Ancestral Process and Diffusion Model with Selection
نویسنده
چکیده
Abstract. The ancestral selection graph in population genetics introduced by Krone and Neuhauser (1997) is an analogue to the coalescent genealogy. The number of ancestral particles, backward in time, of a sample of genes is an ancestral process, which is a birth and death process with quadratic death and linear birth rate. In this paper an explicit form of the number of ancestral particle is obtained, by using the density of the allele frequency in the corresponding diffusion model obtained by Kimura (1955). It is shown that fixation is convergence of the ancestral process to the stationary measure. The time to fixation of an allele is studied in terms of the ancestral process.
منابع مشابه
Duality, ancestral and diffusion processes in models with selection.
The ancestral selection graph in population genetics was introduced by Krone and Neuhauser [Krone, S.M., Neuhauser, C., 1997. Ancestral process with selection. Theor. Popul. Biol. 51, 210-237] as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph, followed backwards in time, is a birth and death process with q...
متن کاملA coalescent dual process in a Moran model with genic selection.
A coalescent dual process for a multi-type Moran model with genic selection is derived using a generator approach. This leads to an expansion of the transition functions in the Moran model and the Wright-Fisher diffusion process limit in terms of the transition functions for the coalescent dual. A graphical representation of the Moran model (in the spirit of Harris) identifies the dual as a str...
متن کاملModelling selection via multiple ancestors
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals first choose a (random) number of potential parents from the previous generation and then, from the selected pool, they inherit the type of the fittest parent...
متن کاملBalanced clusters and diffusion process in signed networks
In this paper we study the topology effects on diffusion process in signed networks. Considering a simple threshold model for diffusion process, it is extended to signed networks and some appropriate definitions are proposed. This model is a basic model that could be extended and applied in analyzing dynamics of many real phenomena such as opinion forming or innovation diffusion in social netwo...
متن کاملThe coalescent process in models with selection.
Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the anc...
متن کامل