Multilocus tetrasomic linkage analysis using hidden Markov chain model

Abstract

The availability of reliable genetic linkage maps is crucial for functional and evolutionary genomic analyses. Established theory and methods of genetic linkage analysis have made map construction a routine exercise in diploids. However, many evolutionarily, ecologically, and/or agronomically important species are autopolyploids, with autotetraploidy being a typical example. These species undergo much more complicated chromosomal segregation and recombination at meiosis than diploids. In addition, there is evidence of polyploidy-induced and highly dynamic changes in the structure of the genome. These polysomic characteristics indicate the inappropriateness of the theory and methods of linkage analysis in diploids for use in these species and a gap in the theory and methodology of tetraploid map construction. This paper presents a theoretical model and statistical framework for multilocus linkage analysis in autotetraploids for use with dominant and/or codominant DNA molecular markers. The theory and methods incorporate the essential features of allele segregation and recombination under tetrasomic inheritance and the major challenges in statistical modeling and marker data analysis. We validated the method and explored its statistical properties by intensive simulation study and demonstrated its utility by analysis of AFLP and SSR marker data from an outbred autotetraploid potato population.autotetraploid species | tetrasomic inheritance | outbred populations | map construction P olyploidization, the simultaneous duplication of all genes in a genome, has been ubiquitous in plant evolutionary history, with ≈70% of angiosperms being polyploids (1). Allopolyploids display disomic inheritance and their genetic analysis follows the same principles as diploids, whereas autopolyploids display more complicated polysomic inheritance. Among autopolyploids exist important autotetraploids including agricultural crops, notably cultivated potato, and aquaculture animals such as Atlantic salmon and trout, for which active genome projects are underway. These projects will generate abundant genetic polymorphisms and, thus, enable construction of genetic maps, which are essential for dissecting quantitative trait loci (QTL) and, in turn, for improving efficiency of breeding programs through marker assisted selection.Genetic linkage maps exist or are becoming rapidly available in almost all important diploid animal and plant species and humans, providing an essential starting point for an insightful genomic investigation. In sharp contrast, progress in autopolyploid linkage analysis, the theoretical kernel for map construction, lags far behind. In autopolyploids, multivalent meiotic pairing of homologous chromosomes, followed by crossing over between the locus and spindle attachment, may cause double reduction, in which sister chromatids enter into the same gamete (2). Recombination frequency between a pair of loci can be as high as 0.75 under a tetrasomic model (compared to 0.5 in diploids), and double reduction can occur at a fr...

Probabilistic Multilocus Haplotype Reconstruction in Outcrossing Tetraploids

“…Remarkably, our nonmechanistic model produces very good estimations of double reduction (Figure 3), indicating that the marker data (200 offspring and 75 markers within the linkage group) provide enough information on double reduction. Also, the accurate estimation may be due to the equivalence between the transition probability matrix of gamete genotypes in our model and that derived by Leach et al (2010) based on the 136 two-locus gamete genotypes, although the transition in our model refers to the 16 phased (ordered) genotypes from one locus to the next, instead of the 10 unphased genotypes in Leach et al (2010).…”

“…Fisher (1947) proposed a conceptual twolocus tetrasomic model where all 136 gamete genotypes are classified into 11 modes of gamete formation according to the occurrence of double-reduction and recombination events between two loci. Luo et al (2004) established a deterministic relationship between the coefficient of double reduction at two linked loci and the recombination fraction between them, which subsequently has been applied to two-and multilocus linkage analysis (Luo et al 2006;Leach et al 2010).…”

“…In contrast to Leach et al (2010), we have built a simpler model of quadrivalent pairing, assuming that the ancestral origins along a chromosome follow a time-homogeneous Markov chain independently between two homologous (homeologous) chromosomes of a diploid gamete. Remarkably, our nonmechanistic model produces very good estimations of double reduction (Figure 3), indicating that the marker data (200 offspring and 75 markers within the linkage group) provide enough information on double reduction.…”

“…Hackett et al (2013) developed a similar HMM, except that their model assumes bivalent pairing and does not account for quadrivalent pairing. Leach et al (2010) developed multilocus autotetrasomic linkage analysis using a HMM for traditional AFLP and SSR marker data conditional on marker ordering and parental linkage phases; their method accounts for a mixture of random bivalent and quadrivalent pairing, and it also may be used for ancestral inference in autotetraploids.We assume a given genetic linkage map, i.e., the ordering of SNP markers and the intermarker genetic distances, that may be constructed from two-locus linkage analysis (Luo et al 2001(Luo et al , 2006Hackett et al 2013). Specifically, for each linkage group, the two-locus analysis produces the recombination fraction and the LOD score for all pairs of markers, which can be used to construct the map using, e.g., the least-squares procedure implemented in JoinMap software (Stam 1993).…”

“…Hackett et al (2013) developed a similar HMM, except that their model assumes bivalent pairing and does not account for quadrivalent pairing. Leach et al (2010) developed multilocus autotetrasomic linkage analysis using a HMM for traditional AFLP and SSR marker data conditional on marker ordering and parental linkage phases; their method accounts for a mixture of random bivalent and quadrivalent pairing, and it also may be used for ancestral inference in autotetraploids.…”