Formal Links between Feature Diversity and Phylogenetic Diversity

Area of Science:

• Biodiversity conservation
• Evolutionary biology
• Quantitative ecology

Background:

• Phylogenetic diversity (PD) and feature diversity (FD) are crucial metrics in biodiversity conservation.
• The congruence between PD and FD is a debated topic, impacting conservation strategies.
• Understanding their relationship is vital for effective biodiversity assessments.

Purpose of the Study:

• To mathematically formalize the conditions under which feature diversity (FD) equals phylogenetic diversity (PD).
• To identify the primary reasons for discrepancies between FD and PD.
• To explore the relationship between PD and FD indices derived from Shapley values.

Main Methods:

• Formal mathematical analysis of diversity metrics.
• Development of conditions for the equivalence of FD and PD.
• Investigation of Shapley value-based indices for PD and FD.

Main Results:

• Established a precise mathematical condition for FD to coincide with PD.
• Identified feature evolution/loss patterns and inappropriate temporal branch lengths as causes for divergence.
• Demonstrated that PD and FD indices (Fair Proportion and a simple FD index) can be identical by adjusting branch lengths.

Conclusions:

• The alignment of phylogenetic and feature diversity is not guaranteed and depends on specific evolutionary and methodological factors.
• Appropriate selection or transformation of branch lengths can reconcile differences between PD and FD measures.
• This work provides a mathematical framework for understanding and potentially unifying these two important biodiversity metrics.