Individual-Based Rarefaction — rarefy • spacc

Compute individual-based rarefaction curves for Hill numbers at any order q. This complements the sample-based accumulation in spacc().

Usage

rarefy(x, n_individuals = NULL, q = 0, n_boot = 100L)

Arguments

x: A site-by-species matrix with abundance data (not presence/absence).
n_individuals: Integer vector. Sample sizes to compute expected diversity for. Default NULL computes for all levels from 1 to total.
q: Numeric. Order of Hill number. Default 0 (species richness). q=1 gives rarefied Shannon diversity, q=2 gives rarefied Simpson diversity.
n_boot: Integer. Number of bootstrap replicates for CI. Default 100.

Value

An object of class spacc_rare containing:

n: Sample sizes
expected: Expected diversity (Hill number of order q)
sd: Standard deviation
lower, upper: 95 percent confidence bounds
q: Order of diversity used

Details

For q=0 (species richness): uses the Hurlbert (1971) formula.

For q=1 (Shannon diversity): rarefied Shannon entropy is computed and converted to effective number of species via exponentiation.

For q=2 (Simpson diversity): rarefied Simpson concentration is computed and converted to effective number of species via inversion.

References

Hurlbert, S.H. (1971). The nonconcept of species diversity: a critique and alternative parameters. Ecology, 52, 577-586.

Chao, A., Gotelli, N.J., Hsieh, T.C., et al. (2014). Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies. Ecological Monographs, 84, 45-67.

Examples

# \donttest{
abundance_matrix <- matrix(rpois(50 * 30, 2), nrow = 50)
rare <- rarefy(abundance_matrix)
plot(rare)

# Shannon rarefaction
rare_q1 <- rarefy(abundance_matrix, q = 1)
plot(rare_q1)
# }