A gene functioning across a range of species would exhibit variation upon comparing DNA sequences from different organisms. There are two kinds of trees lying behind such genetic variation: the gene trees tracing common ancestry of the sampled gene copies, and the species tree representing the evolutionary history of the group of extant species in question. These two kinds of trees should be modeled as random trees to reflect the stochastic nature of the underlying evolutionary forces and a variety of unknown factors influencing the speciation process. The established approach is to use coalescent processes to model gene trees for a single species and branching processes to model the species trees. Such stochastic models are very important tools in modern Population Genetics and Systematic Biology. The aim of this project is to develop the existing models for the gene and species trees by incorporating new biologically relevant features. With the gene tree models, we are interested in coalescent approximation for age-dependent populations in random environment. (Previously, we successfully studied the age-dependent case in constant environment and the geographically structured case in random environment.) A range of questions concerning species trees will be addressed within the framework of the Crump-Mode-Jagers (CMJ) branching processes using among other methods our own technique for studying the asymptotic behavior of critical CMJ-processes with random characteristics.
at Mathematical Sciences, Mathematical Statistics
Funding years 2011–2013