A statistical model for QTL mapping in polysomic autotetraploids underlying double reduction

Abstract

As a group of economically important species, linkage mapping of polysomic autotetraploids, including potato, sugarcane and rose, is difficult to conduct due to their unique meiotic property of double reduction that allows sister chromatids to enter into the same gamete. We describe and assess a statistical model for mapping quantitative trait loci (QTLs) in polysomic autotetraploids. The model incorporates double reduction, built in the mixture model-based framework and implemented with the expectation-maximization algorithm. It allows the simultaneous estimation of QTL positions, QTL effects and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We performed computer simulation to examine the statistical properties of the method and validate its use through analyzing real data in tetraploid switchgrass.

Genetic mapping in polyploids

“…Double reduction has been known about for almost a century and theories of how it should be modelled have been considered by some of the early pioneers of statistical genetics (Haldane, 1930;Mather, 1935;Fisher, 1947). It is quite common nowadays for authors to assert that double reduction is required for a complete and accurate description of autopolyploid inheritance (and by extension, that it be ignored at great peril) (Luo et al, 2004;Wu et al, 2004;Wu and Ma, 2005;Li et al, 2010;Lu et al, 2012;Xu et al, 2013). On the other hand, a number of recent reviews of allo-and autopolyploid meiosis completely fail to mention it Lloyd and Bomblies, 2016).…”

“…Previous studies have attempted to incorporate double reduction in their QTL models without providing sufficient motivation for such models apart from the completeness of their model (Xie and Xu, 2000;Li et al, 2010;Xu et al, 2013). As demonstrated here and elsewhere Zheng et al, 2016), estimation of the rates of double reduction per parental chromosome as well as the frequency of multivalent pairing are now relatively straightforward given modern high-density marker datasets.…”

“…In that sense the bias is positional, but unlike true segregation distortion that may be associated with alleles or allelic combinations of a particular locus, DR is combinatorically a random process which occurs with equal frequency on all homologues. As mentioned in Chapter 1, some authors like to emphasise the importance of including DR in their models for completeness (often castigating those who do not), but so far all have failed to substantiate these claims with actual data (Luo et al, 2004;Wu et al, 2004;Wu and Ma, 2005;Luo et al, 2006;Li et al, 2010;Lu et al, 2012;Xu et al, 2013).…”

“…More complete models of polysomic inheritance that include double reduction are often developed under the assumption of completely-informative marker systems (e.g. (Xie and Xu, 2000;Li et al, 2010;Xu et al, 2013)), thereby avoiding the statistical complexities imposed by partially-informative markers (such as dosage-scored SNP markers). In fact, it is quite telling that the only publically-available tools for QTL analysis in autopolyploids have adopted the simplifying assumption of random bivalent pairing (e.g.…”

High-resolution Linkage Map with Allele Dosage Allows the Identification of an Apomixis Region and Complex Traits in Guinea Grass (Megathyrsus maximus)

“…For example, an autotetraploid genotype with the 'abcd' alleles at a locus that can form six expected combinations of gametes, namely, 'ab', 'ac', 'ad', 'bc', 'bd', and 'cd', but a homozygous gamete can be generated, e.g., 'aa', 'bb', 'cc', or 'dd' (Haldane, 1930;Mather, 1935;Haynes and Douches, 1993). How to accommodate DR and its implications in a breeding program as well as the use of these marker loci in linkage mapping has been discussed for a long time (Butruille and Boiteux, 2000;Luo et al, 2000;Xu et al, 2013;Layman and Busch, 2018;Bourke et al, 2019) for some economically important species, such as potato (Bradshaw, 2007;Bourke et al, 2015) and alfalfa (Julier et al, 2003), but has not yet been reported in guinea grass.…”