The distribution of distances between randomly constructed genomes: generating function, expectation, variance and limits.
Based on a large repertoire of chromosomal rearrangement operations, the genomic distance d between two genomes with chi(r) and chi(b) linear chromosomes, respectively, both containing the same (or orthologous) n genes or markers, is d=n + max(chi(r),chi(b))-c, where c is the number of cycles in the breakpoint graph of the two genomes. In this paper, we study the exact probability distribution of c. We derive the expectation and variance, and show that, in the limit, the expectation of d is n - (2chirchib)/(2chir+2chib(-1)) - 1/2ln (n + max(chir,chib))/(chir+chib).
Xu
Wei
W
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario, K1N 6N5, Canada. wxu060@uottawa.ca
D001483:Base Sequence; D002874:Chromosome Mapping / Q000379:methods*; D003198:Computer Simulation; D019143:Evolution, Molecular; D014644:Genetic Variation / Q000235:genetics*; D016013:Likelihood Functions; D015810:Linkage Disequilibrium / Q000235:genetics*; D008957:Models, Genetic; D015233:Models, Statistical; D008969:Molecular Sequence Data; D016415:Sequence Alignment / Q000379:methods*; D017422:Sequence Analysis, DNA / Q000379:methods*; D016008:Statistical Distributions