MIGRATE

MIGRATE estimates effective population sizes, historical migration rates between multiple populations, and assesses population divergence and admixture under a migration-matrix model that accommodates asymmetric migration rates and varying subpopulation sizes.

Key Features:

• Structured Population Models: Compares and orders structured population models using marginal likelihoods to test hypotheses such as whether sampling locations belong to a single randomly mating population or to compare unidirectional versus multidirectional gene flow models.
• Marginal Likelihood Estimation: Implements modified thermodynamic integration and a stabilized harmonic mean estimator for marginal likelihoods, with thermodynamic integration preferred for consistency and robustness with finite Markov chain Monte Carlo run lengths and reduced sensitivity to prior choice.
• Fractional Coalescent (f-coalescent): Incorporates the fractional coalescent with parameter α to model offspring variance and waiting-time patterns under the Cannings population model, capturing potential environmental heterogeneity.
• Model Comparison and Inference: Performs Bayesian inference and model comparison using Bayes factors, with simulation studies demonstrating accurate estimation of α and improved fit over traditional n-coalescent models in analyses such as H1N1 influenza and malaria parasite data.
• Applications in Population Genetics: Evaluates complex population genetic scenarios including testing deviations from Kingman's n-coalescent and assessing structured population dynamics, migration patterns, and genetic diversity across species.

Scientific Applications:

• Model selection for structured populations: Testing whether sampling locations form a single randomly mating population and comparing migration models (unidirectional versus multidirectional).
• Estimation of demographic parameters: Estimating effective population sizes and historical migration rates between subpopulations.
• Detecting deviations from coalescent assumptions: Testing for deviations from Kingman's n-coalescent and estimating the fractional coalescent parameter α.
• Pathogen population analyses: Analyzing viral and parasite datasets, exemplified by applications to H1N1 influenza and malaria parasite data.
• Bayesian hypothesis testing: Ranking and comparing competing population genetic models using marginal likelihoods and Bayes factors.

Methodology:

Uses a migration-matrix model; estimates marginal likelihoods via modified thermodynamic integration and a stabilized harmonic mean estimator with finite Markov chain Monte Carlo run lengths; implements the fractional coalescent (parameter α) within the Cannings population model; and conducts Bayesian inference and model comparison using Bayes factors.