A Single Mechanism to Account for Regular, Random and Aggregated Populations

In studying the spatial arrangement of natural populations of plants it has been customary to distinguish three types of distribution or pattern: random, aggregated and regular. The individuals of a species are said to be at random if the position of each individual plant is independent of that of all the others; aggregated populations are those in which there is a tendency for the individuals of the species to occur in clumps; and in regular populations the plants are more evenly spaced than they would be were they distributed according to chance. Aggregated populations have been found to be very common in nature and two causes have been suggested for this aggregation (Feller 1943). On the one hand seeds may fall at random over an area but if the habitat is not homogeneous the proportion germinating and thriving will vary from site to site so that the density is high in some sites and low in others. On the other hand the habitat may be homogeneous but the individual plants may occur in family groups owing to the fact that they reproduce vegetatively or by seeds with small radius of dispersal. Feller (1943) has shown that it is impossible, by statistical methods alone, to distinguish between these two causes of aggregation; in any case, both might well be operating simultaneously. Regular populations appear to be extremely rare. According to Greig-Smith (1957) a regular pattern would be expected to occur if the members of a population were so abundant that they competed with each other for the available space. A frequency table obtained by quadrat-sampling such a population should be well graduated by a binomial series, as was done, for instance, by Student (1907) who considered the distribution of yeast cells in the squares of a haemacytometer. Several frequency functions have been used to graduate the results obtained by quadrat-sampling aggregated populations, those most favoured being the negative binomial (Greenwood & Yule 1920, Bliss & Fisher 1953), Neyman's type A (Neyman 1939, Archibald 1948) and Thomas's double Poisson (Thomas 1949, Archibald 1950). In none of these, however, is the necessarily finite size of the individual plants taken into account. In studying aggregated plant populations allowance for the effects of plant size appears to have been made only by Skellam (1952) who calculated a distribution based on the assumption that clumps of plants (of the species being investigated) occurred at random but within a clump the individuals exhibited a positive binomial distribution owing to the effects of competition. This series has since been named the Poisson Binomial by McGuire, Brindley & Bancroft (1957).