Untangling Multiple Factors in Spatial Distributions: Lilies, Gophers, and Rocks

Abstract

Despite broad consensus on the power of experiments, correlational studies are still important in ecology, and may become more so as spatial studies proliferate. Conventional correlation analysis, however, (1) fundamentally conflicts with the basic ecological concept of limiting factors, and (2) ignores spatial structure in data, which can produce spuriously high correlations. Especially for field data, bivariate scattergrams often show _factor—ceiling" distributions wherein data points are widely scattered beneath an upper limit, due to the action of other factors. Although most ecological information in such a graph resides in the upper limit, standard correlation/regression does not characterize such limits. If other factors have been measured, path analysis may be useful, but otherwise, direct description of ecological ceilings is desirable. Objective methods for doing so are barely known to ecologists; we review recent proposals for statistical testing and data display. For correcting correlations for spatial patchiness of the variables, another new technique has been proposed by Clifford, Richardson, and Hemon: by reducing the effective sample size to account for the autocorrelation it allows significance tests. We discuss these issues with reference to counts of glacier lily (Erythronium grandiflorum) seedlings, vegetative plants, and flowering plants in a square grid of 256 contiguous $2 \times 2$ m quadrats in subalpine meadow in western Colorado. We also measured soil moisture, pocket gopher activity, and soil rockiness. All six variables showed significant patchiness (spatial autocorrelation) at similar scales. The abundance of flowering plants was positively correlated with rockiness and negatively correlated with moisture and gopher activity. Although limited seed dispersal suggests that seedlings should be spatially associated with flowering plants, no such correlation existed: indeed, examination of the bivariate scatterplot suggests a negative association, in the particular and restricted sense that seedlings are abundant only in quadrats where flowering is low. We hypothesize that seed germination is higher in less rocky areas of deeper, moister soil than in the rocky areas where most seeds land, but that seedlings seldom reach maturity unless they are in a rocky refuge from predation. Results from path analysis are consistent with this hypothesis. Such an ecological situation should weaken natural selection on characters enhancing seed dispersal.