Assessing group differences in biodiversity by simultaneously testing a user-defined selection of diversity indices

Abstract

Comparing diversities between groups is a task biologists are frequently faced with, for example in ecological field trials or when dealing with metagenomics data. However, researchers often waver about which measure of diversity to choose as there is a multitude of approaches available. As Jost (2008, Molecular Ecology, 17, 4015) has pointed out, widely used measures such as the Shannon or Simpson index have undesirable properties which make them hard to compare and interpret. Many of the problems associated with the use of these 'raw' indices can be corrected by transforming them into 'true' diversity measures. We introduce a technique that allows the comparison of two or more groups of observations and simultaneously tests a user-defined selection of a number of 'true' diversity measures. This procedure yields multiplicity-adjusted P-values according to the method of Westfall and Young (1993, Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment, 49, 941), which ensures that the rate of false positives (type I error) does not rise when the number of groups and/or diversity indices is extended. Software is available in the R package 'simboot'.

Figure 1

Mosaic plot of the soil bacteria data set. The columns are ordered by group (forest and grassland) and represent the single replications. The heights of the boxes within each column are proportional to the relative frequencies of the phyla or proteobacterial classes in each replication. The phyla and classes are ordered by decreasing overall abundance. The names of phyla or classes whose total frequency of occurrence falls below 0.02 are replaced by dots. Dashed lines indicate phyla or classes to be missing in this replication.

Figure 2

Rank/abundance plot of the soil bacteria data set. The relative abundances of the phyla and proteobacterial classes are on a logarithmic scale. All replications of the groups (forest and grassland) were summed up.

Figure 3

Correlation structures of the soil bacteria data set. Empirical distributions of 1000 bootstrap test statistics for integral Hill numbers of orders q from −1 to 3 are plotted in pairs. The respective marginal upper 5% quantiles (corresponding to an upper-tailed test) are shaded in light gray, the overlapping area in dark gray. r² is the Pearson correlation coefficient.

Figure 4

Increase of the two-sided 95%-quantile of the soil bacteria data set with multiplicity correction according to Bonferroni and Westfall & Young, respectively, when raising the number of hypotheses tested. The Bonferroni quantiles were estimated from the empirical bootstrap distribution. For −1≤q≤3 the numbers of 2, 3, 5, 9, 41 and 81 indices correspond to Δ_q=4, 2, 1, 0.5, 0.1 and 0.05 (B=99,999).

Figure 5

Mosaic plot of the marine invertebrates data set. The columns are ordered by group (wave-exposed and sheltered) and represent the single replications. The widths of the columns are proportional to the number of individuals in each replication. The heights of the boxes within each column are proportional to the relative frequencies of the species in each replication. The species are ordered by decreasing overall abundance. Only the names of the ten most abundant species are listed, the others are replaced by dots. Dashed lines indicate species to be missing in this replication.

Figure 6

Rank/abundance plot of the marine invertebrates data set. The relative abundances of the species are on a logarithmic scale. All replications of the groups (wave-exposed and sheltered) were summed up.

Figure 7

Correlation structures of the marine invertebrates data set. Empirical distributions of 1000 bootstrap test statistics for integral Hill numbers of orders q from −1 to 3 are plotted in pairs. The respective upper 5% quantiles are shaded in light gray, the overlapping area in dark gray. r² is the Pearson correlation coefficient.

Figure 8

Mosaic plot of the predatory insects data set. The columns are ordered by group (“GM”, “S1”, “S2” and “S3”) and represent the single replications. The numbers above the columns denote the blocks. The widths of the columns are proportional to the number of individuals in each replication. The heights of the boxes within each column are proportional to the relative frequencies of the species in each replication. The species are ordered by decreasing overall abundance. The (abbreviated) names of species whose total frequency of occurrence falls below 0.02 are replaced by dots. Dashed lines indicate species to be missing in this replication.

Figure 9

Rank/abundance plot of the predatory insects data set. The relative abundances of the species are on a logarithmic scale. All replications of the groups (“GM”, “S1”, “S2” and “S3”) were summed up.