The distributions under two species-tree models of the number of root ancestral configurations for matching gene trees and species trees

For a pair consisting of gene tree and species tree, the ancestral configurations at species-tree internal node are distinct sets lineages that can be present node. The enumeration root configurations—ancestral root—assists in describing complexity gene-tree probability calculations evolutionary biology. Assuming match topology, we study distribution number random labeled topology under uniform Yule–Harding models. We employ analytic combinatorics, considering context additive parameters using singularity analysis to evaluate asymptotic growth coefficients generating functions. both models, obtain lognormal distributions for configurations. trees, also mean (∼1.425n) variance (∼2.045n) configurations, paralleling previous results model (mean (4/3)n, ∼1.822n). A methodological innovation is variance, conducted from Riccati differential equation function satisfies—without possessing itself.