A Linear Model for Predicting d 13 C protein William J. Pestle, 1 * Mark Hubbe, 2,3 Erin K. Smith, 1 and Joseph M. Stevenson 1 1 Department of Anthropology, University of Miami, Coral Gables, FL 33124-2005 2 Department of Anthropology, The Ohio State University, Columbus, OH 43210 3 Instituto De Investigaciones Arqueol ogicas Y Museo, Universidad Cat olica Del Norte, San Pedro De Atacama, Chile KEY WORDS bioarchaeology; human biology; behavior; ecology; physiology; anatomy ABSTRACT Objective: Development of a model for the prediction of d 13 C protein from d 13 C collagen and D 13 C ap- co . Model-generated values could, in turn, serve as “consumer” inputs for multisource mixture modeling of paleodiet. Methods: Linear regression analysis of previ- ously published controlled diet data facilitated the devel- opment of a mathematical model for predicting d 13 C protein (and an experimentally generated error term) from isotopic data routinely generated during the analy- sis of osseous remains (d 13 C co and D 13 C ap-co ). Results: Regression analysis resulted in a two-term linear model (d 13 C protein (%) 5 (0.78 3 d 13 C co ) 2 (0.583 D 13 C ap- co ) 2 4.7), possessing a high R-value of 0.93 (r 2 5 0.86, P < 0.01), and experimentally generated error terms of 61.9% for any predicted individual value of d 13 C protein . This model was tested using isotopic data from Formative Period individuals from northern Chile’s Ata- cama Desert. Conclusions: The model presented here appears to hold significant potential for the prediction of the carbon isotope signature of dietary protein using only such data as is routinely generated in the course of stable isotope analysis of human osseous remains. These predicted values are ideal for use in multisource mixture modeling of dietary protein source contribution. Am J Phys Anthropol 000:000–000, 2015. V C 2015 Wiley Periodicals, Inc. Recent advances in multisource mixture modeling of stable isotope systems hold considerable potential for bioarchaeologists interested in the reconstruction of paleodiet. To make such modeling applications useful, however, the user must possess the ability to gauge tissue-specific source-consumer fractionation for all iso- tope systems of interest. These methods, in point of fact, demand quantification of trophic enrichment factors (TEF)/fractionation/discrimination offsets in order for their bioarchaeological promise to be fully realized. While several recent studies have addressed and attempted to quantify the diet-collagen or protein- collagen offset for nitrogen isotope systematics (d 15 N) (e.g. Hedges and Reynard, 2007; O’Connell et al., 2012), far less work (Froehle et al., 2010) has been done to assess such offsets for carbon stable isotopes (d 13 C). Here, employing a corpus of previously published data from controlled diet experiments with rats, mice, and pigs, we present a multiple (two variable) linear model by which the d 13 C value (plus/minus an experi- mentally generated error term) of dietary protein (d 13 C protein ) can be accurately predicted from isotopic data routinely generated during the analysis of osseous remains (d 13 C co and D 13 C ap-co ). By combining the output of this regression with (one of the several) proposed fractionation offsets between dietary protein and bone collagen for d 15 N, one is able to take advantage of mul- tisource mixture modeling software, and thus develop quantitative and probabilistic models of paleodietary mixtures. After presenting this multiple linear regression model for predicting d 13 C protein , we demonstrate its utility by means of a Markov Chain Monte Carlo sim- ulation [using the software package MixSIAR (Stock and Semmens, 2013)] of the diet of individuals drawn from our ongoing research into the Formative Period of the Atacama Desert of northern Chile. The method detailed here permits us to move beyond relative statements of dietary contribution to probabilistic and uncertainty integrated quantification of dietary inputs on an individual-by-individual basis (Semmens et al., 2009). THE NEED FOR QUANTIFICATION IN ISOTOPIC PALEODIETARY STUDIES The past 30 years have witnessed an explosive increase in the use of stable isotope analysis in bioarch- aeology (see Pestle et al., 2014: Fig. 1). Indeed, stable isotope analysis has now become a standard technique used in the reconstruction of ancient humazn paleodiet, paleomobility, and paleoclimate. And yet, with limited recent exceptions (e.g. Ambrose et al., 2003; Kellner and Schoeninger, 2007; Arcini et al., ; Coltrain and Janetski, 2013; Colonese et al., 2014; Fernandes et al., 2012a, 2014; Ugan and Coltrain, 2012), the paleodietary recon- struction facilitated by this analysis has been limited to relative statements about source contributions (e.g. more of food X, less of food Y). Such relative statements are Grant sponsor: FONDECYT; Grant number: 1110702. *Correspondence to: William Pestle, Department of Anthropology, Merrick Hall 102E, University of Miami, Coral Gables, FL 33124- 2005, USA. E-mail:w.pestle@miami.edu Received 23 October 2014; revised 26 February 2015; accepted 1 March 2015 DOI: 10.1002/ajpa.22743 Published online 00 Month 2015 in Wiley Online Library (wileyonlinelibrary.com). Ó 2015 WILEY PERIODICALS, INC. AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 00:00–00 (2015)