# Information Theory and Biological Diversity (UMAP)

### Author: Steven Kolmes and Kevin Mitchell

This module discusses and derives the key properties of one measure of diversity, the entropy function, and illustrates its use by ecologists and animal behaviorists. By the end of this module students will: 1) be familiar with one common measure of diversity; 2) know how to apply this measure to ecological problems, and 3) have a greater appreciation for the Mean Value Theorem.** Table of Contents:INTRODUCTIONBUILDING INTUITIONDIVERSITY DEFINED** Proportions

The Measure of Diversity

Playing with H1

Computing Base-2 Logarithms

The Divergence from Equiprobability

**THE PROOF THAT H1max = log base 2 n**

Properties of x log base 2 x

Using the Mean Value Theorem

Convexity and H1max

**INFORMATION THEORY APPLICATIONS**

Three Applications to Ecological Diversity

Tree species diversity

Bird species diversity

The effect of insecticide application

Fire Ants

Information Theory and Fish Courtship

**SAMPLE PROJECTS**

Diversity of Flowers

Leaf Shape Diversity

Student Migrations

**SOLUTIONS TO EXERCISES**

REFERENCES

ABOUT THE AUTHORS

REFERENCES

ABOUT THE AUTHORS

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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