Bounds on identification of genome evolution pacemakers

Several works have pointed out that the tight correlation between genes’ evolutionary rate is better explained by a model denoted as the Universal Pacemaker (UPM) rather than by a simple rate constancy as manifested by the classical hypothesis of Molecular Clock (MC). Under UPM, the relative evolutionary rates of all genes remain nearly constant whereas the absolute rates can change arbitrarily according to the pacemaker ticks. This evolutionary framework was recently adapted to model epigenetic aging where methylated sites are the analogs of evolving genes. A consequent question to the above finding is the determination of the number of such pacemakers and which gene adheres to which pacemaker. This however turns to be a non trivial task and is affected by the number of variables, their random noise, and the amount of available information. To this end, a clustering heuristic was devised exploiting the correlation between corresponding edge lengths across thousands of gene trees. Nevertheless, no theoretical study linking the relationship between the affecting parameters was done. We here study this question by providing theoretical bounds, expressed by the system parameters, on probabilities for positive and negative results. We corroborate these results by a simulation study that reveals the critical role of the variances.