We consider a hybrid method to simulate the return time to the initial state in a critical-case birth-death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach is to directly simulate the process, unless the simulated time exceeds some threshold and if it does, draw the return time from the tail of the power law.
The phylogenetic effective sample size is a parameter that has as its goal the quantification of the amount of independent signal in a phylogenetically correlatedsample. It was studied for Brownian motion and Ornstein-Uhlenbeck models of trait evolution. Here, we study this composite parameter when the trait is allowedto jump at speciation points of the phylogeny. Our numerical study indicates thatthere is a non-trivial limit as the effect of jumps grows. The limit depends on thevalue of the drift...
We apply multitype, continuous time, Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly, the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models, in order to analyze pathogenicity in a published clinical data set consisting of 251 strains of E....
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