SPIn

SPIn implements algebraic invariant methods to perform model selection in phylogenetics by characterizing equivariant evolutionary models through linear equations on expected leaf-site pattern probabilities.

Key Features:

• Algebraic invariants: Uses algebraic invariants derived from expected probabilities at the leaves to define constraints for evolutionary models.
• Equivariant model characterization: Fully characterizes equivariant models of evolution via a comprehensive set of linear equations.
• Phylogenetic mixture equivalence: Demonstrates that, for most equivariant models, the space of distributions satisfying these equations coincides with distributions arising from mixtures of phylogenetic trees.
• Linearly independent equations: Provides a complete set of linearly independent equations for each equivariant model applicable to any number of taxa.
• Equation-generation algorithm: Implements an explicit algorithm that generates the defining linear equations for various models and taxa.
• Identifiability analysis: Treats the space of phylogenetic mixtures as a linear space to study identifiability of phylogenetic mixtures.

Scientific Applications:

• Model selection in phylogenetics: Selects among equivariant evolutionary models for molecular sequence data using algebraic constraints.
• Assessment of multiple sequence alignments: Tests whether an observed multiple sequence alignment can be modeled by a mixture of phylogenetic trees under an equivariant model via satisfaction of the linear equations.
• Identifiability and model characterization: Analyzes and characterizes identifiability properties of phylogenetic mixtures and evolutionary processes.

Methodology:

Derives linear equations from expected leaf-site pattern probabilities following the framework of J. Felsenstein, computes algebraic invariants and linearly independent equations for equivariant models, and generates these defining equations with an explicit algorithm for specified models and numbers of taxa.