Precise control of chromosome pairing is vital for conferring meiotic, and hence reproductive, stability in sexually reproducing polyploids. Apart from the Ph1 locus of wheat that suppresses homeologous pairing, little is known about the activity of genes that contribute to the cytological diploidization of allopolyploids. In oilseed rape (Brassica napus) haploids, the amount of chromosome pairing at metaphase I (MI) of meiosis varies depending on the varieties the haploids originate from. In this study, we combined a segregation analysis with a maximum-likelihood approach to demonstrate that this variation is genetically based and controlled mainly by a gene with a major effect. A total of 244 haploids were produced from F1 hybrids between a high- and a low-pairing variety (at the haploid stage) and their meiotic behavior at MI was characterized. Likelihood-ratio statistics were used to demonstrate that the distribution of the number of univalents among these haploids was consistent with the segregation of a diallelic major gene, presumably in a background of polygenic variation. Our observations suggest that this gene, named PrBn, is different from Ph1 and could thus provide complementary information on the meiotic stabilization of chromosome pairing in allopolyploid species.

Approximate Bayesian Computational (ABC) methods, or likelihood-free methods,

The Equi-Energy Sampler (EES) introduced by Kou et al. [2006] is based on a population of chains which are updated by local moves and global moves, also called equi-energy jumps. The state space is partitioned into energy rings, and the current state of a chain can jump to a past state of an adjacent chain that has an energy level close to its level. This algorithm has been developed to facilitate global moves between different chains, resulting in a good exploration of the state space by the target chain. This method seems to be more efficient than the classical Parallel Tempering (PT) algorithm. However it is difficult to use in combination with a Gibbs sampler and it necessitates increased storage. In this paper we propose an adaptation of this EES that combines PT with the principle of swapping between chains with same levels of energy. This adaptation, that we shall call Parallel Tempering with Equi-Energy Moves (PTEEM), keeps the original idea of the EES method while ensuring good theoretical properties, and practical implementation. Performances of the PTEEM algorithm are compared with those of the EES and of the standard PT algorithms in the context of mixture models, and in a problem of identification of transcription factor binding motifs.

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