| Chiasmata constitute one of the cornerstones of sexual reproduction in most eukaryotes. They mediate the reciprocal genetic exchange between homologues and are essential to the proper orientation of the homologous centromeres in meiosis. We analyzed the mathematical relationship between frequencies of nonadorned disomic configurations in meiosis (rings, rods and univalents) and the probabilities at which arms of the respective chromosomes are chiasmate. Numerical analyses indicated that conventionally analyzed bivalents with nonidentified arms yield statistically biased estimates of chiasma probabilities under a broad range of circumstances. We subsequently analyzed estimators derived from adorned configurations with ISH-adorned arms, which were found to be statistically superior, and with no assumptions concerning interference across the centromere. The EM algorithm was proposed to extend the analytical methods to other kinds of cytogenetic stocks (e.g., translocation heterozygotes and monotelodisomic translocation heterozygotes). This approach permits one to perform maximum likelihood estimation of chiasmate probabilities in segments defined by centromeres, breakpoints and telomeres, from either unadorned or ISH-adorned meiotic configurations. The analytical method was tested by Monte Carlo simulation using a monotelodisomic translocation heterozygote as a model. With the proposed algorithm, a computer program was written in Mathematica... |
