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Additional Analytical Support for a New Method to Compute the Likelihood of Diversification Models
Giovanni Laudanno1, Bart Haegeman2, Rampal S Etienne3
1Groningen Institute for Evolutionary Life Sciences, Box 11103, 9700 CC, Groningen, The Netherlands. glaudanno@gmail.com.
Bulletin of Mathematical Biology
|January 24, 2020
Summary
This study analytically proves the correctness of a numerical framework for calculating species diversification likelihoods. The findings provide mathematical support for macroevolutionary models dependent on diversity.
Area of Science:
- Evolutionary Biology
- Computational Biology
- Phylogenetics
Background:
- Molecular phylogenies are crucial for understanding species diversification.
- Macroevolutionary models often use analytical likelihood formulas to infer parameters from phylogenies.
- A numerical framework was proposed to compute likelihoods for models with diversity-dependent rates, but its validity was questioned.
Purpose of the Study:
- To analytically validate the correctness of the numerical framework for computing likelihoods in macroevolution.
- To provide mathematical evidence supporting the general framework for species diversification.
Main Methods:
- Analytical mathematical proof.
- Comparison of the numerical framework's results with known analytical formulas for special cases.
Main Results:
- The study analytically demonstrates that the likelihoods computed by the numerical framework are correct for all special cases where analytical formulas exist.
- Numerical evidence previously showed agreement between the framework and analytical formulas.
Conclusions:
- The analytical proofs provide substantial mathematical support for the coherence and correctness of the general numerical framework.
- This validates the use of the framework for inferring macroevolutionary parameters, especially in models with diversity-dependent rates.
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