Bio Ecological Genomics Biodiversity Metrics

Version Compatibility

Reference examples tested with: ggplot2 3.5+, vegan 2.6+

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name to verify parameters

If code throws ImportError, AttributeError, or TypeError, introspect the installed

package and adapt the example to match the actual API rather than retrying.

Biodiversity Metrics

"Calculate species diversity for my ecological samples" → Compute Hill number diversity (richness, Shannon, Simpson) with coverage-based rarefaction/extrapolation using iNEXT, and partition beta diversity into turnover and nestedness components with betapart.

• R: iNEXT::iNEXT() for coverage-based rarefaction and extrapolation
• R: betapart::beta.multi() for beta diversity partitioning

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

Goal: Compare diversity across assemblages standardized by sampling completeness rather than sample size.

Approach: Run iNEXT coverage-based rarefaction/extrapolation for Hill numbers q=0,1,2 and visualize with ggiNEXT.

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

Goal: Estimate diversity at a common coverage level for fair cross-site comparison.

Approach: Use estimateD with a target coverage of 0.95 to produce standardized Hill number estimates.

# 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

Goal: Estimate true community diversity if sampling were complete.

Approach: Extract asymptotic estimates (Chao1, Chao-Shannon, Chao-Simpson) from iNEXT output.

# 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

Goal: Compute diversity across three dimensions: taxonomic, phylogenetic (Faith's PD generalized), and functional (trait space).

Approach: Use iNEXT3D with appropriate diversity facet and supplementary data (phylogenetic tree or trait distance matrix).

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

Goal: Calculate standard alpha diversity indices and rarefaction curves from a community matrix.

Approach: Compute Shannon, Simpson, and inverse Simpson indices with vegan::diversity, then rarefy to the minimum sample size.

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

Goal: Decompose total beta diversity into turnover (species replacement) and nestedness (richness difference) components.

Approach: Apply betapart pairwise and multi-site decomposition on presence/absence and abundance matrices using Sorensen, Jaccard, and Bray-Curtis families.

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

Goal: Visualize the relative contribution of turnover vs nestedness to total beta diversity.

Approach: Plot turnover proportion against total beta diversity for each site pair using ggplot2.

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