Abstract
The universal pacemaker (UPM) model extends the classical molecular clock (MC) model, by allowing each gene, in addition to its individual intrinsic rate as in the MC, to accelerate or decelerate according to the universal pacemaker. Under UPM, the relative evolutionary rates of all genes remain nearly constant whereas the absolute rates can change arbitrarily. It was shown on several taxa groups spanning the entire tree of life that the UPM model describes the evolutionary process better than the MC model. In this work we provide a natural generalization to the UPM model that we denote multiple pacemakers (MPM). Under the MPM model every gene is still affected by a single pacemaker, however the number of pacemakers is not confined to one. Such a model induces a partition over the gene set where all the genes in one part are affected by the same pacemaker and task is to identify the pacemaker partition, or in other words, finding for each gene its associated pacemaker. We devise a novel heuristic procedure, relying on statistical and geometrical tools, to solve the problem and demonstrate by simulation that this approach can cope satisfactorily with considerable noise and realistic problem sizes. We applied this procedure to a set of over 2000 genes in 100 prokaryotes and demonstrated the significant existence of two pacemakers.
Highlights
The Universal PaceMaker (UPM) of genome evolution [1] extends the classical Molecular Clock (MC) model [2] and its various imperative relaxations, by relaxing the rate constancy on one hand, and yet preserving the rate correlation between the various genes
The universal pacemaker (UPM) model is compatible with the large amount of data on fast-evolving and slow-evolving organismal lineages, primarily different groups of mammals [8]
Throughout, we use the notation UPM to refer to the model and the PM term for the pacemaker as an object
Summary
The Universal PaceMaker (UPM) of genome evolution [1] extends the classical Molecular Clock (MC) model [2] and its various imperative relaxations (see e.g. [3,4] among a few), by relaxing the rate constancy (as in MC) on one hand, and yet preserving the rate correlation between the various genes. [3,4] among a few), by relaxing the rate constancy (as in MC) on one hand, and yet preserving the rate correlation between the various genes. Such a model can provide explanation to the striking phenomenon that the distribution of the evolutionary distances between orthologous genes remains remarkably constant across the entire history of life [5,6,7]. In absolute terms the advantage of UPM over MC was small, and both models exhibited considerable evolution rate overdispersion. Throughout, we use the notation UPM to refer to the model and the PM term for the pacemaker as an object
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