Yun‐Xin Fu

Moments of the length of sample genealogy and their applications

The paper investigates the properties of total branch length in genealogies and derives recurrence relations and closed-form expressions for its moments, showing non-normality under constant population size and applications to mutation counts.

The distribution of the number of mutations in the genealogy of a sample from a single population

The paper derives a new sampling formula for the number of mutations in a genealogy under different population models, improving numerical accuracy and efficiency.

The central limit theorem for the number of mutations in the genealogy of a sample from a large population

This paper proves the central limit theorem for the number of mutations in a sample from a large population, showing it approximates a normal distribution under certain evolutionary models.