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Updated: Feb 11, 2026

The Lambda Select cII Mutation Detection System
Published on: April 26, 2018
A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via
Ellen Baake1, Fernando Cordero2, Sebastian Hummel2
1Faculty of Technology, Bielefeld University, Box 100131, 33501, Bielefeld, Germany. ebaake@techfak.uni-bielefeld.de.
Abstract:
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (random) structures inherent in this deterministic model. In a first step, we obtain a representation of the deterministic equation's solution (and, in particular, of its equilibria) in terms of an ancestral process called the killed ancestral selection graph. This representation allows one to understand the bifurcations related to the error threshold phenomenon from a genealogical point of view. Next, we characterise the ancestral type distribution by means of the pruned lookdown ancestral selection graph and study its properties at equilibrium. We also provide an alternative characterisation in terms of a piecewise-deterministic Markov process. Throughout, emphasis is on the underlying dualities as well as on explicit results.
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