Table 6. Comparison of five richness estimators based on 1,000 simulation data sets under a Zipf–Mandelbrot model p_i ∼ C/(i + 10) with S = 1,000 and CV = 1.87.

See Table 1 for the notations of the estimators.

Size n (Observed richness)	Estimator	Average estimate	Bias	Sample s.e.	Average estimated s.e.	Sample RMSE	95% CI coverage rate
1,000 (439.7)	${\hat{S}}_{\mathrm{Chao1}}$	809.2	−190.8	65	63.8	201.6	0.3
	${\hat{S}}_{\mathrm{Jack1}}$	694.1	−305.9	23.8	24.5	306.8	0
	${\hat{S}}_{\mathrm{CB}}$	6,701.4	5,701	42,271	14,418,927	42,612	0.99
	${\hat{S}}_{\mathrm{LB}}$	1,123.1	123.1	291.8	281.3	316.4	0.96
	${\hat{S}}_{\mathrm{GP}}$	953.6	−46.4a	121	121	129.5a	0.95a
2,000 (629.7)	${\hat{S}}_{\mathrm{Chao1}}$	919.4	−80.6	46.1	45.3	92.8	0.64
	${\hat{S}}_{\mathrm{Jack1}}$	915.3	−84.7	24.2	23.9	88.1a	0.07
	${\hat{S}}_{\mathrm{CB}}$	1,612.1	612.1	328.1	305.8	694.4	0.33
	${\hat{S}}_{\mathrm{LB}}$	1,063.6	63.6	152.8	145.6	165.4	0.96a
	${\hat{S}}_{\mathrm{GP}}$	997.2	−2.8a	89.1	88.1	89.1	0.93
4,000 (817.1)	${\hat{S}}_{\mathrm{Chao1}}$	977.4	−22.6	28.5	26.9	36.3a	0.88
	${\hat{S}}_{\mathrm{Jack1}}$	1,059	59	21.1	19.8	62.7	0.16
	${\hat{S}}_{\mathrm{CB}}$	1,089	89	45.1	44.7	99.7	0.51
	${\hat{S}}_{\mathrm{LB}}$	1,020.8	20.8	68.8	64.2	71.8	0.94a
	${\hat{S}}_{\mathrm{GP}}$	1,001.7	1.7a	49.5	47.2	49.5	0.93
8,000 (946.5)	${\hat{S}}_{\mathrm{Chao1}}$	997.3	−2.7	12.3	12.3	12.5a	0.96
	${\hat{S}}_{\mathrm{Jack1}}$	1,070.9	70.9	12.9	13.1	72.1	0
	${\hat{S}}_{\mathrm{CB}}$	1,007.5	7.5	11.3	12.1	13.6	0.94
	${\hat{S}}_{\mathrm{LB}}$	1,006.0	6	23.6	23.5	24.3	0.95a
	${\hat{S}}_{\mathrm{GP}}$	1,000.9	0.9a	18.3	18.6	18.3	0.95a

Notes.

^adenotes the smallest bias, smallest RMSE, and figure closest to 95% coverage.