a popular diversity index in ecology, where abundance data are often not available for the datasets of interest. Because richness does not take the abundance of the types into account, it is not the same thing as diversity, which does take abundance into account. However, if true diversity is calculated with , the effective number of types () equals the actual number of types, which is identical to Richness (). Shannon index The Shannon index has been a popular diversity index in the ecological literature, where it is also known as Shannon's diversity index, Shannon–Wiener index, and (erroneously) Shannon–Weaver index. The measure was originally proposed by Claude Shannon in 1948 to quantify the entropy (hence Shannon entropy, related to Shannon information content) in strings of text. The idea is that the more letters there are, and the closer their proportional abundances in the string of interest, the more difficult it is to correctly predict which letter will be the next one in the string. The Shannon entropy quantifies the uncertainty (entropy or degree of surprise) associated with this prediction. It is most often calculated as follows: where is the proportion of characters belonging to the th type of letter in the string of interest. In ecology, is often the proportion of individuals belonging to the th species in the dataset of interest. Then the Shannon entropy quantifies the uncertainty in predicting the species identity of an individual that is taken at random from the dataset. Although the equation is here written with natural logarithms, the base of the logarithm used when calculating the Shannon entropy can be chosen freely. Shannon himself discussed logarithm bases 2, 10 and , and these have since become the most popular bases in applications that use the Shannon entropy. Each log base corresponds to a different measurement unit, which has been called binary digits (bits), decimal digits (decits), and natural digits (nats) for the bases 2, 10 and , respectively. Comparing Shannon entropy values that were originally calculated with different log bases requires converting them to the same log base: change from the base to base is obtained with multiplication by . The Shannon index ({{math|H'''}}) is related to the weighted geometric mean of the proportional abundances of the types. Specifically, it equals the logarithm of true diversity as calculated with : This can also be written which equals Since the sum of the values