Recombination and sterility in inversion homo- and heterokaryotypes under a general counting model of chiasma interference

It has long been known that the chiasmata are not independently distributed in most organisms, a phenomenon known as chiasma interference. In this paper, I suggest a model of chiasma interference that generalizes the Poisson model, the counting model, the Poisson-skip model, and the two-pathway counting model into a single framework, and use it to derive infinite series expressions for the sterility and recombination pattern probabilities in inversion homo- and heterokaryotypes, and a closed-form expression for the special case of the two-pathway counting model in homokaryotypes. I then use these expressions to perform maximum likelihood parameter estimations for recombination and tetrad data from various species. The results imply that the simpler counting models perform well compared to more complex ones, that interference works in a similar way in homo- and heterokaryotypes, and that the model fits well with data for the latter as well as the former. I also find evidence that the interference signal is broken by the centromere in some species, but not others, suggestions of negative interference in Aspergillus nidulans, and no consistent support for the theory that a second noninterfering chiasma pathway exists only in organisms that require double-strand break for synapsis. I suggest that the latter finding is at least partly due to issues involved in analyzing aggregate data from different experiments and individuals.