The Commonness, And Rarity, of Species

The purpose of this paper is to deduce, from a number of examples and from theoretical considerations, some plausible general law as to how abundance or commonness is distributed among species. Experimentally, this could be done by making a complete census of every species, but, with rare exceptions, this procedure is quite impractical. We therefore attempt to deduce the "universe" from a sample. Commonness, as understood by ecologists, has several rather different meanings: we are here concerned with (1) the total number of living individuals of a given species, which might be called its global abundance, (2) the total number of individuals living at any instant on a given area, such as on an acre or a square mile, which might be called its local abundance, (3) the ratio which the number of individuals or one species bears to that of another species, i.e., its relative abundance, and (4) the number of individuals observed, for example, the number of a moth species counted in a sample from a light trap, its "observed," "apparent," or "sample" abundance. There will not usually be any difficulty in deciding which phase of the subject is under discussion at any time. The Raunkiaer "Index of Frequency" is a measure of ubiquity rather than of commonness as above defined: its relation to our other concepts is discussed later. As a rule, we are interested in a sample only in so far as it throws light upon the "universe" that is being sampled. The sample will be a sufficiently accurate replica of the universe provided (1) it is a perfectly "random" sample, and (2) no species is represented in the sample by less than 20 or 30 individuals. In most ecological work condition (2) will never obtain, and much of the present paper will center on this difficulty. Condition (1) will not usually obtain in the broadest sense, and needs a moment's consideration. A geologist sampling an ore-body, whose boundaries have been delimited accurately by previous exploration, has a known "universe" and merely needs information on composition. His universe is permanent. But in ecological work, the "universe" changes rapidly. The moths flying tonight are not those that flew a month ago, or will fly a month hence. Those flying this year are a vastly different association from those that flew last year in the same area. The same thing is true of rodent populations, of birds, and of plants. We are dealing with a fleeting and fluctuating assemblage, a "universe" continually expanding, contracting, and changing in composition. Thus it is important to recognize at the outset that, for the purposes of our present investigation, the "universe" from which the sample is drawn is that universe declared to us by the sample itself, and not our preconceived notion of what the universe ought to be. Further, it is important to recognize that the randomness we seek is merely randomness with respect to commonness or rarity. A light trap is satisfactory in this respect and samples its own universe appropriately. It is definitely selective in respect of phototropism, but it is random in respect of commonness, i.e., it does not care which of two moths, equally phototropic, it catches, though one may be a great rarity and the other of a very common species. On the other hand, an entomologist, or even an intelligent boy, with a net, is not a satisfactory collector, for he will go after the rarity. For this reason we have to reject Corbet's ('41)