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Measuring the Flow of Goods with Archaeological DataAuthor(s): John R. ClarkSource: Economic Geography, Vol. 55, No. 1 (Jan., 1979), pp. 1-17Published by: Clark UniversityStable URL: http://www.jstor.org/stable/142729 .Accessed: 24/01/2011 05:36

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ECONOMIC GEOGRAPHY VOL. 55 JANUARY, 1979 No. 1

.IEASURING THE FLOW OF GOODS WITH ARCHAEOLOGICAL DATA*

JOHN R. CLARK

University of California, Los Angeles

Ian Hodder and Colin Renfrew have hypothesized that the nature of ancient trading systems can be deduced from the curvature of distance decay gradients derived from the dispersal of artifacts recovered at archaeo- logical sites. They identify three types of exchange: "local," with a gradient convex to the origin in a single-log interaction model, "down-the-line," with a linear gradient, and "random-walk," with a gradient concave to the origin. The random-walk pattern is said to be characteristic of complex trading networks. Roman period coins excavated at Dura Europus in Syria were used to test these ideas. The trading system was complex, therefore ran- dom-walk curvature was anticipated, but the curves were highly convex to the origin, contrary to expectations. This could be the result of circula- tion across the boundary of the region where the coins had value as money. Interaction values would have been artificially raised within the monetary zone and depressed outside of it, producing strong curvature. The pattern of steepness of the gradients conforms to expectations based on the value and transportability of the coins. It is also likely that political conditions and Roman monetary policy influenced the gradients.

Archaeologists have long been inter- ested in economic prehistoiy and in re- cent years have been increasingly inter- ested in modeling the archaeological evidence [5; 12]. A number of method- ologies, including those commonly used by geographers, have been identified and applied to their data. Nearest neighbor and quadrat analysis have been used to examine settlement patterns [8; 12, pp. 30-52]; central place theory has been applied to settlement hierarchies [15;

* I wish to acknowledge the support of the Regents of the University of California for this study and the valuable help of Dr. W. A. V. Clark in the preparation of the manuscript.

21]; and network analysis [14] and dis- tance decay models [11; 12, pp. 98-125, 183-97; 24; 26; 29] have been used to study exchange systems. The latter are particularly interesting, for many archae- ologists [9; 14; 23; 28; 34] feel that they are important markers of social evolu- tion.

Archaeologists have asked two basic but interrelated questions concerning ex- change: what was the early history of the technology of moving goods over space, and what was the early history of the social organization of exchange sys- tems? It is obvious that the two are closely intertwined, for, like the physical

ECONOMIC GEOGRAPHY

mode of transport, the organization of exchange systems is itself a technology, a social technology. Certainly it has the result of easing the movement of goods, which can be measured by the distance decay gradient in a variety of interac- tion models. Tracing the social evolution of trading systems on the basis of mute archaeological remains is obviously more difficult than measuring the ease with which they are moved, yet Hodder and Renfrew [11; 12, pp. 109-15; 26, pp. 77- 82; 27, pp. 466-701 are attempting to do this.

This effort to delineate social change through the application of geographic models is intriguing, but it faces a num- ber of problems. Many stem from the scarcity and doubtful quality of data, which makes it hard to estimate the value of model parameters, to show that sample statistics are significantly differ- ent from zero, or that several values in a time series are significantly different from one another, thus indicating a tem- poral trend.

Archaeologists share many of the problems faced by geographers inter- ested in the study of a particular region. Their training focuses their attention on the problems of a particular period in a particular region and they are, for the most part, forced to make do with the data that either happen to be available or that they can generate themselves. When geographers became interested in theory and modeling, the problem got turned around. The models, intended to be general, were not supposed to be sensitive to period and place specific phenomena. Thus, data were sought which met the requirements of the mod- els; and as the sophistication of the mod- els increased so did the sophistication of the data requirements. As a result, a lot of work has been done on places like Cedar Rapids or Malmo where "good" data are available.

If a similar trend is to be followed in the study of the geography of the dis- tant past, data must be sought which

meet the minimum requirements of even a simple model. Accordingly, my pur- pose here is to explore Renfrew's and Hodder's ideas with the aid of data that are archaeological but have been chosen for their ability to fit the needs of the models discussed by the two archaeolo- gists. In this case the data are coins of the Roman period excavated at Dura Europus in Syria [11].

THE MODEL

The relative ease of movement of goods, whether the result of social organ- ization or transport technology, can be measured with the distance decay gradi- ent of an interaction model; for a given good, the more gentle the gradient the more easily distance is being overcome. Tracing the social evolution of exchange systems is more difficult, but Renfrew and Hodder [11; 12; 26] state that we can use the shape of the curvature of the distance decay gradient to detelmine the nature of the exchange system. The cur- vature of the gradient can be measured by a, which is the power to which the distance data must be raised to make the relationship between interaction and dis- tance linear in a simple regression [31]. Both the distance decay gradient and a can be derived from a single-log interac- tion model [10; 31], which has been ap- plied to a large number of modern situa- tions [10; 22; 31] and is also the model chosen by Hodder and Renfrew to ex- amine archaeological data (Table 1).

The simplest form of the single-log model is:

log lj - a - b Dij (1)

where:

log I,j - the logarithm of the interac-

tion between two places, i and j;

Dj == the distance between i and j.

2

3 ARCHAEOLOGICAL FLOWS

TABLE 1

HODDER'S b AND OK VALUES FROM NEOLITHIC AND ROMAN PERIOD

ARCHAEOLOGICAL MATERIALS

Article

British Stone

Axes: Group I

Group VI

Lizard Head Pottery

Anatolian Obsidian

Picrite Hammers

Oxford Pottery

New Forest Pottery

Rowland's Castle Pottery

Malvern Pottery

Savernake Pottery

Fine/Coarse b(=log I/km.)

F

F

F

F

C

F

F

C

C

C

-.03

-.05

-.027

-.124

-.024

-.03

-.05

-.10

-.21

< .1

>2.5

1.6

.9

.6

1.0

< .1

1.1

.2

.4

Source: Hodder [11].

In an empirical examination of the movement of goods, the value of the dis- tance decay gradient, b, can be affected by at least three things: the efficiency of the transport system, the perishability of the objects, and the value per weight of the objects transported. As a transport system becomes more efficient the abso- lute value of b declines for any item. However, in all systems the absolute value of b is higher for cheap, bulky goods than it is for valuable, compact ones [26, p. 77]. If the efficiency of trade is to be measured, it must be measured through the movement of a standard commodity. Conversely, if the transport- ability of various goods is to be mea- sured, they should be flowing through the same transport system.

The model assumes that the data are linear once the basic form of the model has been chosen. This is seldom true, so the practice of transforming the dis- tances by raising them to a power to make the relationship between interac- tion and distance linear has been adopted. The transformation' appears

1 Usually, distance decay slopes (b) are cal- culated from untransformed data (a =- 1), for slopes from data transformed by different a would no longer be comparable [11, p. 1791.

as:

logij = a-bDj (2)

An iterative algorithm to determine alpha has been outlined by Taylor [31, pp. 231-3], and a similar procedure has been followed here.2

2 In each case alpha was found by the fol- lowing five steps:

1. The raw distance data were transformed to fit equation (3) by raising them to succes- sive powers ranging from -3 to +3, but ex- cluding zero. After step 3 (below), if alpha proved to lie outside this range, higher or lower powers were tried, until the minimum standard error of b was found to lie between two of the values tested.

2. Before regressions were run to try to bracket the minimum standard error, the newly transformed distance data as well as the inter- action data were converted to z-scores (x - 0, s.d.x - 1). If this is not done, the raising of distance to successive powers changes its dis- tribution by stretching it out, which changes the regression slope (b), making its absolute value smaller as ao gets larger. As b gets smaller, its standard error also gets smaller and will not reach a minimum unless the data are converted to z-scores first.

3. Regressions were run to try to bracket the minimum standard error between two integer values of oa.

Era

Neolithic

Roman

ECONOMIC GEOGRAPHY

Several hypotheses about a have been advanced by Renfrew [26, pp. 77-85]. The first postulates a "down-the-line" mode of exchange where a group receiv- ing trade objects from a source outside their community keeps a fixed propor- tion and trades the rest to communities in a one-dimensional chain of exchang- ing communities farther from the source.

At any distance D, the amount passed on (I) is:

I 1I, e-7D (3)

where o1 is the amount leaving the source area and k is the proportion ( <1) passed on per unit of distance. In its linear folrnn,

log I = log Io- kD (4)

D is not raised to any power, therefore a - 1.

A second hypothesis is that in more complex trading systems where goods might move in any direction, not just away from the source or in a one-dimen- sional chain of exchange, a random walk would be approximated. Renfrew de- rives the equation:

I e -bD (5)

which has the linear form:

logI = log Io = bD2 (6)

where b can be a regression coefficient. In this case the distance is squared, therefore a = 2.

The third hypothesis stems from Hod-

4. If the minimum was not bracketed, the program was sent back to step I to choose new trial values for a.

5. Once bracketed, say between I and 2, a succession of a values incremented by 0.1 (1.1, 1.2, ..., 1.9) were tried and run through steps 1-3, to find the power which generated the smallest standard error of b. This power was accepted as the value of a, determined to the nearest tenth.

der's [11] derivation of a values that were 0.6 or smaller, including some that were probably negative, although he did not test for values of a less than 0.1. Renfrew [26, p. 84] explained these alphas as representing "supply zone" ex- change, and noted Hodder's conclusion that these were associated with steep distance decay slopes. This doesn't fit well with Renfrew's diagrams [26, p. 78; 27, pp. 466-70] which show "supply zone" slopes to be both very gentle and concave to the origin. A better explana- tion is that these represent trade in items that have only local distribution. This fits with both the steep attenuation slopes and Hodder's observation [11, p. 182] that many of the items in this cate- gory were produced in small quantities, probably for local consumption.

The gradients for the coin data exam- ined in the present study should be rela- tively gentle (since coins are high-value items) compared to the cases examined by Hodder (Table 1), which for the most part were either stone or ceramic goods which were relatively hard to transport. The a values should be near 2.0, for the coins are moving in a rela- tively complex trading system.

DATA PROBLEMS

The quality of data is a major prob- lem for the spatial modeling of archaeo- logical material. If we are unsure that a set of data fulfills the requirements of a particular model, then any tests of that model made with these data will be equally unsure. Data problems facing the archaeologist attempting to work with distance decay models have been outlined by Hodder and Orton [21, pp. 104-8] and Wright [33]. They can be summarized as follows:

1. Regional differences in field work. If the intensity of field work varies from area to area, the areas of more intensive field work will turn up more data and thus more "interaction" with the sources of the objects, than will areas where field

4

ARCHAEOLOGICAL FLOWS

work is scanty. This can be a particular problem when using site or material den- sity as the interaction variable. Hodder and Orton [12, p. 105] proposed record- ing of "negatives" (contemporaneous sites without the item being studied) to control for variations in field work in- tensity.

2. Variations in the sampling of as- semblages recovered at different sites. In the course of digging a site, some archaeologists select what they will keep on the basis of variable criteria, while others keep everything. If one uses the percentage of pottery produced at a cer- tain kiln that was found at a site as a measure of the intensity of interaction between the kiln and site, anything that is thrown away will influence the "inter- action" value. Also, whatever is dug from a part of a site might not be representa- tive of the entire settlement.

3. Variation in sample size. Hodder and Orton found that pottery samples from Romano-British sites varied from 10 sherds to over 500. Percentages calcu- lated from small samples are unreliable, and raising the minimum size of assem- blages accepted for inclusion in a study raises the consistency of the results, but also means that fewer sites will be in- cluded and information lost.

4. Difficulty of dating collections. Even pottery from historic contexts such as Roman Britain can often only be dated to within - 60 years. An assem- blage representing a period when the production of a given type was abun- dant would tend to have a higher per- centage of that style than another site which represents a period of smaller out- put. The relative abundance of the style at a site could thus be the result of either patterns of production or trade. Without firm dating of the production of the ob- jects and the period of habitation of the site, there is no solution to this problem [12, p. 106].

5. Measurement of interaction. It is simpler to count the items than to weigh them, and IHodder and Orton [12, p.

106] state that if there is no evidence of systematic bias, counts should be used. Wright [33, pp. 172-3] took the opposite view for obsidian studies, stating that obsidian objects get consistently smaller farther from the source of the material, and recommended that weights be used exclusively. The choice rests with the type of material under study and the availability of appropriate data.

None of these problems is trivial, for each could introduce unknown bias into the data. Thus, one should choose data that avoid as many of these problems as possible.

All of the data sets used by Hodder (Table 1) share these problems to some extent, but as mentioned earlier, archae- ologists have usually been interested in the problems of a particular era and re- gion and have taken data applicable to the models that attract them. When the usefulness of a model is in doubt, it's best to seek out data which are as free from bias as possible and where many things about the data and its context are known, so that the behavior predicted by the model can be checked against re- ality.

The new data chosen for the present analysis are the bronze coins minted by Greek cities in the Asiatic parts of the Roman Empire excavated at Dura Euro- pus by the French and American expedi- tions of 1926-1937 [1]. These data offer several advantages:

1. They came from a single site so there is little variation in the standards of field work.

2. Coins are thought to be valuable by all archaeologists so none are thrown away. Some disintegrate, which might introduce bias, but at least this is not the result of the excavator's on-the-spot de- cisions.

3. The sample size (8619 coins) is large.

4. The chronology of the coins (dated by emperor's portraits) is well known. Most coins can be dated within -- 10 years. Since the data used here cover a

5

ECONOMIC GEOGRAPHY

period of about 280 years, we know that the site existed during the entire produc- tion of all the items (1 item = the coins of 1 emperor) except the last (coins of Valerian and Gallienus) which will be excluded from the study.

5. Counts can be used, for coins are discrete units, both to us and to the peo- ple who made them. The range of weight for the bronze issues is relatively small, the largest weighing about 12 times the smallest, and weight does not vary with distance from the site of pro- duction.

6. The value of the bronze in the coins was probably fairly constant, thus the variations in b over time should be the result of changes in either interac- tion conditions or sampling error and not the value of the objects.

7. The provenance of the coins is known, for each coin was minted with the name of the city which issued it.

8. It is possible to estimate the total production of each city's or region's coins by counting the number of each contained in major collections. This is not an exact method, but at least its re- sults can be tested against other data that we have about these places.

9. We know a lot about social and economic conditions of the period, there- fore b should vary in a predictable way [4] and a should remain fairly constant (near 2), since in this case we are deal- ing with a well-developed trading net- work.

A major drawback of this particular data set is that there are no "close in" contacts. Since much of Taylor's [31] discussion of distance transformation concerns short distance interaction, this is unfortunate, but unavoidable.

DATA PREPARATION

Calibrating the parameters under in- vestigation here requires two variables: one representing interaction, the other distance. In the studies by Hodder and Renfrew, interaction between the source

of an object and its destination was mea- sured as a proportion of the objects of a given class (pottery, stone) that came from a particular source (potsherds from the Oxford kilns or obsidian from Cap- padocia). With the Dura material, in- stead of dealing with a single source and many destinations, we have many sources and a single destination. This makes little difference except that we need an estimate of the production of objects at each source. The production estimates used here are the published coin holdings of the British Museum (BMC) [3]. Use of the collection is jus- tified if it is a representative sample of what was actually produced. Since the coins were struck with handmade dies which must have had some rate of wear and breakage [7, pp. 640-707], cities or regions which issued large numbers of coins must have used many dies repre- senting a variety of imperial portraits and reverse types. A large reference col- lection contains selection of types and dies which, if large enough, should be representative of the real production of these places. Listings of all known types (corpi) of the coinages of only 15 of the cities in the Near East have been pub- lished [2; 13; 16; 17; 18; 19; 25; 30]. The advantage of using the BMC as opposed to the corpi, is that it gives nearly com- plete geographic coverage of the Greek coinage; almost every city that produced coins is represented there. The present study covers all the possible sources of the coins recovered at the archaeological site, the coins produced in 359 cities of the Asiatic provinces of the Roman Em- pire between 27 B.C. and 276 A.D.

If the material in the BMC is repre- sentative of what was produced, then there should be a strong positive rela- tionship between the number of types listed in the corpi and the size of the BMC holdings of the same 15 cities. The correspondence should hold over time as well as space, thus the coins in both data sets were grouped into 30 regnal periods and midpoints for each reign

6

to to ° f 0 w

" > > > > o Q £

o O

u b b b P

.

oo 1 Ilium Ca 00

oo 2. Alexandria Troas

c; o 3. Antioch in Pisidia

0o ,- 4. Caesarea Cappadociae

ca o 5. Aelia Capitolina (Jerusalem)

o co 6. Akko-Ptolemais

-4 7. Caesarea Maritima

o' ° 8. Adramytion

c0 o 9. Apollonia

C o 0 10. Attaia

o> 0 11. Hadrianeia

0 o12. Hadrianoi

o 0 13. Hadrianotherai

0 o14. Kame

o 1 15. Priene

SAkO7Ij 7VJ)IOO7O1VHOUV

0

CJ

o

o

-to

01

o

o

o

o

0

0

z

0

tH

0

0

03

00

GO

co

Co

0

0

0

0

to-

o0

Q-

0

00

0

0

0

0

0

Cq

Ca t-i

00

0

oo

co

o

CID

LIZ

Cal

0O

00

TABLE 8

NUMBER OF TYPES, BY PERIOD, LISTED IN THE COIRPI OF 15 CITIES IN THE STUDY AREA*

City

C / 0 M C Xi

10 B.C.-70 A.D. 15" 0 4 6 0 15 19 2 0 0 0 0 0

70-150 A.D. 16 2 24 64 42 12 19 5 28 21 7 18 18 4 1 a

15$0-210 A.D. 110Q 125 171 89 SS 44 5 43 51 85 20 18 20

210-20 AD 13 50 29 104 65 46 4 21 10 5 6 0

.l 0 $c

20-25 AD . 12 42 B150 20 41 29 90 2 12 0 15 7 4 0

2532 A.. - 1 2 , Si 7 6 n14 B 6 B B 8

Period ,-4 (N co 0 i^ c l; o

10B.C.-70A.D. 15 0 4 6 0 15 19 2 0 0 0 0 0 0 4

70-150 A.D. 16 2 24 64 42 12 19 5 28 21 7 18 13 4 16

150-210 A.D. 110 125 171 89 55 44 35 43 51 35 20 18 20 4 4

210-230 A.D. 13 50 29 104 65 46 34 21 10 5 6 5 0 0 3

230-253 A.D. 12 42 130 20 41 29 90 22 12 0 15 7 4 0 6

253-276 A.D. 4 69 127 1 2 43 33 7 6 0 0 6 0 0 8

I Sources listed in brackets after city names.

ARCHAEOLOGICAL FLOWS

were determined. The data were then grouped into six periods of 80, 80, 60, 20, 23, and 23 years (Tables 2 and 3). The data were relatively scanty in the earlier periods, thus longer spans of time were needed to assemble enough coins for a meaningful analysis. The coins of the in- dividual regnal periods were assigned to the six longer periods on the basis of location of the regnal period's midpoint. All non-zero values in the corpi and the corresponding cells in the BMC table were incremented by one and trans- formed to logarithms, for the raw data have the strong positive skew charac- teristic of city-size distributions. Then both raw and transformed data were correlated. There is a fairly strong re- semblance between the BMC and the corpi: r2 : 0.64 for raw data and r2 = 0.72 for transformed data (both signifi- cant at .001 level).

If the number of types is the best available measure of production, it could be argued that it would be better to weed out the duplicates and use the number of types in the BMC as the populations rather than the total number in the collection. This might be true, but given the state of the coins (poor strikes, wear, illegible inscriptions) it is fre- quently impossible to determine whether coins are duplicates. Reference to a corpus would help, but only about 4 percent of the cities listed in the BMC have corpi. Thus, it is not certain how many types are represented. Counting, while perhaps not ideal, is at least re- producible. The same arguments apply to the treatment of the Dura material.

For use as population data the BMC coins from the 359 cities that could be reached by land from Dura (to avoid the noise generated by inclusion of two modes of transport) from the first five periods were grouped into 18 regions. Twelve of the regions included the 353 cities outside Mesopotamia (Figure 1). This was done to control for "negatives" [11, p. 105] (cities that produced coins but which were not represented at

Dura); while we know that Dura re- ceived coins from 58 cities in the region, coins of 301 other cities were not found.

I have done city-by-city analysis else- where [4], but I now find it unsatisfac- tory; while between 17 and 55 cities whose coins were found at Dura were included in the analysis for each period, upwards of 150 cities with interaction values of zero were excluded. Their in- clusion would have resulted in the spec- ification of a variable with no variation in the bulk of its cases, which violates the assumptions of any analytical tech- nique that I am aware of. I think that the solution to the problem is that the coins recovered should be thought of as a sample of all of the coins that Dura could have possibly received from a re- gion rather than from the particular cities whose coins were recovered there. Dura also received a large number of coins from its neighbor cities in Meso- potamia; "negatives" do not exist there, so these cities can be treated as individ- ual cases. Inclusion of individual cities and large regions as cases in the same data set might risk comparison of non- comparable items. I think that individ- ual cities can be treated as small regions. This is similar to studies of interstate flows where small regions dominated by a single city are included in the same analysis with large multicity regions. Disparity in size of regions is probably more of a problem when the flows are being measured by whether or not they cross the boundaries of a set of interact- ing regions. In that situation large re- gions show fewer "migrations" than ex- pected, because many trips can be com- pletely contained within their bound- aries [20]. In the present study only the fact of a coin's arrival at Dura is be- ing measured.

Once the two matrices representing coins retrieved at Dura (Table 4) and the holdings of the BMC (Table 5) were assembled, 0.5 was added to each cell of the BMC matrix where it had a zero but there was a non-zero value in the

9

ECONOMIC GEOGRAPHY

Fig. 1. Source regions and cities for coins found at Dura.

corresponding cell in the Dura matrix. This was to avoid division by zero. Since the data were to be converted to logs, the zero values had to be dealt with. Cells with zeros in both matrices were ignored, for if there was no production in a region during a period, there was no possibility of interaction. However, if no coins of a producing region were recovered at Dura, this is real informa- tion, which cannot be ignored. To create

the interaction table (Table 6), data in Table 5 were divided by corresponding data in Table 6, and then one-half of the minimum non-zero value of each row was substituted for each zero in the new matrix where there was a non-zero value in the corresponding cell of the BMC matrix. This gave a set of "zero" values for each period that was constant and lower than any of the other values.

A vector of distances (Table 6, top

10

TABLE 4

COINS BY SOURCE AND PERIOD FOUND AT DURA

Source region

II III IV V VI VII VIII IX

0 0 0 0 229 1 0 6

0 38 0 8 261 60 40 19

10 1321 3 13 15 6 43 6

1 7 4 12 533 64 7 26

2 2 2 44 416 1 32 0

X

1

0

2

2

0

Source: Bellinger [1].

XI XIH 13 14 15 16 17 18

17 0 0 0 0 0 0 0

2 2 0 1 0 0 0 0

0 0 2 270 203 0 17 0

1 1 0 4 950 922 0 0

0 0 0 299 1788 414 36 381 >

0

0 g0

LI

TABLE 5

COINS I THE BMC BY REGION AND PERIOD

Region

Period I II III IV V VI VII VIII IX X XI XII 13 14 15 16 17

10 B.C.-70 A.D. 361 243 6 23 0 58 2 0 57 4 74 2 0 0 0 0 0

70-150 A.D. 501 257 109 61 23 114 52 59 106 6 388 47 0 0 0 0 0

150-210 A.D. 1173 485 207 107 25 22 42 40 123 27 191 43 2 48 31 0 3

210-230 A.D. 302 190 65 62 16 93 31 5 294 3 125 36 0 5 77 10 6

230-253 A.D. 488 502 29 214 42 51 8 10 59 25 174 19 0 10 49 22 32

Source: British Museum [3].

Period

10 B.C.-70 A.D.

70-150 A.D.

150-210 A.D.

210-230 A.D.

230-253 A.D.

2

0

2

0

0

r

u:

18

0

0

0

0

15

TABLE 6

DISTANCES AND INTERACTION VALUES BETWEEN SOURCE REGIONS AND DURA

Region: I II HI IV V VI VII VIII IX X XI XII

Distance (km.): 1217 927 738 570 379 442 450 365 485 425 602 516

Interaction values:

10 B.C.-70 A.D. .00554 .00277 .00277 .00277 * 3.948 .5 4 .1053 .250 .2297 .00277

70-150 A.D. .00258 .00258 .3486 .00258 .3478 2.290 1.154 .6780 .1972 .00258 .00515 .0426

150-210 A.D. .00170 .0206 6.382 .0280 .520 .6818 .1429 1.075 .0488 .0741 .00085 .00085 0

210-230 A.D. .00263 .00526 .1077 .0645 .750 5.731 2.064 1.400 0.884 .6667 .00800 .0278 z 0

230-253 A.D. .00199 .00398 .0690 .00936 1.048 8.157 .1250 3.200 .00199 .00199 .00199 .00199 g Q

Region:

Distance (km.):

Interaction values:

10 B.C.-70 A.D.

70-150 A.D.

150-210 A.D.

210-230 A.D.

230-253 A.D.

13

819

14

279

a

1.0

at

15

319

*

16

239

17

259

a a

2.0 a

5.625 6.548 a 5.667

.800 1.234 9.220 .00263

29.90 36.490 18.818 1.125

* Cells with zero values in both Tables 4 and 5.

18

202

25.40

25.40

0

0

) O ©l

ARCHAEOLOGICAL FLOWS

row) from the centroid of each source region was measured from the map. Since some regions are large there is some possibility of error. I felt that this was an acceptable trade-off for the re- duction in the number of zeros in Table 4.

Since the bivariate scatter plots of the distance and interaction data showed a high degree of convexity to the origin, I decided to run both single- and double- log least squares regressions. The dou- ble-log model (often called the gravity model) has the form:

log lij = a-b log Dij (7)

This was done because this model prob- ably fits the data more closely than the single-log model, and it would also fa- cilitate comparison of the present study with those employing the gravity model.

RESULTS

The single-log distance decay gradi- ents (Table 7) conform to the hypoth- esis. All of the Dura gradients are smaller than all but one of those derived by Hodder for stone tools and pottery. However, the a values are strikingly dif- ferent than what was expected from a well-developed trading network. Four of the five values are negative and none is greater than one. This result was not predicted by Renfrew's theory, although

the values are clearly not impossible. They suggest a model of the form:

a logI = a-bD

where a is negative. This kind of model would fit a situa-

tion where interaction dropped off very steeply near the source of an article but a small number of them managed to travel a great distance. This would be characteristic of the circulation of na- tional currencies, where the coins of a particular country would be very com- mon within its territory, drop off sharply at the border, and then represented by fewer and fewer strays carried by trav- elers as souvenirs farther away from the border. Although we don't know how people regarded the currency value of these particular coins, it could have been that either through government decree or common practice only the coins of certain nearby cities or regions were ac- cepted as legal money and all others were mere curiosities. The large issues of Pontus (205-207 A.D.) which appear in abundance at Dura and the large number of coins of Gordian III (238- 244 A.D.) from Mesopotamian mints which predominate in Dura's currency at the very end of its existence are evi- dence that the Roman government minted coins to circulate in certain re- gions. Coins apparently also had value as souvenirs. A contingent of Spartan

(8)

TABLE 7

ALPHA VALUES AND REGRESSION RESULTS OF SINGLE- AND DOUBLE-LOG MODELS

Single-log Double-log

a b r2 a b r

.613 -.00617 .336 28.93 -5.041 .416*

- .7 1.041 -.00654

-1.6 1.894 -.00719

.6 2.375 -.00755

.368*

.342*

.394*

- .7 3.374 -.0102 .462*

25.47 -4.494

27.66 -4.789

25.12 -4.336

37.23 -6.397

.4150

.423*

.387*

.590*

* Significant at 0.05 level.

alpha

-5.1

Period

10 B.C.-70 A.D.

70-150 A.D.

150-210 A.D.

210-230 A.D.

230-253 A.D.

13

ECONOMIC GEOGRAPHY

soldiers brought to Dura by Caracalla in 215 A.D. left at least 95 Pelopon- nesian coins that were found at Dura [1, p. 207]. Apparently these soldiers saw some reason to carry their own local money that far.

This "bounded circulation" was not anticipated by Renfrew, but this does not discredit his ideas, it only means that the situation is more complicated than what he had envisioned. Objects such as coins, to which special limited values are attached by society, might move in very different ways than those which are traded on the basis of their utility alone.

In addition to tests of the hypothesis of the overall efficiency of the trade net- work, the Dura material can be used to measure changes in the efficiency of trade over time (Table 7). Only the double-log gradient of the last period is significantly different from any of the others. This indicates a long period of stable conditions of trade with a sharp rise in its apparent difficulty at the end. I think that there are three possible ex- planations for this steepening of the gradient. One is that the political up- heavals of the third century inhibited trade and that the growing weakness of the imperial government prevented it from paying soldiers from distant sources [1, p. 209]. Thus, the frontiers of the Empire were increasingly depen- dent on local sources for their coinage. The second explanation is that the rise in the gradient reflects the speed of movement of the coins. Crawford [6, p. 77] argues that a coin could travel long distances within a year of its issue. This might be useful for the dating of hoards; knowing it for a certainty surely would, but it's probably that each issue of coins went through a cycle: first they were found only near the source, but as time passed the standard radius of their dis- tribution increased and they became in- creasingly common in places far from their source. After a longer period, the coins either wore out, were lost, melted

down, or de-monetized, becoming in- creasingly rare. If we know the final date at which a site was occupied (as we do at Dura), the closer in time to that date that a coin was made, the less time it had to reach Dura before the city was abandoned. In the case of the most re- cent coins, there would only be large numbers of those produced at the near- est mints, but successively earlier issues would show wider distributions of sources. Thus, we would expect the dis- tance decay gradients to get progres- sively steeper toward the end of the site's occupation. The third possibility is that the Roman government might have decided to supply the frontier with coins from mints in the nearby Mesopotamian cities [1, pp. 207-8].

In an attempt to unravel this problem, the last 50 years of Dura's existence were examined in greater detail (Figure 2, Table 8). The gradients do not conform to the expectations (dotted line) of the circulation hypothesis. The peak, ca. 240, could be the result of the presence of large numbers of coins of Gordian III (238-244 A.D.) found at Dura that were minted at nearby cities, which might have made the regression line steeper than it otherwise would have been. This tends to reinforce the "government de- cision" hypothesis. Since there is no clear pattern to indicate that the steeper gradient was the result of the speed of circulation, it is more likely that the change was caused either by worsening economic conditions or by Roman mone- tary policies.

CONCLUSION

Perhaps more questions have been raised than answers given here, but at least two things are clear: that the dis- tance decay gradient appears to work well to determine how efficiently goods were moving and that Renfrew's theories need further elaboration before they will fit much of the available data.

The distance decay gradients fall into

14

220

15 ARCHAEOLOGICAL FLOWS

Single-Log 's -- - Double-Log b's .............. Circulation hypothesis

* Significant observation O Non-Significant Observation

.010

.008

a)

( I

g) .006

-J 0)

c .004

.002

0205 210

N

N1%

240

8 c

6 0 (a)

4

2

0 250

DATE (A.D.)

Fig. 2. Single- and double-log distance decay slopes for coins found at Dura, 205-250 A.D. The dotted line represents the pattern expected in the speed of circulation hypothesis.

Dates Coins of: (A.D.)

Septimius Severus and Family 193-217

Macrinus through Elagabalus 217-222

Severus Alexander 222-235

Maximinus and Gordian III 235-244

Philip through Trebonnianus Gallus 244-253

* Significant at the 0.05 level.

TABLE 8

REGRESSIONS FOR THIRD CENTURY

Single-Log

a b °2

1.538

.942

1.149

2.939

1.301

-.00651

-.00391

-.00642

-.00929

-.00600

.8010

.275*

.268

.452*

.368*

Double-Log

b

25.37

12.24

22.88

34.96

23.19

-4.42

-2.17

-4.08

-6.03

-4.06

.386*

.252*

.326*

.628*

.484*

ECONOMIC GEOGRAPHY

a pattern that is reasonable in light of the history of the Roman Empire. Also they can be used to help distinguish what the cause of a particular change might be. In this case, the speed of cir- culation was not likely to have been the cause of the steepening gradient of the mid-third century, which means that coins probably moved fairly rapidly. Thus, two hypotheses are left as possi- bilities: that government monetary poli- cies or worsening conditions of trade acted to steepen the gradient.

The a values derived here do not fit Renfrew's theory, yet they do fit into a plausible scheme, that of exchange over a boundary. Within the boundary, the goods have a special cultural status, in the case of these coins a monetary value greater than the intrinsic value of the metal they contain. Outside the bound- ary, their value is less, so there was probably a tendency to send them back into the area where they had monetary value. Certainly, modern money works this way. Also, there are many things beside money that have value in specific cultures, whether they are objects used in religious ceremonies or tools that are useful in some economies, but not in others. A set of theories that explains cultural evolution through the move- ment of goods should cover situations where certain classes of goods have cul- ture-specific value.

I should stress that these conclusions are only as firm as the data that they rest upon. Those used here have been stretched about to their limit. For in- stance, it would have been desirable to have finer divisions of time in the first and second centuries, but when this was attempted the abundance of zeros in the data made any meaningful analysis im- possible. Larger data sets are now avail- able; particularly promising is the In- ventory of Greek Coin Hoards [32] which lists approximately 2,400 coin hoards deposited between 600 and 30 B.C., representing the issues of over 600 mints. Analysis of this material is under

way, and hopefully firmer conclusions can be drawn from it.

LITERATURE CITED

1. Bellinger, Alfred R. The Excavations at Dura Europus Final Report Vol. VI: The Coins. New Haven: Yale University, 1949.

2. Bellinger, Alfred R. Troy: The Coins. Princeton: Princeton University Press, 1961.

3. British Museum. A Catalogue of the Greek Coins in the British Museum (London). The following volumes were used for this study: B. V. Head. Caria, Cos, Rhodes, etc. 19 (1897), Lydia 22 (1901), Phrygia 25 (1906); G. F. Hill. Lycia Pamphylia and Pisidia 18 (1897), Lycaonia, Isauria and Cilicia 21 (1900), Phoenicia 26 (1910), Palestine 27 (1914), Arabia, Mesopotamia and Persia 28 (1922); W. Wroth. Pontus, Paphlagonia, Bithynia and the Kingdom of Bosporus 13 (1889), Mysia 14 (1892), Troas, Aeolis and Lesbos 17 (1894), Ga- latia, Cappadocia and Syria 20 (1899).

4. Clark, John R. "Measuring the Ease of Trade with Archaeological Data: An Anal- ysis of Coins Found at Dura Europus in Syria," Professional Geographer, Vol. 30 (1978), pp. 256-63.

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16

ARCHAEOLOGICAL FLOWS

12. Hodder, Ian and Clive Orton. Spatial Anal- ysis in Archaeology. Cambridge: Cam- bridge University Press, 1976.

13. Imhoof-Blumer, F. and Hans von Fritze. Die Antiken Miinzen Mysiens. Berlin: Georg Reimer, 1913.

14. Irwin-Williams, Cynthia. "A Network Model for the Analysis of Prehistoric Trade," Exchange Systems in Prehistory. Edited by T. K. Earle and J. E. Ericson. New York: Academic Press, 1977.

15. Johnson, Gregory A. Local Exchange and Early State Development in Southwestern Iran. Museum of Anthropology, University of Michigan, Anthropological Papers, no. 51, 1973.

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27. Renfrew, Colin. The Emergence of Civili- zation. London: McHaven, 1972.

28. Renfrew, Colin. "Trade and Culture Pro- cess in European Prehistory," Current An- thropology, 10 (1969), pp. 151-69.

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31. Taylor, Peter S. "Distance Transformation and Distance Decay Functions," Geo- graphical Analysis, 3 (1971), pp. 221-38.

32. Thompson, Margaret, Otto Morkholm, and Colin M. Kraay. An Inventory of Greek Coin Hoards. New York: American Numis- matic Society, 1973.

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34. Wright, Henry and Melinda Zeder. "The Simulation of a Linear Exchange System under Equilibrium Conditions," Exchange Systems in Prehistory. Edited by T. K. Earle and J. E. Ericson. New York: Aca- demic Press, 1977.

17