FORTRAN IV program to compute diversity indices from information theory

Indices of diversity, especially those adopted from information theory, are useful measures of the structure of ancient communities in which post-mortem transportation and destruction of skeletal remains are judged to have been of minor importance. In the study of communities of living organisms, the number of individuals found per unit area or volume is useful information. However, application of indices of diversity presents special problems to geologists. In fossil communities, for example, the number of individuals per unit volume of sediment is affected by density during life, rate of sedimentation, differential longevity, and rate of replacement of individuals. In order to compare diversities of collections of fossils, it is appropriate therefore to base the diversities on a constant number of individuals. Pielou (1966a, 1966b, 1966c, 1967, 1969, 1974, 1975) reviewed diversity indices and related statistics (Table 1) and has suggested conditions under which the use of each is appropriate. Use of H' (equation 1) (Shannon and Weaver, 1949) depends on the assumption that the community being sampled is large enough to be regarded as infinite and that the proportions in which the various species occur are known. The equation for H (equation 2) (Brillouin, 1962) gives the true value, not an estimate, of the diversity of a fully censused collection of organisms. The approximate equation (3) for H" has been used as a substitute for both H and H', but it is not particularly well suited for either purpose. H" is a biased estimator of H and always gives values of diversity that are too high. The larger the Nj's (number of individuals in each species), the less the bias; but collections of fossils are likely to include some rare species that contribute to bias. Briliouin's H is to be preferred for determining the diversity of a fully censused collection of fossils. H" can be used to estimate H', but it is necessary to apply a correction term that includes s, the number of species. In practice, s cannot be known, making the use of H" to estimate H' impossible. In most geological examples, Brillouin's H is the preferred index of diversity. The program described here computes diversity indices and related statistics of the total collection and of a randomly selected subset of size determined by the user. The program consists of four principal sections: input, random sampling procedure, computation of diversity and equitability, and output. One subroutine, DIVERS, is used in the computation of diversity and equitability. The procedure for random sampling selects a specified number of individuals from the collection, monitoring their species designations. This new random sample is treated similarly to the total collection in computations of diversity, as is described next. The sampling is based on two systems functions, ISEED and RCM, at The University of Kansas Computation Center. ISEED generates a ten-digit seed number from the time of day. RCM is a random-number generator that takes the seed and generates a decimal between zero and one, excluding one. Users should consult their respective computation centers for functions that will give comparable results. If desired, the seed number may be derived manually from a random-number table and read directly into the computer. The structure of the data deck is explained thoroughly in the comments at the beginning of the program. After the program listing a sample data deck for Ostracoda from the Beil Member (Pennsylvanian, Virgilian) (Brondos and Kaesler, 1976) is presented as a model. A glossary of variables is located at the beginning of the program.