#### Consortium for Mathematics and its Applications

Product ID: 99705
Supplementary Print

# 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.

INTRODUCTION

BUILDING INTUITION

DIVERSITY 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

UMAP Module
34 pages

Calculus

#### Application Areas:

Environment & Sustainability , Life Sciences & Medicine , Biology, Ecology

#### Prerequisites:

Mean Value Theorem; logarithms and their derivatives; first and second derivatives; L'Hopital's rule