UNTANGLING MULTIPLE FACTORS IN SPATIAL DISTRIBUTIONS - LILIES, GOPHERS, AND ROCKS

Despite broad consensus on the power of experiments, correlational stu dies 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 sca ttergrams often show ''factor-ceiling'' distributions wherein data poi nts are widely scattered beneath an upper limit, due to the action of other factors. Although most ecological information in such a graph re sides in the upper limit, standard correlation/regression does not cha racterize such limits. If other factors have been measured, path analy sis may be useful, but otherwise, direct description of ecological cei lings is desirable. Objective methods for doing so are barely known to ecologists; we review recent proposals for statistical testing and da ta display. For correcting correlations for spatial patchiness of the variables, another new technique has been proposed by Clifford, Richar dson, and Hemon: by reducing the effective sample size to account for the autocorrelation it allows significance tests. We discuss these iss ues with reference to counts of glacier lily (Erythronium grandiflorum ) seedlings, vegetative plants, and flowering plants in a square grid of 256 contiguous 2 x 2 m quadrats in subalpine meadow in western Colo rado. We also measured soil moisture, pocket gopher activity, and soil rockiness. All six variables showed significant patchiness (spatial a utocorrelation) at similar scales. The abundance of flowering plants w as positively correlated with rockiness and negatively correlated with moisture and gopher activity. Although limited seed dispersal suggest s that seedlings should be spatially associated with flowering plants, no such correlation existed: indeed, examination of the bivariate sca tterplot suggests a negative association, in the particular and restri cted sense that seedlings are abundant only in quadrats where flowerin g is low. We hypothesize that seed germination is higher in less rocky areas of deeper, moister soil than in the rocky areas where most seed s 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 natu ral selection on characters enhancing seed dispersal.