Ma, “A general framework for statistical linkage analysis in multivalent tetraploids,” Genetics, vol. 170, no. 2, pp. 899–907, 2005.
[26]
C. A. Hackett, J. E. Bradshaw, and J. W. McNicol, “Interval mapping of quantitative trait loci in autotetraploid species,” Genetics, vol. 159, no. 4, pp. 1819–1832, 2001.
[27]
D. Cao, B. A. Craig, and R. W. Doerge, “A model selection-based interval-mapping method for autopolyploids,” Genetics, vol. 169, no. 4, pp. 2371–2382, 2005.
[28]
K. G. Haynes and D. S. Douches, “Estimation of the coefficient of double reduction in the cultivated tetraploid potato,” Theoretical and Applied Genetics, vol. 85, no. 6-7, pp. 857–862, 1993.
[29]
R. Wu, M. Gallo-Meagher, R. C. Littell, and Z. B. Zeng, “A general polyploid model for analyzing gene segregation in outcrossing tetraploid species,” Genetics, vol. 159, no. 2, pp. 869–882, 2001.
[30]
E. S. Lander and S. Botstein, “Mapping mendelian factors underlying quantitative traits using RFLP linkage maps,” Genetics, vol. 121, no. 1, pp. 185–199, 1989.
[31]
D. Cao, T. C. Osborn, and R. W. Doerge, “Correct estimation of preferential chromosome pairing in autotetraploids,” Genome Research, vol. 14, no. 3, pp. 459–462, 2004.
