Chromosome painting: How recombination mixes ancestral colors

We consider a Moran model with recombination in haploid population of size N. At each birth event, probability 1−ρNR the offspring copies one parent’s chromosome, and ρNR she inherits chromosome that is mosaic both parental chromosomes. assume at time 0 individual has her painted different color we study partition asymptotically fixed large population, when look portion such ρ:=limN→∞ρNN 2→∞. To do so, follow backwards ancestry randomly sampled individual. This yields Markov process valued partitions half-line, was introduced by Esser, Probst Baake (J. Math. Biol. 73 (2016) 161–197), which blocks can merge split, called partitioning process. Its stationary distribution closely related to our recombination. are able provide an approximation this ρ≫1 error bound. allows us show (renormalised) length leftmost block (i.e., region carries same as 0) converges exponential distribution. In addition, geometry be described terms Poisson point explicit intensity measure.