Using geometry to rank evenness measures: Towards a deeper understanding of divergence

Area of Science:

• Ecology
• Biodiversity Science
• Mathematical Ecology

Background:

• Divergence is a key framework for understanding ecological evenness.
• Existing research lacks exploration into the relationships between families of divergence-based evenness measures.
• Understanding these relationships is crucial for accurate ecological analysis.

Purpose of the Study:

• To geometrically demonstrate that families of divergence-based evenness measures nest when order and richness are constant.
• To establish a ranking of these measures based on their reactivity to changes in even and uneven assemblages.
• To explore the relationship between distance-based measures and this ranking, and introduce a novel family of measures.

Main Methods:

• Geometric analysis to demonstrate the nesting property of divergence-based evenness measures.
• Ranking of evenness measures based on their sensitivity to changes in relative abundances.
• Derivation of a new family of distance-based measures using angular distance.

Main Results:

• Families of divergence-based evenness measures are shown to nest, allowing for a reactivity-based ranking.
• The relationship of distance-based measures (for orders q=2 and q=1) to this ranking is explored.
• A new family of distance-based measures, highly reactive to changes in even assemblages, is derived.

Conclusions:

• The nesting property provides a framework for ordering evenness measures by their sensitivity.
• The derived measures offer new tools for assessing ecological evenness.
• Further research is needed to determine which divergence measure best reflects the concept of evenness in empirical or theoretical contexts.