# Multidimensional $\Lambda$-Wright-Fisher processes with general frequency-dependent selection

## TL;DR

This paper introduces a flexible population model that incorporates complex selection mechanisms and extreme reproductive events, extending existing processes to include non transitive interactions and providing insights into fixation and stochastic differential equation solutions.

## Contribution

It generalizes $ ext{Lambda}$-Fleming-Viot processes to include general frequency-dependent selection and non transitive interactions, broadening the scope of population genetics models.

## Key findings

- Established fixation properties for the new processes.
- Derived conditions for realization as solutions of stochastic differential equations.
- Extended the model to include extreme reproductive events and complex selection rules.

## Abstract

We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample potential parents in the previous generation before choosing the 'strongest' one, by allowing individuals to use any rule to choose their real parent. Via a large population limit, we obtain a generalisation of $\Lambda$-Fleming Viot processes allowing for non transitive interactions between types. We provide fixation properties, and give conditions for these processes to be realised as solutions of stochastic differential equations.