We have presented a mathematical model relating ceramic use and discard, and have applied this model to modern cooking vessels in the Peruvian Andes. The age distribution of in-use vessels allows calculation of vessel discard; the difference between vessels in use for successive time intervals is the vessel discard rate. Uselife is defined as the mean age for vessel discard. Two pathways for discard are described, accident and service wear, resulting in different patterns for vessel age during use and vessel discard. Accidental breakage results in equal vessel uselife and in-use vessel mean age. Service-wear breakage results in significantly greater vessel uselife than in-use vessel mean age.

Data on modern vessel usage were obtained from 199 Wanka households. With these data, we sought relations between ceramic discard and household size. Three variables potentially affecting the rate of ceramic discard were considered: vessel numbers, vessel volume, and vessel uselife. A typical Wanka cooking vessel assemblage consists of four or five ollas, two large ollas, one chata, one tostadera, and one tetera. The number of ollas per family increases slightly with household size, whereas the number of chatas per family decreases. The number of tostaderas is nearly constant at about one per family. Overall, an increasing number of vessels (ceramic and metal) is observed with household size, at a rate of .15 vessels per person. The mean volume of all ollas also correlates with household size, with a slope of. 15 liters per person. Larger families expand their cooking capacity by having a few more vessels and slightly larger vessels. Between small (2 to 3 persons) and large (9 to 10 persons) families, the combined cooking capacity increase due to having more and larger vessels is only about 11 liters. The age distribution for ollas in use does not fall exponentially with age (unlike the accidental breakage model in Figure 2); instead their peak discard occurs at two years of age (similar to the service-wear breakage model in Figure 3). However, informants report accidental breakage more often (81 percent) than service-wear breakage (17 percent). Several causes of breakage that we classified as accidental could alternatively be considered use-related breakage, and there may be many use-related injuries that don't immediately break the vessel and so are unreported in our data. Repeated thermal shock is one example that may leave older vessels susceptible to weak impacts (accidents) that would not break new vessels. The annual discard of ceramic ollas correlates with household size with a rate of .06 ollas/person, and ollas account for the highest discard level, with a mean of 1.15 ollas per family-year. Accounting for replacement by metal ollas, the olla discard rate would be 1.87 ollas per family-year. The mean annual discard for ceramic chatas is .48 per family-year, and for tostaderas it is .75 tostadera per family-year. Total sherd accumulation is more consistent per family than per person, suggesting that the number of families is more easily obtained from bulk archaeological sherd data. Additional knowledge of household size is required to determine population size from ceramic data.

An independent survey of vessel discard for 223 Wanka families tests the predictions of the usage survey. Using the discard rate for each vessel morphology independently, a range of 91 to 183 family-years was calculated, compared to the actual figure of 223 families reporting discard for somewhat less than one year. With relations between discard and household size for several vessel morphologies, household size can be calculated from the relative proportion of discard for two or more vessel morphologies. Using discard data from three vessels (ollas, chatas, and tostaderas), the calculated household size is 5.0 (versus 5.7 actual), and the number-of-households time product is 171 family-years (versus < 223 family-years actual). Ceramics remain a vital part of food preparation and serving in the Mantaro Valley of the Peruvian Andes, the continuation of a long ceramic tradition. A large-scale survey approach to studying ceramic use and discard has provided intriguing data and suggested new approaches to studying these data. The challenge now is to apply these observations to Wanka archaeological data.

Acknowledgments We thank Andres Moya and his family of Ataura, Peru, for assistance in the field. We acknowledge the many Mantaro families who revealed the ways they use and discard their pots. Melissa Hagstrum's research in the Mantaro was supported by a Fulbright-Hays grant, the UCLA Friends of Archaeology, and the UCLA Department of Anthropology Research and Travel Fund. Her ethnoarchaeological research was part of the Upper Mantaro Archaeological Research Project funded by the National Science Foundation (BNS-8203723). We are grateful to Carmen Thays and Maritza PĂ©rez who drafted Figure 4 in Peru and Jo Griffith and Georgia Greaves for finishing these drawings in ink. We thank Guillermo Algaze, Warren DeBoer, Gary Feinman, Charles Kolb, Barbara Mills, and several anonymous reviewers for helpful comments on the manuscript.

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