tools-only Biodiversity Metrics
Calculates alpha diversity using Hill numbers, coverage-based rarefaction/extrapolation, and beta diversity partitioning into turnover and nestedness components.
Hill Numbers Framework
Hill numbers unify diversity indices into a single parametric family controlled by order q:
| Order (q) | Name | Sensitivity | Equivalent Index |
|---|---|---|---|
| q = 0 | Species richness | Rare species only | S (species count) |
| q = 1 | Shannon diversity | Equal weight all | exp(H') Shannon exponential |
| q = 2 | Simpson diversity | Dominant species | 1/D Simpson inverse |
Higher q values downweight rare species. q = 1 weights species by frequency and is the most balanced measure.
iNEXT Coverage-Based Rarefaction
Coverage-based rarefaction standardizes by completeness rather than sample size, enabling fair comparison of assemblages sampled with different effort (Chao & Jost 2012).
library(iNEXT)
# abundance data: named list of species abundance vectors per site
abundance_data <- list(
site_A = c(100, 45, 23, 12, 8, 5, 3, 2, 1, 1),
site_B = c(80, 60, 40, 30, 20, 15, 10, 8, 5, 3, 2, 1),
site_C = c(200, 10, 5, 2, 1, 1, 1)
)
# q=c(0,1,2): compute all three Hill numbers
# datatype='abundance': raw counts (use 'incidence_freq' for detection/non-detection)
# nboot=200: bootstrap replicates for confidence intervals
result <- iNEXT(abundance_data, q = c(0, 1, 2), datatype = 'abundance', nboot = 200)
# Rarefaction/extrapolation curves
ggiNEXT(result, type = 1) + theme_bw()
# Sample completeness profiles (coverage vs sample size)
ggiNEXT(result, type = 2) + theme_bw()
# Coverage-based rarefaction curves (diversity vs coverage)
ggiNEXT(result, type = 3) + theme_bw()
Point Estimates at Standardized Coverage
# Estimate diversity at a common coverage level
# coverage=0.95: typical target for adequate sampling
# 0.95 means 95% of individuals in the community belong to detected species
est <- estimateD(abundance_data, datatype = 'abundance',
base = 'coverage', level = 0.95)
est
Asymptotic Diversity Estimation
# Chao1 (q=0), Chao-Shannon (q=1), Chao-Simpson (q=2)
# Asymptotic = estimated true diversity if sampling were complete
asymptotic <- iNEXT(abundance_data, q = c(0, 1, 2), datatype = 'abundance')
asymptotic$AsyEst
iNEXT.3D: Taxonomic, Phylogenetic, and Functional Diversity
library(iNEXT.3D)
# Taxonomic diversity (TD) - standard Hill numbers
td <- iNEXT3D(abundance_data, diversity = 'TD', q = c(0, 1, 2), datatype = 'abundance')
# Phylogenetic diversity (PD) - requires ultrametric tree
# PD generalizes Faith's PD via Hill numbers on branch lengths
pd <- iNEXT3D(abundance_data, diversity = 'PD', q = c(0, 1, 2),
datatype = 'abundance', PDtree = phylo_tree)
# Functional diversity (FD) - requires species distance matrix
# FD captures trait space coverage via Hill numbers
fd <- iNEXT3D(abundance_data, diversity = 'FD', q = c(0, 1, 2),
datatype = 'abundance', FDdistM = trait_dist_matrix, FDtype = 'AUC')
Classic Diversity with vegan
library(vegan)
# community_matrix: sites (rows) x species (columns)
richness <- specnumber(community_matrix)
shannon <- diversity(community_matrix, index = 'shannon')
simpson <- diversity(community_matrix, index = 'simpson')
invsimpson <- diversity(community_matrix, index = 'invsimpson')
# Classic rarefaction to minimum sample size
# Rarefies to the smallest sample, discarding extra reads
raremin <- min(rowSums(community_matrix))
rarecurve(community_matrix, step = 20, sample = raremin)
rare_richness <- rarefy(community_matrix, sample = raremin)
Beta Diversity Partitioning with betapart
Decomposes total beta diversity (Sorensen or Jaccard) into turnover (species replacement) and nestedness (richness difference) components:
library(betapart)
# Presence/absence matrix required
pa_matrix <- ifelse(community_matrix > 0, 1, 0)
# --- Pairwise decomposition ---
# Sorensen family: beta.sim (turnover) + beta.sne (nestedness) = beta.sor (total)
pair_sor <- beta.pair(pa_matrix, index.family = 'sorensen')
pair_sor$beta.sim # turnover component
pair_sor$beta.sne # nestedness component
pair_sor$beta.sor # total beta diversity
# Jaccard family: beta.jtu (turnover) + beta.jne (nestedness) = beta.jac (total)
pair_jac <- beta.pair(pa_matrix, index.family = 'jaccard')
# --- Multi-site decomposition ---
multi <- beta.multi(pa_matrix, index.family = 'sorensen')
multi$beta.SIM # multi-site turnover
multi$beta.SNE # multi-site nestedness
multi$beta.SOR # multi-site total
# --- Abundance-based beta diversity ---
pair_abund <- beta.pair.abund(community_matrix, index.family = 'bray')
pair_abund$beta.bray.bal # balanced variation (analogous to turnover)
pair_abund$beta.bray.gra # abundance gradient (analogous to nestedness)
Interpreting Beta Diversity Components
| Dominance | Ecological Meaning |
|---|---|
| Turnover >> Nestedness | Species replacement along gradients; distinct communities |
| Nestedness >> Turnover | Poor sites are subsets of rich sites; nested pattern |
| Both similar | Mixed processes driving community differences |
Visualization
library(ggplot2)
# Beta diversity triangle plot (turnover vs nestedness proportions)
beta_df <- data.frame(
turnover = as.vector(pair_sor$beta.sim),
nestedness = as.vector(pair_sor$beta.sne),
total = as.vector(pair_sor$beta.sor)
)
beta_df$turn_prop <- beta_df$turnover / beta_df$total
ggplot(beta_df, aes(x = total, y = turn_prop)) +
geom_point(alpha = 0.5) +
geom_hline(yintercept = 0.5, linetype = 'dashed') +
labs(x = 'Total beta diversity (Sorensen)',
y = 'Turnover proportion') +
theme_bw()
Related Skills
- edna-metabarcoding - Generate species tables from eDNA data
- community-ecology - Constrained ordination of assemblages
- microbiome/diversity-analysis - 16S microbiome diversity metrics
- data-visualization/ggplot2-fundamentals - Customize diversity plots