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Heuristic Mining of Hierarchical Genotypes and Accessory Genome Loci in Bacterial Populations

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Phylogenetic Diversity Indices from an Affine and Projective Viewpoint.

V Moulton¹, A Spillner², K Wicke³

¹School of Computing Sciences, University of East Anglia, Norwich, UK.

Bulletin of Mathematical Biology

|July 9, 2024

Summary

This study introduces generalized phylogenetic diversity indices derived from species clusters and splits, offering a unified framework for conservation. These new indices accommodate uncertainty in evolutionary history, enhancing biodiversity assessments.

Keywords:

Fair Proportion index Cluster system Phylogenetic diversity Phylogenetic tree Shapley value Split system

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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.