An evaluation of flexible shortest path adjustment in the ordination of community data with high beta diversity

Background/Question/Methods

In community data of high beta diversity, many pairs of sampling units (SUs) have no species in common.  Dissimilarity measures that are effective for analysis of community data (e.g., the Bray-Curtis index), take their maximum value for all such disjunct pairs.  Although disjunct SUs may have different degrees of separation along underlying ecological gradients, their dissimilarities contain no information about these differences.  Ordination methods that assume a linear relationship between dissimilarity and inter-point distance, such as principal coordinates analysis (PCoA) and metric multidimensional scaling (MMDS), attempt to assign equal distances to all disjunct pairs, resulting in the well-known horseshoe effect.  Flexible shortest path adjustment (FSPA), which re-estimates dissimilarities between disjunct SUs as the sum of dissimilarities along the shortest pathway through SUs that do share species, has been suggested as a solution to this problem.  Preliminary evaluations of FSPA using simulated data suggested the adjustment is sensitive to sampling.  Furthermore, nonmetric multidimensional scaling (NMDS) has been shown to successfully ordinate community data of high beta diversity without any adjustment of dissimilarities.  I performed a multi-factorial experiment to compare the effectiveness of PCoA, MMDS, and NMDS, each applied with and without FSPA, in recovering the gradient structure of simulated community data.

Results/Conclusions

Ordination performance (as measured by the Procrustes badness-of-fit between the ordination and the configuration of SUs in the simulated ecological gradient space) was significantly improved by FSPA for both linear methods (PCoA and MMDS), provided that sampling was dense and relatively even.  With sparse or uneven sampling, FSPA generally overestimated the degree of difference between disjunct SUs, resulting in deterioration of ordination performance.  This occurs because the lack of SUs in some regions of gradient space necessitates the use of sequences of SUs to re-estimate dissimilarities between disjunct SUs that lie along nonlinear pathways.  Improvements in performance of linear ordination methods by FSPA were greatest at higher beta diversities, especially when the beta diversities of simulated gradients were unequal.  NMDS performed well without FSPA, and further improvements in fit due to FSPA were generally modest.  Significantly, NMDS without FSPA often gave results that were better, or at least no worse, than the linear methods with FSPA.  The robust assumption of a monotonic fit between ordination distances and dissimilarities allows NMDS to utilize information in the smaller dissimilarities to resolve the ambiguity of dissimilarities among disjunct SUs.  Consequently, FSPA is not required for effective ordination of high beta diversity data.