The concepts of bias, precision and accuracy, and their use in testing the performance of species richness estimators, with a literature review of estimator performance

Ecography

Volumn 28, Issue 6, 2005, Pages 815-829

  Walther, Bruno A ^a,b   Moore, Joslin L ^c  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b STELLENBOSCH UNIVERSITY   (South Africa)

^c Zoology Department   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY ASSESSMENT; ESTIMATION METHOD; PRECISION; SAMPLING BIAS; SPECIES RICHNESS;

EID: 28744451104     PISSN: 09067590     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.2005.0906-7590.04112.x     Document Type: Review

References (109)

1. Anderson, D. R., Burnham, K. P. and Thompson, W. L. 2000. Null hypothesis testing: problems, prevalence, and an alternative. - J. Wildl. Manage. 64: 912-923.
2. Anon. 2002. Species diversity and richness III. Ver. 3.0, 〈http://www.pisces-conservation.com/indexsoftdiversity.html〉.
3. Bainbridge, T. R. 1985. The Committee on Standards: precision and bias. - ASTM Standardization News 13: 44-46.
4. Baltanás, A. 1992. On the use of some methods for the estimation of species richness. - Oikos 65: 484-492.
5. Bohannan, B. J. M. and Hughes, J. 2003. New approaches to analyzing microbial biodiversity data. - Curr. Opinion Microbiol. 6: 282-287.
6. Boulinier, T. et al. 1998. Estimating species richness: the importance of heterogeneity in species detectability. - Ecology 79: 1018-1028.
7. Brose, U. 2002. Estimating species richness of pitfall catches by non-parametric estimators. - Pedobiologia 46: 101-107.
8. Brose, U. and Martinez, N. D. 2004. Estimating the richness of species with variable mobility. - Oikos 105: 292-300.
9. Brose, U., Martinez, N. D. and Williams, R. J. 2003. Estimating species richness: sensitivity to sample coverage and insensitivity to spatial patterns. - Ecology 84: 2364-2377.
10. Bunge, J. and Fitzpatrick, M. 1993. Estimating the number of species: a review. - J. Am. Stat. Assoc. 88: 364-373.
11. Burkholder, D. L. 1978. Point estimation. - In: Kruskal, W. H. and Tanur, J. M. (eds), International encyclopedia of statistics. Free Press, New York, USA, pp. 251-259.
12. Burnham, K. P. and Anderson, D. R. 1998. Model selection and inference: a practical information-theoretic approach. - Springer.
13. Burnham, K. P. and Anderson, D. R. 2001. Kullback-Leibler information as a basis for strong inference in ecological studies. - Wildl. Res. 28: 111-119.
14. Cam, E. et al. 2002. On the estimation of species richness based on the accumulation of previously unrecorded species. - Ecography 25: 102-108.
15. Cao, Y., Larsen, D. P. and White, D. 2004. Estimating regional species richness using a limited number of survey units. - Ecoscience 11: 23-35.
16. Casella, G. and Berger, R. L. 1990. Statistical inference. - Duxburry Press, Belmont.
17. Chao, A. 2001. An overview of closed capture-recapture models. - J. Agricult. Biol. Environ. Stat. 6: 158-175.
18. Chao, A. 2005. Species richness estimation. - In: Balakrishnan, N., Read, C. B. and Vidakovic, B. (eds), Encyclopedia of statistical sciences, 2nd ed. Wiley, in press.
19. Chao, A. and Lee, S.-M. 1992. Estimating the number of classes via sample coverage. - J. Am. Stat. Assoc. 87: 210-217.
20. Chao, A. and Tsay, P. K. 1998. A sample coverage approach to multiple-system estimation with application to census undercount. - J. Am. Stat. Assoc. 93: 283-293.
21. Chao, A., Chu, W. and Hsu, C. H. 2000. Capture-recapture when time and behavioural response affect capture probabilities. - Biometrics 56: 427-433.
22. Chao, A., Shen, T.-J. and Hwang, W.-H. 2005. Application of Laplace's boundary mode approximation to estimate species and shared species richness. - Aust. N. Z. J. Stat., in press.
23. Chazdon, R. L. et al. 1998. Statistical methods for estimating species richness of woody regeneration in primary and secondary rain forests of northeastern Costa Rica. - In: Dallmeier, F. and Comiskey, J. A. (eds), Forest biodiversity research, monitoring and modeling: conceptual background and Old World case studies. Parthenon Publ. Group, Paris, pp. 285-309.
24. Chiarucci, A., Maccherini, S. and De Dominicis, V. 2001. Evaluation and monitoring of the flora in a nature reserve by estimation methods. - Biol. Conserv. 101: 305-314.
25. Chiarucci, A. et al. 2003. Performance of nonparametric species richness estimators in a high diversity plant community. - Div. Distrib. 9: 283-295.
26. Christen, J. A. and Nakamura, M. 2000. On the analysis of accumulation curves. - Biometrics 56: 748-754.
27. Colwell, R. K. 2000. EstimateS: statistical estimation of species richness and shared species from samples. - 〈http://viceroy.eeb.uconn.edu/ EstimateS〉.
28. Colwell, R. K. and Coddington, J. A. 1994. Estimating terrestrial biodiversity through extrapolation. - Phil. Trans. R. Soc. B 345: 101-118.
29. Colwell, R. K., Mao, C. X. and Chang, J. 2004. Interpolating, extrapolating, and comparing incidence-based species accumulation curves. - Ecology 85: 2717-2727.
30. Davison, A. C. and Hinkley, D. V. 1997. Bootstrap methods and their application. - Cambridge Univ. Press.
31. Debanne, S. M. 2000. The planning of clinical studies: bias and precision. - Gastrointestinal Endoscopy 52: 821-822.
32. Díaz-Francés, E. and Gorostiza, L. G. 2002. Inference and model comparisons for species accumulation functions using approximating pure birth processes. - J. Agricult. Biol. Environ. Stat. 7: 335-349.
33. Efron, B. and Gong, G. 1983. A leisurely look at the bootstrap, the jackknife, and cross-validation. - Am. Stat. 37: 36-48.
34. Efron, B. and Tibshirani, R. 1986. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. - Stat. Sci. 1: 54-77.
35. Flather, C. H. 1996. Fitting species-accumulation functions and assessing regional land use impacts on avian diversity. - J. Biogeogr. 23: 155-168.
36. Foggo, A. et al. 2003a. Estimating marine species richness: an evaluation of six extrapolative techniques. - Mar. Ecol. Progr. Ser. 248: 15-26.
37. Foggo, A. et al. 2003b. The net result: evaluating species richness extrapolation techniques for littoral pond invertebrates. - Freshwater Biol. 48: 1756-1764.
38. Gimaret-Carpentier, C. et al. 1998. Sampling strategies for the assessment of tree species diversity. - J. Veg. Sci. 9: 161-172.
39. Good, I. J. 1953. On the population frequencies of species and the estimation of population parameters. - Biometrika 40: 237-264.
40. Gorostiza, L. G. and Díaz-Francés, E. 2001. Species accumulation functions and pure birth processes. - Stat. Prob. Lett. 55: 221-226.
41. Gotelli, N. J. and Colwell, R. K. 2001. Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. - Ecol. Lett. 4: 379-391.
42. Gotelli, N. J. and Entsminger, G. L. 2001. Ecosim: null models software for ecology, Ver. 7.0. - Acquired Intelligence and Kesey-Bear, Burlington, VT 05465, USA, 〈http://homepages.together.net/~gentsmin/ecosim.htm〉.
43. Gould, W. R. and Pollock, K. H. 1997. Catch-effort maximum likelihood estimation of important population parameters. - Can. J. Fish. Aquat. Sci. 54: 890-897.
44. Gould, W. R., Stefanski, L. A. and Pollock, K. H. 1997. Effects of measurement error on catch-effort estimation. - Can. J. Fish. Aquat. Sci. 54: 898-906.
45. Hellmann, J. J. and Fowler, G. W. 1999. Bias, precision, and accuracy of four measures of species richness. - Ecol. Appl. 9: 824-834.
46. Herzog, S. K., Kessler, M. and Cahill, T. M. 2002. Estimating species richness of tropical bird communities from rapid assessment data. - Auk 119: 749-769.
47. Hines, J. E. et al. 1999. COMDYN: software to study the dynamics of animal communities using a capture-recapture approach. - Bird Study Suppl: 209-217, 〈http://www.mbr-pwrc.usgs.gov/software/comdyn.html〉.
48. Hubálek, Z. 2000. Measures of species diversity in ecology: an evaluation. - Folia Zool. 49: 241-260.
49. Hughes, J. B. et al. 2001. Counting the uncountable: statistical approaches to estimating microbial diversity. - Appl. Environ. Microbiol. 67: 4399-4406 (erratum 2002, 68: 448).
50. Izsák, J. 1997. DIVERSI. Ver. 1.1. A program package to calculate diversity indices, their jackknifed estimates with confidence intervals, similarity indices and fitting abundance models. - Abstracta botanica.
51. Jones, C. B. 1997. Geographical information systems and computer cartography. - Longman.
52. Keating, K. A. et al. 1998. Estimating the effectiveness of further sampling in species inventories. - Ecol. Appl. 8: 1239-1249.
53. Kotz, S. and Johnson, N. L. 1982-1988. Encyclopedia of statistical sciences. Vol. 1-9. - Wiley.
54. Krebs, C. J. 1999. Ecological methodology. - Benjamin/Cummings.
55. Lande, R. 1996. Statistics and partitioning of species diversity, and similarity among multiple communities. - Oikos 76: 5-13.
56. Lehmann, E. L. 1983. Theory of point estimation. - Wiley.
57. Longino, J. T., Coddington, J. and Colwell, R. K. 2002. The ant fauna of a tropical rain forest: estimating species richness three different ways. - Ecology 83: 689-702.
58. Ludwig, J. A. and Reynolds, J. F. 1988. Statistical ecology: a primer on methods and computing. - Wiley.
59. Manly, B. F. J. 1997. Randomization, bootstrap and Monte Carlo methods in biology. - Chapman and Hall.
60. Mao, C. X. and Colwell, R. K. 2005. Estimation of species richness: mixture models, the role of rare species, and inferential challenges. - Ecology 86: 1143-1153.
61. Mao, C. X., Colwell, R. K. and Chang, J. 2005. Estimating the species accumulation curves using mixtures. - Biometrics 61: 433-441.
62. Marriott, F. H. C. 1990. A dictionary of statistical terms, 5th ed. - Wiley.
63. Martin, J. L., Gaston, A. J. and Hitier, S. 1995. The effect of island size and isolation on old growth forest habitat and bird diversity in Gwaii Haanas (Queen Charlotte Islands, Canada). - Oikos 72: 115-131.
64. McAleece, N. et al. 1997. BioDiversity Professional Beta Release 1. - 〈http://www.sams.ac.uk/dml/projects/benthic/bdpro/index.htm〉.
65. Melo, A. S. and Froehlich, C. G. 2001. Evaluation of methods for estimating macroinvertebrate species richness using individual stones in tropical streams. - Freshwater Biol. 46: 711-721.
66. Melo, A. S. et al. 2003. Comparing species richness among assemblages using sample units: why not use extrapolation methods to standardize different sample sizes? - Oikos 101: 398-410.
67. Mood, A. M., Graybill, F. A. and Boes, D. C. 1974. Introduction to the theory of statistics. - MacGraw-Hill.
68. Mouillot, D. and Lepêtre, A. 1999. A comparison of species diversity estimators. - Res. Popul. Ecol. 41: 203-215.
69. Nakamura, M. and Peraza, F. 1998. Species accumulation for beta distributed recording probabilities. - J. Agricult. Biol. Environ. Stat. 3: 17-36.
70. Nichols, J. D. and Conroy, M. J. 1996. Estimation of species richness. - In: Wilson, D. E. et al. (eds), Measuring and monitoring biological diversity. Standard methods for mammals. Smithsonian Inst. Press, pp. 226-234.
71. Norris, J. L. and Pollock, K. H. 1996. Non-parametric MLE under two closed capture-recapture models with heterogeneity. - Biometrics 52: 639-649.
72. Norris, J. L. and Pollock, K. H. 1998. Non-parametric MLE for Poisson species abundance models allowing for heterogeneity between species. - Environ. Ecol. Stat. 5: 391-402.
73. Novotny, V. and Basset, Y. 2000. Rare species in communities of tropical insect herbivores: pondering the mystery of single-tons. - Oikos 89: 564-572.
74. O'Hara, R. B. 2005. Species richness estimators: how many species an dance on the head of a pin? - J. Anim. Ecol. 74: 375-386.
75. Otis, D. L. et al. 1978. Statistical inference from capture data on closed animal populations. - Wildl. Monogr. 62: 1-135.
76. Palmer, M. W. 1990. The estimation of species richness by extrapolation. - Ecology 71: 1195-1198.
77. Palmer, M. W. 1991. Estimating species richness: the second-order jackknife reconsidered. - Ecology 72: 1512-1513.
78. Petersen, F. T. and Meier, R. 2003. Testing species-richness estimation methods on single-sample collection data using the Danish Diptera. - Biodiv. Conserv. 12: 667-686.
79. Petersen, F. T., Meier, R. and Larsen, M. N. 2003. Testing species richness estimation methods using museum label data on the Danish Asilidae. - Biodiv. Conserv. 12: 687-701.
80. Peterson, A. T. and Slade, N. A. 1998. Extrapolating inventory results into biodiversity estimates and the importance of stopping rules. - Div. Distrib. 4: 95-105.
81. Picard, N., Karembé, M. and Birnbaum, P. 2004. Species-area curve and spatial pattern. - Ecoscience 11: 45-54.
82. Pledger, S. 2000. Unified maximum likelihood estimates for closed capture-recapture models using mixtures. - Biometrics 56: 434-442.
83. Pledger, S. and Schwarz, C. J. 2002. Modelling heterogeneity of survival in band-recovery data using mixtures. - J. Appl. Stat. 29: 315-327.
84. Poulin, R. 1998. Comparison of three estimators of species richness in parasite component communities. - J. Parasitol. 84: 485-490.
85. Rexstad, E. and Burnham, K. P. 1991. User's guide for interactive program CAPTURE. Abundance estimation of closed animal populations. - Colorado State Univ. Fort Collins, CO, 〈http://www.mbr-pwrc.usgs.gov/software.html〉.
86. Rosenberg, D. K., Overton, W. S. and Anthony, R. G. 1995. Estimation of animal abundance when capture probabilities are low and heterogeneous. - J. Wildl. Manage. 59: 252-261.
87. Rosenzweig, M. L. et al. 2003. Estimating diversity in unsampled habitats of a biogeographical province. - Conserv. Biol. 17: 864-874.
88. Ross, G. J. S. 1987. Maximum likelihood program. Ver. 3.08. - Numerical Algorithm Group, Downers Grove, IL, 〈http://sci.agr.ca/sthyacinthe/biblio/ i/n/m003032.htm〉.
89. Samu, F. and Lövei, G. L. 1995. Species richness of a spider community (Araneae): extrapolation from simulated increasing sampling effort. - Euro. J. Entomol. 92: 633-638.
90. Soberon, M. J. and Llorente, B. J. 1993. The use of species accumulation functions for the prediction of species richness. - Conserv. Biol. 7: 480-488.
91. Sokal, R. R. and Rohlf, F. J. 1995. Biometry: the principles and practice of statistics in biological research. - Freeman.
92. Stanley, T. R. and Burnham, K. P. 1998. Estimator selection for closed-population capture-recapture. - J. Agricult. Biol. Environ. Stat. 3: 131-150.
93. Stark, P. B. 1997-2002. SticiGui: statistics tools for internet and classroom instruction with a graphical user interface. - Dept of Statistics, Univ. of California, Berkeley, USA, 〈http://www.stat.berkeley.edu/users/ stark/SticiGui/Text/index.htm〉.
94. Stuart, A. and Ord, J. K. 1991. Kendall's advanced theory of statistics, volume 2: classical inference and relationships - Edward Arnold.
95. Thomas, G. 2000. Bio-dap diversity indices. - 〈http://detritus. inhs.uiuc.edu/wes/populations.html〉.
96. Tietjen, G. L. 1986. A topical dictionary of statistics - Chapman and Hall.
97. Turner, W., Leitner, W. and Rosenzweig, M. 2001. ws2m: software for the measurement and analysis of species diversity. - 〈http://eebweb.arizona. edu/diversity/〉.
98. Wagner, H. H. and Wildi, O. 2002. Realistic simulation of the effects of abundance distribution and spatial heterogeneity on non-parametric estimators of species richness. - Ecoscience 9: 241-250.
99. Walsh, S. J. 1997. Limitations to the robustness of binormal ROC curves: effects of model misspecification and location of decision thresholds on bias, precision, size and power. - Stat. Medicine 16: 669-679.
100. Walther, B. A. et al. 1995. Sampling effort and parasite species richness. - Parasitol. Today 11: 306-310.
101. Walther, B. A. 1997. Comparative studies of ectoparasite communities of birds. - Ph. D. thesis, Oxford Univ., Oxford.
102. Walther, B. A. and Morand, S. 1998. Comparative performance of species richness estimation methods. - Parasitology 116: 395-405.
103. Walther, B. A. and Martin, J. L. 2001. Species richness estimation of bird communities: how to control for sampling effort? - Ibis 143: 413-419.
104. West, M. J. 1999. Stereological methods for estimating the total number of neurons and synapses: issues of precision and bias. - Trends Neurosci. 22: 51-61.
105. White, G. C. and Burnham, K. P. 1999. Program MARK: survival estimation from populations of marked animals. - Bird Study Suppl., 46: 120-138, 〈http://www.cnr. colostate.edu/~gwhite/mark/mark.htm〉.
106. Williams, B. K., Nicholls, J. D. and Conroy, M. J. 2001. Analysis and management of animal populations: modeling, estimation, and decision making. - Academic Press.
107. Winklehner, R., Winkler, H. and Kampichler, C. 1997. Estimating local species richness of epigeic Collembola in temperate dry grassland. - Pedobiologia 41: 154-158.
108. Zar, J. H. 1996. Biostatistical analysis. - Prentice Hall.
109. Zelmer, D. A. and Esch, G. W. 1999. Robust estimation of parasite component community richness. - J. Parasitol. 85: 592-594.