title: A continuous analog of run length distributions reflecting accumulated fractionation events.
abstract: BACKGROUND
  We propose a new, continuous model of the fractionation process (duplicate gene deletion after polyploidization) on the real line. The aim is to infer how much DNA is deleted at a time, based on segment lengths for alternating deleted (invisible) and undeleted (visible) regions.
  
  
  RESULTS
  After deriving a number of analytical results for "one-sided" fractionation, we undertake a series of simulations that help us identify the distribution of segment lengths as a gamma with shape and rate parameters evolving over time. This leads to an inference procedure based on observed length distributions for visible and invisible segments.
  
  
  CONCLUSIONS
  We suggest extensions of this mathematical and simulation work to biologically realistic discrete models, including two-sided fractionation.
authors.affiliation: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario, K1N 6N5, Canada.
authors.forename: Zhe
authors.initials: Z
authors.lastname: Yu
authors.affiliation: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario, K1N 6N5, Canada. sankoff@uottawa.ca.
authors.forename: David
authors.initials: D
authors.lastname: Sankoff
mesh_terms: D017353:Gene Deletion; D020440:Gene Duplication; D023281:Genomics; D008962:Models, Theoretical
keywords: Analysis of runs; Duplicate gene deletion; Genomics; Probability modeling; Whole genome duplication