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PLOS ONE  2012 

Estimating the Richness of a Population When the Maximum Number of Classes Is Fixed: A Nonparametric Solution to an Archaeological Problem

DOI: 10.1371/journal.pone.0034179

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Abstract:

Background Estimating assemblage species or class richness from samples remains a challenging, but essential, goal. Though a variety of statistical tools for estimating species or class richness have been developed, they are all singly-bounded: assuming only a lower bound of species or classes. Nevertheless there are numerous situations, particularly in the cultural realm, where the maximum number of classes is fixed. For this reason, a new method is needed to estimate richness when both upper and lower bounds are known. Methodology/Principal Findings Here, we introduce a new method for estimating class richness: doubly-bounded confidence intervals (both lower and upper bounds are known). We specifically illustrate our new method using the Chao1 estimator, rarefaction, and extrapolation, although any estimator of asymptotic richness can be used in our method. Using a case study of Clovis stone tools from the North American Lower Great Lakes region, we demonstrate that singly-bounded richness estimators can yield confidence intervals with upper bound estimates larger than the possible maximum number of classes, while our new method provides estimates that make empirical sense. Conclusions/Significance Application of the new method for constructing doubly-bound richness estimates of Clovis stone tools permitted conclusions to be drawn that were not otherwise possible with singly-bounded richness estimates, namely, that Lower Great Lakes Clovis Paleoindians utilized a settlement pattern that was probably more logistical in nature than residential. However, our new method is not limited to archaeological applications. It can be applied to any set of data for which there is a fixed maximum number of classes, whether that be site occupancy models, commercial products (e.g. athletic shoes), or census information (e.g. nationality, religion, age, race).

References

[1]  Magurran A (2004) Measuring Biological Diversity. Oxford: Blackwell.
[2]  Chao A (2005) Species estimation and applications. In: Balakrishnan N, Read CB, Vidakovic B, editors. Encyclopedia of statistical sciences, 2nd Edition, Vol 12. New York: Wiley. pp. 7907–7916.
[3]  Colwell R, Chao A, Gotelli N, Lin S, Mao C, et al. (2012) Models and estimators linking individual-based and sample-based rarefaction, extrapolation, and comparison of assemblages. J Plant Ecol: 5: 3–21.
[4]  Gotelli N, Colwell R (2011) Estimating species richness. In: Magurran A, McGill B, editors. Frontiers in measuring biodiversity. New York: Oxford University Press. pp. 39–54.
[5]  Gotelli N, Chao A (2012) Measuring and estimating species richness, species diversity, and biotic similarity from sampling data. The Encyclopedia of Biodiversity, 2nd edition. Elsevier. N.Y.
[6]  Colwell R, Mao C, Chang J (2004) Interpolating, extrapolating, and comparing incidence-based species accumulation curves. Ecology 85: 2717–2727.
[7]  Hughes J, Hellmann J, Ricketts T, Bohannan B (2001) Counting the uncountable: statistical approaches to estimating microbial diversity. Appl Environ Microbiol 67: 4399–4406.
[8]  Colwell R, Coddington J (1994) Estimating terrestrial biodiversity through extrapolation. Philos T R Soc B 345: 101–118.
[9]  Sanders H (1968) Marine benthic diversity: a comparative study. The Am Nat 102: 243.
[10]  Hurlbert S (1971) The nonconcept of species diversity: a critique and alternative parameters. Ecology 52: 577–586.
[11]  Heck K , van Belle G, Simberloff D (1975) Explicit calculation of the rarefaction diversity measurement and the determination of sufficient sample size. Ecology 56: 1459–1461.
[12]  Gotelli N, Colwell R (2001) Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecol Lett 4: 379–391.
[13]  Bunge J, Fitzpatrick M (1993) Estimating the number of species: a review. J Am Stat Assoc 88: 364–373.
[14]  Chao A (1984) Non-parametric estimation of the number of classes in a population. Scand J Stat 11: 265–270.
[15]  Grismer J, Grismer L (2010) Who’s your mommy? Identifying maternal ancestors of asexual species of Leiolepis Cuvier, 1829 and the description of a new endemic species of asexual Leiolepis Cuvier, 1829 from Southern Vietnam. Zootaxa 2433: 47–61.
[16]  Roosmalen M, Roosmalen T, Mittermeier R (2002) A taxonomic review of the Titi Monkeys, Genus Callicebus Thomas, 1903, with the description of two new species, Callicebus bernhardi and Callicebus stephennashi, from Brazilian Amazonia. Neotropical Primates 10 (Sppl.). pp. 1–53.
[17]  Baxter M (2001) Methodological issues in the study of assemblage diversity. Am Antiquity 66: 715–725.
[18]  Cochrane W (2003) Artefact attribute richness and sample size adequacy. J Archaeol Sci 30: 837–848.
[19]  Eerkens J, Ferguson J, Glascock M, Skinner C, Waechter S (2007) Reduction strategies and geochemical characterization of lithic assemblages: a comparison of three case studies from western North America. Am Antiquity 72: 585–597.
[20]  Grayson D, Cole S (1998) Stone tool assemblage richness during the Middle and Early Upper Palaeolithic in France. J Archaeol Sci 25: 927–938.
[21]  Kaufman D (1998) Measuring archaeological diversity: an application of the Jackknife technique. Am Antiquity 63: 73–85.
[22]  Kintigh K (1984) Measuring archaeological diversity by comparison with simulated assemblages. Am Antiquity 49: 44–54.
[23]  Leonard R, Jones G (1989) Quantifying Diversity in Archaeology. Cambridge: Cambridge University Press.
[24]  Simek J, Price H (1990) Chronological change in Perigord lithic assemblage diversity. In: P InMellars, editor. editor. The Emergence of Modern Humans: An Archaeological Perspective. Edinburgh: University of Edinburgh Press. pp. 243–261.
[25]  Thomas D (1988) The Archaeology of Monitor Valley: 3. Survey and Additional Excavations. New York: Anthropological Papers 66(2), American Museum of Natural History.
[26]  Bradley J, Spiess A, Boisvert R, Boudreau J (2008) What’s the point? Model forms and attributes of Paleoindian bifaces in the New England-Maritimes region. Archaeol Eastern North Amer 36: 119–172.
[27]  Ellis C, Deller D (1988) Some distinctive Paleo-Indian tool types from the Lower Great Lakes area. Midcontinental J Archaeol 13: 111–158.
[28]  Jackson L (1998) The Plainville Point: description of a Late-Paleoindian type. Current Research in the Pleistocene 15: 23–25.
[29]  Shott M (1997) Activity and formation as sources of variation in Great Lakes Paleoindian assemblages. Midcontinental J Archaeol 22: 197–236.
[30]  Eren MI, Redmond B (2011) Clovis Blades at Paleo Crossing (33ME274), Medina County, Ohio. Midcontinental J Archaeol 36: 173–194.
[31]  Eren MI, Vanderlaan S, Holland J (2011) Overshot flaking at the Arc Site, Genesee County, New York: Examining the Clovis-Gainey Connection. The Open Anthropol J 4: 40–52.
[32]  Tomenchuk J, Storck PL (1997) Two newly recognized Paleoindian tool types: single- and double-scribe compass gravers and coring gravers. Am Antiquity 62: 508–522.
[33]  Bisson M (2000) Nineteeth Century tools for Twenty-First Century archaeology? Why the Middle Paleolithic typology of Francois Bordes must be replaced. J Archaeol Meth Th 7: 1–48.
[34]  Fish P (1978) Consistency in archaeological measurement and classification: a pilot study. Am Antiquity 43: 86–89.
[35]  Whittaker J, Caulkins D, Kamp K (1998) Evaluating consistency in typology and classification. J Archaeol Meth Th 5: 129–164.
[36]  Dunnell R (1971) Systematics in Prehistory. New York: The Free Press.
[37]  O’Brian M, Lyman R (2000) Applying Evolutionary Archaeology: A Systematic Approach. New York: Kluwer Academic/Plenum.
[38]  O’Brien M, Lyman R (2003) Cladistics and Archaeology. Salt Lake City: University of Utah Press.
[39]  Eren MI (2011) Behavioral Adaptations of Human Colonizers in the North American Lower Great Lakes Region. Unpublished Ph.D. Dissertation, Department of Anthropology, Southern Methodist University, Dallas, TX.
[40]  Chao A (1987) Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43: 783–791.
[41]  Meltzer D (2009) First Peoples in a New World: Colonizing Ice Age America. Berkeley: University of California Press.
[42]  Chao A, Shen T-J, Hwang W-H (2006) Application of Laplace’s boundary-mode approximations to estimate species and shared species richness. Aust NZ J Stat 48: 117–128.
[43]  Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7: 1–26.
[44]  Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap. New York: Chapman and Hall.
[45]  Shen T-J, Chao A, Lin C-F (2003) Predicting the number of new species in further taxonomic sampling. Ecology 84: 798–804.
[46]  Bettinger R (1991) Hunter-Gatherers: Archaeological and Evolutionary Theory. New York: Plenum Press.
[47]  Schiffer M (1975) The effects of occupation span on site content. In: M InSchiffer, J House, editors. editors. The Cache River Archaeological Project: An Experiment in Contract Archaeology. Fayetteville: Arkansas Archaeological Survey, Research Series 8. pp. 265–269.
[48]  Surovell T (2009) Toward a Behavioral Ecology of Lithic Technology: Cases from PaleoindianArchaeology. Tucson: The University of Arizona Press.
[49]  Kent S (1992) Studying variability in the archaeological record: an ethnoarchaeological model for distinguishing mobility patterns. Am Antiquity 57: 635–660.
[50]  Plog S (1989) Ritual, exchange, and the development of regional systems. In: W InLipe, M Hegmon, editors. editors. The Architecture of Social Integration. Cortez: Occasional Paper No. 1 Crow Canyon Archaeological Center. pp. 143–154.
[51]  Reid J (1982) Analystic procedures for interassemblage-settlement system analysis. In: J InReid, editor. editor. Introduction and Special Studies. Tucson: Cholla Project Archaeology, Vol. 1, Archaeological Series No. 1. pp. 193–216.
[52]  Schlanger S (1990) Artifact assemblage composition and site occupation duration. In: P InMinnis, C Redman, editors. editors. Perspectives on Southwestern Prehistory. Boulder: Westview Press. pp. 103–121.
[53]  Thomas D (1989) Diversity in hunter-gatherer cultural geography. In: R InLeonard, G Jones, editors. editors. Quantifying Diversity in Archaeology. Cambridge: Cambridge University Press. pp. 85–91.
[54]  Yellen J (1977) Archaeological Approaches to the Present: Models for Reconstructing the Past. New York: Academic Press.
[55]  MacKenzie D, Nichols J, Lachman G, Droege S, Royle J, et al. (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83: 2248–2255.

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