Evolution with mass extinction on $\mathbb{T}_d^+$

TL;DR

This paper introduces a stochastic model for population evolution on a tree structure, analyzing conditions for survival and extinction based on mutation and selection dynamics.

Contribution

It presents a novel mathematical framework modeling evolution on a tree with explicit criteria for population survival or extinction.

Findings

Derived sharp conditions for extinction and survival

Model captures evolution fitness landscape dynamics

Provides mathematical insights into population persistence

Abstract

We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain sharp and distinct conditions on the set of parameters for extinction and survival.