Work

Sackin indices for labeled and unlabeled classes of galled trees

Year: 2025

Type: article

Abstract: The Sackin index is an important measure for the balance of phylogenetic trees. We investigate two extensions of the Sackin index to the class of galled trees and two of its subclasses, namely simplex galled trees and normal galled trees, where for all classes we consider both labeled and unlabeled galled trees. In all cases, we show that the mean of the Sackin index for a network which is uniformly sampled from its class is asymptotic to $$\mu n^{3/2}$$ for an explicit constant $$\mu $$ . In addition, we show that the scaled Sackin index converges weakly and with all its moments to the Airy distribution.

Source: Journal of Mathematical Biology

DOI: 10.1007/s00285-025-02205-0

Authors: Michael Fuchs, Bernhard Gittenberger

Institutions: National Chengchi University, TU Wien

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Science and Technology Council, National Chengchi University, National Science and Technology Council