On the Estimation of Intron Evolution

Miklós Csu2rös PLoS Computational Biology recently published an article about spliceosomal intron evolution by Nguyen, Yoshihama, and Kenmochi [1]. The authors were unaware of some earlier independent results. Foremostly, the main point of the article—that of estimating the density of potential intron sites—is not novel. It was described more than three months earlier [2]. The numerical results are virtually identical in the two publications, which is not surprising, since they apply the same model to the same data [3]. A recent article points to the model’s validity. Raible and coauthors [4] report that introns in the protostome Platynereis dumerilii are almost as abundant as in humans, and many introns are in homologous positions between the two species. The shared positions indicate that at most one-third of human introns were gained in the vertebrate lineage, in agreement with the estimates of [2] and [1]. In contrast, parsimony estimates [3] should change significantly when including P. dumerilii. To estimate ancestral intron losses and gains, Nguyen and coauthors use an exponential-time procedure, which is practical only for a few species. In reality, the estimation can be done in linear time [2], as described briefly below. We are modeling intron presence and absence in homologous sites across organisms related by a known phylogeny. Presence and absence are encoded by 1 and 0, respectively. Introns evolve independently, by a Markov model for a binary character. On branch e, an intron is lost with probability pe(1 ! 0) and an intron is gained with probability pe(0 ! 1) at every site. Assuming a continuous-time Markov process, peð0 ! 1Þ 1⁄4 k k þ l k k þ l e tðkþlÞ peð1 ! 0Þ 1⁄4 l k þ l l k þ l e tðkþlÞ ð1Þ