An Ecological Distribution Akin to Fisher's Logarithmic Distribution

Abstract

In several publications (e.g. [1947] [1950]) C. B. Williams has used the properties of Fisher's logarithmic distribution (see Fisher, Corbet and Williams, [1943]) to characterise the abundance of species of animals or plants in a sampling area. The distribution has been used to describe data consisting of the number of species of which one or more members have been in a sampling area or time. The logarithmic or log distribution implies that the number of species of which n members have been caught is proportional to x'/n where x is a positive constant less than one. The coefficient of proportionality is usually written ae and called the index of diversity. It is a measure of the richness of the biological association in the area and it is independent of the nature of the sampling. The constant x however depends on such things as the time spent in sampling and the volume of the sample (e.g. the size of a quadrat or the size of a light trap). It is sometimes impossible or inconvenient for all the individuals of a sample to be counted. Often it is only practicable to observe whether or not a species has occurred at all. Two examples of such data have come the author's way. In the first example the data were the different numbers of moss species that had been found in one, two, three, four, five, or all of the principal islands of Hawaii. These data were kindly supplied by Professor A. R. Gemmell of the University College of North Staffordshire, England, in 1949. The moss species were of three reproductive kinds, dioecious, monoecious, and sterile. Some of the dioecious species were found in only a few of the islands, some in nearly all the islands, while a smaller number were found in about half the islands. The monoecious species were mostly found in only a few islands although there were a few found in nearly all.