Estimating the Total Number of Species in a Biological Community

Abstract

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/Hmax (in the case of Shannon-Wiener). Unless reliable knowledge of S* can be obtained, misleading conclusions regarding a community's diversity could result.

The Estimation of Species Richness by Extrapolation

“…3. Integration of the lognormal distribution .. -The graph of number of species as a function of logarithm (base 2) of abundance in a sample often resembles a Gaussian curve (Preston 1948, Slocomb and Dickson 1978, Miller and Wiegert 1989. The left tail of the distribution is usually truncated.…”

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Numerous methods have been proposed for estimating the number of species, or species richness (SR) in a community. Most methods assume taxa are sampled as "individuals" (e.g., Fisher et al 1943, Efron and Thisted 1976, Slocomb and Dickson 1978. This may be approporiate for animals, which occur as discrete individuals, but it is inappropriate for plants, which often exhibit clonal reproduction.

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“…With these methods, abundance or presence of each species is recorded in randomly located quadrats. Estimators ofSR fall into four categories: (1) number of observed species, (2) extrapolations of species-area curves, (3) integration of the lognormal distribution, and (4) nonparametric estimators.The performance ofSR estimators has been assessed either by comparing the estimator to the measured SR at one or a few areas (Arrhenius 1923, Kilburn 1966, Miller and Wiegert 1989, or by simulation (Slocomb and Dickson 1978, Heltshe and Forrester 1983, Smith and van Belle 1984. The problem with the former approach is that the sample size is insufficient to establish the validity of a method.…”

“…The performance ofSR estimators has been assessed either by comparing the estimator to the measured SR at one or a few areas (Arrhenius 1923, Kilburn 1966, Miller and Wiegert 1989, or by simulation (Slocomb and Dickson 1978, Heltshe and Forrester 1983, Smith and van Belle 1984. The problem with the former approach is that the sample size is insufficient to establish the validity of a method.…”

How important are rare species in aquatic community ecology and bioassessment?

“…Many workers routinely delete rare species from their data sets, believing that rare species contribute little to community analysis but add noise to statistical solutions (Austin and Greig-Smith 1968;Gauch 1982;Marchant 1989;Boulton et al 1992;Barbour and Gerritsen 1996;Reynoldson and Rosenberg 1996;Rodriguez and Lewis 1997;Brazner and Beals 1997). Others have criticized this strategy because valuable information can be lost (Goodall 1969;Fore et al 1996: Courtemanch 1996Karr and Chu 1997) and because it lacks biological justification (Slocomb and Dickson 1978). Cao et al (1997b) argued that the concept of rare species is relative in aquatic communities, dependent on sample size, with the cutoff points often being determined arbitrarily.…”