*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. *S*_{obs}
= 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

**where:**

*S*_{est} = estimated
species richness

*Q*_{j} = number
of species that occur in exactly j samples

*m* = total number
of samples

*S*_{freq} = number
of frequent species (each found in more than 10 samples)

*S*_{inf} = number
of infrequent species (each found in 10 or fewer samples)

*C*_{ice} = sample
incidence coverage estimator:

*N*_{inf} = total
number of occurrences of infrequent species:

_{ice}^{2}
estimates the coefficient of variation of the *Q*j's:

*m*_{inf} = number
of samples that have at least one infrequent species

**Species accumulation curves:**

**Michaelis-Menten model**:

**Exponential equation**:

**where:**

*n* = units of sampling

*S*(*n*) = S_{obs}
after *n* units of sampling

*S*_{max} = estimated
total species richness (asymptote)

B, K = fitted constants

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