Statistical and Structural Bias in Birth-Death Models.

Area of Science:

• Phylogenetics
• Evolutionary Biology
• Computational Biology

Background:

• Accurate estimation of speciation (λ) and extinction (μ) rates from phylogenetic trees is crucial for understanding diversification dynamics.
• Existing estimators may be subject to statistical and structural biases, particularly with smaller trees.

Purpose of the Study:

• To identify and quantify sources of bias in speciation and extinction rate estimation.
• To develop corrected estimators that minimize bias in birth-death model inference.

Main Methods:

• Re-derivation of bias in the standard Yule process estimator for speciation rate (λ).
• Application of symbolic regression to the birth-death model to find bias-minimizing estimators for λ and μ.
• Evaluation of corrected estimators on simulated phylogenetic trees.

Main Results:

• The standard speciation rate estimator (λ^) underestimates the true rate (λ) by a factor of (n-2)/(n-1) for the Yule process.
• A new correction for extinction rate (μ) bias depends on sample size and the extinction fraction (μ/λ).
• Corrected estimators significantly improve the accuracy of estimated diversification rates, though net diversification (λ - μ) remains underestimated.

Conclusions:

• Statistical and structural biases in phylogenetic tree-based diversification rate estimation are clarified.
• The developed bias corrections provide a framework for more accurate inference under birth-death models.
• Further refinement is needed to address residual bias in net diversification estimation.