WHAT DO ALL THESE NUMBERS MEAN? MULTIVARIATE GOODNESS-OF-FIT THRESHOLD FOR COMMUNITY SIMILARITY

Paleocommunity researchers often employ ordination to study variations in taxonomic abundance among samples. Ordination permits visualization of multidimensional data, with samples that have more similar taxonomic abundances plotting closer together. However, ordination is not a statistical test. Some less utilized methods (i.e., Mantel Test and the Procrustes Randomization Test (PROTEST)) measure the goodness-of-fit between two ecological datasets. However, the goodness-of-fit values have no definite ecological meaning; the value from 0 to 1 does not indicate whether two datasets would be visually interpreted as “the same”. Moreover, these are measures of overall similarity, which may not capture details important to the research question. The situation is analogous to reporting a correlation r- or p-value but not visually inspecting a scatterplot.

We examined 6000 multivariate, pairwise comparisons of simulated ecological datasets and compared a qualitative assessment of similarity to the corresponding Mantel Test and PROTEST goodness-of-fit values to determine the values at which two paleoecological results would be visually interpreted as the same. For each of the comparisons, we examined the procrustes transformed ordinations of the two datasets and gave a rank of 1, 2, or 3. Rank 1 = two ordinations were almost indistinguishable and would lead to the same interpretations. Rank 2 = two or more samples changed position radically through the ordination or one cluster divided into multiple clusters; the changes may lead to different interpretations. Rank 3 = the points moved considerably along one or both ordination axes; the changes in the groupings and patterns of the points within the ordinations would lead to different interpretations. The mean Mantel Test R-statistic for the rank of 1 was 0.94 (standard deviation = 0.04). For a rank of 2, R = 0.82 (SD = 0.16), and for a rank of 3, R = 0.49 (SD = 0.24). The mean PROTEST m²-value for the rank of 1 was 0.96 (SD = 0.035). For a rank of 2, m² = 0.84 (SD = 0.10), and for a rank of 3, m² = 0.61 (SD = 0.14). The 95% confidence interval resulted in a 0.86 and a 0.89 as the lowest values that may be considered the same (rank of 1) for the Mantel Test and PROTEST, respectively. These values serve as estimates of the threshold between classifying two paleocommunities as different and the same.