# On the information content of discrete phylogenetic characters

## TL;DR

This paper investigates the informational value of discrete characters in phylogenetic inference, analyzing how the number and distribution of character states affect their ability to reveal evolutionary relationships.

## Contribution

It introduces a combinatorial measure of information content for individual characters and examines properties of maximally informative characters in phylogenetics.

## Key findings

- Identifies conditions for characters to maximize phylogenetic information
- Analyzes the impact of the number of states on information content
- Explores how state distribution among taxa influences informativeness

## Abstract

Phylogenetic inference aims to reconstruct the evolutionary relationships of different species based on genetic (or other) data. Discrete characters are a particular type of data, which contain information on how the species should be grouped together. However, it has long been known that some characters contain more information than others. For instance, a character that assigns the same state to each species groups all of them together and so provides no insight into the relationships of the species considered. At the other extreme, a character that assigns a different state to each species also conveys no phylogenetic signal. In this manuscript, we study a natural combinatorial measure of the information content of an individual character and analyse properties of characters that provide the maximum phylogenetic information, particularly, the number of states such a character uses and how the different states have to be distributed among the species or taxa of the phylogenetic tree.