Analyzing maps of dispersal around a single focus

The spatial pattern of organisms may be used to characterize their dispersal, quantify spread or estimate the point of introduction of an alien species. Their distribution may be represented by maps of individuals, or by counts or by presence/absence at known positions within a sampled area. The problems and relative merits of these different forms of data for spatial inference are discussed. Three datasets concerning dispersal from a single focus are analyzed: counts of aphids, Rhopalosiphum padi and Sitobion avenae, on barley plants, Hordeum vulgare, grown in experimental trays; mapped locations of couch grass, Elymus repens, tillers within plots of a field experiment; locations of sightings of the lupin aphid, Macrosiphum albifrons, as it invaded Great Britain between 1981 and 1984. A method for generating maps from counts is proposed to overcome problems caused by recording imprecision. Several statistics are used to quantify dispersal and spatial pattern in the experimental data and together provide a clear picture of the spatial pattern observed; they enabled several effects of the experimental treatments to be identified. The value of the statistics are compared. Estimates of the source of the lupin aphid invasion are obtained using the backtracking methods of Perry (1995b) and do not contradict previous suggestions.