Genotypic frequencies at equilibrium for polysomic inheritance under double-reduction

Abstract

5Polyploids are organisms whose genomes consist of more than two complete sets 6 of chromosomes. Both autopolyploids and allopolyploids may display polysomic 7 inheritance. A peculiarity of polysomic inheritance is multivalent formation during 8 meiosis resulting in double-reduction, which occurs when sister chromatid fragments 9 are segregated into the same gamete. Double-reduction can result in gametes carry-10 ing identical-by-descent alleles and slightly increasing homozygosity. This will cause 11 the genotypic frequencies to deviate from expected values and will thus bias the re-12 sults of standard population genetic analytical methods used in molecular ecology 13 and selective breeding. In this study, we extend existing double-reduction models to 14 account for any even level of ploidy, and derive the symbolic expressions for geno-15 typic frequencies via two methods. Inbreeding coefficients and heterozygosity under 16 double-reduction and inbreeding are also calculated. Numerical solutions obtained 17 by computer simulations are compared with analytical solutions predicted by the 18 model to validate the model.19 20 ing coefficient, heterozygosity.21 3Polyploids are organisms whose genomes consist of more than two complete sets of chromosomes 23 (Madlung, 2013). They represent a significant proportion of plant species, with 30-80% of angiosperm 24 species showing polyploidy (Burow et al., 2001) and most lineages showing evidence of paleoploidy (Otto, 25 2007). Polyploid plants can arise spontaneously in nature by several mechanisms, including meiotic or 26 mitotic failures, and fusion of unreduced gametes (Comai, 2005). 27 There are two distinct mechanisms of genome duplication that result in polyploidy: allopolyploidy 28 and autopolyploidy. Autopolyploids are usually thought to arise within a species by the doubling of 29 structurally similar homologous genomes, whereas allopolyploids arise via interspecific hybridization and 30 subsequent doubling of non-homologous genomes (Parisod et al., 2010). Both autopolyploids and al-31 lopolyploids can be found among both wild and domesticated plant species. Although rare, polyploidy is 32 also found in a few species of vertebrates such as some salmonid fish (Limborg et al., 2017), the weather 33 loach (Misgurnus anguillicaudatus) (Zhou et al., 2016), the common carp (Cyprinus carpio) (David et al., 34 2003), and the African clawed frog (Xenopus laevis) (Session et al., 2016). 35In autopolyploids, more than two homologous chromosomes can pair at meiosis, resulting in the 36 formation of multivalents and polysomic inheritance (Rieger et al., 1968). A peculiarity of polysomic 37 inheritance is the possibility that a gamete inherits a single gene copy twice, termed double-reduction 38 (Butruille and Boiteux, 2000). For example, an autotetraploid individual produces a gamete . 39 In prophase I, crossovers can happen between the locus and the centromere, resulting in an exchange 40 of chromatid fragments between pairing chromosomes. In a multivalent configuration, the...

Performing Parentage Analysis for Polysomic Inheritances Based on Allelic Phenotypes

“…For the genotypic data, the likelihood formulas for all three categories in a parentage analysis, under either self-fertilization or not, are given in Appendix B. For polysomic inheritance, the genotypic frequencies (Pr( )) and transitional probabilities ( ( | ) and ( | , )) need to be properly adjusted, where the formula of Pr( ) under inbreeding and double-reduction is given in Appendix C (or in Huang et al (2019)), and the formulas of ( | ) and ( | , ) are given in Appendix D.…”

“…In order to evaluate these methods, we create some theoretical monoecious populations, each consisting only of individuals with disomic to decasomic inheritance for the genotypic data or disomic to hexasomic inheritance for the phenotypic data. We assumed that the population under scrutiny is genotyped at unlinked loci under the PES model (Huang et al, 2019). The number of loci is set from three to 12 (genotypes) or three to 18 (phenotypes) at an interval of three.…”

“…50% bivalent and 50% multivalent gamete formation, regardless of how complex the nature of meiosis, identical-by-double-reduction (IBDR) alleles will be present in the resulting fertile gametes (Huang et al, 2019). For this reason, a generalized model was proposed, which uses ⌊ /4⌋ double-reduction rates in the calculation of genotypic frequencies and is able to describe meiosis patterns including that for intermediate inheritance (Huang et al, 2019). However, this model is too complex because it has ⌊ /4⌋ more degrees of freedom than the RCS (PRCS or CES) model.…”

“…Several models for polysomic inheritance have been developed, such as double-reduction models (Muller, 1914;Haldane, 1930;Mather, 1935), genotypic frequencies (Fisher, 1943;Geiringer, 1949), and transitional probabilities from a zygote to a gamete (Fisher and Mather, 1943;Field et al, 2017). On the basis of these findings, Huang et al (2019) derived the generalized genotypic frequency and gamete frequency for ploidy levels fewer than 12 and derived the generalized transitional probability from a zygote to a gamete for any ploidy level. These models provide a foundation on which to establish a method of parentage analysis for polyploids.…”

“…Double-reduction arises from a combination of three major events during meiosis: (i) the crossing-over between non-sister chromatids, (ii) an appropriate pattern of disjunction, and (iii) the migration of chromosomal segments carrying a pair of sister chromatids to the same gamete (Darlington, 1929;Haldane, 1930). Geneticists have developed several mathematical models to simulate double-reduction: these are the random chromosome segregation (RCS) model (Muller, 1914), the pure random chromatid segregation (PRCS) model (Haldane, 1930), the complete equational segregation (CES) model (Mather, 1935) and the partial equational segregation (PES) model (Huang et al, 2019). A brief description of each of these models is given in Appendix A.…”