PMLE

PMLE estimates gene flow parameters (θ) in semi-isolated island populations by applying a pseudo maximum likelihood estimator to allele distribution data to quantify migration and effective population size relationships.

Key Features:

• Estimation Methodology: Employs a pseudo maximum likelihood estimator (PMLE) to derive estimates for θ, defined in Wright's discrete-generation island model as 2Nm where N is haploid population size per island and m is the fraction of individuals replaced by immigrants per generation.
• Model Flexibility: Applies to both discrete- and continuous-generation models, with θ in the continuous-generation formulation representing the ratio of immigration rate (φ) to individual birth rate (λ).
• Data Compatibility: Accepts molecular data types including allozymes, microsatellites, and RFLPs, and handles single- and multi-locus genotype data from haploid or diploid organisms.
• Statistical Efficiency: Monte Carlo simulations show PMLE has greater statistical efficiency and lower mean square error than alternative estimators derived from Wright's F-statistics across a wide range of sample sizes and parameter values.

Scientific Applications:

• Island population gene flow analysis: Quantifies migration and subdivision effects in island models to study evolutionary dynamics in semi-isolated populations.
• Empirical estimation in subdivided populations: Applied to estimate θ using mitochondrial DNA (mtDNA) haplotypes and allozymes in case studies such as African elephants and Channel Island foxes.

Methodology:

PMLE is derived from the distribution of alleles across samples from multiple islands and considers both discrete- and continuous-generation models; its statistical properties are compared with alternative estimators using Monte Carlo simulations.