Quantitative Analysis of Directionality in Mammalian Karyotype Evolution.

The ancestral mammalian karyotype had been hypothesized to have had 2n ≈ 80 (the "fusion hypothesis"), 2n = 6-14 (the "fission hypothesis") or a diploid number close to the present mode (the "modal hypothesis"). The fusion hypothesis has long been the dominant paradigm in the study of karyotype evolution, but recent evidence favors the fission hypothesis, and our analysis also strongly supports fission as the predominant rearrangement compared to fusion. To formalize our analysis, we first define $$\overline A$$ chromosomes as a group containing both acrocentrics and telocentrics, and $$\overline M$$ chromosomes as all the rest. Given this dichotomy, we then divide pericentric inversions into three types according to whether they convert $$\overline A$$ chromosomes to $$\overline M$$ , $$\overline M$$ to $$\overline A$$ or make no interchange. Only the first two types, denoted p.i. $$(\overline {AM})$$ and p.i. $$(\overline {MA})$$ , are important for the analysis. If fusion predominates, the direction of karyotype evolution is determined by the overall joint action of centric fusions and p.i. $$(\overline {MA})$$ (the "fusion cycle"), whereas, if fission predominates, the chief rearrangements are fission and p.i. $$(\overline {AM})$$ (the "fission cycle"). The necessary predominance of p.i. $$(\overline {MA})$$ over p.i. $$(\overline {AM})$$ in the fusion cycle makes it extremely unlikely on a priori grounds that this cycle has been very important in mammalian karyotype evolution, because a probabilistic analysis shows that p.i. $$(\overline {AM})$$ should occur many times more often than the reverse rearrangement, especially when the chromosome number is low. Chromosomes will therefore seldom be available for fusion. On the other hand, given duplication of both heterochromatic and centromeric material, there are no obstacles to the operation of the fission cycle. The modal hypothesis is also implausible on a priori grounds because of the many fusions required for most groups. We next define the karyograph as a graph on which karyotypes are plotted in terms of chromosome number (2n) versus arm number (2AN). We determine 2AN by counting one for each $$\overline A$$ and two for each $$\overline M$$ chromosome. Robertsonian changes each alter 2n by one while leaving 2AN constant while p.i. $$(\overline AM)$$ and p.i. $$(\overline MA)$$ do the reverse. An extensive karyograph analysis of the known mammalian karyotypes shows that there is little correlation between karyotypic and morphological level under any of the three hypotheses, and that there is a strong tendency for linear patterns to emerge when families are plotted separately. This linearity consists of either vertical or horizontal lines on the karyograph, or some combination of the two. Such linearity would be unexpected if the fusion cycle dominated mammalian karyotype evolution, but is readily understandable under the fission cycle as resulting from the development of synchrony between large sections of the genome. This synchrony can develop readily under the fission cycle in that fission produces two $$\overline A$$ chromosomes constrained to evolve by inversion for some time. The resulting $$\overline M$$ chromosomes would later become available for fission following duplication of centromeric material and give rise to four $$\overline A$$ chromosomes, again constrained to evolve by inversion for a while also. The frequently observed linearity of family karyograph distributions, and the above argument concerning the development of synchrony, suggests that mammalian karyotypes tend to follow an upwardly zig-zag course (with occasional "back eddies" by centric fusion) during evolution when plotted on the karyograph.