Lineage-through-time plots of birth-death processes

TL;DR

This paper derives formulas for the distribution and expected number of lineages in reconstructed birth-death trees, considering different assumptions about the tree's age, aiding understanding of evolutionary processes.

Contribution

It provides new analytical expressions for lineage counts in birth-death models under various conditioning assumptions.

Findings

Derived density and expectation formulas for lineage counts.

Analyzed effects of conditioning on tree age.

Applicable to evolutionary and phylogenetic studies.

Abstract

We calculate the density and expectation for the number of lineages in a reconstructed tree with $n$ extant species. This is done with conditioning on the age of the tree as well as with assuming a uniform prior for the age of the tree.