Phylogenetic Diversity Indices from an Affine and Projective Viewpoint

Area of Science:

• Ecology
• Evolutionary Biology
• Conservation Biology

Background:

• Phylogenetic diversity (PD) indices are crucial for ranking species/populations in conservation.
• Existing PD indices typically rely on phylogenetic trees (rooted or unrooted) to quantify evolutionary history.

Purpose of the Study:

• To introduce generalized phylogenetic diversity indices applicable to collections of species clusters and splits.
• To provide a unified framework for various PD indices, accommodating uncertainty in phylogenetic tree topology.

Main Methods:

• Development of novel phylogenetic diversity indices based on cluster and split collections.
• Establishment of a link between cluster-based and split-based indices using a discrete analogue of affine and projective geometry.

Main Results:

• Characterization of new indices and their special properties.
• Unified framework encompassing existing tree-based PD indices and their generalizations.
• Introduction of new PD indices as affine or projective variants.

Conclusions:

• The generalized indices offer a flexible approach to PD assessment, particularly when phylogenetic uncertainty exists.
• The unified framework simplifies and extends existing methods for phylogenetic diversity analysis.
• This work provides new tools for conservation biology and evolutionary studies.