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

Abstract

BackgroundEstimating 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 FindingsHere, 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/SignificanceApplication 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).

Neutron activation analysis of 12,900-year-old stone artifacts confirms 450–510+ km Clovis tool-stone acquisition at Paleo Crossing (33ME274), northeast Ohio, U.S.A.

“…This, of course, is not to say that Clovis colonizing foragers had no knowledge of the area whatsoever. Instead, it is entirely possible that a "working knowledge" of the area had been hitherto achieved through earlier scouting trips aimed to target desirable resource areas (Dincauze, 1993;Ellis, 2011;Eren, 2011;Eren et al, 2012).…”

Environment-induced changes in selective constraints on social learning during the peopling of the Americas

“…Here sample coverage (or simply coverage ) is an objective measure of sample completeness originally developed by the founder of modern computer science, Alan Turing, and his colleague I. J. Good545556 (see ref. 41 for details). The estimated coverage values in Table 1a were obtained by an estimator57 that is more accurate than Turing’s original estimator.…”

Species richness and abundance among macromoths: A comparison of taxonomic, temporal and spatial patterns in Oregon and South Korea

“…8.0;Colwell 2006). The Chao 1 estimator is widely accepted as reliable in biodiversity studies since this estimator uses information on the number of rare or infrequent species in the collection to estimate the number of undetected species (Chao et al 2009;Colwell et al 2012;Eren et al 2012).…”