Stylistic variation in evolutionary perspective: Inferences from decorative diversity and...

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Stylistic Variation in Evolutionary Perspective: Inferences from Decorative Diversity andInterassemblage Distance in Illinois Woodland Ceramic AssemblagesAuthor(s): Fraser D. NeimanSource: American Antiquity, Vol. 60, No. 1 (Jan., 1995), pp. 7-36Published by: Society for American ArchaeologyStable URL: http://www.jstor.org/stable/282074Accessed: 04/07/2009 16:22

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STYLISTIC VARIATION IN EVOLUTIONARY PERSPECTIVE: INFERENCES FROM DECORATIVE DIVERSITY AND

INTERASSEMBLAGE DISTANCE IN ILLINOIS WOODLAND CERAMIC ASSEMBLAGES

Fraser D. Neiman

Certain aspects of what archaeologists have traditionally called stylistic variation can be understood as the result of the introduction of selectively neutral variation into social-learning populations and the sampling error in the cultural transmission of that variation (drift). Simple mathematical models allow the deduction of expectations for the dynamics ofthese evolutionary mechanisms as monitored in the archaeological record through assemblage diversity and interassemblage distance. The models are applied to make inferences about the causes of change in decorative diversity and interassemblage distance for Woodland ceramics from Illinois.

Ciertos aspectos de lo que arqueologos han tradicionalminente llamado "variacion de estilo" pueden explicarse como el resultado de la introducion de variacion selectiva neutral en poblaciones de aprendizaje social, y el error de muestreo en la transmission cultural de variacion. Simples modelos matemdticos permiten la deduccion de expectativas para la dindmica de estos mecanismos evolutivos controlados en el registro arqueologico a traves de la diversidad y la distancia entre conjuntos. Los mnodelos de los conjuntos artefactuales son utilizados en inferencias sobre las causas del cambio en la diversidad decorativa y la distancia entre conjuntos cerdmicos del periodo Woodland en Illinois.

T he possibility that Darwinian evolutionary theory might prove the foundation

for a progressive research program in archaeology was first raised in a serious way over a decade ago (Dunnell 1978, 1980). Since then the first explorations have begun to appear of how evolutionary theory might be used to solve the puzzle what the archaeological record means (e.g., Bettinger 1991; Braun 1990; Dunnell 1989a; Leonard 1989; Mithen 1990; Neiman 1990; O'Brien and Holland 1990; Rindos 1984; Teltser 1988). Uniting most of this literature is a focus on the adaptive aspects of archaeological variation; witness the metonym used by some to refer to it: cultural selectionism (e.g., Braun 1990; Leonard 1989; Rindos 1984). This paper takes the exploration of a Darwinian approach to the archaeological record in a dif-

ferent and complementary direction by emphasizing the nonadaptive aspects of phenotypic variation that archaeologists have traditionally called style. In so doing, it con- tributes to the ongoing effort to sketch a useful picture of just what a neo-Darwinian archaeology might look like. The approach is neo-Darwinian in two senses. First, it takes mechanistic processes occurring within populations of interacting individuals as causally fundamental (Sober 1980). Second, it is premised on an understanding of theory building as the development of explicit models of evolutionary mechanisms that cause the differential persistence of transmitted forms in populations of individuals (e.g., Boyd and Richerson 1985; Cavalli-Sforza and Feldman 1981). Such models comprise the foundation on which inferences about the

Fraser D. Neiman n Social Science Statistical Laboratory, Yale University, New Haven, CT 06520-8208

American Antiquity, 60(1), 1995, pp. 7-36. Copyright ? 1995 by the Society for American Archaeology

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causes behind unique historical trajectories are necessarily based (Lewontin 1980).

The starting point is a definition of style entailed by the distinction between stylistic and functional variation and embedded in the larger framework of evolutionary theory (Dunnell 1978). Style and function refer to two classes of difference among alternative variants along a given dimension of culturally transmitted phenotypic variation. Variation along a dimension is stylistic when the fitness values associated with each variant (the expected reproductive success they confer on their bearers) are effectively the same, ren- dering the variants selectively neutral. Vari- ation is functional when different variants have effectively different fitness values (Nei- man 1990:169-170; O'Brien and Holland 1992:47; Pierce 1991). In a neo-Darwinian framework these definitions imply that variation in stylistic variant frequencies in time and space will be affected by a subset of evolutionary forces that introduce selectively neutral cultural variation into populations of social learners, for example, innovation and intergroup transmission, and then sort it stochastically (drift). The frequency of functional traits, on the other hand, will be controlled by forces that sort cultural variation deter- ministically, if population size is large. These include natural selection, as well as different kinds of learning rules or cognitive algo- rithms (Cosmides and Tooby 1987; Tooby and Cosmides 1992), built by natural selection in the context of high-frequency envi- ronmental variation, for example, individual learning, direct bias, complex indirect bias (Boyd and Richerson 1985:110-115,117- 127; Neiman 1990:90-97; Rogers 1988).

Social learning and the translation of what is learned into phenotypic variation both require energy investment (Meltzer 1981:314; Neiman 1990:207; Pierce 1991). Energy in- vested in learning stylistic variants and in their behavioral implementation is not available for other pursuits, any one of which might have positive fitness consequences. Because style in general involves both direct and opportunity costs, investments in it are part of

the selective picture and will be subject to deterministic sorting (e.g., Dunnell 1989a). Hence a complete evolutionary account of style will contain two components: first, models of the mechanisms that introduce and stochastically sort particular selectively neutral variants, and second, models of the deterministic mechanisms responsible for functional variation in overall levels of investment in style. This paper addresses only the first of these issues.

The signal advantage of embedding style in a Darwinian framework is that it becomes possible to make and evaluate inferences about what happened in history. These twin goals are accomplished by developing models of the operation of different evolutionary forces or mechanisms defined by theory. Models in turn deliver expectations concern- ing spatial and temporal distributions of elements that result from the operation of different mechanisms. Given a suite of measurements of real-world phenomena or statistical summaries of them, we are in a position to make inferences about the mechanisms that caused observed values. The inferences can be checked by developing additional models and expectations, based on independent lines of reasoning. Over the long term, the agreement of independent inferences leads to historical knowledge. Thus while model building is an abstract enterprise, the payoff is fundamentally pragmatic.

Archaeologists will recognize the two sorts of statistical summaries that are discussed here - assemblage diversity and interassemblage distance-as old friends. This prior fa- miliarity should not obscure the fact that the meaning of these measures in what follows comes entirely from evolutionary theory. For example, the empirical implications of our theoretical models of stylistic diversity are initially deduced in terms of a statistic that is closely related to Simpson's diversity index, not the Shannon-Weaver statistic, which is more commonly used in archaeology, or some other diversity measure (cf. Bobrowsky and Ball 1989). There is an explicit logical relationship between this particular statisti-

8 [Vol. 60, No. 1, 1995

STYLISTIC VARIATION IN EVOLUTIONARY PERSPECTIVE

cal summary of archaeological variation and the theoretical constructs that we use to make that summary meaningful. This relationship is crucial because it makes our observations of archaeological variation accountable (Kos- so 1992:140-141). The source of their inferential meaning is clear. Accountability re- duces ambiguity over what that meaning is. It eases assessment of the independence of multiple inferences. When independent inferences produce divergent results, there is a conceptual audit trail with which to begin to puzzle out what went wrong.

A first step in developing an evolutionary approach to style is to answer the question, What kinds of spatial and temporal patterns can we expect of stylistic elements? The chances of developing a deductively correct answer are increased if we work with formal models, capable of representation in either mathematical formalism or computer simulation, of the evolutionary mechanisms that govern the distribution of selectively neutral forms in time and space. This is not the course development has taken. Archaeologists ex- ploring an evolutionary approach to style have ignored the powerful inferential engine uniquely offered by formal modeling in favor of a more familiar strategy that relies on natural language. When inquiry is governed by a loose-knit, contradictory, and covert suite of intuitions about the way the world works, as has been the case for much of processual and post-processual archaeology, this approach produces results whose flaws easily escape notice since they can usually be rec- onciled with some aspect of common sense (sensu Dunnell 1982). However, when theory is an explicit set of notions about causal mechanisms, and evolutionary theory is just that, the traditional approach is bound to produce conclusions that are demonstrably incorrect.

Rather than continuing in this tradition, I want to introduce some simple models of the evolutionary mechanisms that in theory govern the distribution of stylistic elements. I will concentrate on two such processes: drift and innovation. Two groups of models are

described in this paper. The first allows inferences to be made about the evolutionary mechanisms responsible for stylistic diversity monitored archaeologically within assemblages. I show how variation in within- assemblage diversity is a function of variation in the parameter values governing these mechanisms: population size and innovation rate. The theory is then used to further our understanding of Woodland social dynamics in Illinois. The second family of models independently works out the implications of these same mechanisms for stylistic distance among assemblages. It therefore offers the opportunity to check the empirical correct- ness of inferences about the trajectory of Il- linois Woodland social change based on the first model and about the evolutionary mechanisms hypothesized to have been at work.

The models employed here were originally developed in population genetics to describe variation in neutral alleles. Only slight mod- ifications are necessary for application to the horizontal, oblique, or vertical transmission of selectively neutral cultural variation.1 In fact the diversity models have already been applied to cultural transmission, to explain geographic variation in song among chaf- finches in New Zealand (Lynch et al. 1989; Lynch and Baker 1993) and surnames among humans in Italy (Yasuda et al. 1974; Piazza et al. 1987) and Sardinia (Zei et al. 1983). The distance models have not previously been used in the exploration of cultural phenomena.

Drift, Innovation, and Diversity

Drift

We start with drift. Drift is sampling error that inevitably accompanies horizontal, oblique, or vertical cultural transmission in finite populations. Consider the following scenario for horizontal cultural transmission: We have a population comprised of N individuals. Each individual is characterized by one of several mutually exclusive cultural prescriptions or variants governing some dimension of behavioral variation. For ex-

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ample, the variants might prescribe different ways of producing a decorative band on a pottery vessel or the proper sizes of the me- dallions on a necktie.

In each time period, each individual con- tacts another individual chosen at random from the population and adopts whatever variant the contacted individual happens to carry with probability (N - 1)/N and retains their own previous variant with probability I/N, in which case the individual in effect learns from themselves. This implies that there are no deterministic forces at work that might cause learners to prefer some variants over others. In this case, the expected frequency of any given variant in a given time period is the frequency in the previous time period. However, the actual frequency is quite likely to be different because, in a finite population, some individuals by chance alone will end up teaching more learners than others. The cultural variants carried by those lucky teachers will increase in frequency. The magnitude of this effect, like other forms of sampling error, is a function of the size of the population. The temporal dynamics created by this simple process can be counterintu- itive. Because the actual frequencies of one time period become the expected frequencies of the next, the effects of sampling error are cumulative over time. This Markov property produces what appear, when filtered through contemporary common sense, to be deterministic trends.

Temporal Dynamics of Drift

The consequences of drift for variant frequencies and their temporal distributions can be illustrated with the help of a simple simulation that duplicates the process described

above. Typical results illustrate two important points about drift. The first is that drift destroys variation. In the realizations illustrated (Figure 1), the populations start off with k = 10 variants whose starting frequencies are equal. As transmission episodes accu- mulate, variants disappear from the population until there is only one left. The second point is that the speed with which variation is destroyed (or the strength of drift) increases as the population size decreases. In the two cases shown, when N =- 20, the population is fixed for a single variant within 45 time periods. With 100 individuals, 176 time periods elapse before fixation takes place.

In principle we can generalize these results to situations with more complex learning structures, where for example some individuals are more likely to be models than others. They can be handled by converting the actual number of individuals in such populations to the "effective number" (Crow and Kimura 1970:109-111; Neiman 1990:206-207). Note that the effective population (Ne) size is likely to be much smaller than the actual population size, making it possible for drift to be a potent force even when nominal population sizes are large. These results also hold for vertical and oblique cultural transmission. In these cases the time periods of the model become successive biological generations. In the vertical case, teachers are parents of learners, while for oblique transmission teachers may also be unrelated individuals drawn from the parental generation.

Homogeneity Under Drift

Now if we are willing to do a little algebra, we can describe this process in a more analytical fashion. First, we require a measure of

-4

Figure 1. Simulation of the effects of drift on cultural variant frequencies in a single population over time. The temporal trajectories of variants are portrayed here in a left-justified seriation diagram. The vertical axis is time. Each series of vertically stacked bars represents the frequency of a variant in 200 successive time periods. During each time period, individuals learn variants from a randomly chosen model or teacher. In (a), population size (N) = 20, while in (b), N = 100. In both cases there are 10 variants whose frequencies in the initial time period are

equal. Comparison between the two illustrations shows how drift destroys variation more quickly in smaller populations.

10 [Vol. 60, No. 1, 1995


Variants and Variant Frequencies


11 Neiman]

a

C/) -0 0

(t)

E

b

Or)

0

EL (D)

a) E

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the amount of variation within a population, either in terms of homogeneity or diversity (its reciprocal). One simple measure of homogeneity is the probability that two randomly chosen individuals in the population carry variants that are copies of a common antecedent variant.

The simulations suggest the rate at which within-population homogeneity (F) will increase is a function of the population size. But what kind of function? To answer this question, well-known results from the theory of neutral alleles (e.g., Crow 1986:43; Crow and Kimura 1970:101-102) can be adapted to the cultural case. Notice that in a given time period the probability of drawing an individual, who learned from the same model as some other randomly selected individual in the previous time period, is 1/N. The probability of getting a second individual who did not learn from the same model is 1 - 1/N. If we do happen to draw such a second individual (i.e., one who learned a variant from a different model in the previous time period), then there is always a chance that this second individual's model learned from the same model as did the first individual's model in a still earlier time period. If we call this chance F,_,, then we can combine all the probabilities into a recursion that predicts homogeneity in a population at a given time period (Ft) as a function of homogeneity at the previous period. We have

1) Ft - + - - yFt-, (1)

This simply says that the amount of increase in homogeneity in each time period is inversely proportional to the effective popula-

tion size. While this result is not very useful by itself, it is a necessary building block for what is to come.

Temporal Dynamics of Drift and Innovation

I now want to introduce a second set of forces into our model, ones that introduce novel, selectively neutral variation into the population. These forces include both in situ innovation that arises within a group and innovation that may be introduced into it from outside, from neighboring groups or demes via intergroup cultural transmission. To explore the effects of innovation we can return to the simulation. We start off with a single variant and now allow the introduction of novel variants at a rate ,i. During each time period, individuals learn from randomly chosen teachers, as before, but now there is also the probability , that they abandon that socially learned variant in favor of one of their own invention.

Now given traditional archaeological pre- occupations, the most striking aspect of curves describing the frequency of variants over time lies in their shape (Figure 2). Despite short- term fluctuations, shapes tend to be lenticular, with the expected maximum frequency of a variant occurring exactly halfway between its origination and termination. The resemblance to the battleship-shaped curves of frequency seriation is obvious. I have explored this aspect of the simulations elsewhere and here simply note that drift and neutral innovation offer a compelling account of one set of causal mechanisms behind the empirical generalizations about the temporal trajectories of stylistic elements on which the seriation method is based (Dunnell

Figure 2. Simulation of the joint effects of drift and neutral innovation on cultural variant frequencies in a single population over time. During each of 400 time periods, individuals learn variants from a randomly chosen model.

They then have the opportunity to replace this variant with a novel variant that has never been seen in the population before. The probability that this happens is the innovation rate (M). In both (a) and (b), the innovation rate (I) =

.01, the population size (N) = 50, and the population contains a single variant in the initial time period. Despite identical parameters, the details of the two realizations differ as a result of chance. In both cases drift and innovation

combine to produce lenticular variant trajectories that resemble the battleship-shaped curves familiar from frequency seriation.

12 [Vol. 60, No. 1, 1995


a

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b

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D,

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Neiman] 13

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1978; Neiman 1990:156-167,181-197; Tel- tser 1995).

Homogeneity Under Drift and Innovation

Drift and innovation are opposing forces: drift increases homogeneity and innovation decreases it. We can characterize the equilibrium that results, again following Crow and Kimura (1970:323; Crow 1986:46) by incor- porating innovation into Equation 1 (see p. 12), which gave the probability that two variants randomly chosen at a given period were copies of a common variant. If innovation is possible, then we need to adjust this probability slightly to take into account the fact that neither of the two chosen variants was replaced by a novel variant after transmission occurred and before we chose them. It is assumed that each newly introduced variant is unique, that it is different from any variant that already exists in the population. If the innovation rate = At, that probability is (1 -

p)2. So we have

F=[N + ( - N)Ft_1 ](

- )2 (2)

The equilibrium homogeneity is reached when Ft = F,_. So setting Ft = F_ , in Equa- tion 2, we get

_ F=(1 - 2

_ (Ne - 1)(l - g)2 (3) Ne

which, assuming A is quite small, is roughly equal to

A _~ 1 (4) 2Ne/ + 1

In other words, the homogeneity of neutral variants within a population is inversely proportional to twice the effective population size times the innovation rate (2NAup), a parameter that I will refer to as 0. This is a result whose usefulness begins to become apparent on the realization that one can also estimate homogeneity of a population empirically as a function of a relative frequency of variants in it:

Here Pi is the relative frequency of the i'th variant in the population. The reasoning here is simple: the probability of choosing a given variant at random is its relative frequency (Pi), which is also the probability of picking another copy of this same variant on the second try. The probability of getting this variant twice in a row is therefore pi2. The total probability of getting any of the i = 1 to k variants twice in a row is the sum of all these probabilities.

Diversity

We can also look at the matter the other way around in terms of diversity, instead of homogeneity. In this case one measure of diversity is called the "effective number" of variants (Crow and Kimura 1970:323-324) and is defined as the reciprocal of F. Esti- mating diversity within a population in these terms means that the population contains the same amount of diversity as would be found in an imaginary population with the effective number of variants at equal frequency. Tak- ing reciprocals in Equation 4, we see that in theory the effective number of variants scales linearly with 6:

ne= 2Ne,I + 1 (6)

Larger populations should contain more diversity at a given level of innovation. Greater diversity is also expected in populations into which new variants are being introduced at higher rates. Furthermore, it is clear that 0 can be estimated empirically by computing the reciprocal of the sum of squares of variant frequencies in a population:

1 tF k - 1

i=l

(7)

We can call such estimates tF, to distinguish them from the actual population values and to remind ourselves they are based on ho-

k

P= 2p i i=1

(5)

14 [Vol. 60, No. 1, 1995


mogeneity (F) in Equation 5. The foregoing algebraic exercise is useful because it reveals how inferences about spatial and temporal variation in 0, the product of twice the effective population size and innovation rate (2NeA), among a suite of populations or demes might be made by tracking variation in the special diversity statistic tF.

Archaeological Application

Taphonomic Considerations

There are, however, two topics that need to be covered before we can make use of this model to make sense of the archaeological record. So far I have described the frequency of variants in a population of social learners, not the frequency of modes in an archaeological assemblage. Clearly these are not the same. Under the appropriate taphonomic circumstances, however, they are surprisingly similar. This argument is developed in more detail elsewhere with the help of computer simulations (Neiman 1990:182-193). The following is relevant for the problem at hand. When the assemblages in question are attri- tional, the product of time averaging over multiple transmission episodes (the time periods of our models) and multiple discard events for the artifacts whose morphology is culturally prescribed, the shapes of mode trajectories estimated on the basis of assemblage contents closely mirror those of the under- lying cultural variants. This is true despite the fact that mode frequencies in assemblages are governed by discard rates, which in the simulations are modeled as culturally transmitted trait values that determine the mean number of times a variant will be represented in an assemblage per unit time period, and those discard rates are allowed to vary as a result of drift by an order of magnitude. Changes in population size and/or innovation rate, which cause alterations in variant frequencies, will be mirrored by changes in mode frequencies and, afortiori, in diversity measures computed from them. These considerations raise the possibility of using the theory outlined above to make inferences

about the mechanisms responsible for stylistic variation monitored in the archaeological record. More specifically, under some conditions, we can expect to get useful insights into variation in 0 values among groups or demes, by using mode frequencies for the Pi in computing tF. This is not to say that these conditions will always prevail. Whether they do or not is a matter for empirical determi- nation on a case-by-case basis.

Diversity and Sample Size

The second topic revolves around the prob- lems we confront when trying to estimate diversity on the basis of a sample derived from a population, and not the entire population. Readers familiar with the large literature that has grown up around the use of diversity indexes in archaeology (e.g., Leonard and Jones 1989) will recognize in Equations 5 and 7 a functional form similar to the Shannon- Weaver information statistic so beloved by archaeologists:

k

H = - , P log(p) i=l

(8)

Equation 5 (or its complement or its reciprocal), known in the ecological literature as Simpson's index (Bobrowsky and Ball 1989; Simpson 1949), has itself seen occasional us- age by archaeologists to describe assemblage homogeneity (or diversity) (e.g., Rothschild 1989). As Grayson and colleagues (Grayson 1981; Jones et al. 1983) first noticed in an archaeological context, and others have con- firmed, measures like these are sensitive to sample-size variation. In fact in many cases, when computed from archaeological data, they appear to measure little else. If we are to put our insights into style and apply them to use, we need to take this artificial sampling effect into account. To date archaeologists have attempted to address this problem in an ad hoc, inductive fashion (Kintigh 1984; McCartney and Glass 1990). In the case at hand, theory points in the direction of a deductive solution.

We have seen how 0 controls the sum of

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squared variant frequencies in a population. This raises the possibility that there might be a characteristic probability distribution of variants whose shape is also controlled by 0. In other words, for a given value of 0, we should be able to predict how many variants occur with certain frequencies. When 0 is low (0<< 1), we should expect that most of the time, a population will be dominated by a few variants, with other variants at low frequencies. When 0 is high (0>> 1), we are more likely to see a large number of variants at low to moderate frequencies. By combining this frequency distribution with the probability that a variant at a given frequency is represented at least once in a sample of a given size drawn at random from the population, it should be possible to deduce how many different variants we can expect to find in a sample of a given size N.

Using this line of reasoning, Ewens (1972) showed that if the variants are selectively neutral, the expected number of different variants (k) found in a sample drawn from a population is a function of the sample size (n) and the parameter 0:

n-I

E(k) =-- .(9) ,i=o 0 + i

Note that this result is intuitively reasonable in that it indicates that the number of variants will be large when either 0 or n (the sample size, not the population size) are large.

Ewens also showed that Equation 9 could be used to produce a maximum likelihood estimate of 0, that is the value of 0 for a population that maximizes the chances of drawing the observed number of variants (k) in a sample of the observed size (n). Although Equation 9 has no analytic solution, we can still use it to estimate 0, iteratively by chang- ing its value until E(k) equals the observed number of variants. I shall call the result of doing this tE, to distinguish the estimates so produced from the actual 0 values and as a reminder that they are estimates based on Ewens's theory. TE is also the minimum-variance, unbiased estimate of 0. These properties imply that this estimate is statis-

tically sufficient in the technical sense. That is, all information regarding the actual value of 0 is contained in the estimate derived from Equation 9. This means that, under drift and neutral innovation, once one knows the values of n and k, the actual frequencies of the different variants in the population provide no useful information about the causal process that generates diversity in the sample. Thus both tF from Equation 7 and tE from Equation 9 offer us special statistical summaries of assemblage diversity that are also estimates of 0. If the conditions are right, there are theoretical reasons for preferring the tE estimates.

Stripped of its mathematical specificity, the skeleton of this argument should have a familiar ring to archaeologists who have considered the issue of the relationship between the size of an assemblage, the frequency distribution of artifacts across classes (even- ness), and the number of classes represented (richness). For example, Dunnell pursued a similar line of reasoning when he recently noted that "sampling interacts with the distribution of ns [artifact numbers] over cs [artifact classes] partly to determine richness" (1989b:146). For Dunnell n and c describe a population of artifacts, while richness is the number of classes represented in an assemblage of artifacts sampled from that population. The analogous quantities in Ewens's work are the variant frequencies and number of variants in a finite population of individuals and the number of variants (k) in a sample of individuals drawn from that population.

Archaeological Sample Size

How can Ewens's work be put to use in archaeological context? If variant frequencies control mode frequencies and mode frequencies are sampled independently of one another, then it is reasonable to anticipate that for a given value of 0, the number of modes in an archaeological sample might increase as a function of archaeological sample size in a fashion similar to the way in which the number of variants represented in a sample

16 [Vol. 60, No. 1, 1995


of individuals increases with the number of individuals sampled, as described in Equa- tion 9. We might expect the tE values that are derived from an assemblage will be correlated with the tE values that would have been derived from a random sample of the population of social learners responsible for the assemblage. Given a suite of archaeological samples, it therefore may be possible to compute for each assemblage an estimate of the key parameter 0, based on the size of the assemblage and the number of modes from a single stylistic dimension of variation represented in it, and to anticipate that those estimates would be correlated with the actual population values across the populations or demes that generated the samples.

There is, however, a potential complica- tion. Equation 9 implies that for a given number of variants or modes (k), tE estimates of 0 will decline as sample size increases. Ob- viously the number of individuals that can be randomly drawn from a population is limited by the size of the population. This lim- itation on sample size places a lower limit on tE values, a limit assumed in the mathematics behind Equation 9. On the other hand, given the time-transgressive character of archaeological samples, there are no such limits on the size of an assemblage that can be generated by that same population. This raises the possibility that tE estimates of 0 and derived from very large archaeological samples that accumulated over long periods of time may be much lower than they should be. For such archaeological samples, tE estimates of 0 based on Equation 7 may be more accurate, despite Ewens's demonstration that for samples of individuals, this is not the case.

Whether tE or tF offers better estimates of 0 for a suite of assemblages should be decid- able on the basis of empirical relationships among them and assemblage size. A negative correlation between tE and assemblage size would betray the possibility of artificial, assemblage-size induced variation in those 0 estimates. On the other hand, as the archaeological diversity literature reminds us, a positive correlation between tF and sample size

would raise similar suspicions about those estimates. These effects taken singly would attenuate the otherwise positive correlation between the two estimates; together they might even be sufficient to make the correlation negative. Another, perhaps a more powerful, indicator of artificial variation in either set of 0 estimates would be change in the difference between them (tF - tE) as a function of assemblage size. This (signed) difference should be positive and decrease in magnitude with assemblage size over the lower range of assemblage sizes. This is the range over which tE, unlike tF, is likely to provide estimates undistorted by size effects. The difference should be negative and increase in magnitude with size over the upper range of assemblage sizes since it is here that the risk of sample-size artifacts is greater for tE and less for tF. There is, of course, no guarantee that a given group of assemblages will exhibit sufficient size variation for these correlations to be detectable. In such cases we can still hope to detect the existence of confounding size effects by measuring the extent to which the (signed) differences between estimates (tF - tE) depart from zero. These relationships offer plenty of opportunity to recognize artificial assemblage-size effects on estimates of 0 and will be put to use later in this paper.

Inferences About Group Size and Innovation Rate

If these tests fail to detect such effects, what substantive inferences can be derived from the model? Recall that 0 is twice the product of the effective population size (Ne) and the innovation rate (,u), where the latter includes the combined effects of both in situ innovation (v) and the introduction of novel variants from other groups (m). If , = v + m, then Ne, = NeV + Nem. Now, it seems reasonable to suppose v, the probability that a group member will introduce a novel variant into their own group in each time period, is roughly constant across demes (e.g., Dunnell 1978: 197; Leone 1968:1150). On the other hand, m, the probability that an individual in a given group learns from a member of another

17 Neiman]

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deme, is likely to be more variable in time and space. Under these circumstances, most of the variation in 0 associated with the parameter A will be caused by variation in intergroup transmission rates. In addition we can expect 0 to be independently affected by variation in Ne. Variation in 0, derived from either or both of these sources, implies variation in the absolute number of intergroup transmission episodes per unit time (Nmn), that is, the number of times local group members learn from members of other groups. Variation in 0 is a conservative measure of intergroup transmission levels because some proportion of donor group members carry variants that already exist in the recipient group as a result of transmission into it in previous time periods.

To sum up then, variation in estimates of 0 derived from selectively neutral modes in archaeological assemblages is likely to be correlated with variation in the absolute number of individuals in the group responsible for the assemblage who learned their cultural variants from individuals derived from other groups. Assemblages associated with relatively small values of 0 were generated by relatively isolated demes, while those with larger values of 0 should come from less isolated demes. Furthermore, changes over time in the mean value of 0 for assemblages from sites scattered across a geographical region should register changes in the absolute amount of cultural transmission among demes within it. However, before such inferences are taken seriously, relationships among estimates of 0, tF, and tE from Equa- tions 7 and 9, respectively, and assemblage size need to be carefully examined for artificial size induced effects.

Woodland Assemblage Diversity

Illinois Woodland Ceramic Data

I argued at the outset that theory building is a fundamentally pragmatic exercise. I now want to make good on that claim by using the models described so far to make inferences about change in the amount of inter-

group transmission within southern Illinois during the Woodland period based on variation in decoration on ceramics. This period covers the rise and decline of the "Hopewell Interaction Sphere" (Caldwell 1964), a phe- nomenon over which archaeologists have puzzled and will continue to puzzle for decades. Important parts of what is rightly re- garded (e.g., O'Brien and Holland 1992:47- 48) as our most sophisticated, anthropological understanding of the historical processes occurring during this period are derived from the ceramic data examined here (Braun 1977. 1985, 1986, 1992; Braun and Plog 1982). Those data are part of a remarkable corpus originally collected by David Braun and published in his dissertation (1977). I will ex- amine variation along a single dimension of decorative variation: lip exterior decoration applied in a band around the top of cooking pots during this period (Braun 1977:149-167). This dimension contains 26 modes or decorative alternatives for which examples occur in the assemblages. The variants distin- guished include cord marking, smoothed cord marking, fabric marking, and punctate and dentate stamping of different sorts. Although such arguments should be used with caution (Binford 1989), it seems highly unlikely that there are significant engineering fitness differences (Burian 1983) among these kinds of alternatives. Hence there is a prima facie war- rant for considering them selectively neutral.

The ceramics come from nine sites occurring in five discrete site clusters or localities in the southern Illinois and Kaskaskia River valleys. The average spacing between adja- cent site clusters is about 130 km, with the closest pair separated by roughly 50 km. Braun's demonstration of a decline in ceramic wall thickness across the Woodland offers a means of dividing assemblages from each site cluster into temporally ordered, time- transgressive subsamples. I used seven thickness classes (2-4 mm, 5 mm, 6 mm 7 mm, 8 mm, 9 mm, 10-14 mm). The thickness classes can be mapped approximately onto cultural-historical periods. The 10 to 14 mm class represents the Early Woodland (before

18 IVol. 60, No. 1, 1995


200 B.C.); the 9 to 6 mm classes represent successively later phases of the Middle Woodland (200 B.C.-A.D. 400); the 5 mm and 2 to 4 mm classes fall largely in the Late Woodland (A.D. 400-800) (Braun 1977, 1985). The seven thickness classes yield samples for the five localities that vary in size from 12 to 171 sherds. Thus samples are gen- erally small, but there is considerable variation among them in size. This is the sort of situation in which it is reasonable to expect useful results from Ewens's approach. The thickness classes have the additional advan- tages of offering reasonably fine-grained temporal resolution while at the same time pro- viding sample sizes that are large enough to apply the distance-based approach described in the next section. To sum up then, we have a collection of sherds that is partitioned among seven temporal periods (the thickness classes) and five localities, making a total of 35 assemblages. I computed two estimates of 0, tF and tE, for each of the 35 assemblages from Equations 7 and 9. As noted above, Equation 9 cannot be solved for 0 analytically, so a numerical solution was derived by incrementing 0 until the resulting estimate of k (the number of variants) converged on the number observed in an assemblage of a given size n.

Woodland Assemblage Diversity

Comparison of the frequency distributions of the two sets of 0 estimates reveals general agreement on the range of values represented in the 35 assemblages. On both measures the middle half of the values is concentrated between 2 and 4 (Figure 3). There is, however, one conspicuous outlier in the tE estimates: 7 mm thick sherds from the Lower Illinois Valley (tE = 9.04). I can offer no explanation for this rogue observation, but note this assemblage also ranks highest among the tF estimates for the 7 mm thickness class (tF =

5.2). This suggests that the actual 0 value behind this assemblage is high, although not as high as tE indicates. Because of the sensitivity of variances and covariances to outliers, this

CZ 4-J .a) c-

F-

10-

9-

8-

7-

6-

5-

4-

3-

2-

0-

1-

0

-*-- -*-

tF tE

Estimator Figure 3. Box plots of the two sets of 9 (diversity) estimates, tF and tE, from Equations 7 and 9, respectively, computed from lip-exterior decoration mode frequencies in 35 Illinois Woodland assemblages from five localities and seven sherd thickness classes. Box ends represent the interquartile range (IQR); the vertical lines (whisk- ers) end at the last observation within a distance of 1.5 times the IQR from the box ends. The single outlier in the tE Equation 9 estimates is the 7 mm thickness class assemblage from the Lower Illinois Valley.

observation has not been used in correlation analyses reported below.

Before our results can be used legitimately to make inferences about Woodland social dynamics, it is necessary to explore the relationships among the two sets of 0 estimates

19 Neiman]

AMERICAN ANTIQUITY

10o

8-

6-

4-

2-

0-

o

0 0 o 0 0 0~~~

o \ o o~~~~~~~~~~ ~~~~~o 0~~~

g

10-14 9 8 7 6 5 2-4

Thickness Class (mm)

Figure 4. Estimates of 0 (diversity), tE from Equation 9, computed from lip-exterior decoration modes for the five localities and seven sherd thickness classes. Esti- mates for individual assemblages are shown as circles. Line segments connect thickness class means and represent the temporal trend in within-assemblage diversity from Early (10-14 mm) to Late (2-4 mm) Woodland.

and assemblage size. The results of our discussion of these relationships in the previous section will be used to look for signs of artificial assemblage size effects on our estimates of 0. Consider first relationships with assemblage size, measured here using Pear- son's r and a log transformation of assemblage size. Artificial assemblage-size effects on tF and tE should be detectable, respectively, in positive and negative correlation with assemblage size. The observed correlation for

tE is strong and positive (r = .47, p = .005), suggesting no artificial size effects of the sort that might result from the time-transgressive character of archaeological samples. By contrast a similarly strong, positive correlation for tF (r = .49, p = .003), leaves open the

possibility of spurious sample-size effects. Such effects, if present, are not sufficiently strong to eliminate a strong positive correlation between the two sets of estimates (r = .76, p<.001).

The relationship between the paired differences (rE - tF) of the two estimates and

assemblage size was also examined. Here the

relationship was in the direction expected, if size artifacts were present in either set of estimates, but the strength of the correlation was indistinguishable from 0 (r = -.14, p =

.42), indicating that whatever effects may be present, presumably in the tF estimates, they are too weak to be detected. The mean of the paired differences (tE - tF) was also computed and found to be statistically indistinguishable from 0 (t = .002, p = .998). These results indicate that 0 estimates from tE are not artificially contaminated by sample size. They also leave open the possibility that the estimates from tF might be weakly influenced by artificial size effects.

If we look more closely, this analysis also tells us something about the substantive processes generating diversity in these archaeological samples. The clue lies in the unex- pected positive correlation between tE estimates and sample size. Apparently there is a real relationship between assemblage size and tE. Its probable cause is easily seen in the foregoing mathematics which make it clear that 0 is a function of population size. If lengths of occupation are roughly constant across assemblages, assemblage size will be controlled by population size. A correlation between assemblage size and tE would result because both assemblage size and the actual 0 values estimated by tE are functions of the same variable: population size. This implies that some of the variation in 0 monitored in these data is a function of variation in group size.2

This evaluation of the two sets of 0 estimates leads to the conclusion that the tE estimates are more reliable in fact, at least in this case, as well as in theory. I shall use them in what follows, although the tF estimates yield the same substantive results. Graphing these estimates against thickness classes allows the identification of temporal trends in this measure of within-assemblage diversity (Figure 4). Thanks to our modeling efforts, the theoretical meaning of this measure is clear. The trend in mean values for tE for each time period represents our best estimate of change in the overall level intergroup transmission

m (D) c-

20 [Vol. 60, No. 1, 1995


among the five localities during the Wood- land Period. The tE values start out low in the Early Woodland thickness class, averaging about 2.5. They increase to a peak in the Middle Woodland classes, somewhere between 3.8 and 4.3, depending on whether the Lower Illinois outlier is included. The Late Woodland witnessed a decline in the mean value of tE to 1.8.3 The inference is that levels of intergroup transmission in the region were low in the Early Woodland, rose to a peak during the Middle Woodland, and then fell to a new low in the Late Woodland.4

Clearly the trail leading from data to inference is long. Many assumptions have to be made if we are to convert our observations on the number of decorative variants and sample size in the archaeological record into a measure of intergroup transmission. Are the variants selectively neutral? Are their frequencies governed by drift and intergroup transmission as the model requires? Are the behavioral and taphonomic processes that intervene between variant frequencies in a population and decorative mode frequencies in the assemblages as well behaved as I have claimed?

Drift, Intergroup Transmission, and Interassemblage Distance

Dynamics of Stylistic Distance between Two Groups

One way to answer these questions is to develop an independent deductive argument that would allow us to check our conclusions about changes in the value of 0 and its components Ne and w. We require a model that converts the operation of drift and innovation into quantities that can be measured empirically but are conceptually unrelated to sample size (n) and number of variants (k), which yield the values of tE.

One promising approach comes from migration matrix models, which in population genetics have proven useful in studying the effects of drift and intergroup genetic transmission on genetic distances among small, localized demes (e.g., Smith 1969; Carmelli

and Cavalli-Sforza 1975). Such models reveal what happens to variant frequencies in a finite number of demes that are subject to the joint effects of drift, whose strength is controlled by the effective size of each population, and intergroup transmission, occurring between demes at constant pairwise rates. Note there is no role in these models for in situ innovation. Hence they offer a means of checking our earlier assumption that variation in 0 is largely a function of intergroup transmission.

The dynamics of migration matrix models can be approached in terms of a simple simulation. Whereas we earlier considered the effects of drift on a single population, here we consider two demes. In the realizations illustrated below, each deme is comprised of N = 100 individuals. As before each individual has an opportunity to contact another individual chosen at random and learn whatever variant the contacted individual happens to carry with probability (N - 1)/N. Only in this case, there is a set probability, the intergroup transmission rate (mi), that the individual contacted is derived from the other group. As before, no deterministic forces favor one variant over another. Hence changes in variant frequencies are once again controlled by sampling error in the learning process in finite populations. In addition, however, the intergroup transmission rate controls the extent to which drift-driven changes in one group affect variant frequencies in the other.

Modeling the results of this process requires a measure of the effects of intergroup transmission on between-group similarity. A simple measure of divergence that has proven useful in both theory and practice is the squared Euclidean distance: the sum of squared differences in variant frequencies between the two groups. The squared Euclidean distance between a pair of demes, i and j, is computed as:

(10) n

d = (Pik - Pjk) k=

where Pk is the frequency of the k'th variant.

21 Neiman]

AMERICAN ANTIQUITY

a

0.35-

0

0

8 o 0

o0 0 a~ Q

0

0

o

o 0 0

8

0 0

0

0u u

?8o ? 8 Q 8

0 89~ 0 0 0 0 0 oo 08? o 0

o a 8 0

0 0

0 8 8 a 0 0

0 ~~~~~~~0o8~~~~~ 5

~~8 80 8 00 0 0

0

I I I I I I

0 0

?o 0

0 8

o 8

0 0

0

o 8

o 0

o o 0 0

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80 0

o 8 0 o 0 0 8 8

0 0 0 0

o

o

8 8

0 0 8

0 0

o o 8

I I I I I I I I I I

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time Figure 5. Simulation of the effects of drift on the squared Euclidean distance in successive time periods between stylistic variant frequencies in two groups comprised of 100 individuals. In the initial time period, the frequencies of 20 variants in the two groups are identical. During each period, individuals learn variants from a model chosen at random from the other group with probability m and from their own group with probability (1 - m). Intergroup transmission rates (m) are symmetric for the two groups. Circles represent the outcome of 20 realizations from

The effects of intergroup transmission and drift on between-group distance are shown in Figure 5, where squared Euclidean distances from 20 realizations are plotted against time. In each realization there are initially 20 variants whose starting frequencies in the two groups are identical, randomly drawn from a uniform distribution. The distance between groups is therefore zero. However, as time passes, the distance increases up to a quasi-

stationary equilibrium. The equilibrium is only quasi-stationary because the groups are finite and there is no innovation: if the simulations are continued for a sufficient number of time periods, a single variant is fixed and as a result the between-group distance reverts to zero. The equilibrium holds over the period during which the opposing forces of drift, locally reducing variation within each group, and intergroup transmission, introducing po-

C/) C) cl

4-o CD 0

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0.25 -

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0.10 -

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0

22 [Vol. 60, No. 1, 1995

A


b

0.35

0 0

o

0

0

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0

8

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0 o

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o 0 o

o o 0 o

0 0 8 Q 8

8 o? 8 8

8 o8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time simulation, while the line is the approximation of the expected distance given by Equations 11 and 12. In (a), m =

.025, while in (b), m = .05. Drift causes the two groups to diverge until an equilibrium between-group distance is reached, usually within 10 to 20 time periods. The magnitude of the equilibrium distance and the speed with which it is reached are controlled by the intergroup transmission rate. Higher intergroup transmission causes lower equilibrium distances, which are reached more rapidly.

tentially novel variation into each group from the other, are balanced, before drift globally depletes all variation in both groups.

As comparison of the two plots in Figure 5 reveals, higher levels of intergroup transmission will lower the equilibrium level of divergence, while lower levels of intergroup transmission raise it. Although not illustrated here, it is also the case that lower effective sizes for either or both groups will raise the

equilibrium amount of divergence since, as we have seen, the effects of drift scale with Ne, the effective population size. Of course, larger group sizes will lower the equilibrium distance.

There are two other points worth noting about the equilibrium distance. The first is the speed with which it is reached. Although it is apparent that the equilibrium distance is attained more rapidly when intergroup

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0.30

0.25

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23 Neiman]

AMERICAN ANTIQUITY

transmission rates are higher, in both cases the distance approaches the equilibrium after a few time periods. The speed with which equilibrium is achieved indicates how quickly changes in Ne or in will be registered in changes in between-group distance. Just how rapidly this occurs in real time, of course, depends on how the time periods of our models map onto calendar years. The most important factor is whether cultural transmission is horizontal, vertical, or oblique. If transmission is horizontal, then there may be multiple transmission episodes or model time periods per year, and equilibrium may occur in a few years or less. Under vertical and oblique transmission, there is a one-to-one relationship between biological generations and model time periods and equilibrium may require several centuries. It is important to realize that the equilibrium is a global one. Although the model is derived in terms of differentiation among initially identical groups, the same equilibrium is approached by a group of initially divergent groups when intergroup transmission is initiated among them.

Stylistic Distances for Multiple Groups

Since the real world is likely to be better represented in terms of more than two groups learning from one another, it is useful to know what happens in the multiple-group case. The intergroup transmission component of the model is now described by a matrix of intergroup transmission rates (M), whose elements mj give the proportion of the i'th deme that learned from the j'th deme and whose diagonal elements are the proportion of each deme that learned from its own members. The evolution of the system, characterized in terms of a matrix of squared Euclidean distances, is controlled by the intergroup transmission matrix and the effective population sizes of each group.

Wood (1986), building on earlier work, has recently offered an elegant, analytical treatment of the general multiple-group case. As

in the simulation, we start with the assumption that all the groups initially have the same variant frequencies. This means that the expected frequencies for each group in any time period are identical and equal to the starting frequency. Drift-driven departures from this expectation for a given deme can be characterized analytically in terms of a variance. Since there are multiple demes in the system, their joint evolution must be handled in terms of a matrix of variances and covariances V(t)- Each diagonal element i// of V(t) is a variance: the square of the departure of the variant frequency in the i'th deme at time t from its starting frequency when the demes were identical, standardized by the variance of that starting frequency. Similarly, each v)) is a covariance: the product of the departures of the variant frequencies in each pair of demes i and j, again standardized by the variance of the starting frequency.

The relevance of this to the case at hand lies in the fact that the matrix of variances and covariances at a given time t (V(t) = viA)) is in turn a function of the effective sizes of each group and the intergroup transmission matrix. The function in question is approx- imated by:

t-1

Vt) = 2 MrU(Mr)' r=0

(11)

Here r indexes the successive time periods, while U is a square matrix containing the reciprocals of the effective population sizes (1/Ne) on its diagonal and O's elsewhere.

Equation 11 says that in the first time period, the covariance between two groups is a function of the sum of products of the intergroup transmission rates from all groups to those two groups and the reciprocal of their two effective population sizes. In later time periods, as individuals who learned from non- group members are in turn distributed among the other groups, the intergroup transmission rates from each group to all the others as- sumes increasing importance. The resulting cumulative effect of the indirect movement of variants among groups is handled by suc-

24 [Vol. 60, No. 1, 1995


cessively powering the intergroup transmission matrix.

The magnitude of the covariance between two groups will scale inversely with their sizes and positively with the intergroup transmission rates. High levels of intergroup transmission, either directly or through an inter- mediate group, will mean that whatever departures from the initial frequency occur, they will be similar and in the same direction, hence the covariance between the groups will be high. On the other hand, if either or both group sizes are low, causing drift to play a stronger role, variant frequencies are less likely to depart from initial frequencies in a similar fashion, hence the covariance will be low.

Once the matrix of variances and covariance has been obtained, it can be converted into a matrix of squared Euclidean distances using:

d''= v + v) - 2v( (12)

This too makes intuitive sense. If both groups are associated with large variances (the effects of drift are important) and low covariance (the effects of drift are different in each), they should have very different variant frequencies and be far apart. On the other hand, if they are both associated with small variances (effects of drift are unimportant) and high covariances (effect of drift similar in each), they should be close together.

The accuracy of the approximation sup- plied by Equations 11 and 12 can be judged in Figure 5, where the solid line portrays the result of solving them for successive values of t for two populations with the same parameters used in the simulations. As these figures suggest and Wood (1986) has noted, the approximation deteriorates as t approaches 20. However, as the simulations and Wood's results indicate, the squared Euclid- ean distance between the demes usually approaches equilibrium before this point. The advantage of Equations 11 and 12 over the simulation is their generality. They reveal that for any number of groups with fixed Ne and any matrix of intergroup transmission rates,

the equilibrium distances are completely de- termined as a sum of products of Ne and mi for each of the groups. Herein lies the link between interassemblage distance and within-assemblage diversity as characterized by estimates of 0. Distance and diversity are functions of the products of the same parameters: the effective population size and the intergroup transmission rate. It is also apparent that for any number of populations the entries in the squared Euclidean distance matrix converge rapidly to equilibrium values and so, afortiori, does their mean, which can serve as a useful summary measure of differentiation. Therefore in the general multiple-deme case, the mean of the squared Eu- clidean distance matrix among groups should track change in the overall level of intergroup transmission among them. High levels of intergroup transmission will cause low mean squared distance, while low levels will cause a high mean squared distance.

Woodland Interassemblage Distance

Trends in Interassemblage Distance

The migration matrix approach can be applied to the problem of Woodland ceramic diversity by computing a matrix of squared Euclidean distances between the five localities for each of the seven thickness classes. We expect to find that the overall level of differentiation among localities, as measured by the mean of the squared Euclidean distances, is the mirror image of our estimates of 0. A plot of the N(N - 1)/2 = 10 pairwise distances for each thickness class, along with their means, reveals this expected pattern (Figure 6). The mean level of divergence starts out high in the Early Woodland thickness classes at .37, decreases to a minimum in the Middle Woodland classes at about .21, and then increases to a maximum of .44 in the Late Woodland classes5. Thus inference from Wood's migration matrix formulation regarding the pattern of change in the overall level of intergroup transmission in the region matches precisely the picture derived from

25 Neiman]

AMERICAN ANTIQUITY

1.2-

<D 1 0-

oC

C: c a)

0.6-

0,4-

23 LL

a0 A4 - (D

0 - o) 0.2-

0.0-

0

o0

0o ~~~~~~~0 o 00

0o o

o

00 /

8 o o c

10-14 9 8 7 6 5 2-4

Thickness Class (mm)

Figure 6. Estimates of the squared Euclidean distance between the assemblages from the five localities for each of seven sherd-thickness classes. For each thickness class, the between-assemblage distances of 5 x (5 - 1) + 2 = 10 were computed from lip-exterior decoration mode frequencies. Line segments connect the mean between-assemblage distance for each thickness class and represent the temporal trend in interassemblage distance from Ear- ly (10-14 mm) to Late (2-4 mm) Woodland.

our earlier examination of change in diversity in terms of 0 estimates.

Diversity and Distance for Individual Assemblages

A further evaluation of the agreement between the two models is possible, based on comparing their deliverances regarding the consequence of variation in levels of intergroup transmission among individual groups. It is helpful to think of the mean squared distance

n

d2 = d2/(n - 1), i - j, (13) j=1

between one group and all the others at a given time period as a function of two sets of quantities. The first is comprised of intergroup transmission rates from each of the other groups to the group in question (the rows of the intergroup transmission matrix) along with the effective population size of that group. The second includes the intergroup transmission rates to each of the other

groups, from not only the group in question, but also from all the others, along with their effective population sizes. Now the estimates of 0 for a given group are completely deter- mined by the first set of quantities. Because these same quantities partially determine d2, the mean squared distance associated with a given group, it seems reasonable to expect, under certain circumstances, an inverse correlation between the estimate of 0 for a group and the mean squared distance from that group to the others. Groups that are well con- nected, in that individuals in them frequently learn from individuals from other demes, should have higher estimated values of 0 and lower mean squared distances dj than groups that are more isolated.6

This line of reasoning allows another evaluation of the agreement between our two models. In the Woodland case for each thickness class, we can expect to find a correlation across assemblages between our estimates of 0 and the mean squared distance from each assemblage to the other four. Failure to detect the correlation would imply either that the sampling error that accompanies our empirical estimates of mean squared distance and of 0 has erased all trace of the expected relationship, or that our modeling efforts are incorrect. Detecting a correlation would strengthen our confidence in both the diversity and migration matrix models.

Now with only five localities, any empirical estimate of the correlation for a single thickness class may be largely a function of sampling error and hence useless for our purpos- es. However, a statistically more powerful approach is available. It is based on computing for each thickness class the locality- specific deviations from the mean of tE on the one hand and the corresponding locality- specific deviations from the mean of the squared Euclidean distances d2 on the other. Taking deviations from the means for each thickness class removes the nonlinear secular trend in both the interassemblage distance and within-assemblage diversity, which would confound simultaneous evaluation of the relationship between the two measures

26 [Vol. 60, No. 1, 1995


across all thickness classes. A scatter plot of the 35 points (Figure 7) reveals the expected negative relationship and a single outlier: again the 7 mm assemblage from the Lower Illinois Valley. The correlation (Pearson's r) between the two measures, computed with the outlier excluded, is -.62 (p < .001). To sum up then, not only is there agreement on the overall trend in intergroup transmission across time between the two models, but there is also agreement on the fine-grained geographic pattern of variation in levels of intergroup transmission during all time periods.

Discussion

Stylistic Variation and Social Dynamics

How far have we come? I have argued that variation in the frequencies of lip exterior decoration modes in Woodland Illinois was controlled by two forces: drift and intergroup transmission. Theory about the mechanisms affecting the trajectories of selectively neutral variants was employed to construct two independent deductive arguments. The first argument led from drift, in situ innovation, and intergroup transmission to two measures of within-assemblage diversity, tF and tE. It indicated that when mode frequencies are selectively neutral, and therefore controlled by drift and neutral innovation, within-assemblage diversity scales with the product of the effective population size and the rate at which innovation occurs. To the extent that variation in the innovation rate is controlled by variation in the rate of intergroup transmission, variation in diversity is a function of the number of intergroup transmission episodes per time period. High stylistic diversity means high levels of intergroup transmission, while low diversity means low levels of intergroup transmission. The second deductive argument led from drift and intergroup transmission to a measure of interassemblage distance, the squared Euclidean distance. Equilibrium distances among a set of groups are also a function of their effective population sizes and intergroup transmission rates.

0.3-

c)

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C)

0.1 a)

-c

0.0

-0 a) CZ -0.1 - CT

) -

-0.3

o

o o

0 0 ? o o0

0 0 0 0

0 ? 0 o ? o

o 0

-3 -2 -1 0 1 2

Theta 3 4 5

Figure 7. Relationship between estimates of 0 (diversity) - tE from Equation 9-for each assemblage and the mean of the squared Euclidean distances, de, from that assemblage to each of four others in the same thickness class. Both the diversity and the mean distance values for each assemblage are reexpressed as deviations from their respective thickness class means, thus removing the confounding effects of the temporal trends in both measures.

Large distances mean low levels of intergroup transmission, while small distances mean high levels of such transmission. Thus when drift and neutral innovation are at work, we can expect within-assemblage diversity and interassemblage distance to be inversely correlated.

We have discovered this inverse relationship in stylistic mode frequencies in Illinois Woodland assemblages. In other words, theory-driven measurements of diversity and distance have lead to identical inferences about temporal and spatial variation in the operation of two evolutionary mechanisms: drift and neutral innovation. The agreement warrants the conclusion that these forces, in- voked in the models, were at work in the past. As a result, and it is here that the theoretical exercise finds its primary justification, it is possible to make a reasonable claim to have gotten a chunk of history right: during the Woodland Period in Illinois, levels of intergroup transmission began at low levels, rose to a maximum in the Middle Woodland, and then declined to new lows in the Late Wood- land.

Neiman] 27

o

AMERICAN ANTIQUITY

To the extent that movement of individuals from one deme to another would have been a necessary condition for learning to take place, change in intergroup transmission in turn implies change in the number of individuals moving among demes in the region. As we saw in the analysis of assemblage size and 0 estimates, there is evidence that some of this variation, perhaps a quarter of the variance in tE, is caused by variation in group size. It seems unlikely that all of the remain- der is accounted for in terms of random error variance associated with the estimates themselves. If true, this would imply correlated variation in intergroup transmission rates that scales with population size. In other words, the absolute amount of intergroup transmission rose and then fell because both effective population size and intergroup transmission rates rose and fell.

The explicitness of our mechanistic approach makes it possible to be a bit more specific. The stylistic variation monitored here occurs on cooking pots. Hence inferences about intergroup transmission are about intergroup transmission among individuals responsible for the decoration of cooking pots. Empirical generalization from ethnoarchaeo- logical work suggests that successful transmission of style in the context of pottery manufacture requires some form of perdur- ing relationship between teacher and learner (e.g., Bunzel 1929; DeBoer 1989). If this pattern applies to Illinois Woodland groups, the changes in intergroup transmission occurred in the context of changes in levels of long- term residential movement by potters among groups. Clearly this is an area that requires further inferential work.

The resulting picture contradicts the current canonical understanding of social dynamics during the period, an understanding that is based on the same data I have used here (Braun 1985, 1986, 1992; Braun and Plog 1982; cf. Tainter 1977). Braun and Plog argued that the Hopewell Interaction Sphere arose as a result of the need to buffer temporal variation in resource availability for local groups in the context of sedentism. Reduc-

tion of risk was achieved via increased levels of supralocal integration mediated by exchange. In this scenario the disappearance of exotic trade goods at the end of the Middle Woodland marked the replacement of inter- mittent ties among groups, requiring repeat- ed affirmation by gift exchange, by more stable, long-term social relationships that did not require extraordinary prestations for their maintenance. Thus the Late Woodland is al- leged to be a period of increased regional integration characterized by more frequent and thus routine interaction and communication among groups. The archaeological evidence for this scenario allegedly resides in patterns of ceramic assemblage decorative diversity measured by the Shannon-Weaver index. However, given the results described above, it is likely that the measurements of regional diversity on which this interpretation turns are misleading artifacts of sample-size variation7. While the picture I have developed conflicts with the view developed in the wake of the New Archaeology, it resembles the previously received wisdom about the period that was developed by culture historians during the 1940s and 1950s (e.g., Streuver 1964; Wray 1952). In this case, the culture historians were right. The Hopewell climax does correspond with the highest levels of movement within the region, as documented by ordinary ceramics, while the ensuing period emerges as one of marked social isola- tion among potters in different demes. Dur- ing the Late Woodland, groups were more isolated than they had been during the Early Woodland.

Limitations

It is important to be clear about the limits of the models presented here, both with regard to the scope of their application and the circumstances under which they make inferences possible. Clearly the models are not able to handle functional variation. There are several outstanding issues intimately con- nected to the style-related social dynamics in

28 [Vol. 60, No. 1, 1995


the Illinois Woodland that require functional treatment. Among the most pressing are the linked questions of whose movement is being monitored (i.e., males or females) and why levels of movement might have been chang- ing. Getting the answers is going to require inferential arguments about such selectively important matters as sexual dimorphism in subsistence and reproductive strategies and variation in levels of energy investment in style in general. Such inferences, when they are made, are going to be based on the same kinds of methods I have attempted here for selectively neutral traits. They will depend on the development of imaginary models that portray the dynamic consequences of the operation of a relatively small set of evolutionary mechanisms that can explain unique historical trajectories. However, in the case of functional variants, the mechanisms in question will be those that sort variants deter- ministically, not stochastically.

The fact that the models have been applied successfully to decorative variation in Wood- land Illinois does not mean that decorative variation is selectively neutral in all historical contexts and hence always under the control of neutral innovation and drift. I have left open the matters of whether and under what conditions decorative variation might be functional and therefore subject to deterministic sorting (e.g., O'Brien and Holland 1990: 58, 1992:47), and the evolutionary mechanisms that might be responsible for this. If historical circumstances exist in which decorative variation is functional, the models presented here will not apply in those cases. In other words, the goal of this paper has not been to peddle a universal view of what decoration means in all times and places. Instead the models outlined here are intended to allow us to determine, by looking at variation in the archaeological record, when neutral innovation and drift are important determinants, and to make possible inferences about social dynamics in those particular historical contexts only. Lip exterior decoration on Il- linois Woodland cooking pots is apparently one such context.

Concluding Remarks

A Little Metaphysics

The approach to style pursued here is a departure from most recent archaeological work on the topic. The divergence deserves examination. It is best understood as the expression of a fundamental, metaphysical difference, nicely captured in the late Wilfrid Sellar's distinction between the manifest and scientific images of the world, two different ways of imagining what kinds of things exist and how they change (Sellars 1962). Under the manifest image, phenomena are inter- preted in the way in which we commonly understand persons. Empirical dynamics are thought to result from intentions, beliefs, and desires. Under the scientific image, the met- aphor of personhood is rejected in favor of understanding in terms of physical systems whose dynamics are caused by mechanistic forces. Theory consists of descriptions of those mechanisms and the way they work, cast in prose or, more powerfully, in mathematics. The manifest image is the framework in which people the world over have understood phenomena since the beginning of documented history, and presumably long before. The scientific image is a recent development, with its origins in the sixteenth century. From this perspective, the history of science chronicles the shrinkage of knowledge domains inter- preted in the terms of manifest image.

Although they include a wide variety of interpretations of what style is, the vast ma- jority of recent archaeological treatments of the topic are crafted in the manifest image. Symptomatic and fundamental is their lack of any account of mechanisms that cause stylistic variation. The notions that style is "a means of non-verbal communication to ne- gotiate identity" (Wiessner 1990:108, 1985), or that style resides in "choices" among "equivalent alternatives, of equally viable options, for attaining a given end" (Sackett 1990:33, 1982), or, most ephemerally, that style is simply "a way of doing" (Hodder 1990:45) are high-level abstractions drawn from commonsense associations of the word

29 Neiman]

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"style" and thus rendered in the intention- laden language of persons. Given the foundation in common sense, the definitions seem unproblematic and the question of underly- ing causal mechanisms appears otiose.

The implications of Sellars's distinction for archaeological practice are worked out in more detail elsewhere (Dunnell 1992; Nei- man 1990:38-42). The aspect to which I wish to call attention here is the contrast between empirical patterning in the knowledge produced by the two approaches. The scientific image produces knowledge that over time is cumulative at both a theoretical and empirical level (Dunnell 1982; Hesse 1978). New theory does not wholly replace earlier theory, but subsumes it in a more encompassing framework. From the perspective of the new framework, earlier theory is often seen to offer useful approximations under a limited range of parameter values (Wimsatt 1980). By contrast the knowledge products of the manifest image are ephemeral (Gergen 1986). New interpretations do not offer more powerful frameworks that encompass their pre- decessors, just different ones. Wylie recog- nizes the difference as follows: "There does seem to be a relatively stable core of obser- vational claims, quasifoundational causal principles and low-level empirical generalizations, particularly in the biophysical sciences, which persist through successive episodes of theory change and which find continuous application in practice" (1989: 100, emphasis added).

Although a definitive account clearly awaits further archaeological work over the next decade, there are hints that this practical contrast will characterize the products of recent archaeological and evolutionary approaches to style. To the extent that successive for- mulations about style in archaeology are grounded in the manifest image, they will be incommensurate and noncumulative. Con- sider for example the intuitively attractive idea that style results when people compare "their ways of making and decorating artifacts with those of others and then imitate, differentiate, ignore, or in some way com-

ment on how aspects of the maker or bearer relate to their own social or personal iden- tities" (Wiessner 1985:160). Application of this abstract notion to a particular case requires interpretation. The formulation in the language of personhood and intentionality invites elaboration in terms of the common sense of the interpreter. Because human goals, desires, and common sense are socially variable, they give rise to fundamentally conflicting glosses of when and how people should imitate, differentiate, ignore, and comment on other people and what they might say (e.g., Wiessner 1990:111).

Given their origins in common sense, such conflicting glosses cannot be resolved. The reasons for this are twofold. First, there is no motivation for resolution. Different interpretations are bound up with different visions of how the world is or should be (Hesse 1978). Those visions are intimately tied to group interests. Social allies are loathe to invest energy in any enterprise that might subject their interested glosses to serious risk of rejection in favor of glosses derived from the visions of a competing group. Second, even if par- tisans of conflicting glosses were able to agree to place their own positions in real jeopardy, the use of common sense in the role of theory pushes the chances of success in such an enterprise toward zero. The lack of explicitly rendered theory positing causal mechanisms means that it is very difficult to derive empirical consequences which may be used to evaluate particular interpretations. There is simply no way to produce a formal model by which the implications of commonsense notions (e.g., that style is a way of commenting) for empirical variation (e.g., stylistic diversity, interassemblage distance, and their relationship) might be deduced. It therefore comes as no surprise that archaeologists wed- ded to the manifest image have recently con- cluded that they must "abandon the hope for a unified theory of style" (Conkey and Has- torf 1990:3). If theory development is con- strained to occur in the manifest image, they are right.

30 [Vol. 60, No. 1, 1995


The Promise of an Evolutionary Approach

If the hallmark of inquiry guided by the scientific image is the subsumption of prag- matically useful results from earlier research programs under more encompassing and powerful frameworks, then the development of an evolutionary approach to style looks like a very promising enterprise (Neiman 1990:196-197; Teltser 1995). That this kind of relationship exists between aspects of traditional archaeological practice and the theory presented here is suggested by the correspondence noted above between evolutionary and culture-historical inferences concern- ing Illinois Woodland social dynamics. The instructive aspect of this correspondence lies not simply in the substantive agreement about what happened in history, but at the methodological level that makes this agreement predictable. Culture-historical interpretations of the Woodland period in Illinois rest- ed on interpretive conventions or methods that were modal in the discipline at the time. Culture history was grounded in the interpretation of the record in terms of homologous similarity. Explanations therefore tend- ed to invoke processes that involved cultural transmission-migration, exchange, "diffu- sion" (Dunnell 1986). The early ceramic so- ciology studies that helped launch the New Archaeology had a similar foundation (Deetz 1965; Hill 1966; Longacre 1964), although here the spatial scale over which stylistic sim- ilarities were considered was smaller, their measurement numerical, and their interpretation in terms of "interaction" often more abstract (e.g., Plog 1976). An evolutionary framework subsumes earlier practice by showing when and why these kinds of interpretive conventions are likely to provide useful approximations.

Evolutionary theory isolates the kind of similarity that is likely to be homologous. When the similarity in question actually is stylistic (that is, reckoned using selectively neutral variants), interpretations that invoke some form of cultural transmission among social-learning populations are likely to be

correct, at least in a general way. Selective neutrality means that drift and the introduction of variation, either from within a group or from other groups, will be among the primary determinants of culturally transmitted variant trajectories. The Markovian structure of drift makes it likely that isolated groups will diverge from identical starting frequencies, even in the absence of innovation that is historically unique to each group. Selective neutrality raises the probability that, at a given level of design complexity, innovations will be historically unique. Under these circumstances only some form of cultural transmission among groups causes increased similarity. Within groups, similarity over time is a function of the number of transmission episodes and hence the temporal interval between samples.

The idea that drift might have something to do with stylistic variation has emerged in the discipline several times over the past 30 years. It received its earliest and most sus- tained expression in Binford's work on met- rical differences among the contents of Late Archaic point caches from Michigan (1963). Since then it has resurfaced occasionally either as a possibility for consideration in the interpretation of empirical work, whose primary theoretical motivation lay elsewhere (Graves 1981, 1985), or in an entirely theoretical context (Hill 1985; O'Brien and Hol- land 1990, 1992). Modal reaction in the discipline has not been sanguine, as witnessed by a recent surveyor of archaeological approaches to style who rightly concludes, "most archaeologists shy away from explaining at least most cultural change as random" (Braun 1992:265). Given the ease with which traditional archaeological interpretative conventions regarding style can be subsumed under an evolutionary approach, the reticence to explore seriously the analytical possibili- ties offered by evolutionary theory emerges as a puzzle. Sellars's distinction helps resolve it.

Although the possibility of a mechanistic treatment of style was repeatedly glimpsed in the field, it quickly palled because it was met-

31 Neiman]

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aphysically incompatible with unquestioned assumptions about the way the world should be understood. As long as archaeology was anthropology, and anthropology was the study of persons conceived in the manifest image, the idea that drift might be responsible for some aspects of archaeological variation could never be more than a passing fancy, uncon- nected to mainstream theoretical develop- ments, and therefore not seriously explored. Results obtained here indicate that further exploration of the effects of drift on archaeological variation and an evolutionary approach to style would lead to real payoffs in historical knowledge. However, their realization depends on a fundamental alteration in the kind of explanation archaeologists are willing to entertain.

,4cknowledgments. An earlier version of this paper was presented in a symposium entitled "Building Method- ology for an Evolutionary Archaeology," organized by Patrice Teltser at the 57th Annual Meeting of the Society of American Archaeology, Pittsburgh, Pennsylvania. I am very grateful to Teltser for the opportunity to write the paper and for encouragement along the way. Several people were kind enough to offer helpful comments on the manuscript at different stages. They were Cliff Boyd, Robert Dunnell, David Braun. Michael Graves, James N. Hill, Martha Hill, Michael Kline, Jon Marks, Michael O'Brien, Patrice Teltser, Janet Walker, and one anony- mous reviewer. I am also grateful to Rolando Portocar- erro for preparing the Spanish version of the abstract. Of course the usual disclaimers apply, and none of these people should be held responsible for any muddled thinking or prose that remains.

References Cited

Bettinger, R. L. 1991 Hunter Gatherers: Archaeological and Evolu-

tionary Theory. Plenum Press, New York. Binford, L. R.

1963 "Red Ochre" Caches from the Michigan Area: A Possible Case of Cultural Drift. Southwestern Journal of Anthropology 19:89-108.

1989 Styles of Style. Journal of Anthropological Ar- chaeology 8:51-67.

Bobrowsky, P. T., and B. F. Ball 1989 The Theory and Mechanics of Archaeological

Diversity in Archaeology. In Quantifying Diversity in Archaeology, edited by R. D. Leonard and G. T. Jones, pp. 4-12. Cambridge University Press, Cam- bridge.

Boyd, R., and P. J. Richerson. 1985 Culture and the Evolutionary Process. Univer-

sity of Chicago Press, Chicago. Braun, D. P.

1977 Middle Woodland-Early Late Woodland So- cial Change in the Prehistoric Central Midwestern U.S. Ph.D. dissertation, University of Michigan, University Microfilms, Ann Arbor.

1985 Ceramic Decorative Diversity and Illinois Woodland Regional Integration. In Decoding Pre- historic Ceramics, edited by Ben A. Nelson, pp. 128- 153. Southern Illinois University Press, Carbon- dale.

1986 Midwestern Hopewellian Exchange and Su- pralocal Interaction. In Peer Polity Interaction and Socio-Political Change, edited by C. Renfrew and J. Cherry, pp. 117-126. Cambridge University Press, Cambridge.

1990 Selection and Evolution in Nonhierarchical Organization. In The Evolution of Political Systems: Socio-politics in Small-Scale Sedentary Societies, edited by S. Upham, pp. 62-86. Cambridge Uni- versity Press, New York.

1992 Why Decorate a Pot? Midwestern Household Pottery, 200 B.C.-A.D. 600. Journal of Anthropo- logical Archaeology 10:360-397.

Braun, D. P., and S. Plog 1982 Evolution of "Tribal" Social Networks: The-

ory and Prehistoric North American Evidence. American Antiquity 47:504-525.

Bunzel, R. 1929 The Pueblo Potter. Columbia University Press,

New York. Burian, R. M.

1983 Adaptation. In Dimensions of Darwinism, edited by M. Grene, pp. 287-314. Cambridge Uni- versity Press, Cambridge.

Caldwell, J. R. 1964 Interaction Spheres in Prehistory. In Hope-

wellian Studies, edited by J. R. Caldwell and R. L. Hall, pp. 133-143. Illinois State Museum Scientific Papers 12.

Cavalli-Sforza, L. L., and M. W. Feldman 1981 Cultural Transmission and Evolution. Prince-

ton University Press, Princeton. Carmelli, D., and L. L. Cavalli-Sforza

1975 Some Models of Population Structure and Evolution. Theoretical Population Biology 9:329- 359.

Conkey, M. W., and C. A. Hastorf 1990 Introduction. In The Uses of Style in Archae-

ology, edited by M. Conkey and C. Hastorf, pp. 1- 4. Cambridge University Press, Cambridge.

Cosmides, L., and J. Tooby 1987 From Evolution to Behavior: Evolutionary

Psychology as the Missing Link. In The Latest on the Best, Essays on Evolution and Optimality, edited by John Dupre, pp. 277-306. MIT Press, Cam- bridge.

32 [Vol. 60, No. 1, 1995


Crow, J. F. 1986 Basic Concepts in Population, Quantitative and

Evolutionary Genetics. W. H. Freeman, San Fran- cisco.

Crow, J. F., and M. Kimura 1970 An Introduction to Population Genetics Theory.

Harper Row, New York. De Boer, W. R.

1989 Interaction, Imitation, and Communication as Expressed in Style: The Ucayali Experience. In The Uses of Style in Archaeology, edited by M. Conkey and C. Hastorf, pp. 82-104. Cambridge University Press, Cambridge.

Deetz, J. D. F. 1965 The Dynamics of Stylistic Change in Arikara

Ceramics. Illinois Studies in Anthropology 4. Uni- versity of Illinois Press, Urbana.

Dunnell, R. C. 1978 Style and Function: A Fundamental Dichoto-

my. American Antiquity 43:192-202. 1980 Evolutionary Theory and Archaeology. In Ad-

vances in Archaeological Method and Theory, vol. 3, edited by M. B. Schiffer, pp. 35-99. Academic Press, New York.

1982 Science, Social Science, and Common Sense: The Agonizing Dilemma of Modem Archaeology. Journal of Anthropological Research 38:1-25.

1986 Five Decades of American Archaeology. In American Archaeology: Past and Future, edited by D. J. Meltzer, D. D. Fowler and J. A. Sabloff, pp. 23-49. Smithsonian Institution Press, Washington.

1989a Aspects of the Application of Evolutionary Theory in Archaeology. In Archaeological Thought in the Americas, edited by C. C. Lamberg-Karlov- sky, pp. 35-49. Cambridge University Press, Cam- bridge.

1989b Diversity in Archaeology: A Group of Mea- sures in Search of Application? In Quantifying Di- versity in Archaeology, edited by R. D. Leonard and G. T. Jones, pp. 142-149. Cambridge University Press, Cambridge.

1992 Archaeology and Evolutionary Science. In Quandaries and Quests: Visions of Archaeology's Future, edited by LuAnn Wansnider, pp. 209-224. Center for Archaeological Investigations, Occasion- al Paper No. 20.

Ewens, W. J. 1972 The Sampling Theory of Selectively Neutral

Alleles. Theoretical Population Biology 3:87-112. Gergen, K. J.

1986 Correspondence vs. Autonomy in the Lan- guage of Understanding Human Action. In Metath- eory in Social Science, edited by D. W. Fiske and R. A.Schweder, pp. 136-162. University of Chicago Press, Chicago.

Grayson, D. K. 1981 The Effects of Sample Size on Some Derived

Measures in Vertebrate Faunal Analysis. Journal of Archaeological Science 8:77-88.

Graves, M. W. 1981 Ethnoarchaeology ofKalinga Ceramic Design.

Ph.D. dissertation, University of Arizona. Univer-

sity Microfilms, Ann Arbor. 1985 Ceramic Design Within a Kalinga Village:

Temporal and Spatial Processes. In Decoding Pre- historic Ceramics, edited by B. A. Nelson, pp. 9-34. Southern Illinois University Press, Carbondale.

Hanushek, E. A., and J. E. Jackson 1977 Statistical Methods for Social Scientists. Aca-

demic Press, New York. Hesse, Mary

1978 Theory and Value in the Social Sciences. In Action and Interpretation: Studies in the Philosophy of the Social Sciences, edited by C. Hookway and P. Pettit, pp. 1-16. Cambridge University Press, Cambridge.

Hill, J. A. 1966 A Prehistoric Community in Eastern Arizona.

Journal of Southwestern Anthropology 22:9-30. 1985 Style: A Conceptual Evolutionary Framework.

In Decoding Prehistoric Ceramics, edited by B. A. Nelson, pp. 362-388. Southern Illinois University Press, Carbondale.

Hodder, I. 1990 Style as Historical Quality. In The Uses of Style

in Archaeology, edited by M. Conkey and C. Has- torf, pp. 44-51. Cambridge University Press, Cam- bridge.

Jones, G. T., D. K. Grayson, and C. Beck 1983 Artifact Class Richness and Sample Size in Ar-

chaeological Surface Assemblages. In Lulu Linear Punctated: Essays in Honor of George Irving Quim- by, edited by R. C. Dunnell and D. K. Grayson, pp. 55-73. Anthropological Papers No. 72. Museum of Anthropology, University of Michigan, Ann Arbor.

Kintigh, K. W. 1984 Measuring Archaeological Diversity by Com-

parison with Simulated Assemblages. American An- tiquity 49:44-54.

Kosso, P. 1992 Reading the Book of Nature. Cambridge Uni-

versity Press, Cambridge. Leonard, R. D.

1989 Resource Specialization, Population Growth, and Agricultural Production in the American South- west. American Antiquity 54:491-503.

Leonard, R. D., and G. T. Jones 1987 Elements of an Inclusive Evolutionary Model

for Archaeology. Journal of Anthropological Ar- chaeology 6:199-219.

Leonard, R. D., and G. T. Jones (eds.) 1989 Quantifying Diversity in Archaeology, Cam-

bridge University Press, Cambridge. Leone, M. B.

1968 Neolithic Economic Autonomy and Social Distance. Science 162:1150-1151.

Lewontin, R. C. 1980 Theoretical Population Genetics in the Evo-

33 Neiman]

AMERICAN ANTIQUITY

lutionary Synthesis. In The Evolutionary Synthesis, edited by E. Mayr and W. B. Provine, pp. 58-68. Harvard University Press, Cambridge.

Longacre, W. A. 1964 Sociological Implications of the Ceramic Anal-

ysis. In On the Prehistory of Eastern Arizona, II, pp. 155-167. Fieldiana; Anthropology Vol. 55. Field Museum of Natural History, Chicago.

Lynch, A., G. M. Plunkett, A. J. Baker, and P. F. Jenkins 1989 A Model of the Cultural Evolution of Chaffinch

Song Derived from the Meme Concept. American Naturalist 133:634-653.

Lynch, A., and A. J. Baker 1993 A Population Memetics Approach to Cultural

Evolution in Chaffinch Song: Meme Diversity With- in Populations. American Naturalist 141:597-620.

McCartney, P. H., and M. F. Glass 1990 Simulation Models and the Interpretation of

Archaeological Diversity. American Antiquity 55: 521-536.

Meltzer, D. J. 1981 A Study of Style and Function in a Class of

Tools. Journal of Field Archaeology 8:313-326. Mithen, S.

1990 Thoughtful Foragers, A Study of Prehistoric De- cision Making. Cambridge University Press, Cam- bridge.

Neiman, F. D. 1990 An Evolutionary Approach to Archaeological

Inference. Aspects of Architectural Variation in the 17th-Century Chesapeake. Ph.D. dissertation, Yale University. University Microfilms, Ann Arbor.

O'Brien, M. J., and T. D. Holland 1990 Variation, Selection, and the Archaeological

Record. In Archaeological Method and Theory, vol. 2, edited by M. B. Schiffer, pp. 31-79. University of Arizona Press, Tucson.

1992 The Role of Adaptation in Archaeological Ex- planation. American Antiquity 57:36-59.

Piazza, A., S. Rendine, G. Zei, A. Moroni, and L. L. Cavalli-Sforza

1987 Migration Rates of Human Populations from Surname Distributions. Nature 129:714-716.

Pierce, C. 1991 Distinguishing Style and Function in Poverty

Point Objects. Paper presented at the 56th Annual Meeting of the Society for American Archaeology, New Orleans.

Plog, S. 1976 Measurement of Prehistoric Interaction Be-

tween Communities. In The Early Mesoamerican Village, edited by K. V. Flannery, pp. 255-272. Ac- ademic Press, New York.

Rindos, D. 1984 The Origins of Agriculture. An Evolutionary

Perspective. Academic Press, New York. Rogers, A.

1988 Does Biology Constrain Culture? American Anthropologist 90:819-831.

Rothschild, N. A. 1989 The Effect of Urbanization on Faunal Diver-

sity: A Comparison Between New York City and St. Augustine, Florida, in the Sixteenth to Eighteenth Centuries. In Quantifying Diversity in Archaeology, edited by R. D. Leonard and G. T. Jones, pp. 92- 99. Cambridge University Press, Cambridge.

Sackett, J. 1982 Approaches to Style in Lithic Archaeology.

Journal of Anthropological Archaeology 1:59-110. 1990 Style and Ethnicity in Archaeology. In The Uses

of Style in Archaeology, edited by M. Conkey and C. Hastorf, pp. 32-43. Cambridge University Press, Cambridge.

Sellars, W. 1962 Philosophy and the Scientific Image of Man.

In Frontiers of Science and Philosophy, edited by R. G. Colodny, pp. 5-78. University of Pittsburgh Press, Pittsburgh.

Simpson, E. H. 1949 Measurement of Diversity. Nature 163:688.

Smith, C. A. B. 1969 Local Fluctuations in Gene Frequencies. An-

nals of Human Genetics 32:251-260. Snedecor, G. W., and W. G. Cochran

1978 StatisticalMethods. Iowa State University Press, Ames.

Sober, E. 1980 Evolution, Population Thinking and Essen-

tialism. Philosophy of Science 47:350-383. Streuver, S.

1964 The Hopewell Interaction Sphere in Riverine- Western-Great Lakes Cultural History. In Hope- wellian Studies, edited by J. R. Caldwell and R. L. Hall, pp. 87-106. Illinois State Museum Scientific Papers, Vol. 12.

Tainter, J. A. 1977 Woodland Social Change in West-Central Il-

linois. Midcontinental Journal of Archaeology 2:67- 98.

Teltser, P. A. 1988 The Mississippian Archaeological Record on the

Malden Plain, Southeast Missouri: Local Variability in Evolutionary Perspective. Ph.D. dissertation, University of Michigan. University Microfilms, Ann Arbor.

1995 Culture History, Evolutionary Theory, and Frequency Seriation. In Evolutionary Archaeology, Methodological Issues, edited by P. A. Teltser, pp. 51-68. University of Arizona Press, Tucson.

Tooby, J., and L. Cosmides 1992 The Psychological Foundations of Culture. In

The Adapted Mind, Evolutionary Psychology and the Generation of Culture, edited by J. Barkow, L. Cos- mides, and J. Tooby, pp. 19-136. Oxford University Press, New York.

Wiessner, P. 1985 Style or Isochrestic Variation? A Reply to

Sackett. American Antiquity 50:160-166.

34 [Vol. 60, No. 1, 1995


1990 Is There a Unity to Style? In The Uses of Style in Archaeology, edited by M. Conkey and C. Has- torf, pp. 105-112. Cambridge University Press, Cambridge.

Wylie, A. 1989 Matters of Fact and Matters of Interest. In Ar-

chaeological Approaches to Cultural Identity, edited by S. Shennan, pp. 94-108. Allen Unwin, London.

Wimsatt, W. 1980 Reductionist Research Strategies and Their Bi-

ases in the Units of Selection Controversy. In Sci- entific Discovery: Case Studies, edited by T. Nickles, pp. 213-259. D. Reidel, Dordrecht.

Wood, J. W. 1986 Convergence of Genetic Distances in a Migra-

tion Matrix Model. American Journal of Physical Anthropology 71:209-219.

Wray, D. E. 1952 Archaeology of the Illinois Valley: 1950. In

Archaeology of Eastern North American, edited by J. B. Griffin, pp. 152-164. University of Chicago Press, Chicago.

Yasuda, N., L. L. Cavalli-Sforza, M. Skolnick, and A. Moroni

1974 The Evolution of Surnames: An Analysis of Their Distribution and Extinction. Theoretical Pop- ulation Biology 5:123-142.

Zei, G., R. G. Matessi, E. Siri, A. Moroni, and L. Cavalli- Sforza

1983 Surnames in Sardinia: Fit of Frequency Dis- tribution for Neutral Alleles and Genetic Population Structure. Annals of Human Genetics 47:329-352.

Notes

'The terms horizontal, oblique, and vertical were introduced by Cavalli-Sforza and Feldman (1981). They refer respectively to cultural transmission among individuals of the same biological generation, from members of one generation to members of the next generation who are not their offspring, and from parent to child. 2 The inference raises a puzzle. The archaeological diversity literature indicates that at least over the small to moderate assemblage sizes observed here, tF estimates should be influenced artificially by assemblage size. The foregoing theoretical arguments indicate they should also be affected by real 0 values. Thus we expect that tF should be more highly correlated with assemblage size than tE: Ne determines the former suite of estimates along two paths-assemblage size and actual 0 values-while the latter suite of estimates is influenced by N, along only the second of these paths. However, as we have seen, the correlations between the two sets of 0 estimates and sample size are practically indistinguishable.

The explanation for this conundrum lies in Ewens's work. In theory tE is a minimum-variance estimator. Other estimators, particularly those like Equation 7 that

incorporate extraneous information about variant fre-

quencies, contain additional error variance. This theoretical expectation appears to be met in this sample. The variance of the 35 tF values is 2.53, while that of the corresponding tE values is 2.46. However, the latter is

greatly inflated by the outlier. When it is removed, the

tE variance estimate shrinks to 1.44. Statistical evaluation of the difference between the two variances, computed without the outlier and taking into account the correlation between the variables (Snedecor and Cochran 1978:196), indicates it is unlikely an artifact of sampling error (rDs = .39, p = .02). It is this large, additional component of error variance contained in the tF estimates that dilutes the expected higher correlation with assemblage size. 3 Given the small number of localities, it is desirable to evaluate the importance of sampling error in producing the temporal pattern of increase followed by decrease. A simple way to do this is to fit by least squares a qua- dratic regression to the point scatter, using thickness class values and their squares to predict tF. If the regression coefficients associated with both the first- and second- degree terms are significantly different from 0, then we can reject the hypothesis that the curvature in the data is an artifact of sampling error. After deletion of the outlier, t-tests of the null hypotheses that both thickness class and its square are associated with zero coefficients produced encouragingly low values (p = .013 and .014, respectively). The accuracy of these probability values depends on the assumption, often violated with time- series data, that the errors from the regression equation are independently and identically distributed. However in this case the assumption is supported by a Durban- Watson statistic of 2.09, indicating no serial correlation among error terms (Hanushek and Jackson 1977:164- 168).

There remains the ambiguity of whether the signifi- cance of both the first- and second-order terms arises in the context of a trend that is nonlinear but monotonic, as opposed to a trend characterized by increase followed by decrease. These alternatives can be discriminated by fitting a simple linear regression to the point scatter. If the first alternative were true, the predominant monotonic component should result in a slope significantly different from 0. A slope statistically indistinguishable from 0 would be compatible with the second alternative. A t-test reveals that the departure of a straight line fit by least squares from a slope of 0 under the null hypothesis is likely an artifact of sampling error (p = .71). Evaluation of the results in the framework of traditional hypothesis testing points to the conclusion that the pattern of increase followed by decrease is not explicable as a sampling artifact. 4 Although space constraints forbid a full treatment here, it is important to note that the same temporal trend emerges in tE values computed for a second dimension of stylistic variation reported by Braun (1977:151-167). This second dimension, designated "exterior decoration band 1," describes motifs that occur in a decorative band

35 Neiman]

AMERICAN ANTIQUITY

that lies below the lip-exterior decoration on Illinois Woodland cooking pots. 5 The same temporal trend is found in interassemblage distances computed from mode frequencies for a second dimension of stylistic variation: exterior decoration band 1 (see note 4). 6 Several questions immediately arise in the context of this argument. Is it deductively correct? What parameters control the strength of the correlation between the mean squared distance and 0? How large a correlation can be expected? Answers to these questions can be had with the help of Equations 11, 12, and 13. We proceed as follows. To simplify matters, we will continue to assume that there is no variation among groups in the in situ innovation rates. Hence variation in 0 is entirely driven by variation in Ne and mi,. We also assume that group sizes are the same. The two equations can be used to compute the expected value of the correlation between the mean squared distance d2 from a given group to the others and 0 for that group under a variety of parameter values. By varying those parameters, we can determine numerically how sensitive the strength of the correlation is to variation in the different parameters.

Expected values for the correlation were obtained numerically by averaging estimates of Pearson's r between 0 (= 2Ne,(1 - m,,)) and d2 computed on the basis of Equations 11, 12, and 13. An estimate of r was computed for each of multiple realizations of intergroup transmission matrices whose diagonal elements mij were randomly drawn from a uniform distribution with mean (I -

A) and range s. The off-diagonal elements were obtained by randomly apportioning, again using a uniform distribution, the intergroup transmission rate 1 - mii among the off-diagonal elements along each row. While a full analysis of the problem is beyond our current needs, the following results are relevant. The correlation is controlled by the number of groups, along with the mean A

and range s of the intergroup transmission rate. As the number of groups increases, so does the correlation. Since in the case we are examining, there are five groups, the expected correlations derived from the five-group case offer a useful clue to what we can expect to observe in the Woodland data. Although the expected correlations are affected by interaction between A and s, the values lie in a range between -.65 and -.89 for a large range

of realistic parameter values (.025 < , < .10, .025 < s < .20), with most of the values lying in the more negative half of this interval. 7 Braun pursued his argument using two measures of decorative mode variation, which he called "local" and "regional diversity." Local diversity was measured by computing the Shannon-Weaver statistic for an assemblage from a given locality and thickness class. Thus Braun's local diversity is a measure of within-assemblage diversity, like tE Braun measured regional diversity by combining relative frequencies for assemblages from the five localities into a single 'average' assemblage for each thickness class and then computing the Shannon-Weaver statistic for this average assemblage. Thus his regional diversity is an attempt to measure the amount of variation among assemblages (Braun 1985:150-152), like the mean of the squared Euclidean distances used here. Braun detected a trend in local diversity that matches the pattern of increase followed by decrease in within-assemblage diversity that I describe here. However, he also noted that his measure of regional diversity behaved in the same way: it rose and then declined as well, leading to the conclusion that "supralocal connectedness" (1985: 147) decreased and then increased. This conclusion contradicts the inference made here, from the temporal trend in the mean of the Euclidean distances, that in levels of intergroup, transmission increased and then decreased.

Along with the arguments adduced in the body of this paper, two pieces of evidence indicate the contradiction must be resolved in favor of inferences based on the mean of the Euclidean distances. Braun's regional diversity is a misleading measure of among-assemblage variation because it is sensitive to within-assemblage diversity as well. It thus confounds these two fundamentally different sources of variation. More important, variation in Braun's regional diversity is almost certainly an unwelcome sample-size artifact: the correlation (Pear- son's r) between sample size and regional diversity for lip exterior decoration is .87 (p = .01) for the seven thickness classes considered by Braun (1985:148).

Received July 10, 1992; accepted September 15, 1994.

36 [Vol. 60, No. 1, 1995

Stylistic variation in evolutionary perspective: Inferences from decorative diversity and...

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