Karyotype distributions in a stochastic model of reciprocal translocation

A random process of reciprocal translocation for a fixed number k of chromosomes (or arms) will have an equilibrium distribution of chromosome lengths. In this paper we calculate this distribution, by analytical means for k = 2 and partially for k = 3, and simulate the means of the marginal distributions for higher k. We compare this with a random (i.e., ahistorical) distribution of genomic DNA among k chromosomes and to a selection of karyotypes of real organisms. The results motivate a revised model where translocations giving rise to undersize chromosomes are disadvantaged.