We apply our general method of duality, introduced in [10], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman’s type, as well as for models with finite population size. Next, using SU(1, 1) raising an...

Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the distribution of the number of original alleles still segregating in the population at a given time in the past. The turnover of alleles is considered for specific cl...

Biological fitness is not an observable quantity and must be inferred from population dynamics. Bayesian inference applied to the Moran process and variants yields a robust inference method that can infer fitness in populations evolving via a Moran dynamic and generalizations. Information about fitness is derived solely from birth-events in birthdeath and death-birth processes in which selectio...

This research focuses on analyzing selection amplifiers in population genetics. Since the structure of a population graph can influence selection, this paper focuses on finding undirected graphs that can amplify selection. To clearly demonstrate the idea, the paper will briefly discuss the basic Moran model at first. Then it will analyze the star graph as an example of selection amplifiers that...