[Paper Review] Branch lengths on Yule trees and the expected loss of phylogenetic diversity

Arne Ø. Mooers, Olivier Gascuel+3 more|arXiv (Cornell University)|Nov 25, 2010

Evolution and Paleontology Studies45 references3 citations

TL;DR

This paper challenges the widely cited claim that 80% of phylogenetic diversity (PD) survives 95% species loss by showing that under realistic Yule and birth-death models—unlike coalescent-based models—pendant and interior branch lengths are nearly equal, leading to a near-linear loss of PD with species extinction. The key result is that phylogenetic redundancy in the Tree of Life is substantially lower than previously thought, especially under conditioning on tree size and age.

ABSTRACT

Diversification is nested, and early models suggested this could lead to a great deal of evolutionary redundancy in the Tree of Life. This result is based on a particular set of branch lengths produced by the common coalescent, where pendant branches leading to tips can be very short compared to branches deeper in the tree. Here, we analyze alternative and more realistic Yule and birth-death models. We show how censoring at the present both makes average branches one half what we might expect and makes pendant and interior branches roughly equal in length. Although dependent on whether we condition on the size of the tree, its age, or both, these results hold both for the Yule model and for birth-death models with moderate extinction. Importantly, the rough equivalency in interior and exterior branch lengths means the loss of evolutionary history with loss of species can be roughly linear. Under these models, the Tree of Life may offer limited redundancy in the face of ongoing species loss.

Motivation & Objective

• To reassess the robustness of the Nee and May (1997) claim that 80% of PD survives 95% species loss, which relies on coalescent-based tree models with highly unequal branch lengths.
• To investigate how conditioning on tree size (n), age (t), or diversification rate (λ) affects expected branch lengths in Yule and birth-death trees.
• To evaluate whether the assumption of high phylogenetic redundancy in the Tree of Life holds under biologically plausible diversification models.
• To quantify the expected loss of phylogenetic diversity (PD) as species go extinct under these models, particularly under moderate extinction rates.

Proposed method

• Uses the Yule process (pure-birth model) and birth-death processes to model tree diversification, with branching events occurring at rate λ and extinction at rate μ.
• Applies conditioning on tree size (n), depth (t), or both, to reflect real-world sampling scenarios where trees are observed at a fixed number of extant species.
• Derives analytical expressions for expected pendant edge length (pₙ) and interior edge length (iₙ) using results from Steel and Mooers (2010), extended to birth-death models.
• Computes expected phylogenetic diversity (PD) as Lₙ = n·pₙ + (n−2)·iₙ to assess loss under species extinction.
• Analyzes the impact of censoring at the present time on branch length expectations, showing that this conditioning reduces average edge length to half the naive expectation (1/(2λ)).
• Evaluates the 'push of the past' effect and non-uniform diversification (e.g., adaptive radiations) to assess their impact on branch length distribution and PD loss.

Experimental results

Research questions

• RQ1 How do expected branch lengths in Yule trees change when conditioned on the number of tips (n), tree depth (t), or both?
• RQ2 To what extent do pendant and interior branch lengths differ in Yule and birth-death trees under realistic sampling conditions?
• RQ3 How does the expected loss of phylogenetic diversity (PD) scale with species extinction under Yule and birth-death models, compared to the coalescent model?
• RQ4 Does the inclusion of moderate extinction (μ > 0) alter the conclusion that PD loss is nearly linear with species loss?
• RQ5 How do empirical patterns—such as negative gamma statistics in real phylogenies—support or contradict the assumption of high phylogenetic redundancy?

Key findings

• The expected average edge length in a Yule tree is 1/(2λ), half the naive expectation of 1/λ, due to conditioning on tree size at the present.
• Pendant and interior branch lengths are nearly equal in expectation under the Yule model, meaning there is little phylogenetic redundancy in branch length distribution.
• Under Yule and birth-death models with moderate extinction, the loss of phylogenetic diversity is nearly linear with species loss, contradicting the Nee and May (1997) claim of 80% PD retention after 95% extinction.
• The 'push of the past' and non-uniform diversification (e.g., adaptive radiations) further reduce interior branch lengths, diminishing any potential redundancy.
• Coalescent-based models overestimate redundancy because they produce very short pendant edges; real trees, which tend to have longer terminal branches, do not support the same level of PD resilience.
• Even under moderate extinction (μ/λ < 1), the expected loss of PD remains steep, and the ratio π(s) of expected PD loss to species loss approaches 1 only in the critical case (μ = λ), which is biologically unrealistic for surviving trees.