A branching process approach to level‐k phylogenetic networks. Issue 2 (26th November 2021)

• Record Type: Journal Article
• Authors: Stufler, Benedikt
• Is Part Of: Random structures & algorithms. Volume 61:Issue 2(2022)
• Page Start: 397
• Page End: 421
• Publication Date: 2021-11-26
• Subjects: branching processes -- phylogenetic networks -- random graphs; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.21065
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach appears to be new in this context. Our main results focus on random level‐ k networks with n labeled leaves. Although the number of reticulation vertices in such networks is typically linear in n, we prove that their asymptotic global and local shape is tree‐like in a well‐defined sense. We show that the depth process of vertices in a large network converges towards a Brownian excursion after rescaling by n − 1 / 2 . We also establish Benjamini–Schramm convergence of large random level‐ k networks towards a novel random infinite network.