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Mittwoch, 15.05.2019 | 14.15 - 15.45 Uhr | A 3.339

OS Stochastik: Prof. Dr. Ellen Baake, Universität Bielefeld

Vortrag: Ancestral lines under selection and mutation

Abstract: We consider an interacting particle system that describes the joint action of mutation and selection in biological populations; it is equivalent to the biased voter model on the complete graph that also allows for change of opinion. We revisit the ancestral selection graph, which is the standard tool to trace back ancestral lines of individuals sampled from the population at present. We then introduce two new concepts, namely, the killed ancestral selection graph and the pruned lookdown ancestral selection graph. The killed ancestral selection graph gives a representation of the type of a random individual from a stationary population, based upon the individual’s potential ancestry back until the mutations that define the individual’s type. The pruned lookdown ancestral selection graph allows to trace the ancestry of individuals from a stationary distribution back into the distant past, thus leading to the stationary distribution of ancestral types. We illustrate the results by applying them to a prototype model for the error threshold phenomenon, which is equivalent to a phase transition of the underlying voter model.
This is joint work with Fernando Cordero and Sebastian Hummel.
 

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