Chapter 6 Diversity Measures
How diverse is this site? many sites? region?
Let’s examine the “diversity” of our sites and study area.
Diversity can encompass any sort of variation, e.g., taxonomic, trait, or phylogenetic.
Here we assume that spe is a species abundance matrix where rows = sites, columns = taxa, and values must not be negative or missing.
Recall that we did a validity test on the spe data table in Section 5, ensuring there weren’t any NA values. We could do a similar test looking for negative values.
6.1 Gamma (regional) diversity
The total number of species in a given region.
## [1] 56NOTE: there are other approaches to calculating gamma diversity that incorporate both richness and evenness, such as Shannon, Simpson, and Hill indices. We will not cover these calculations today, but you should be aware of them and investigate them for the future. Below is an example of calculating Shannon gamma.
6.2 Alpha (per-site) diversity
The number of species in a plot, averaged over all plots for Whittaker’s alpha.
### Alpha (per-site) diversity
alpha <- rowSums(spe > 0) # within-site
avgalpha <- mean(alpha) # average within-site
avgalpha## [1] 6.2680416.3 Beta (among-site) diversity: Whittaker’s
The calculation below is for a classic Whittaker’s beta diversity measure, but we’ve subtracted a value of 1 from the ratio of gamma and avgalpha. This is because if we didn’t subtract 1 and there was no turnover, then beta would equal 1, which can be confusing.
## [1] 7.9342116.4 Beta diversity: dust bunny indices (DBI)
McCune and Root (2015) proposed two model-free measures of how strongly multivariate species data exhibit a “dust bunny” distribution, that is, departure from multivariate normality because of many zero abundances due to few species occurring in any given sample unit. In other words, the DBI measures how much of the community matrix consists of “dust” - i.e., rare species, low abundances, and empty cells. High values indicate that most species occur in few sites and/or at low relative abundance. Low values indicate broadly distributed and abundant taxa. This information is important because many multivariate methods become harder to interpret, and potentially invalid, when matrices have high dust-bunny values (many rare species and zeros), which is common in community ecology datasets.
Calculate the proportion of zeros in the matrix, independent of abundance
propzero <- sum(spe < .Machine$double.eps) / prod(dim(spe))
cat('Proportion of zeros in matrix:', propzero, '\n')## Proportion of zeros in matrix: 0.8880707Calculate the dust-bunny index (DBI) for the matrix, including abundances
The code below includes many steps in one line. Here’s what’s going on:
vegan::decostand(spe, method='max')= max-standardize each species column, i.e., divides each column by its maximum value, so each species abundance has a maximum value of 1as.matrix(...)= treats the output of the max-stadnardization as amatrixmean(as.matrix(...))= calculates the overall average abundance for all species at all sites1 - mean(...)= results in an index where a value of 0 indicates a dense matrix, with few zeros, where most species are common and a value of 1 indicates a sparse matrix, with many zeros, where rare species dominate
## Dust bunny index: 0.9325203