There is well-known evidence that in many eukaryotes, different species have different karyotypes (e.g. n=1-47 in ants and n=3-51 in mammals). Alternative (fusion and fission) hypotheses have been proposed to interpret this chromosomal diversity. Although the former has long been accepted, accumulating molecular genetics evidence seems to support the latter. We investigated this problem from a stochastic viewpoint using the Monte Carlo simulation method under the minimum interaction theory. We found that the results of simulations consistently interpreted the chromosomal diversity observed in mammals, ants and wasps, and concluded that chromosome evolution tends to evolve as a whole toward increasing chromosome numbers by centric fission. Accordingly, our results support the fission hypothesis. We discussed the process of chromosome evolution based on the latest theory of the molecular structure of chromosomes, and reconfirmed that the fission burst is the prime motive force in long-term chromosome evolution, and is effective in minimizing the genetic risks due to deleterious reciprocal translocations and in increasing the potential of genetic divergence. Centric fusion plays a biological role in eliminating heterochromatin (C-bands), but is only a local reverse flow in contrast to the previously held views. Copyright 2001 Academic Press.