The Use of Plant-to-Neighbour Distances for the Detection of Competition

Abstract

If intraspecific competition is taking place within a plant population, unsuccessful competitors will either be small and stunted, or else completely unable to establish themselves. Also, the closer two plants are to each other, the more intensely will they compete with each other. The fact that the plants are competing with one another may therefore manifest itself in two ways: (i) the distance between any plant and its nearest neighbour will be positively correlated with the sum of their sizes, and (ii) there may be a lower limit to the distance between any plant and its nearest neighbour, or in other words, each successful plant may have around it its own 'territory' within which no new colonizers can establish themselves. In a population of fairly low density, weak competition might produce result (i) only; unsuccessful competitors would be stunted but not suppressed. Where competition is more intense, (ii) would be expected to occur as well as (i). The fact that (i) does indeed occur has been shown for two populations of trees described earlier (Pielou 1960, 1961). It will be shown in this paper that result (ii) may also be detected in populations in which competition is intense. Even if each plant in a population pre-empts an appreciable area as its own territory, a regular pattern for the population as a whole will not necessarily result. For one thing, competition may actually cause a population to be aggregated, owing to the crowding of small plants in the gaps left vacant among the territories of the large well-established ones (Pielou 1960). Alternatively, the regularity that might be expected to occur within high-density patches may be obscured if the population, considered as a whole, is aggregated because of some other cause such as familial clumping or heterogeneity of the habitat. It is for these reasons, presumably, that regular populations are so rare in nature, a fact that has been commented upon by, for example, Goodall (1952) and Greig-Smith (1957). Evidently, then, the fact that competition is taking place will seldom be detectable from a consideration of the pattern of a population of large area. Moreover, detection of regularity within dense clumps by the usual methods of examining pattern, would require that these clumps be recognized and delimited; in natural populations the investigator would have to judge subjectively which clumps were to be treated as dense and where their boundaries lay. One method of determining the pattern of a population consists in measuring a sample of distances, r, from randomly chosen individuals to their nearest neighbours. Taking as variate the square of this distance co (= r2), in a random population co will have the distributionf(cw) = Ae-AX where A denotes the mean density of the population in terms of numbers of individuals per circle of unit radius (Skellam 1952). In an aggregated population in which the density varies from point to point as a type III variate so that f(A) = ePAk-pk/F(k), co would have the distribution f(co) = kpkI(p+co)k+l (Maguire, Pearson & Wynn 1952). This latter curve would be appropriate if the proportions of low