Spatial Density Dependence in Populations of a Cynipid Gall-Former Andricus Quercuscalicis

Abstract

Summary 1. Patterns of spatial density dependence in mortality factors affecting the sexual generation of Andricus quercuscalicis (Burgsdorf 1783) on Quercus cerris (L.) were investigated as part of a long-term study of the population dynamics of the gall wasp. Experimental enhancement of gall density was used to increase the range of densities observed in the field. 2. We present a new application of logistic regression for detecting spatial density dependence in single-sample collections of galls or leaf-mines. The test, first described by Cox (1970) uses GLIM with binomial errors. The performance of the test and the frequency of Type I and Type II errors were assessed by computer simulation of a variety of different ecological circumstances including density independence, mild and severe, direct and inverse density dependence, and proved satisfactory in most respects. 3. In our field data, statistically significant spatial density dependence was detected in about 15% of cases. Out of 62 cases of significant density dependence, 66% were of inverse density dependence. In particular, the gall wasp data demonstrate a preponderance of inverse density dependence in rates of parasitism. Only predation of galls by birds exhibited a consistent pattern of direct density dependence. There was marked variation in the intensity of all mortality factors from tree to tree. 4. As spatial scale is increased from catkins, through buds, shoots and twigs, so the sample size declines and the range of densities increases. Since reducing the sample size reduces the probability of detecting significant density dependence, but increasing the range of densities increases the likelihood of detecting density dependence, the overall effect of changing spatial scale on the probability of detecting density dependence is difficult to predict. Even when density dependence was detected at the smallest scale, the frequency of detection at higher scales declined, and this may be due in part to spatial heterogeneity in the action of density dependence. Thus, it is not obvious whether changes in the rate of detection of density dependence at different spatial scales are statistical artefacts or reflect real changes in the ecology of the organisms involved. 5. There are two potential problems in applying logistic regression to such data sets. First, overdispersion may occur if p (the probability of mortality) varies significantly within the sample. One way of dealing with this is to rescale the model, according to the degree of aggregation. Second, apparent underdispersion may occur if both p and n are low because, with small sample sizes, variation in p may be undetectable. The most obvious solution in this case is to increase the sample size n, though this may be difficult at larger spatial scales. 6. Enhancing gall densities by caging agamic females directly onto the branches of the host tree led to an increase in mean gall density and in the range of gall densities. This, in turn, led to an increase in the detection of inverse density dependence (mainly through parasitoid attack) but had no significant impact on the detection of direct density dependence. The use of experimentally enhanced gall densities appears to hold considerable potential for demonstrating the importance of spatial density dependence, so long as care is taken to ensure that the highest densities are not unrealistic. 567