Biometrika

Biometrika 1953 40(3-4):237-264; doi:10.1093/biomet/40.3-4.237
© 1953 by Biometrika Trust

This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by GOOD, I. J. Search for Related Content Social Bookmarking          What's this?

THE POPULATION FREQUENCIES OF SPECIES AND THE ESTIMATION OF POPULATION PARAMETERS

I. J. GOOD

A random sample is drawn from a population of animals of various species. (The theory may also be applied to studies of literary vocabulary, for example.) If a particular species is represented r times in the sample of size N, then r/N is not a good estimate of the population frequency, p, when r is small. Methods are given for estimating p, assuming virtually nothing about the underlying population. The estimates are expressed in terms of smoothed values of the numbers n_r (r= 1, 2, 3, ...), where n_r is the number of distinct species that are each represented r times in the sample. (n_r may be described as ‘the frequency of the frequency r’.) Turing is acknowledged for the most interesting formula in this part of the work. An estimate of the proportion of the population represented by the species occurring in the sample is an immediate corollary. Estimates are made of measures of heterogeneity of the population, including Yule's ‘characteristic’ and Shannon's ‘entropy’. Methods are then discussed that do depend on assumptions about the underlying population. It is here that most work has been done by other writers. It is pointed out that a hypothesis can give a good fit to the numbers n_r but can give quite the wrong value for Yule's characteristic. An example of this is Fisher's fit to some data of Williams's on Macrolepidoptera.

CiteULike    Connotea    Del.icio.us    What's this?

This article has been cited by other articles:

				H. J. Mills, E. Hunter, M. Humphrys, L. Kerkhof, L. McGuinness, M. Huettel, and J. E. Kostka Characterization of Nitrifying, Denitrifying, and Overall Bacterial Communities in Permeable Marine Sediments of the Northeastern Gulf of Mexico Appl. Envir. Microbiol., July 15, 2008; 74(14): 4440 - 4453. [Abstract] [Full Text] [PDF]

				T. Brad, M. Braster, B. M. van Breukelen, N. M. van Straalen, and W. F. M. Roling Eukaryotic Diversity in an Anaerobic Aquifer Polluted with Landfill Leachate Appl. Envir. Microbiol., July 1, 2008; 74(13): 3959 - 3968. [Abstract] [Full Text] [PDF]

				E. Allers, C. Niesner, C. Wild, and J. Pernthaler Microbes Enriched in Seawater after Addition of Coral Mucus Appl. Envir. Microbiol., May 15, 2008; 74(10): 3274 - 3278. [Abstract] [Full Text] [PDF]

				C. U. Schwermer, G. Lavik, R. M. M. Abed, B. Dunsmore, T. G. Ferdelman, P. Stoodley, A. Gieseke, and D. de Beer Impact of Nitrate on the Structure and Function of Bacterial Biofilm Communities in Pipelines Used for Injection of Seawater into Oil Fields Appl. Envir. Microbiol., May 1, 2008; 74(9): 2841 - 2851. [Abstract] [Full Text] [PDF]

				H. Urakawa, Y. Tajima, Y. Numata, and S. Tsuneda Low Temperature Decreases the Phylogenetic Diversity of Ammonia-Oxidizing Archaea and Bacteria in Aquarium Biofiltration Systems Appl. Envir. Microbiol., February 1, 2008; 74(3): 894 - 900. [Abstract] [Full Text] [PDF]

				S. Beier, K.-P. Witzel, and J. Marxsen Bacterial Community Composition in Central European Running Waters Examined by Temperature Gradient Gel Electrophoresis and Sequence Analysis of 16S rRNA Genes Appl. Envir. Microbiol., January 1, 2008; 74(1): 188 - 199. [Abstract] [Full Text] [PDF]

				A. Lijoi, R. H. Mena, and I. Prunster Bayesian Nonparametric Estimation of the Probability of Discovering New Species Biometrika, December 1, 2007; 94(4): 769 - 786. [Abstract] [PDF]

				B. C. Crump, C. Peranteau, B. Beckingham, and J. C. Cornwell Respiratory Succession and Community Succession of Bacterioplankton in Seasonally Anoxic Estuarine Waters Appl. Envir. Microbiol., November 1, 2007; 73(21): 6802 - 6810. [Abstract] [Full Text] [PDF]

				D. A. de Carcer, M. Martin, U. Karlson, and R. Rivilla Changes in Bacterial Populations and in Biphenyl Dioxygenase Gene Diversity in a Polychlorinated Biphenyl-Polluted Soil after Introduction of Willow Trees for Rhizoremediation Appl. Envir. Microbiol., October 1, 2007; 73(19): 6224 - 6232. [Abstract] [Full Text] [PDF]

				A.-D. G. Wright, C. H. Auckland, and D. H. Lynn Molecular Diversity of Methanogens in Feedlot Cattle from Ontario and Prince Edward Island, Canada Appl. Envir. Microbiol., July 1, 2007; 73(13): 4206 - 4210. [Abstract] [Full Text] [PDF]

				B. Diez, K. Bauer, and B. Bergman Epilithic Cyanobacterial Communities of a Marine Tropical Beach Rock (Heron Island, Great Barrier Reef): Diversity and Diazotrophy Appl. Envir. Microbiol., June 1, 2007; 73(11): 3656 - 3668. [Abstract] [Full Text] [PDF]

				C. R. Cox and M. S. Gilmore Native Microbial Colonization of Drosophila melanogaster and Its Use as a Model of Enterococcus faecalis Pathogenesis Infect. Immun., April 1, 2007; 75(4): 1565 - 1576. [Abstract] [Full Text] [PDF]

				M. S. Payne, M. R. Hall, L. Sly, and D. G. Bourne Microbial Diversity within Early-Stage Cultured Panulirus ornatus Phyllosomas Appl. Envir. Microbiol., March 15, 2007; 73(6): 1940 - 1951. [Abstract] [Full Text] [PDF]

				N. N. Perreault, D. T. Andersen, W. H. Pollard, C. W. Greer, and L. G. Whyte Characterization of the Prokaryotic Diversity in Cold Saline Perennial Springs of the Canadian High Arctic Appl. Envir. Microbiol., March 1, 2007; 73(5): 1532 - 1543. [Abstract] [Full Text] [PDF]

				A. Edlund and J. K. Jansson Changes in Active Bacterial Communities before and after Dredging of Highly Polluted Baltic Sea Sediments Appl. Envir. Microbiol., October 1, 2006; 72(10): 6800 - 6807. [Abstract] [Full Text] [PDF]

				P. L. Worthen, C. J. Gode, and J. Graf Culture-independent characterization of the digestive-tract microbiota of the medicinal leech reveals a tripartite symbiosis. Appl. Envir. Microbiol., July 1, 2006; 72(7): 4775 - 4781. [Abstract] [Full Text] [PDF]

				C Manichanh, L Rigottier-Gois, E Bonnaud, K Gloux, E Pelletier, L Frangeul, R Nalin, C Jarrin, P Chardon, P Marteau, et al. Reduced diversity of faecal microbiota in Crohn's disease revealed by a metagenomic approach Gut, February 1, 2006; 55(2): 205 - 211. [Abstract] [Full Text] [PDF]

				E. M. Bik, P. B. Eckburg, S. R. Gill, K. E. Nelson, E. A. Purdom, F. Francois, G. Perez-Perez, M. J. Blaser, and D. A. Relman Molecular analysis of the bacterial microbiota in the human stomach PNAS, January 17, 2006; 103(3): 732 - 737. [Abstract] [Full Text] [PDF]

				M. A. J. Hullar, L. A. Kaplan, and D. A. Stahl Recurring Seasonal Dynamics of Microbial Communities in Stream Habitats Appl. Envir. Microbiol., January 1, 2006; 72(1): 713 - 722. [Abstract] [Full Text] [PDF]

				O. Nercessian, M. G. Kalyuzhnaya, S. B. Joye, M. E. Lidstrom, and L. Chistoserdova Analysis of fae and fhcD Genes in Mono Lake, California Appl. Envir. Microbiol., December 1, 2005; 71(12): 8949 - 8953. [Abstract] [Full Text] [PDF]

				S. G. Acinas, R. Sarma-Rupavtarm, V. Klepac-Ceraj, and M. F. Polz PCR-Induced Sequence Artifacts and Bias: Insights from Comparison of Two 16S rRNA Clone Libraries Constructed from the Same Sample Appl. Envir. Microbiol., December 1, 2005; 71(12): 8966 - 8969. [Abstract] [Full Text] [PDF]

				Y. Hongoh, P. Deevong, T. Inoue, S. Moriya, S. Trakulnaleamsai, M. Ohkuma, C. Vongkaluang, N. Noparatnaraporn, and T. Kudo Intra- and Interspecific Comparisons of Bacterial Diversity and Community Structure Support Coevolution of Gut Microbiota and Termite Host Appl. Envir. Microbiol., November 1, 2005; 71(11): 6590 - 6599. [Abstract] [Full Text] [PDF]

				O. Nercessian, E. Noyes, M. G. Kalyuzhnaya, M. E. Lidstrom, and L. Chistoserdova Bacterial Populations Active in Metabolism of C1 Compounds in the Sediment of Lake Washington, a Freshwater Lake Appl. Envir. Microbiol., November 1, 2005; 71(11): 6885 - 6899. [Abstract] [Full Text] [PDF]

				C. P. Ridley, D. John Faulkner, and M. G. Haygood Investigation of Oscillatoria spongeliae-Dominated Bacterial Communities in Four Dictyoceratid Sponges Appl. Envir. Microbiol., November 1, 2005; 71(11): 7366 - 7375. [Abstract] [Full Text] [PDF]

				M. Timke, N. Q. Wang-Lieu, K. Altendorf, and A. Lipski Community Structure and Diversity of Biofilms from a Beer Bottling Plant as Revealed Using 16S rRNA Gene Clone Libraries Appl. Envir. Microbiol., October 1, 2005; 71(10): 6446 - 6452. [Abstract] [Full Text] [PDF]

				D. A. Pearce, C. J. van der Gast, K. Woodward, and K. K. Newsham Significant changes in the bacterioplankton community structure of a maritime Antarctic freshwater lake following nutrient enrichment Microbiology, October 1, 2005; 151(10): 3237 - 3248. [Abstract] [Full Text] [PDF]

				B. M. Jedynak and S. Khudanpur Maximum Likelihood Set for Estimating a Probability Mass Function Neural Comput., July 1, 2005; 17(7): 1508 - 1530. [Abstract] [Full Text] [PDF]

				H. J. Mills, R. J. Martinez, S. Story, and P. A. Sobecky Characterization of Microbial Community Structure in Gulf of Mexico Gas Hydrates: Comparative Analysis of DNA- and RNA-Derived Clone Libraries Appl. Envir. Microbiol., June 1, 2005; 71(6): 3235 - 3247. [Abstract] [Full Text] [PDF]

				B. Lawley, S. Ripley, P. Bridge, and P. Convey Molecular Analysis of Geographic Patterns of Eukaryotic Diversity in Antarctic Soils Appl. Envir. Microbiol., October 1, 2004; 70(10): 5963 - 5972. [Abstract] [Full Text] [PDF]

				H. J. Mills, R. J. Martinez, S. Story, and P. A. Sobecky Identification of Members of the Metabolically Active Microbial Populations Associated with Beggiatoa Species Mat Communities from Gulf of Mexico Cold-Seep Sediments Appl. Envir. Microbiol., September 1, 2004; 70(9): 5447 - 5458. [Abstract] [Full Text] [PDF]

				P. D. Schloss, B. R. Larget, and J. Handelsman Integration of Microbial Ecology and Statistics: a Test To Compare Gene Libraries Appl. Envir. Microbiol., September 1, 2004; 70(9): 5485 - 5492. [Abstract] [Full Text] [PDF]

				B. J. Giri, N. Bano, and J. T. Hollibaugh Distribution of RuBisCO Genotypes along a Redox Gradient in Mono Lake, California Appl. Envir. Microbiol., June 1, 2004; 70(6): 3443 - 3448. [Abstract] [Full Text] [PDF]

				W. F. M. Roling, I. R. Couto de Brito, R. P. J. Swannell, and I. M. Head Response of Archaeal Communities in Beach Sediments to Spilled Oil and Bioremediation Appl. Envir. Microbiol., May 1, 2004; 70(5): 2614 - 2620. [Abstract] [Full Text] [PDF]

				J. Lu, U. Idris, B. Harmon, C. Hofacre, J. J. Maurer, and M. D. Lee Diversity and Succession of the Intestinal Bacterial Community of the Maturing Broiler Chicken Appl. Envir. Microbiol., November 1, 2003; 69(11): 6816 - 6824. [Abstract] [Full Text] [PDF]

				A. Orlitsky, N. P. Santhanam, and J. Zhang Always Good Turing: Asymptotically Optimal Probability Estimation Science, October 17, 2003; 302(5644): 427 - 431. [Abstract] [Full Text] [PDF]

				R. T. Anderson, H. A. Vrionis, I. Ortiz-Bernad, C. T. Resch, P. E. Long, R. Dayvault, K. Karp, S. Marutzky, D. R. Metzler, A. Peacock, et al. Stimulating the In Situ Activity of Geobacter Species To Remove Uranium from the Groundwater of a Uranium-Contaminated Aquifer Appl. Envir. Microbiol., October 1, 2003; 69(10): 5884 - 5891. [Abstract] [Full Text] [PDF]

				J. E. M. Stach, L. A. Maldonado, D. G. Masson, A. C. Ward, M. Goodfellow, and A. T. Bull Statistical Approaches for Estimating Actinobacterial Diversity in Marine Sediments Appl. Envir. Microbiol., October 1, 2003; 69(10): 6189 - 6200. [Abstract] [Full Text] [PDF]

				A. Taton, S. Grubisic, E. Brambilla, R. De Wit, and A. Wilmotte Cyanobacterial Diversity in Natural and Artificial Microbial Mats of Lake Fryxell (McMurdo Dry Valleys, Antarctica): a Morphological and Molecular Approach Appl. Envir. Microbiol., September 1, 2003; 69(9): 5157 - 5169. [Abstract] [Full Text] [PDF]

				J. R. Marchesi and A. J. Weightman Comparing the Dehalogenase Gene Pool in Cultivated {alpha}-Halocarboxylic Acid-Degrading Bacteria with the Environmental Metagene Pool Appl. Envir. Microbiol., August 1, 2003; 69(8): 4375 - 4382. [Abstract] [Full Text] [PDF]

				K. J. Purdy, D. B. Nedwell, and T. M. Embley Analysis of the Sulfate-Reducing Bacterial and Methanogenic Archaeal Populations in Contrasting Antarctic Sediments Appl. Envir. Microbiol., June 1, 2003; 69(6): 3181 - 3191. [Abstract] [Full Text] [PDF]

				J. Lu, S. Sanchez, C. Hofacre, J. J. Maurer, B. G. Harmon, and M. D. Lee Evaluation of Broiler Litter with Reference to the Microbial Composition as Assessed by Using 16S rRNA and Functional Gene Markers Appl. Envir. Microbiol., February 1, 2003; 69(2): 901 - 908. [Abstract] [Full Text] [PDF]

				M. P. Mehta, D. A. Butterfield, and J. A. Baross Phylogenetic Diversity of Nitrogenase (nifH) Genes in Deep-Sea and Hydrothermal Vent Environments of the Juan de Fuca Ridge Appl. Envir. Microbiol., February 1, 2003; 69(2): 960 - 970. [Abstract] [Full Text] [PDF]

				M. A. Furlong, D. R. Singleton, D. C. Coleman, and W. B. Whitman Molecular and Culture-Based Analyses of Prokaryotic Communities from an Agricultural Soil and the Burrows and Casts of the Earthworm Lumbricus rubellus Appl. Envir. Microbiol., March 1, 2002; 68(3): 1265 - 1279. [Abstract] [Full Text] [PDF]

				H. W. Stokes, A. J. Holmes, B. S. Nield, M. P. Holley, K. M. H. Nevalainen, B. C. Mabbutt, and M. R. Gillings Gene Cassette PCR: Sequence-Independent Recovery of Entire Genes from Environmental DNA Appl. Envir. Microbiol., November 1, 2001; 67(11): 5240 - 5246. [Abstract] [Full Text]

				S.-P. Huang and B. S. Weir Estimating the Total Number of Alleles Using a Sample Coverage Method Genetics, November 1, 2001; 159(3): 1365 - 1373. [Abstract] [Full Text] [PDF]

				D. R. Singleton, M. A. Furlong, S. L. Rathbun, and W. B. Whitman Quantitative Comparisons of 16S rRNA Gene Sequence Libraries from Environmental Samples Appl. Envir. Microbiol., September 1, 2001; 67(9): 4374 - 4376. [Abstract] [Full Text] [PDF]

				B. Diez, C. Pedros-Alio, and R. Massana Study of Genetic Diversity of Eukaryotic Picoplankton in Different Oceanic Regions by Small-Subunit rRNA Gene Cloning and Sequencing Appl. Envir. Microbiol., July 1, 2001; 67(7): 2932 - 2941. [Abstract] [Full Text] [PDF]

				R. Massana, E. F. DeLong, and C. Pedrós-Alió A Few Cosmopolitan Phylotypes Dominate Planktonic Archaeal Assemblages in Widely Different Oceanic Provinces Appl. Envir. Microbiol., May 1, 2000; 66(5): 1777 - 1787. [Abstract] [Full Text]

				I. Kroes, P. W. Lepp, and D. A. Relman Bacterial diversity within the human subgingival crevice PNAS, December 7, 1999; 96(25): 14547 - 14552. [Abstract] [Full Text] [PDF]

				K. Ravenschlag, K. Sahm, J. Pernthaler, and R. Amann High Bacterial Diversity in Permanently Cold Marine Sediments Appl. Envir. Microbiol., September 1, 1999; 65(9): 3982 - 3989. [Abstract] [Full Text]

				A. E. McCaig, L. A. Glover, and J. I. Prosser Molecular Analysis of Bacterial Community Structure and Diversity in Unimproved and Improved Upland Grass Pastures Appl. Envir. Microbiol., April 1, 1999; 65(4): 1721 - 1730. [Abstract] [Full Text]

				V. Chazalet, J.-P. Debeaupuis, J. Sarfati, J. Lortholary, P. Ribaud, P. Shah, M. Cornet, H. V. Thien, E. Gluckman, G. Brücker, et al. Molecular Typing of Environmental and Patient Isolates of Aspergillus fumigatus from Various Hospital Settings J. Clin. Microbiol., June 1, 1998; 36(6): 1494 - 1500. [Abstract] [Full Text]

				T.M. Cocks and B.C. Brookes Sichel's unification of bibliometric frequency distributions Journal of Information Science, January 1, 1986; 12(1-2): 45 - 51. [Abstract] [PDF]

Online ISSN 1464-3510 - Print ISSN 0006-3444

Copyright © 2008 Biometrika Trust

Oxford Journals Oxford University Press

• Site Map
• Privacy Policy
• Frequently Asked Questions

Other Oxford University Press sites: Oxford University Press Oxford Journals Japan American National Biography Booksellers' Information Service Children's Fiction and Poetry Children's Reference Corporate & Special Sales Dictionaries Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks Humanities International Education Unit Law Medicine Music Online Products Oxford English Dictionary Reference Rights and Permissions Science School Books Social Sciences Very Short Introductions World's Classics