The Density-Dependence of Spatial Behaviour and the Rarity of Randomness

Abstract

1. Spatial distribution was analysed in 156 sets of field data comprising more than 200,000 sample units in 3840 samples from 102 species. 2. Taylor's model, proposing that spatial variance is proportional to a fractional power of mean population density, provided an appropriate description of 147 sets of data. 3. Iwao's mean crowding model provided a rather less adequate alternative but with marked limitations. 4. The negative binomial with a common k was not satisfactory. 5. Two data sets only were judged random at all population densities. 6. In all other sets of samples, only at or near the lowest densities was disposition indistinguishable from random and the range of spacing between individuals progressively and disproportionately changed as mean density increased. 7. Spatial disposition is thus density-dependent and we deduce that spatial behaviour is also density-dependent as required by Taylor and Taylor's delta-model for intrinsic population contril by movement. 8. The sepcies examined range from Protista through annelids, molluscs, crustaceans, arachnids, insects, echinoderms, fish, birds and quadrupeds to men and orchids. 9. The sampling scales range from ciliates on the surface of a flat-worm to the human population of the United States of America and include temporally stable and unstable populations. 10. The sampling methods range from quadrat counts, through trap, net and grab samples to volumetric samples and complete censuses.