Meiotic pairing in autohexaploid Lathyrus: a mathematical model

Abstract

A mathematical meiotic pairing and chiasma model is described for a hexaploid. It estimates, on the basis of observations on chromosome associations at metaphase I of meiosis, the frequencies of initial hexavalent, quadrivalent and bivalent pairing, as well as the frequency of chiasmate association of the two chromosome arms, both after multivalent and after bivalent pairing. These estimates use all nine degrees of freedom available (10 configuration types distinguished). Although potential complications like multiple pairing partner exchange and interstitial chiasma formation are not accommodated by the model, a very close fit is found between the configuration frequencies observed in Lathyrus palustris (2n = 6x = 42) and those reconstructed on the basis of the model. This does not necessarily imply that the model fully represents biological reality, but at least it shows that the arms are significantly different in respect of chiasma formation and that chiasma frequencies may differ between multivalent and bivalent pairing. The hexavalent pairing frequency, as estimated by correcting metaphase frequencies for failure of chiasma formation, was only slightly lower than theoretically expected for an autohexaploid. However, the pairing of the six homologous chromosomes as a quadrivalent + a bivalent was considerably lower than with random pairing. The frequency of pairing as three bivalents was correspondingly higher.

Estimation of allele frequencies in polyploids under certain patterns of inheritance

“…There are several recent papers on this subject, both from a cytogenetic and a mathematical modelling point of view (Sybenga, 1994(Sybenga, , 1995(Sybenga, , 1996(Sybenga, , 1999Jackson and Jackson, 1996). The evidence suggests that these situations should be characterised by a general polyploid inheritance model with no complete preference to homologous or homeologous paring (Wu et al, 2001).…”

A Bivalent Polyploid Model for Mapping Quantitative Trait Loci in Outcrossing Tetraploids

“…In other factor. The preferential pairing factor (p) is defined as the propensity of bivalent pairings between more similar words, for fully informative markers, results from the autopolyploid model will be similar to those from the rather than less similar chromosomes (Sybenga 1988(Sybenga , 1994(Sybenga , 1995(Sybenga , 1996. Different values of this parameter, ranggeneral polyploid model.…”

“…where lines indicate the individual chromosomes on which the QTL is bracketed by the two markers and mosomes (Sybenga 1992(Sybenga , 1994(Sybenga , 1995 and such a is the Kronecker product. The specific linkage phase difference is defined as the preferential pairing factor, decombination of parents P and Q, which is not known a noted by p, that is bounded by [0, 2 ⁄ 3 ] (Sybenga 1988).…”

“…nomes. It is observed that for many polyploids there is Suppose there is a full-sib family of size n derived a higher probability of pairing between more similar from two heterozygous tetraploid parents P and Q. Conchromosomes than between less similar chromosomes sider two fully informative markers ᏹ and ᏹ ϩ1 , which (Hickok 1978;Sybenga 1988Sybenga , 1994Sybenga , 1995 Allendorf each have eight different alleles assigned to the four and Danzmann 1997). By implementing powerful exchromosomes of parents P and Q, respectively.…”

Interval Mapping for Autopolyploids

“…Specifically, autopolyploids may undergo either bivalent pairing (two homologs pair) or multivalent pairing (more than two homologues pair), and it varies in different species (Rieseberg and Doyle 1989;Sybenga 1995). Furthermore, the manner in which the paired chromosomes segregate during meiosis, especially for multivalent pairing, also varies among species (Jackson and Jackson 1996).…”