ANALYSIS OF COMPLEX AND PATCHY PALEOECOLOGIC GRADIENTS USING FLEXIBLE SHORTEST PATH ADJUSTMENT OF ECOLOGIC DISTANCES

A variety of multivariate techniques are available to ordinate quantitative paleoecologic data (i.e., the abundances of species in paleoecologic samples). The simplest, like principal components analysis, are subject to the “horseshoe” or “arch” effect because the measured distance between two samples equals a maximum value (often one unit) when no species are shared, regardless of the actual ecologic separation along the gradient. Thus, measured ecologic distances can reveal small-scale structure, but large-scale structure is distorted and folded. Flexible shortest path adjustment (FSPA; Bradfield and Kenkel 1987; De'ath 1999) is a method of unfolding this large-scale structure. First, all pairwise distances above some threshold are deleted from the distance matrix because they represent indeterminately large ecologic distances. Each deleted value is replaced by the minimum sum of distances between the two samples and one or more intermediate data points. Thus, the measured distances between data points correspond more closely to the true distance along a gradient. Traditional multivariate methods can be used on the resulting distance matrix. FSPA should be a valuable supplement to other techniques used in paleoecology because it can effectively reveal the existence of a variety of patterns beyond simple gradients, such as two-dimensional gradients, branching gradients, and patches. This is particularly important in paleoecology because we cannot directly observe the environmental variations that largely control the distributions of species (modern ecologists can often use methods that presuppose a one-dimensional gradient because they can observe and measure the generating gradient in temperature, altitude, water depth, etc.). The value of FSPA in revealing paleoecologic patterns beyond simple gradients will be demonstrated with simulated and real data, including some from the Late Devonian of the Appalachian Basin.