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Bioinformatics 2008 24(16):i146-i152; doi:10.1093/bioinformatics/btn295
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Poisson adjacency distributions in genome comparison: multichromosomal, circular, signed and unsigned cases

Wei Xu *, Benoît Alain and David Sankoff

Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada

*To whom correspondence should be addressed.


  Abstract

The number of common adjacencies of genetic markers, as a measure of the similarity of two genomes, has been widely used as indicator of evolutionary relatedness and as the basis for inferring phylogenetic relationships. Its probability distribution enables statistical tests in detecting whether significant evolutionary signal remains in the marker order. In this article, we derive the probability distributions of the number of adjacencies for a number of types of genome—signed or unsigned, circular or linear, single-chromosome or multichromosomal. Generating functions are found for singlechromosome cases, from which exact counts can be calculated. Probability approaches are adopted for multichromosomal cases, where we find the exact values for expectations and variances. In both cases, the limiting distributions are derived in term of numbers of adjacencies. For all unsigned cases, the limiting distribution is Poisson with parameter 2; for all signed cases, the limiting distribution is Poisson with parameter 1/2.

Contact: wxu060{at}uottawa.ca


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