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

Eren, Metin I. and Chao, A. and Hwang, W-H. and Colwell, R.K. (2012) Estimating the Richness of a Population When the Maximum Number of Classes Is Fixed: A Nonparametric Solution to an Archaeological Problem. PLoS ONE, 7 (5). e34179. ISSN 1932-6203. (Full text available)

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http://dx.doi.org/10.1371/journal.pone.0034179

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).

Item Type: Article
Subjects: H Social Sciences
Divisions: Faculties > Social Sciences > School of Anthropology and Conservation > Social and Cultural Anthropology
Depositing User: Shelley Malekia
Date Deposited: 13 Aug 2012 11:06
Last Modified: 12 Mar 2013 16:38
Resource URI: http://kar.kent.ac.uk/id/eprint/30102 (The current URI for this page, for reference purposes)
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