tree shape statistics

tree shape statistics evaluates the discriminative power of tree shape statistics using a resolution function that quantifies their ability to distinguish among phylogenetic tree shapes and assesses convergence of linear combinations as tree size increases.

Key Features:

• Resolution Function: A resolution function that assesses the ability of different tree shape statistics to differentiate phylogenetic tree shapes and is optimized to reduce computational time and memory.
• Tree Shape Statistics: Numerical representations that encode phylogenetic tree morphology into scalar values and are evaluated for their capacity to capture nuances of tree shape.
• Linear Combination Class: A class of tree shape statistics formed as linear combinations of two existing optimal statistics with respect to the resolution function.
• Convergence Property: Demonstrates that the linear-combination class converges toward a limiting linear combination as phylogenetic tree size increases.

Scientific Applications:

• Speciation and Extinction Patterns: Inferring historical patterns of speciation and extinction from phylogenetic tree shape analysis.
• Comparative Phylogenetics: Distinguishing tree shapes to support comparative studies across taxa and assess evolutionary relationships.

Methodology:

Encode phylogenetic trees with shape statistics and evaluate those statistics using the resolution function.