Variance and the Large Scale Spatial Stability of Aphids, Moths and Birds

(1) Ninety-seven species of aphids, 263 species of moths and 111 species of birds were sampled simultaneously over an area of about 2300 km2, for up to eleven, thirteen and fifteen years at up to twenty-four, 126 and 210 sites, respectively. (2) Aphid sites were uniform farmland; bird sites were segregated into farmland and woodland; moth sites were highly diverse. (3) Aphids were sampled by suction traps, moths by light traps and birds by direct observation. (4) By analogy with temporal variance, spatial variance (S2) was used as a measure of spatial stability and in most species was found to be proportional to a fractional power of mean population density (ms). (5) Estimates of the parameter b, in S,2 = amb, ranged from 1.29 to 2-95, 0.95 to 3.32 and 1.19 to 2.69 in aphids, moths and birds respectively, and from 1.20 to 3.32 within a single genus (Apamea). (6) Estimates of the parameter a (in S2 = amb) were different in farmland and woodland for nearly half the bird species examined. This difference may be due to environmental components of variance. (7) Taylor's (1961) power model fitted well in 95/ of species and, on logarithmic scales, mean population density accounted for more than 70o of the spatial variance in more than 90/ of species. This suggests that species' behaviour is a major component of spatial stability, being the only common property in all the environmentally varied samples. No species showed evidence of reaching an upper limit of density constraining variance.