Abstract
Chromosomes evolve through genome rearrangement events, including inversions, transpositions, and inverted transpositions, that change the order and strandedness of genes within chromosomes. In this paper we present a method for estimating evolutionary histories for chromosomes based upon such events. The fundamental mathematical challenge of our approach is to estimate the true evolutionary distance between every pair of chromosomes, where the true evolutionary distance is the number of rearrangement events that took place in the evolutionary history between the chromosomes. We present two techniques, Exact- and Approx-IEBP, for estimating true evolutionary distances and prove guarantees about the accuracy of these techniques under a very general stochastic model of chromosomal evolution. We then show how we can use these estimated distances to obtain highly accurate estimates of chromosomal evolutionary history, significantly improving upon the previous best techniques.
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