On the Eve property for CSBP

TL;DR

This paper investigates the Eve property in continuous state branching processes, classifying all possible long-term behaviors based on the branching mechanism, which enhances understanding of ancestral dominance in populations.

Contribution

It provides a comprehensive classification of long-term behaviors related to the Eve property in CSBP based on different branching mechanisms.

Findings

Classified all possible Eve property behaviors in CSBP

Linked behaviors to specific branching mechanisms

Enhanced understanding of ancestral dominance in population models

Abstract

We consider the population model associated to continuous state branching processes and we are interested in the so-called Eve property that asserts the existence of an ancestor with an overwhelming progeny at large times, and more generally, in the possible behaviours of the frequencies among the population at large times. In this paper, we classify all the possible behaviours according to the branching mechanism of the continuous state branching process.