The style-function dichotomy lies at the heart of the evolutionary archaeology research program. It also is the source of much disagreement about how we should conceive of the processes of culture change. Evolutionary archaeologists tend to view archaeological attributes as either functional, if they respond to selection, or stylistic, if they do not. Others tend to see style and function as operating simultaneously. A resolution to this problem is proposed through development of a formal mathematical model of style- and function-based evolution using a hypothetical example of temporal patterns of ceramic decoration within a community of household-based potters. Simple replicator equations are proposed to describe the household-scale dynamics of change in the relative frequency of ceramic decoration. These low-level dynamics can be distinguished on the basis of whether or not change is correlated with some measure of performance, utility, or payoff. The replicator equations are then used to derive several versions of the Price Equation (Price 1970), a very general and powerful statement about total evolutionary change in any system. At this scale of analysis, total change is similarly partitioned into payoff-correlated (functional) and payoff-independent (stylistic) contributions and it is shown that these processes are likely to operate simultaneously. Tests of the model against simulated data show that it is possible to estimate with considerable accuracy the strength of functional and stylistic contributions to culture change under ideal conditions of site preservation. Further theoretical work is needed, however, to understand how diverse site formation and disturbance processes might impact application of the model in real archaeological settings.
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