Computing likelihoods for coalescents with multiple collisions in the infinitely many sites model

Area of Science:

• Mathematical Genetics
• Population Genetics
• Evolutionary Biology

Background:

• Classical population genetics models like Wright-Fisher and Moran assume binary ancestral collisions (Kingman's coalescent).
• Generalised Lambda-Fleming-Viot processes and Lambda-coalescents allow for multiple simultaneous ancestral collisions.
• These generalized models may better represent populations with extreme reproductive strategies, such as marine species.

Purpose of the Study:

• To extend existing inference methods for population genetics to accommodate general Lambda-coalescents.
• To develop a likelihood-based approach for inferring evolutionary parameters from DNA samples under these more general models.
• To identify and utilize a relevant subfamily of Lambda-coalescents (Beta(2 - alpha, alpha)-coalescents) for practical applications.

Main Methods:

• Extension of inference techniques developed by Ethier and Griffiths, and Griffiths and Tavaré.
• Development of a method to compute approximate likelihood surfaces for observed genetic type probabilities.
• Application of the method to simulated datasets for parameter estimation.

Main Results:

• A novel likelihood-based inference method for general Lambda-coalescents has been established.
• The method enables the computation of approximate likelihood surfaces for genetic data.
• Maximum-likelihood estimators for mutation and demographic parameters were obtained using simulated data.

Conclusions:

• The developed method provides a powerful tool for inferring population evolutionary parameters under generalized coalescent models.
• The Beta(2 - alpha, alpha)-coalescent family offers a relevant and parametrisable subset for such inferences.
• This approach enhances the ability to model and understand populations with complex reproductive dynamics.