The Moran process, as studied by Lieberman, Hauert and Nowak (2005) [1] , is a birth-death process that models the spread of mutations in two-type populations (residents-mutants) whose structure defined digraph. process' central notion probability randomly placed mutant will occupy whole vertex set (fixation probability). We extend this model considering type-specific graphs, consequently prese...

Jia Shao, Sergey V. Buldyrev, Reuven Cohen, Maksim Kitsak, Shlomo Havlin, and H. Eugene Stanley Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel Minerva Center and Departme...

We consider a multi-type Moran model (in continuous time) with selection and typedependent mutation. This paper is concerned with the evolution of genealogical information forward in time. For this purpose we define and analytically characterize a pathvalued Markov process that contains in its state at time t the extended ancestral lines (adding genealogical distances) of the population alive a...