Squaring within the Colless index yields a better balance index

Area of Science:

• Phylogenetics
• Computational Biology
• Evolutionary Biology

Background:

• The Colless index is a popular measure of phylogenetic tree balance.
• It is widely used due to its simplicity and discriminatory power.
• However, the original index has analytical limitations and can be ambiguous in identifying maximally balanced trees.

Purpose of the Study:

• To address the drawbacks of the traditional Colless index.
• To develop a more analytically tractable and powerful phylogenetic balance index.
• To improve the study of phylogenetic tree distributions under probabilistic models.

Main Methods:

• Modification of the Colless index by replacing absolute differences with squared differences.
• Analytical investigation of the new index's properties.
• Comparison of the modified index with the original Colless index in terms of power and discrimination.

Main Results:

• The modified index overcomes the analytical difficulties associated with the original Colless index.
• The new index is shown to be more powerful and discriminating than the original.
• The squared difference approach facilitates analytical study of distributions under probabilistic models.

Conclusions:

• The squared Colless index offers a superior alternative for phylogenetic tree balance assessment.
• This modification enhances the analytical tractability and discriminatory power of phylogenetic shape indices.
• The findings contribute to a better understanding of phylogenetic tree shapes and their evolutionary implications.