Extracting gradients from community data with multiple stressors and empty plots: A case study and simulations

Ecological community data are used to infer levels of environmental stressors; for example, epiphytic lichen communities can be used to estimate levels of air pollutants. If stressors are so severe that the community of interest disappears altogether, then “empty” plots are recorded. The problem compounds when multiple environmental stressors strongly influence the community. We explore this problem using simulated data and a case study of epiphytic lichens in the Sierra Nevada mountains of the United States. This area experiences relatively high amounts of nitrogen (N) deposition that can suppress lichen communities, but this signal is confounded at high elevations where epiphytic lichens become absent. This combination of severe stressors interferes with extracting a lichen community gradient that corresponds with the air quality gradient for the full elevation range in this study area. We evaluated three general approaches: (1) methods of nonmetric multidimensional scaling that allow inclusion or exclusion of empty plots, (2) the “dummy species” method that populates empty plots with a consistent low abundance, and (3) bypassing problematic distance measures by nonparametric regression of the environmental parameter of interest (N deposition) against total abundance. In the simulated gradient, we added stressors at one or both ends of a dataset with a dominant environmental gradient to demonstrate the effect of extreme suppression of communities by environmental conditions. With lichen and simulated data that are “stressed” at one or both ends of the community gradients, Euclidean and Gower distances distorted the primary gradients in a circular manner that weakened relationships with environmental variables. This is similar to the “horseshoe effect” that is recognized as a problem in ordinations of ecological communities. If one excluded empty plots, ordination axes represented the underlying gradients better with quantitative Sørensen (Bray–Curtis) distance than with Euclidean and Gower distances, but this limits the scope of its application in bioindication. The distortion of environmental gradients can be revealed with ordination phase plots, a new method of projecting environmental gradients, whether linear or nonlinear, onto any community ordination space. The regression-based alternative to ordination extracted the strongest relationship between N deposition and lichen community data, and included empty plots.