K. Bartoszek

Limit distribution of the quartet balance index for Aldous’s β ≥ 0-model

The paper analyzes the limit distribution of a new balance index for phylogenetic trees under Aldous’s β ≥ 0-model, showing it converges to a fixed point of a contraction operator.

Exact and approximate limit behaviour of the Yule tree’s cophenetic index

The paper analyzes the limit distribution of the cophenetic index under the Yule tree model and proposes hypothesis testing methods for phylogenetic trees.

A Central Limit Theorem for Punctuated Equilibrium

The paper derives a Central Limit Theorem for punctuated equilibrium, showing that dramatic phenotypic change must be rare for weak convergence to hold under fast adaptation.