The gene-orientation structure of eukaryotes

It is shown that the sequence of gene orientations of four eukaryotes-for those that are presently known-are well modeled by a two-state, two-parameter (first order) Markov chain. These include the six chromosomes of nematodes (C. elegans), the 16 chromosomes of yeast (S. cerevisiae), the five chromosomes of Arabidopsis (A. thaliana), and the 19 scaffolds of fruit flies (D. melanogaster). Moreover, they are reasonably well modeled, more simply, by a one-parameter symmetric version of the Markov chain. Further, compelling statistical evidence is presented which suggests that the parameters particularizing the Markov chain are organism dependent rather than merely chromosome dependent. This surprising observation begs an appropriate biological explanation. Does there exist some kind of mechanism of "communication" among a eukaryote's chromosomes that serves to maintain common values for all of the chromosomal parameters? Or are the common parameter values merely a consequence of a common environment of origin for all of the chromosomes of an organism? (If so, why so?) A third possible explanation is ruled out: while there exists within the class of Markov chain models under consideration, a case that could be described as equivalent to "flipping a fair coin," a thorough-random-shuffling-of-the-genes explanation, via mutations, does not hold up to statistical scrutiny.