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**Published:** Jan 1978

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**Source: **STP652-EB

The lognormal distribution has figured prominently in the description of species-abundance relationships and in assessing effects of perturbation on aquatic ecosystems. Diatom communities, in particular, have been shown to conform relatively well to a normal law subsequent to grouping individuals on a logarithmic scale. Fitting of the distribution to sample data entails estimation of location and scale parameters. A more interesting and, indeed, ecologically important estimate that can be obtained is the total number of species in the community, *S*^{*}. Unfortunately, estimates of *S*^{*} are currently unsatisfactory since an estimator of the variance of *S**, var (*S**), is not available. Moreover, it is often the case that several different theoretical distributions are found to fit the same sample data equally well but provide discrepant estimates of *S**. On this basis then, comparisons between different communities are impossible. In addition, a cautious attitude is warranted in certain applications of the Shannon-Wiener diversity index where knowledge of *S*^{*} is required.

The purpose of this paper is to report on the results of a computer simulation study which was designed to mimic the sampling and identification of diatom species from idealized, fully censused collections where the value of *S*^{*} was known as was the proportional abundance of each species. Each simulation run consisted of sampling the idealized collections a total of 100 (independent) times; each sample being fit by a lognormal distribution and an estimate of *S*^{*} calculated. It was thus possible to compute an estimate of var (*S~*^{*}) and monitor its behavior as the sample sizes for various types of communities were increased. The results indicate that the precision of *S~*^{*} depends on the relative size of the sample and that var (*S~*^{*}) decreases asymptotically as the number of species sampled approaches *S*^{*}. It is shown that, for some types of communities, species sample sizes on the order of *S* = 0.8 (*S*^{*}) yield imprecise estimates of *S*^{*}. The implications of these results have importance for the biologist who is faced with distinguishing between two or more similarly diverse communities on the basis on an index of evenness such as *H/H*^{max} (in the case of Shannon-Wiener). Unless reliable knowledge of *S*^{*} can be obtained, misleading conclusions regarding a community's diversity could result.

**Keywords:**

ecology, environments, lognormal distribution, total species, simulation, species diversity, species evenness

**Author Information:**

Slocomb, J *Graduate research assistant and assistant director, Center for Environment Studies, Virginia Polytechnic Institute and State University, Blacksburg, Va*

Dickson, KL *Graduate research assistant and assistant director, Center for Environment Studies, Virginia Polytechnic Institute and State University, Blacksburg, Va*

**Committee/Subcommittee:** D19.02

**DOI:** 10.1520/STP35655S