Journal of Bioinformatics and Computational Biology Vol. 6, No. 1 (2008) 125–162 c  Imperial College Press LIKELIHOOD OF A PARTICULAR ORDER OF GENETIC MARKERS AND THE CONSTRUCTION OF GENETIC MAPS S. TEWARI Department of Statistics, University of Georgia Athens, GA 30602-1952, USA statsusant@yahoo.com J. ARNOLD * Department of Genetics, University of Georgia Athens, GA 30602-7223, USA arnold@uga.edu S. M. BHANDARKAR Department of Computer Science, University of Georgia Athens, GA 30602-7404, USA suchi@cs.uga.edu Received 20 July 2007 Accepted 24 August 2007 We model the recombination process of fungal systems via chromatid exchange in meio- sis, which accounts for any type of bivalent conﬁguration in a genetic interval in any speciﬁed order of genetic markers, for both random spore and tetrad data. First, a probability model framework is developed for two genes and then generalized for an arbitrary number of genes. Maximum likelihood estimators (MLEs) for both random and tetrad data are developed. It is shown that the MLE of recombination for tetrad data is uniformly more eﬃcient over that from random spore data by a factor of at least 4 usually. The MLE for the generalized probability framework is computed using the expectation-maximization (EM) algorithm. Pearson’s chi-squared statistic is computed as a measure of goodness of ﬁt using a product-multinomial setup. We implement our model with genetic marker data on the whole genome of Neurospora crassa. Simulated annealing is used to search for the best order of genetic markers for each chromosome, and the goodness of ﬁt value is evaluated for model assumptions. Inferred map orders are corroborated by genomic sequence, with the exception of linkage groups I, II, and V. Keywords : Recombination; genetic map; tetrad analysis; EM algorithm; simulated annealing; MLE. * Corresponding author. 125