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Confidence Intervals in the Analysis of Mortality and Survivorship Curves in Zooarchaeology

Published online by Cambridge University Press:  20 January 2017

Max Price*
Affiliation:
Department of Anthropology, Harvard University, Cambridge, MA 02138
Jesse Wolfhagen
Affiliation:
Interdepartmental Doctoral Program in Anthropological Sciences, Stony Brook University, Stony Brook, NY 11794
Erik Otárola-Castillo
Affiliation:
Department of Anthropology, Purdue University, West Lafayette, IN 47907

Abstract

The analysis of age-at-death data, derived from epiphyseal fusion and dental eruption/wear patterns, is one of the most powerful tools at the disposal of zooarchaeologists studying past hunting and herd management practices. Zooarchaeologists typically analyze age-at-death data by constructing survivorship and mortality curves in order to allow insight into a variety of ecological and economic relationships between humans and animals. Since adopting such practices in the middle of the twentieth century, zooarchaeologists have proposed several methods for analyzing these curves, including visual examination and hypothesis testing. Creating confidence intervals is complementary to these two methods, allowing practitioners to graphically represent survivorship and mortality while testing hypotheses and accounting for sample sizes, which are often small in zooarchaeological assemblages. We discuss the basic concepts behind the nature of age-at-death data and the analysis of mortality and survivorship curves. We then describe how to calculate confidence intervals using bootstrapping techniques for both dental eruption/wear data and epiphyseal fusion data. To enable future users to replicate our methods, we introduce the freely available online R package “zooaRch” (http://cran.r-project.org/web/packages/zooaRch/ ), which includes a vignette to guide first-time users.

El análisis de los datos de edad a la muerte derivada de la fusion de las epífisis y la erupción dental o patrones de desgaste, es una de las herramientas más potentes a disposición de zooarqueólogos quienes estudian las prácticas de caza en el pasado y la gestión de los rebaños. Curvas de supervivencia y mortalidad que se pueden derivar de estos datos, permiten comprender una variedad de relaciones ecológicas y económicas entre humanos y animales. Desde el comienzo del uso de esta metodología a mediados del siglo 20, los zooarqueólogos han propuesto varios métodos para el análisis de datos de sobrevivencia y mortalidad, incluyendo exámenes visuales o pruebas de hipótesis. La creación de los intervalos de confianza se complementa con ambos métodos, lo cual permite a los investigadores representar a los datos de sobrevivencia o mortalidad a través de gráficas, y deja que al mismo tiempo puedan probar la hipótesis y tomar en cuenta el tamaño de la muestra, la cual es normalmente pequeña en los casos de zooarqueología. Después de una discusión sobre los conceptos básicos detrás del análisis de sobrevivencia, se describe cómo calcular intervalos de confianza para los gráficos de estas curvas utilizando tanto los datos de la erupción / desgaste dental y los datos de fusión de las epífisis a través de técnicas de bootstrapping. Para que los usuarios futuros puedan replicar nuestros métodos, se introduce el paquete gratis de R “zooaRch” (http://cran.r-project.org/web/packages/zooaRch/), que se puede encontrar en su pagina de web que incluye una viñeta para guiar los usuarios probando el programa por primera vez.

Type
Reports
Copyright
Copyright © 2016 by the Society for American Archaeology.

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References

References Cited

Arbuckle, Benjamin S. 2009 Chalcolithic Caprines, Dark Age Dairy, and Byzantine Beef: A First Look at Animal Exploitation at Middle and Late Holocene Çadir Höyük, North Central Turkey. Anatolica 35:180224.Google Scholar
Atici, Levent, Kansa, Sarah Whitcher, Lev-Tov, Justin S., and Kansa, Eric C. 2013 Other People’s Data: A Demonstration of the Imperative of Publishing Primary Data. Journal of Archaeological Method and Theory 20:663681.Google Scholar
Borgan, Ørnulf, and Liestøl, Knut 1990 A Note on Confidence Intervals and Bands for the Survival Function Based on Transformations. Scandinavian Journal of Statistics 17:3541.Google Scholar
Bréhard, Stéphanie, Radu, Valentin, Martin, Alexis, Hanot, Pauline, Popovici, Dragomir, and Balasescu, Adrian 2014 Food Supply Strategies in the Romanian Eneolithic: Sheep/Goat Husbandry and Fishing Activities from Harsova Telland Bordusani-Popina (5th Millennium BC). European Journal of Archaeology 17:407433.Google Scholar
Brochier, J.E. 2013 The Use and Abuse of Culling Profiles in Recent Zooarchaeological Studies: Some Methodological Comments on “Frequency Correction” and Its Consequences. Journal of Archaeological Science 40:14161420.CrossRefGoogle Scholar
Bunn, Henry T., and Pickering, Travis Rayne 2010 Bovid Mortality Profiles in Paleoecological Context Falsify Hypotheses of Endurance Running-Hunting and Passive Scavenging by Early Pleistocene Hominins. Quaternary Research 74:395404.Google Scholar
Byers, David A., and Hill, Brenda L. 2009 Pronghorn Dental Age Profiles and Holocene Hunting Strategies at Hogup Cave, Utah. American Antiquity 74:299321.CrossRefGoogle Scholar
Carter, Rickey E., and Huang, Peng 2009 Cautionary Note Regarding the Use of CIs Obtained from Kaplan-Meier Survival Curves. Journal of Clinical Oncology 27:174175.Google Scholar
Chaplin, Raymond E. 1971 The Study of Animal Bones from Archaeological Sites. Seminar Press, New York.Google Scholar
Chernick, Michael R. 2008 Bootstrap Methods: A Guide for Practitioners and Researchers. 2nd ed. Wiley-Interscience, Hoboken, New Jersey.Google Scholar
Cox, D. R. and Oakes, D. 1984 Analysis of Survival Data. Chapman and Hall, New York.Google Scholar
Crabtree, Pam J. 1996 Production and Consumption in an Early Complex Society: Animal Use in Middle Saxon East Anglia. World Archaeology 28:5875.Google Scholar
Crema, Enrico R. 2011 Modelling Temporal Uncertainty in Archaeological Analysis. Journal of Archaeological Method and Theory 19:440461.Google Scholar
Cumming, Geoff, Fidler, Fiona, and Vaux, David L. 2007 Error Bars in Experimental Biology. Journal of Cell Biology 177:711.CrossRefGoogle Scholar
Deevey, Edward S. 1947 Life Tables for Natural Populations of Animals. The Quarterly Review of Biology 22:283314.Google Scholar
Deniz, Esref, and Payne, Sebastian 1982 Eruption and Wear in the Mandibular Dentition as a Guide to Ageing Turkish Angora Goats. In Ageing and Sexing Animal Bones from Archaeological Sites, edited by Bob Wilson, Caroline Grigson, and Sebastian Payne, pp. 155205. BAR British Series 109. British Archaeological Reports, Oxford.Google Scholar
Discamps, Emmanuel, and Costamagno, Sandrine 2015 Improving Mortality Profile Analysis in Zooarchaeology: A Revised Zoning for Ternary Diagrams. Journal of Archaeological Science 58:6276.CrossRefGoogle Scholar
Dyson, Robert H. 1953 Archaeology and the Domestication of Animals in the Old World. American Anthropologist 55:661673.Google Scholar
Efron, Bradley, and Tibshirani, Robert J. 1986 Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science 1:5477.Google Scholar
Frison, George C. 1984 The Carter/Kerr-Mcgee Paleoindian Site: Cultural Resource Management and Archaeological Research. American Antiquity 49:288314.Google Scholar
Gardner, Martin J., and Altman, Douglas G. 1986 Confidence Intervals Rather than P Values: Estimation Rather than Hypothesis Testing. British Medical Journal 292:746750.Google Scholar
Grant, Annie 1978 Variation in Dental Attrition in Mammals and Its Relevance to Age Estimation. In Research Problems in Zooarchaeology, edited by D. Borthwell, K. D. Thomas, and J. Clutton-Brock, pp. 103106. Occasional Publication No. 3. University College London Institute of Archaeology, London.Google Scholar
Grant, Annie 1982 The Use of Tooth Wear as a Guide to the Age of Domestic Ungulates. In Ageing and Sexing Animal Bones from Archaeological Sites, edited by Bob Wilson, Caroline Grigson, and Sebastian Payne, pp. 91108. BAR British Series 109. British Archaeological Reports, Oxford.Google Scholar
Greenfield, Haskel J. 1986 The Paleoeconomy of the Central Balkans (Serbia): A Zooarchaeological Perspective on The Late Neolithic and Bronze Age (ca. 4500–1000 B.C.). BAR International Series 304. British Archaeological Reports, Oxford.Google Scholar
Greenfield, Haskel J. 1988 The Origins of Milk and Wool Production in the Old World: A Zooarchaeological Perspective from the Central Balksms. Current Anthropology 29:573593.Google Scholar
Hall, Wendy J., and Wellner, Jon A. 1980 Confidence Bands for a Survival Curve from Censored Data. Biometrika 67:133143.CrossRefGoogle Scholar
Hole, Frank, Flannery, Kent V., and Neely, James A. 1969 Prehistory and Human Ecology of the Deh Luran Plain. Memoirs of the Museum of Anthropology 1. University of Michigan Press, Ann Arbor.CrossRefGoogle Scholar
Jones, Gillian G. 2006 Tooth Eruption and Wear in Live Sheep from Butser Hill, the Cotswold Farm Park and Five Farms in the Pentland Hills, UK. In Recent Advances in Ageing and Sexing Animal Bones, edited by Deborah Ruscillo, pp. 155178. Oxbow Books, Oxford.CrossRefGoogle Scholar
Kaplan, Edward L., and Meier, Paul 1958 Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association 53:457481.Google Scholar
Klein, Richard G. 1978 Stone Age Predation on Large African Bovids. Journal of Archaeological Science 5:195217.Google Scholar
Klein, Richard G. 1982 Age (Mortality) Profiles as a Means of Distinguishing Hunted Species from Scavenged Ones in Stone Age Archaeological Sites. Paleobiology 8:151158.Google Scholar
Klein, Richard G., and Cruz-Uribe, Kathryn 1984 The Analysis of Animal Bones from Archaeological Sites. University of Chicago Press, Chicago.Google Scholar
Knight, Richard R. 1966 Bone Changes with Aging Elk. Journal of Wildlife Management 30:369374.CrossRefGoogle Scholar
Kurtén, Björn 1954 Population Dynamics: ANew Method in Paleontology. Journal of Paleontology 28:286292.Google Scholar
Landon, David B. 1993 Feeding Colonial Boston: A Zooarchaeological Study. Historical Archaeology 30:i-vii, 1153.Google Scholar
Lee, Elisa T. 2013 Statistical Methods for Survival Data Analysis. 4th ed. Wiley, Hoboken, New Jersey.Google Scholar
Lubinski, Patrick M. 2000 A Comparison of Methods for Evaluating Ungulate Mortality Distributions. Archaeozoologia 11:121134.Google Scholar
Lyman, R. Lee 1987 On the Analysis of Vertebrate Mortality Profiles: Sample Size, Mortality Type, and Hunting Pressure. American Antiquity 52:125142.Google Scholar
Lyman, R. Lee 2008 Quantitative Paleozoology. Cambridge University Press, Cambridge.Google Scholar
Marciniak, Arkadiusz 2014 The Secondary Products Revolution, Mortality Profiles, and Practice of Zooarchaeology. In Animal Secondary Products: Archaeological Perspectives on Domestic Animal Exploitation in the Neolithic and Bronze Age, edited by Haskel J. Greenfield, pp. 186205. Oxbow Books, Oxford.Google Scholar
Marom, Nimrod, and Bar-Oz, Guy 2009 Culling Profiles: The Indeterminacy of Archaeozoological Data to Survivorship Curve Modelling of Sheep and Goat Herd Maintenance Strategies. Journal of Archaeological Science 36:11841187.Google Scholar
Meadow, Richard H. 1980 Animal Bones: Problems for the Archaeologist Together with Some Possible Solutions. Paléorient 6:6577.CrossRefGoogle Scholar
Meadow, Richard H. 1989 Osteological Evidence for the Process of Animal Domestication. In The Walking Larder: Patterns of Domestication, Pastoralism, and Predation, edited by Juliet Clutton-Brock, pp. 8090. Unwin-Hyman, London.Google Scholar
Millard, Andrew R. 2006 A Bayesian Approach to Ageing Sheep/Goats from Toothwear. In Recent Advances in Ageing and Sexing Animal Bones, edited by Deborah Ruscillo, pp 145154. Oxbow Books, Oxford.Google Scholar
Munro, Natalie D. 2004 Zooarchaeological Measures of Hunting Pressure and Occupation Intensity in the Natufian. Current Anthropology 45:S5S33.Google Scholar
Munson, Patrick J. 2000 Age-Correlated Differential Destruction of Bones and Its Effect on Archaeological Mortality Profiles of Domestic Sheep and Goats. Journal of Archaeological Science 27:391407.Google Scholar
O’Connor, Terry P. 2008 The Archaeology of Animal Bones. Texas A&M University Press, College Station,Texas.Google Scholar
Otárola-Castillo, Erik, Wolfhagen, Jesse, and Price, Max D. 2015 zooaRch: Analytical Tools for Zooarchaeological Data. R package version 1.0. Electronic resource, http://CRAN.R-project.org/package=zooaRch, accessed November 12, 2015.Google Scholar
Payne, Sebastian 1973 Kill-Off Patterns in Sheep and Goats: The Mandibles from Asvan Kale. Anatolian Studies 23:281303.Google Scholar
Pearl, Raymond, and Miner, John R. 1935 Experimental Studies on the Duration of Life. XIV. The Comparative Mortality of Certain Lower Organisms. Quarterly Review of Biology 10:6079.Google Scholar
Popkin, Peter R. W., Baker, Polydora, Worley, Fay, Payne, Sebastian, and Hammon, Andy 2012 The Sheep Project (1): Determining Skeletal Growth, Timing of Epiphyseal Fusion and Morphometric Variation in Unimproved Shetland Sheep of Known Age, Sex, Castration Status and Nutrition. Journal of Archaeological Science 39:17751792.Google Scholar
Price, Max D., Buckley, Mike, Kersel, Morag, and Rowan, Yorke M. 2013 Animal Management Strategies during the Chalcolithic in the Lower Galilee: New Data from Marj Rabba. Paléorient 39:183200.CrossRefGoogle Scholar
R Core Team 2014 R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Electronic document, http://www.R-project.org/, accessed November 12, 2015.Google Scholar
Redding, Richard 1981 Decision Making in Subsistence Herding of Sheep and Goats in the Middle East. Ph.D. dissertation, Departments of Anthropology and Biological Sciences, University of Michigan, Ann Arbor.Google Scholar
Reitz, Elizabeth, and Wing, Elizabeth 2008 Zooarchaeology. 2nd ed. Cambridge University Press, Cambridge.Google Scholar
Ringrose, Trevor J. 1993 Bone Counts and Statistics: A Critique. Journal of Archaeological Science 20:121157.Google Scholar
Schoville, Benjamin J., and Otárola-Castillo, Erik 2014 A Model of Hunter-Gatherer Skeletal Element Transport: The Effect of Prey Body Size, Carriers, and Distance. Journal of Human Evolution 73:114.Google Scholar
Severinghaus, C. William 1949 Tooth Development and Wear Criteria of Age in White-Tailed Deer. Journal of Wildlife Management 13:195216.Google Scholar
Silver, I. A. 1969 The Ageing of Domestic Animals. In Science in Archaeology, edited by Don Brothwell, and Eric S. Higgs, pp. 283302. Thames and Hudson, London.Google Scholar
Speth, John D. 1983 Bison Kills and Bone Counts: Decision Making by Ancient Hunters. University of Chicago Press, Chicago.Google Scholar
Steele, Teresa E. 2005 Comparing Methods for Analysing Mortality Profiles in Zooarchaeological and Palaeontological Samples. International Journal ofOsteoarchaeology 15:404420.Google Scholar
Steele, Teresa E. 2015 The Contributions of Animal Bones from Archaeological Sites: The Past and Future of Zooarchaeology. Journal of Archaeological Science 56:168176.Google Scholar
Steele, Teresa E., and Weaver, Timothy D. 2002 The Modified Triangular Graph: A Refined Method for Comparing Mortality Profiles in Archaeological Samples. Journal of Archaeological Science 29:317322.Google Scholar
Stiner, Mary C. 1990 The Use of Mortality Patterns in Archaeological Studies of Homonid Predatory Adaptations. Journal of Anthropological Archaeology 9:305351.Google Scholar
Stiner, Mary C. 1994 Honor Among Thieves: A Zooarchaeological Study of Neandertal Ecology. Princeton University Press, Princeton, New Jersey.Google Scholar
Twiss, Katheryn C. 2008 An Assessment of the Archaeological Applicability of Faunal Ageing Methods Based on Dental Wear. International Journal of Osteoarchaeology 18:329351.Google Scholar
Voorhies, Michael R. 1969 Taphonomy and Population Dynamics of an Early Pliocene Vertebrate Fauna, Knox County, Nebraska. Contributions to Geology, Special Paper No. 1. University of Wyoming, Laramie.Google Scholar
Watson, J. P. N. 1978 The Interpretation of Epiphyseal Fusion Data. In Research Problems in Zooarchaeology, edited by Don R. Brothwell, Kenneth D. Thomas, and Juliet Clutton-Brock, pp. 97101. Occasional Publication No. 3. University College London Institute of Archaeology, London.Google Scholar
Weaver, Timothy D., Boyko, Ryan H., and Steele, Teresa E. 2011 Cross-Platform Program for Likelihood-Based Statistical Comparisons of Mortality Profiles on a Triangular Graph. Journal of Archaeological Science 38:24202423.Google Scholar
White, Tim D., Black, Michael T., and Folkens, Pieter Arend 2012 Human Osteology. 3rd ed. Academic Press, New York.Google Scholar
Zeder, Melinda A. 2001 A Metrical Analysis of a Collection of Modern Goats (Capra hircus aegargus and C. h. hircus) from Iran and Iraq: Implications for the Study of Domestication. Journal of Archaeological Science 28:6179.CrossRefGoogle Scholar
Zeder, Melinda A. 2006 Reconciling Rates of Long Bone Fusion and Tooth Eruption in Sheep (Ovis) and Goat (Capra). In Recent Advances in Ageing and Sexing Animal Bones, edited by Deborah Ruscillo, pp. 87118. Oxbow Books, Oxford.Google Scholar
Zeder, Melinda A., and Hesse, Brian 2000 The Initial Domestication of Goats (Capra hircus) in the Zagros Mountains 10,000 Years Ago. Science 287:22542257.Google Scholar
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