The Use of Log-Normal Statistics to Describe the Benthos of Lochs Etive and Creran

Abstract

One of us (Gage 1972a) has examined the diversity of the macrobenthos of Loch Etive, Loch Creran and the Firth of Lorne on the west coast of Scotland, using the rarefaction method of Sanders (1968). The other (Tett 1973) has attempted to characterize the abundance and diversity of phytoplankton populations from Loch Etive and the Firth of Lorne by means of estimates of the parameters of a log-normal model fitted to sample distributions of taxon abundances. Although Lie (1969) has shown that the abundances distribution of infaunal benthic species from Puget Sound correspond reasonably well to a truncated log-normal distribution, there is no convincing theoretical reason why this should be so. In the case of phytoplankton populations the origin of a log-normal distribution can be explained, theoretically, in terms of simple processes of exponential growth (see e.g. Macarthur 1960). It was thus of interest to test the application of the log-normal distribution to further benthic data, by use of techniques based on the method of Hald (1949) for estimating the parameters of a truncated normal distribution. It was further hoped that it might be possible to make use of log-normal statistics to compare macrobenthic populations in the same way as Tett (1972) compared phytoplankton populations. Two different approaches have become apparent in community ecology (see e.g. Pielou 1969; Hurlbert 1971); The first consists of representing a community characteristic, for example diversity, in terms of a parameter of a fitted theoretical model. The use of the log series a (Fisher, Corbet & Williams 1943), and the use of log-normal statistics, are examples of this approach. The second approach consists of the use of empirical methods, which, it is claimed, are independent of a priori assumptions about the structure of the community studied. Examples of this approach are the use of the indices proposed by Hurlbert (1971) and the Sanders (1968) rarefaction method. Similar virtues have been claimed for the various information statistics (see e.g. Margalef 1958 and Pielou 1969), but whether they are independent of a priori assumptions is arguable. By attempting to use log-normal statistics to describe the same populations as Gage (1972a) has analysed with Sanders' rarefaction method, it was hoped that a useful comparison between the two approaches could be made,