Segregation and Symmetry in Two-Species Populations as Studied by Nearest- Neighbour Relationships

Much work has been done in recent years on the spatial patterns of natural populations of plants, and it has been customary to study one species only at a time. Suppose, however, an investigator were concerned with a population containing two co-dominant species. Then, besides determining the density and spatial pattern of each of the codominant species considered separately it would also be interesting to know how the individuals of one species were arranged with respect to the individuals of the other species. The two species could be described as 'unsegregated' if any individual plant of one of the species was as likely to be found growing close to members of the other species as to members of its own species. Conversely, the two species could be described as 'segregated' if they had a tendency, however slight, to occur in one-species clumps, so that any individual was more likely to be found near members of its own species than near members of the other. In studying the relationship between two species growing in the same area it has been usual to sample the area with quadrats and then determine whether the number of joint occurrences of the two species in the same quadrat was significantly greater (or less)) than chance expectation; if so, the two species were said to be positively (or negatively) associated. However, as Greig-Smith (1957, Ch. 4) has shown, the result obtained inevitably depends on the size of quadrat used. It is thus meaningless to assert that a pair of species is, say, positively associated, unless at the same time one specifies at what scale this positive association manifests itself. Nevertheless, the degree to which the individuals in a two-species population are, colloquially speaking, 'mingled together' is clearly an intrinsic property of the whole population, and one independent of scale. Furthermore, it should be possible to measure this property in such a way that the result obtained is independent of any arbitrary characteristic (such as quadrat size), of the sampling method. It is for this purpose that the concept of segregation, as described in the previous paragraph, is proposed. The smaller the degree of 'mingled-togetherness' of a pair of species, the greater will be their degree of segregation. A population of two species, A and B, may exhibit two entirely different types of pattern, as shown in Fig. 1. One type of pattern, the 'unsegregated' type, is shown in Figs. la and lb. In Fig. la the two species are present as two co-extensive random populations. In Fig. lb the population as a whole is clumped, but within every clump the individuals of species A and the individuals of species B are present in the same proportions and are arranged independently of each other. Figs. lc, 1d, le and If show examples of the second, or 'segregated', type of pattern.