A simple way to improve multivariate analyses of paleoecological data sets

Abstract

Multivariate methods such as cluster analysis and ordination are basic to paleoecology, but the messy nature of fossil occurrence data often makes it difficult to recover clear patterns. A recently described faunal similarity index based on the Forbes coefficient improves results when its complement is employed as a distance metric. This index involves adding terms to the Forbes equation and ignoring one of the counts it employs (that of species found in neither of the samples under consideration). Analyses of simulated data matrices demonstrate its advantages. These matrices include large and small samples from two partially overlapping species pools. In a cluster analysis, the widely used Dice coefficient and the Euclidean distance metric both create groupings that reflect sample size, the Simpson index suggests large differences that do not exist, and the corrected Forbes index creates groupings based strictly on true faunal overlap. In a principal coordinates analysis (PCoA) the Forbes index almost removes the sample-size signal but other approaches create a second axis strongly dominated by sample size. Meanwhile, species lists of late Pleistocene mammals from the United States capture biogeographic signals that standard ordination methods do recover, but the adjusted Forbes coefficient spaces the points out more sensibly. Finally, when biome-scale lists for living mammals are added to the data set and extinct species are removed, correspondence analysis misleadingly separates out the biome lists, and PCoA based on the Dice coefficient places them to the edge of the cloud of fossil assemblage data points. PCoA based on the Forbes index places them in more reasonable positions. Thus, only the adjusted Forbes index is able to recover true biological patterns. These results suggest that the index may be useful in analyzing not only paleontological data sets but any data set that includes species lists having highly variable lengths.

Compositional turnover and ecological changes related to the waxing and waning of glaciers during the late Paleozoic ice age in ice-proximal regions (Pennsylvanian, western Argentina)

“…Different analyses have shown that NMDS is as good as or better than other ordination techniques in recovering the underlying structure of the data (Minchin 1987; Bush and Brame 2010). Recently, Alroy (2015) proposed that principal coordinates analysis using a novel modification of the Forbes index was a best solution for paleoecological ordination. Using PCO and the Forbes index, or another common ordination technique such as detrended correspondence analysis, gave virtually identical results.…”

Binary Coefficients Redux

“…The author observed few differences among results from several types of ordination and choice of coefficients, including the modified Forbes coefficient of Alroy (2015b) and Bray and Curtis dissimilarity.…”

Vegetation Response to Wildfire and Climate Forcing in a Rocky Mountain Lodgepole Pine Forest Over the Past 2500 Years

“…Second, to investigate the relationships between vegetation compositional change over time and to interpret the response of pollen assemblages to fire events over millennial scales, I used Kruskal's nonmetric multidimensional scaling (NMDS) to reduce the dimensionality of the dataset and map vegetation change (Alroy, 2015). This analysis was carried out using the MASS package in R and pollen data was transformed using the Bray-Curtis distance measure, a common distance metric in ecological research (Beals, 1984).…”