Ecological Archives E084-057-A1

Ulrich Brose, Neo D. Martinez, and Richard J. Williams. 2003. Estimating species richness: sensitivity to sample coverage and insensitivity to spatial patterns. Ecology 84:2364–2377.

Appendix A. A comparison of formulas for the estimators of species richness. Sobs = the number of species observed.

Non-parametric estimators:

Chao2: The incidence-based estimator of species richness

Jack1: The first-order jacknife estimator

Jack2: The second-order jacknife estimator

Jack3: The third-order jacknife estimator


Jack4: The fourth-order jacknife estimator

Jack5: The fifth-order jacknife estimator

ICE: The incidence-based coverage estimator


Sest = estimated species richness

Qj = number of species that occur in exactly j samples

m = total number of samples

Sfreq = number of frequent species (each found in more than 10 samples)

Sinf = number of infrequent species (each found in 10 or fewer samples)

Cice = sample incidence coverage estimator:

Ninf = total number of occurrences of infrequent species:

ice2 estimates the coefficient of variation of the Qj's:  

minf = number of samples that have at least one infrequent species

Species accumulation curves:

Michaelis-Menten model:

Exponential equation:


n = units of sampling

S(n) = Sobs after n units of sampling

Smax = estimated total species richness (asymptote)

B, K = fitted constants

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