54 citations · 62 across the 8 of their papers we have counts for
6 papers · 1 filter
A small noise approximation for Muller's Ratchet
Carola Sophia Heinzel, Peter Pfaffelhuber, Anton Wakolbinger
We consider an infinite system of SDEs with Fleming-Viot noise indexed by , whose parameters , and are the (deleterious) selection coefficient, the (uni-dir…
Optimal strategies in the all-heads coin game
Peter Pfaffelhuber
We study a sequential coin-flipping game: a player starts with ~coins, each heads with probability~, and in each round flips all remaining coins and must set aside at least o…
Formalization of Brownian motion in Lean
Rémy Degenne, David Ledvinka, Etienne Marion +1
Brownian motion is a building block in modern probability theory. In this paper, we describe a formalization of Brownian motion using the Lean theorem prover. We build on the exist…
Fixation probabilities and hitting times under low levels of frequency-dependent selection
Peter Pfaffelhuber, Anton Wakolbinger
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities…
Muller's ratchet with compensatory mutations
P. Pfaffelhuber, P. R. Staab, A. Wakolbinger
We consider an infinite-dimensional system of stochastic differential equations describing the evolution of type frequencies in a large population. The type of an individual is the…
An approximate sampling formula under genetic hitchhiking
Alison Etheridge, Peter Pfaffelhuber, Anton Wakolbinger
For a genetic locus carrying a strongly beneficial allele which has just fixed in a large population, we study the ancestry at a linked neutral locus. During this ``selective sweep…