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Chiasma: a Mathematica application for analysis of chromosome pairing

M. Humberto Reyes-Valdes
Organization: Texas A&M University
David M. Stelly
Organization: Texas A&M University
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This application estimates probabilities of at least one chiasma in subchromosomal segments between centromeres, telomeres and breakpoints. The input data are observed frequencies of meiotic configurations or groups of meiotic configurations, the possible combinations of chiasmate segments for each class, and an initial set of starting values for the chiasma probabilities in the involved segments. The program uses the EM algorithm to do maximum likelihood estimations of the parameters (Reyes-Valdes and Stelly, PNAS, 1995). By performing first and second partial derivatives and inversion of the expected information matrix, the program evaluates the asymptotic variances of the estimates. The chiasma probabilities are converted to map distances in centimorgans via Haldane, Kosambi, and Carter and Falconer mapping functions. Observed and expected frequencies of meiotic classes are compared by the chi-square test for goodness of fit and by the Neyman-Pearson test. Log-likelihood graphics are presented for each individual parameter to check for one- and two-dimension maxima. The program permits analysis of virtually any kind of cytogenetic stock with disomic pairing, either unmarked or ISH-marked, e.g. normal bivalents, heterozygous translocations, monotelodisomic translocations and tertiaty monosomics. This work was supported by Pioneer Hi-Bred International, Inc., the Universidad Autonoma Agraria Antonio Narro, Mexico and Texas A&M University.

*Science > Biology

Genetics, Chiasma, Meiosis
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data.txt (518 B) - ASCII file with data sample for chiasma.m
chiasma.m (12.7 KB) - Mathematica application
tutorial.nb (872 KB) - Mathematica notebook tutorial for chiasma.m

Files specific to Mathematica 2.2 version:
tutorial.ma (325.5 KB) - Mathematica notebook tutorial for chiasma.m