Natural Resource BiometricsMeasures of DiversityFormated version of this page for printingShannonWiener IndexThis diversity measure is based on information theory; simply, the measure of order (or disorder) within a particular system. For our uses, this order could be characterized by the number of species and/or the number of individuals in each species, within our sample plot. By applying these numbers to the ShannonWiener equations we can determine what is referred to as the degree of uncertainty. With this number we can then specify our degree of diversity. In questioning how difficult it would be to predict correctly the species of the next individual collected, we define uncertainty, in turn defining diversity. For example, if our number of uncertainty is low, ie. we feel confident in naming the next individual's species, our types of species are few. And, of course, vice versa... if our number of uncertainty is high, the number of species are greater and our chances of knowing the next individual's species are low.
ShannonWiener indexwhere H = Information content of sample, Index of species diversity, or Degree of Uncertainty, c = Number of categories(species) pi = Proportion of total sample belonging to ith category(species)
Alternative FormAn alternative form for ShannonWiener index:where N_{1} is the number of equally common categories (species) for the diversity H'. The equations varies depending on the type of logarithms used to calculate the H'.
Measures of EvennessThe maximum ShannonWiener index for a given number of categories(species) can be calculated as:The minimum ShannonWiener index for a given data set can be calculated as: Where:
The evenness of the sample can be calculated by the following two equations:
Base conversion with LogarithmsTo convert from known log bases to any other log base use: where b is the base value, loge is the natural logarithm, and x is the value to be transformed. For example to take a log base 2 you would use:
Other Hints
Also See: Chapter 10  Species Diversity Measures pages 361367 in:

Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons AttributionShareAlike 4.0 International License . Author: J. Mark Travis and Dr. David R. Larsen Created: October 11, 1995 Last Updated: July 29, 2014 