## Satellite Symposium 5: Molecular Breeding

#### Description

Polyploidy plays an important role in the evolution of species and many cultivated species, particularly in angiosperms, are polyploids (Bever and Felber, 1992; Gallais, 2003). Autopolyploid species that show a tetrasomic inheritance have complex genetics. However, some theoretical models were built for: (1) genetic mapping (Hackett* et al*., 1998), (2) quantitative genetics (Gallais, 2003) and (3) population genetics (Ronfort* et al*., 1998). But in practice, most data analyses ignore one essential feature of tetrasomic inheritance that is double-reduction. Indeed, in an autotetraploid species, homologous chromosomes can form tetravalents at meiosis. In this case, a double-reduction is observed if crossing-over occurs between a locus and its centromere, and if the sister chromatids migrate to the same pole at anaphase I. The gametes may, thus, carry a pair of sister alleles. Double-reduction frequency is represented by the index of separation (α) (Demarly, 1963; Mather, 1935; Mather, 1936). The parameter α is considered as a product of four probabilities: α = q e a s (Gallais, 2003) in which “ q ” is the probability of multivalent formation, “ e ” the probability of first equational division, related to the frequency of crossing-over, “ a ” is the probability of non-disjunction at first anaphase and “s” is the probability of having two sister chromatids in the same gamete. If separation during anaphase II is random, s = ½. Consequently, α will be low for a gene located in the vicinity of the centromere and will increase with distance between the gene and the centromere. It was demonstrated that double-reduction events alter the rate of progression towards equilibrium under inbreeding or under random mating, modify the recombination rate between loci and also alter the rate of decay of linkage disequilibrium under random mating (Bever and Felber, 1992). Current theoretical models allow drawing genetic maps taking into account double-reduction (Luo *et al*., 2004). Thus, it is possible to estimate α for codominant loci in tetraploid species. To date, we have few estimates of the double-reduction frequency. Haynes and Douches (1993) on potato and Julier* et al*. (2003) on lucerne found that double-reduction occurs sporadically. In both studies, the low number of progenies hampered a precise estimation of α. The aim of our study was to estimate the frequency of double-reduction in a mapping population of lucerne that includes a large number of individuals.

#### Included in

Agricultural Science Commons, Agronomy and Crop Sciences Commons, Plant Biology Commons, Plant Pathology Commons, Soil Science Commons, Weed Science Commons

Estimation of the Coefficient of Double-Reduction in Autotetraploid Lucerne

Polyploidy plays an important role in the evolution of species and many cultivated species, particularly in angiosperms, are polyploids (Bever and Felber, 1992; Gallais, 2003). Autopolyploid species that show a tetrasomic inheritance have complex genetics. However, some theoretical models were built for: (1) genetic mapping (Hackett* et al*., 1998), (2) quantitative genetics (Gallais, 2003) and (3) population genetics (Ronfort* et al*., 1998). But in practice, most data analyses ignore one essential feature of tetrasomic inheritance that is double-reduction. Indeed, in an autotetraploid species, homologous chromosomes can form tetravalents at meiosis. In this case, a double-reduction is observed if crossing-over occurs between a locus and its centromere, and if the sister chromatids migrate to the same pole at anaphase I. The gametes may, thus, carry a pair of sister alleles. Double-reduction frequency is represented by the index of separation (α) (Demarly, 1963; Mather, 1935; Mather, 1936). The parameter α is considered as a product of four probabilities: α = q e a s (Gallais, 2003) in which “ q ” is the probability of multivalent formation, “ e ” the probability of first equational division, related to the frequency of crossing-over, “ a ” is the probability of non-disjunction at first anaphase and “s” is the probability of having two sister chromatids in the same gamete. If separation during anaphase II is random, s = ½. Consequently, α will be low for a gene located in the vicinity of the centromere and will increase with distance between the gene and the centromere. It was demonstrated that double-reduction events alter the rate of progression towards equilibrium under inbreeding or under random mating, modify the recombination rate between loci and also alter the rate of decay of linkage disequilibrium under random mating (Bever and Felber, 1992). Current theoretical models allow drawing genetic maps taking into account double-reduction (Luo *et al*., 2004). Thus, it is possible to estimate α for codominant loci in tetraploid species. To date, we have few estimates of the double-reduction frequency. Haynes and Douches (1993) on potato and Julier* et al*. (2003) on lucerne found that double-reduction occurs sporadically. In both studies, the low number of progenies hampered a precise estimation of α. The aim of our study was to estimate the frequency of double-reduction in a mapping population of lucerne that includes a large number of individuals.