big sites.short time: accumulation rates in archaeological...

Journal of Archaeological Science (2003) 30, 297–316doi:10.1006/jasc.2002.0838

Big Sites—Short Time: Accumulation Rates inArchaeological Sites

Julie K. Stein and Jennie N. Deo

Department of Anthropology, University of Washington, Seattle, WA 98195-3100, U.S.A.

Laura S. Phillips

Archaeology Department, Burke Museum, Seattle, WA 98195-3010, U.S.A.

(Received 10 December 2001, revised manuscript accepted 3 April 2002)

Large, complex archaeological sites are often characterized by only a handful of radiocarbon dates. This practiceencourages indiscriminant dating of sites for the sole purpose of determining age. If a more rigorous dating scheme isemployed and accumulation rates are calculated, otherwise invisible aspects of human behaviour become apparent.Issues central to settlement pattern analysis, such as abandonment and reoccupation events, population fluctuations,building activities, and activity areas are more easily identified when accumulation rates are calculated. In this study,accumulation rates are calculated for seven shell midden sites found in the San Juan Islands, Washington. Thecollections are stored at the Burke Museum of Natural History and Culture, University of Washington, Seattle,Washington. Eighty-two charcoal pieces were selected according to a comprehensive horizontal and vertical samplingregime and radiometrically dated. Accumulation rate calculations suggest that large archaeological sites, like these shellmiddens, do not always represent continuous human occupation characterized by gradual accumulation of material.Rather, these large complex sites accumulated during short-duration occupations that were repeated infrequently in thesame area. This research recommends that numerical accumulation rates be calculated using at least two calculations;the excavation unit accumulation rate and the entire site accumulation rate, and that the excavation unit accumulationrate is the more useful scale for interpreting settlement history. Calculations of these rates focus the multifacetedinteraction between human behaviour and natural processes in a way that qualitative guesses cannot.

� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: ACCUMULATION RATES, SHELL MIDDEN, RADIOCARBON DATING, SETTLEMENTPATTERN, NORTHWEST COAST, GEOARCHAEOLOGY.

H umans occupy their landscape in a dynamicmanner, often altering their spatial organiz-ation and subsistence practices in response to

changes in climate, technology, population size, andother factors that fluctuate through time. Archaeolo-gists seek to unravel this complex story of humanoccupation by examining cultural deposits that accu-mulate sequentially over time. Determining the time-frame of the depositional sequence of cultural deposits,therefore, is intrinsic to any interpretation of pasthuman behaviour on a landscape. An effective tech-nique for analysing that timeframe is to calculate therate of accumulation for the sequence, which requiresthe measurement of ages and thicknesses of thecultural deposits. We suggest a method whereby ar-chaeologists can calculate accumulation rates withinarchaeological sites to better measure the changinguse of a landscape through time and to understandstratigraphically complex deposits.

2970305–4403/03/$-see front matter

Accumulation rates often support behavioural inter-pretations of sites, especially studies of settlementpattern. Settlement pattern research has been import-ant in archaeology since the pioneering efforts ofWilley and Chang (Billman & Feinman, 1999; Chang,1968; Vogt & Leventhal, 1983; Willey, 1956). Settle-ment archaeology was predicated on the assumptionthat sites were occupied during specific time intervals,which in turn were determined by assuming accumu-lations rates. This research continues today (e.g.,Anderson & Gillam, 2000; Clark & Herdrich, 1993;Ford & Fedick, 1992; Hiscock & Hughes, 2001;McWeeney & Kellogg, 2001; Smyth et al., 1995), asdoes the researchers’ dependence on assumptionsconcerning accumulation rates.

Archaeologists determine accumulation rates in oneof two ways: relatively or absolutely. Relative accumu-lation rates (e.g. fast versus slow) are based on fieldobservations and are useful for qualitative research

� 2002 Elsevier Science Ltd. All rights reserved.

298 J. K. Stein et al.

questions that are focused less on settlement dynamicsand more on presence or absence of human occupationand activities occurring at one location. Absoluteaccumulation rates (e.g. 4·5 mm/yr) are based on quan-titative data and are useful for interpreting intensity ofhuman occupation in a certain location and acrossregions. The absolute method is explored in this studyin the context of interpreting stratigraphically complexsites, such as shell middens. The accurate calculation ofabsolute accumulation rates relies on the depth and ageof each sample, and considers factors of precision andaccuracy, sample and site sizes, and potential errors.

This report is not the first publication to considerusing accumulation rate calculations. Archaeologistsconcerned with alluvial, rockshelter and cave contextshave reported previously on calculations of accumula-tion rates (Brown, 1997; Butzer, 1977; Farrand, 1993,2000; Ferring, 1986; Ferring & Peter, 1987; Fullagaret al., 1996; Gladfelter, 1985; Jerardino, 1995;Parkington, 1988; Waters, 1992), as have archaeologistsinvestigating occupational intensity (Edwards, 1992;Morwood, 1981). Ferring (1986) most thoroughlyexplained accumulation rates by radiometrically datingcultural material in Holocene alluvial settings of NorthAmerican. He notes that rapid sedimentation ratesresult in clear distinctions between archaeologicalassemblages, and slow sedimentation rates provide noseparation of artifacts from different occupations. Wehave built upon Ferring’s example by expanding thediscussion to a different depositional context (shellmiddens) and by considering the consequences of calcu-lating rates at both site and unit scales (the term‘‘unit’’, throughout this paper, refers to a rectangularhole excavated by archaeologists). The calculationmethodology, however, is applicable to scholars exca-vating most types of stratigraphically complex sites.

Several archaeologists have recognized the specificneed for shell midden accumulation rate research(Fladmark, 1982; Lyman, 1991; Stein, 1992; Sullivan,1984), but little work has actually been performed onthis front. The research reported here attempts torectify that gap and focuses on large, complex, lateHolocene sites from the North American NorthwestCoast.

Shell middens have a long history of challengingtraditional archaeological methods and interpretationsbecause of their large matrix-to-artifact ratio with themajority of the matrix composed of cultural material(e.g., shell and fire-cracked rock). Researchers whofocus on shell middens have developed methods toextract information about diets, palaeoecology,palaeoshorelines, technology, and depositional andpost-depositional histories (Ambrose, 1967; Claassen,1998; Hall & McNiven 1999; Stein, 1992; Waselkov,1987). Since the 1940s, various scholars on the North-west Coast have attempted to distill the complexstratigraphy of shell middens into a manageable set ofdata using various recovery techniques (e.g., in chrono-logical order: King, 1950; Carlson, 1960; Bryan, 1963;

Borden, 1970; Mitchell, 1971; Abbott, 1972; Burley,1980; Stein, 1986, 1992; Coupland, 1991; Couplandet al., 1993; Stucki, 1993; Cannon, 2000; Erlandson &Moss, 2001). Early in that history, methods includedusing 20 cm arbitrary excavation levels, discarding allbut a small sample of shell, and saving only largesignificantly modified objects. More recently, methodshave changed to emphasize: excavating by layers (suchas facies) to maximize the extraction of complex strati-graphic information relevant to depositional processes,acquiring more radiometric samples rather than relyingonly on cultural phases and estimated ages of artifacttypes, using coring whenever possible, and obtainingstatistically significant sample sizes. Accumulation ratecalculations fit nicely into the methodological rigorthat has become standard in shell midden research, butare seldom-used by researchers in this field.

Our sample of eighty-two dates from shell middensin the San Juan Islands, Washington (Figure 1), fur-thers the relatively recent understanding of shellmidden accumulation dynamics in this area. In the lastdecade, Northwest Coast archaeologists have begun tomove away from equating very deep shell midden siteswith long, continuous human occupation. Sites like theWest Point site in Seattle, Washington, established thatlarge shell middens can accumulate very rapidly andare often accompanied by a complex history ofoccupation and abandonment (Larson & Lewarch,1995). Our results suggest that calculating accumula-tion rates provides archaeologists with a powerful toolto interpret the past.

Calculating Accumulation RatesGeoscientists have determined a way to actually calcu-late a rate of accumulation using numerical values. Onemust determine the radiocarbon age and depth belowsurface of at least two points in the depositionalrecord. The rate of accumulation is calculated bydividing the thickness of the accumulation (in centime-tres) by the duration of the accumulation (in years).The total accumulation is the difference in depths ofthe two samples. The duration of accumulation is thedifference between the mean radiocarbon ages of anytwo samples. This method assumes a constant rate ofsedimentation between the two points.

Figure 2 illustrates this method with a series ofhypothetical accumulation rates. Line A representsan extremely gradual rate of sediment accumulation,graphically represented by zero accumulation.Whether it took place 1000 years ago or 100,000 yearsago, an archaeological site that receives little sedimen-tation except from low-density human occupationmight approximate this extreme profile. Line C indi-cates a very rapid rate of accumulation; a relativelylarge quantity of material deposited over a short periodof time. Graphically, this is depicted as an infinite rate.Behaviourally, it represents a single dumping of a large

Big Sites—Short Time 299

Figure 1. Location of the San Juan Islands, Washington, and archaeological sites mentioned in the text.


amount of material. Sampling can be critical to detectdepositional sequences approaching Line C. Forexample, if only one date is measured at the base of thesequence, then the whole sequence could be misinter-preted as accumulating slowly and continuously fromthat date to the present. When it actually was depositedin one event, very rapidly. Line B corresponds toan intermediate accumulation rate of X cm/yr andrepresents one of many possible accumulation ratesbetween zero and infinity. In reality, most sites will

display a pattern more like Line B than either A or C.And lastly, Line D signifies a negative accumulationrate (�X cm/yr), or simply, erosion and new deposi-tion. Negative rates of accumulation result from trans-port agents moving an object whose date of death isolder than the age of deposition for the whole unit,signaling some kind of disturbance.

Examples from Northwest Coast ShellMiddensCharcoal samples from six archaeological sites in theSan Juan Islands, Washington (Figure 1), were selectedfrom collections owned by the Burke Museum ofNatural History and Culture and the National ParkService. The San Juan Islands are located at theconvergence of the Strait of Juan de Fuca, PugetSound, and the Strait of Georgia, at the borderbetween Canada and the United States. These archivedcollections were chosen because they offered an abun-dance of datable material, comprehensive field notes,and a geographical distribution throughout the SanJuan Islands. The shell middens themselves are locatedon the shorelines of several different islands and collec-tively represent several thousand years of lateHolocene human occupation. The sites include: 45SJ1(Cattle Point), 45SJ24 (English Camp, Operation A),45SJ24 (English Camp, Operation D), 45SJ254(Fisherman Bay), 45SJ278 (Mud Bay), and 45SJ280(Watmough Bay). See Table 1 for site-specificexcavation information.

Figure 2. Hypothetical accumulation rates: radiometric age as afunction of sample depth. Line A models zero accumulation, Line Bmodels a positive accumulation rate, Line C models an infiniteaccumulation rate, and Line D models a negative accumulation rate.

Table 1. Archaeological site information for San Juan Island sites included in this study

Site name Site no. ExcavatorYear

excavated IslandExcavation

intervalsTopomap References

Cattle Point 45SJ1 Arden King 1946 San Juan 13·2 cm (6 in) Figure 3 King, 1950English Camp, Op A 45SJ24 Julie Stein 1983–91 San Juan 3-pt provenience Figure 4 Stein, 1992, 2000English Camp, Op D 45SJ24 Julie Stein 1983–91 San Juan 3-pt provenience Figure 5 Stein, 1992, 2000Fossil Bay 45SJ105 Robert Kidd 1955–56 Sucia 20 cm Figure 6 Kidd, 1971Fisherman Bay 45SJ254 David Munsell 1967–68 Lopez 3-pt provenience N/A Field notebooks, Burke Museum,

Accn. 1997-115Mud Bay 45SJ278 David Munsell 1968 Lopez 20 cm Figure 7 Field notebooks, Burke Museum,

Accn. 1996-121Watmough Bay 45SJ280 David Munsell 1968 Lopez 20 cm Figure 8 Field notebooks, Burke Museum,

Accn. 1996-11

Sampling strategySingle pieces of charcoal were removed from level bagsand field specimens with the goal of maximizing hori-zontal and vertical sampling within each site. Thesamples consisted of burned segments of branch ortwig wood, as identified by palaeoethnobotanist NancyStenholm of Botana Labs, Inc. Beta Analytic Inc.performed the radiometric analysis. When combinedwith Stein’s previously submitted English Campsamples (Stein, 1992), 82 radiometric ages wereincluded in this study.


While shells and bones are ubiquitous in thesearchaeological sites, they were not selected for radio-metric analysis. The problems associated with shellinvolving local marine reservoir effects in the PugetSound/Gulf of Georgia region are being investigatedusing paired charcoal and shell from many of the sitesmentioned in this report (Deo et al., manuscript sub-mitted). Recent research in California indicates thatreservoir age corrections for radiocarbon-datedshell vary not only by region, but also through time(Kennett et al., 1997; Ingram, 1998). Such temporalvariations are a relatively recent discovery and aremost likely based on differences in deep ocean up-welling between regions. Since late Holocene fluctu-ations in Gulf of Georgia reservoir ages are not yetdocumented, shell dates are considered a less reliablesource of chronometric data. Bone in these shell mid-dens is primarily fish, bird, and mammal, all of whichcan lack sufficient collagen to date conventionally. Theexpense of AMS dating was minimized by selectingcharcoal over bone.

DataThe radiocarbon dates are displayed in Table 2,arranged by site and sample number. Many sampleswere too small to undergo conventional analysis andwere therefore selected for extended counting (EC) orAccelerator-Mass Spectrometry (AMS) dating, asnoted. All dates discussed in this text are 2� calibratedresults.

Accumulation rates were computed on two differentscales: entire site and individual excavation units.Calculation of the site accumulation rates (Table 3)entailed plotting all samples from an entire site,according to each sample’s mean 2� calibrated radio-carbon age and mean depth of sample (see Table 2 andFigures 3–8 for results). A regression equationdescribes the most parsimonious relationship betweensamples, and a correlation coefficient (R2) describes thedegree of fit. The slope of the equation represents theaccumulation rate (in cm/yr). The unit accumulationrates were calculated in the same manner (Table 3),with the difference of using only samples within agiven excavation unit. If a unit contained only onedated sample, a unit accumulation rate could not becalculated.

Although the shell middens in our study are notalluvial deposits, we also performed the pairwise cal-culation recommended by Ferring (1986) for com-parison purposes (in Table 3, see ‘‘accumulation rateby pair’’). The results show wildly fluctuating accumu-lation rates within many units. For instance, in 45SJ1,Unit 100–105N, 530–535W, the pairwise accumulationrates are 13·45 cm/100 yr, �65·31 cm/100 yr, and2·49 cm/100 yr. The rates do not provide a clearpattern of deposition over time, but instead provideinsight into specific deposition rates between layers.This is valuable for determining one layer’s accumu-

lation rates, but as the table shows the fluctuations aregreat and appropriate for only questions asked at thescale of layer. If the research questions require a scalelarger than layer, then excavation unit accumulationrates, or site accumulation rates, are more useful.

The correlation coefficient R2 is indicative not nec-essarily of the accumulation dynamics present at thecurrent site, but may be a function of the variety ofscales over which the value was calculated and thesample size used in the calculation. A low R2, whencalculated from the entire site (all excavation units),indicates that there are variable accumulation ratesthroughout the depositional sequence. This rate maybe a result of different intensities of use for differentparts of the site, or may be a function of fluctuatingperiods of sediment accumulation. On the other hand,a low R2, when calculated from individual excavationunits, indicates a non-uniform accumulation ofmaterials between stratigraphic layers but allows cor-relation from excavation unit to unit. The calculationof R2 using two samples will result in a correlationcoefficient equal to ‘‘1·0’’, and is meaningless becauseof its predictable correlation. Therefore, a sampleshould be greater than two to provide conclusiveresults.

45SJ1, Cattle PointCalculations show an overall site accumulation rateof 0·66 cm/100 yr and an R2 of 0·01 (see Table 3and Figure 3). The accumulation rate of this siteapproaches line A in Figure 2 and therefore reflects avery slow accumulation. There is relatively low corre-lation (0·01), compared to other rate calculations inthis study. This pattern, however, is expected sincegreat horizontal distances exist between units.

The individual unit accumulation rates (Figure 3)are greater than the site rate, and are probably moreaccurate in light of their higher correlation coefficients.Unit 105–110N, 15–20W, exhibits a 21·58 cm/100 yrrate, with a R2 of 1·00, since only two samples weredated. Unit 100–105N, 530–535W, accumulated at arate of 6·56 cm/100 yr and had a R2 of 0·66. Therelatively high correlation and inclusion of foursamples lends confidence to the accuracy of the Unit100–105N, 530–535W rate. The horizontal distances ofhundreds of metres between excavation units is prob-ably the cause for the individual unit accumulationrates to be more meaningful than the overall siteaccumulation rate. These widely spaced areas wereconsidered together because they were recorded in 1946as one site and only small amounts of charcoal areavailable in this old collection.

45SJ24, Operation A, English CampEnglish Camp, excavated recently, was considered astwo separate areas within one site. Originally recordedin 1948, the two areas were excavated at different times

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Table 3. Calculated accumulation rates for sites mentioned in text. Accumulation rates by overall site were calculated using all dated samples fromthat site (‘‘accumulation rate by site’’) and are noted in the shaded rows. Accumulation rates by individual units were calculated using all samplesfrom one unit (‘‘accumulation rate by unit’’). Accumulation rates were also calculated between each sample pair (‘‘accumulation rate by samplepair’’). R2 represents the correlation coefficient of the regression equation

Site UnitNumber of

samples Sample IDs

Accumulation rateby pair

(cm/100 yr)

Accumulation rateby site and unit

(cm/100 yr) R2

45SJ1 All 8 0·66 (site) 0·01

45SJ1 105–110N, 15–20W 2 00102 21·58 21·58 1·0000104

45SJ1 100–105N, 530–535W 4 00105 13·45 6·56 0·6600106 �65·3100108 2·4900110

45SJ1 375–380N, 460–465E 1 00111 N/A N/A N/A45SJ1 370–375N, 465–470E 1 00112 N/A N/A N/A

45SJ24—Op A All 20 0·64 (site) 0·01

45SJ24—Op A 294, 270 1 294,270fF#18 N/A N/A N/A45SJ24—Op A 310, 300 5 310,300fB1#1 �10·00 8·68 0·98

310,300fB1#9 5·00310,300fC#7 21·39

310,300fN#25 7·60310,300fR3#4

45SJ24—Op A 310,302 3 310,302fD1#1 80·00 �2·62 1·00310,302fD2#6 �2·52310,302fE1#1

45SJ24—Op A 310, 304 4 310,304fB1#1 3·11 12·31 0·47310,304fD1#5 41·18310,304fD3#6 �13·33310,304f2#26

45SJ24—Op A 310, 306 2 1983#3 206·67 206·67 1·001983#4

45SJ24—Op A 306, 300 4 QL-4153 7·44 10·28 0·93QL-4154 12·50QL-4155 �5·17QL-4156

45SJ24—Op A 306, 302 1 QL-4157 N/A N/A N/A

45SJ24—Op D All 22 5·36 (site) 0·06

45SJ24—Op D 105, 365 3 105B7 8·37 �13·22 0·12105O1 �33·37

105T1C45SJ24—Op D 111, 349 3 111P1 �2·69 17·04 0·55

111W1 19·17111EE2

45SJ24—Op D 123, 347 2 123A5 8·00 8·00 1·00123I1

45SJ24—Op D 130, 352 3 130C1 156·00 53·23 0·76130H1 22·40130K1

45SJ24—Op D TAB 5 TABC1 �50·77 25·01 0·37TABD2 53·57TAB003 �4·08TAB004 7·22TAB007

45SJ24—Op D TCD 1 TCD002 N/A N/A N/A45SJ24—Op D TEF 2 TEF0073 3·75 3·75 1·00

TEF007745SJ24—Op D TGH 3 TGHB3 3·64 �9·31 0·39

TGH008 �11·69TGH009

45SJ105 All 12 1·22 (site) 0·02

Continued on next page


using different strategies and large numbers of datesfor each area were measured. For this study they arecompared separately.

The all unit site accumulation rate of English CampOperation A (Table 3, Figure 4) is relatively low(0·64 cm/100 yr) and is accompanied by a weak corre-lation coefficient. The site rate approximates the LineA model in Figure 2, or a slow accumulation.

Higher rates and much stronger correlations areapparent when individual unit accumulation ratesare calculated, with the exception of Unit 310,302(Figure 4). The high individual unit rates rangefrom 10·28 to 206·67 cm/100 yr, reflecting the Line Baccumulation model (Figure 2). These rates, coupledwith their strong correlations, suggest that this site

accumulated under an intermediate to rapid scheme.The rapid accumulation of Unit 310,306, however, isrepresented by only two samples and may be afunction of inadequate sample size. The exception,Unit 310,302, is interesting in that it reflects a nega-tive accumulation rate similar to the Line D modelin Figure 2. Evidence of erosion in the form of alarge pit is clear in the profile of the unit (seephotograph of pit profile in Stein, 1996, Figure 19).Older charcoal was deposited over younger charcoalas pit fill.

Table 3. Continued

Site UnitNumber of

samples Sample IDs

Accumulation rateby pair

(cm/100 yr)

Accumulation rateby site and unit

(cm/100 yr) R2

45SJ105 2·5N, 5E 3 10501 3·07 4·61 0·7710502 103·2310504

45SJ105 7·5N, 7·5E 4 10506 60·00 �1·37 0·0610507 2·0810508 �2·8910509

45SJ105 2·5N0, 2·5N, 2·5W 5 10510 �11·51 35·04 0·5510511 34·5310513 15·3810514 �266·6710516

45SJ254 All 3 5·46 (site) 0·88

45SJ254 Pit A 3 25401 4·65 5·46 0·8825402 �9·0325403

45SJ278 All 8 3·58 (site) 0·40

45SJ278 3N, 2W 1 27801 N/A N/A N/A45SJ278 15N, 2W 3 27803 6·11 3·37 0·99

27804 3·0827805

45SJ278 21N, 2W 2 27806 58·54 58·54 1·0027809

45SJ278 54N, 0E 1 27810 N/A N/A N/A45SJ278 66N, 0E 1 27811 N/A N/A N/A

45SJ280 All 9 4·14 (site) 0·51

45SJ280 12S, 0E 1 28001 N/A N/A N/A45SJ280 0N, 24W 3 28007 10·00 14·92 0·80

28008 133·3328009

45SJ280 1N, 9W 4 28010 3·91 5·03 0·8928012 �15·5928013 13·8828014

45SJ280 9N, 3W 1 28015 N/A N/A N/A

45SJ24, Operation D, English CampAn all unit site rate for English Camp Operation D of5·36 cm/100 yr is represented by a weak correlation of


0·06 (Table 3, Figure 5). The individual unit rates weregenerally higher and more strongly correlated, exceptfor two units with negative accumulation rates. For themost part, the individual units show intermediate torapid accumulation, as represented by Line B in Figure2. The negative rates in Unit 105,365 and Unit TGHmay again reflect disturbance, but a more likely possi-bility is that the charcoal and other particles accumu-lated so rapidly in these units that the time representedin the counting errors inherent in radiometric agedetermination overlaps the time it took for the depositsto accumulate and cause the negative values. Note thatvery little difference in age is seen among the samples,especially in Unit 105,365.

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Figure 3. 45SJ1, Cattle Point site. Topographic map of the site and location of excavation units, accompanied by accumulation rate data.Graphs show depth below surface versus 2� calibrated radiocarbon age () for (1) all units and (2) individual units. Slopes of regressionequations represent accumulation rates in cm/yr.

45SJ105, Fossil BayA very different impression of cultural materialaccumulation is apparent for the Fossil Bay site whenviewed from site versus unit perspectives (Table 3,

Figure 6). The all unit site accumulation rate is quitelow (1·22 cm/100 yr), similar to the Line A model ofslow accumulation (Figure 2), and exhibits a weakcorrelation of 0·02.

The site contains distinct and widely separatedareas of artifact concentrations (200–300 m), as indi-cated by Kidd’s separation of the areas into Locali-ties A and B. Although recorded as one site,considering these areas separately produces a muchclearer and more accurate picture of the accumula-tion rate. In Locality A, one excavation unit (2·5N,5E) displays a unit accumulation rate similar to theLine B model (Figure 2), an intermediate accumula-tion. The other excavation unit in Locality A (Unit7·5N, 7·5E) approximates Line A in the model(Figure 2), which represents no accumulation toslightly negative accumulation. In Locality B the unitaccumulation rate of 2·5N0, 2·5N, 2·5W is alsosimilar to the Line B model, but reflects a more rapidaccumulation scheme approaching Line C.


45SJ254, Fisherman BayThis site is represented by only three dated samplesfrom one unit, and therefore our calculation serves asboth the all unit site and individual unit rates (Table 3).The accumulation rate is intermediate at 5·46 cm/100 yr and is accompanied by a high correlation (0·88).This site’s accumulation rate is similar to the inter-mediate accumulation of the Line B model (Figure 2).

45SJ278, Mud BayCalculations indicate an all unit site rate of 3·58 cm/100 yr and an intermediate correlation of 0·40 (Table 3,Figure 7). The all unit site rate approximates Line Baccumulations (Figure 2). The individual unit ratessuggest that different accumulation rates characterizethis site, depending on location. Calculations of Unit15N, 2W give an intermediate rate (3·37 cm/100 yr)and high correlation (0·99), while Unit 21N, 2Wreflects a very high rate (58·54 cm/100 yr) and perfectcorrelation (1·00). Considering the low sample size ofUnit 15N, 2W, it is unclear as to whether this high rate

reflects the true accumulation character of this part ofthe site. In this case, the all unit site rate is prob-ably more accurate, as it is almost identical to theaccumulation rate in Unit 15N, 2W.

45SJ280, Watmough BayCalculations reveal an all unit site accumulation rate of4·14 cm/100 yr and a correlation of 0·51 (Table 3,Figure 8). Individual unit rates for Unit 0N, 24W andUnit 1N, 9W are intermediate (14·92 and 5·03, respect-ively) and correlations are very strong (0·80 and 0·89).The high correlations and large sample size supportthe interpretation that Watmough Bay accumulatedaccording to different rates, depending on the loca-tion, but both of the rates conform to a Line B model(Figure 2) of intermediate accumulation.

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Figure 4. 45SJ24, English Camp, Operation A site. Topographic map of the site and location of excavation units, accompanied byaccumulation rate data. Graphs show depth below surface versus 2� calibrated radiocarbon age () for (1) all units and (2) individual units.Slopes of regression equations represent accumulation rates in cm/yr.

Interpreting the CalculationAlthough very few problems are associated with thecalculation of accumulation rates, many factors should


be considered when interpreting the calculation.Specifically, the factors are: (1) size of the deposit beingdated, (2) period of time (duration) over which theaccumulation occurred, (3) number of samples dated,(4) horizontal and vertical distribution of samplesacross the deposit, (5) the date of deposition versusthe actual sample age, and (6) difference betweenconventional C-14 age and calibrated age.

Factor 1—Size of the depositThe size of the deposit under consideration dictateswhether calculating a site accumulation rate or multipleexcavation unit accumulation rates is more appropriate.The sites considered in this research are extremely largeand contain layers of variable thickness. Therefore,individual excavation unit accumulation rate calcu-lations are more appropriate. Unit accumulation ratesdescribe more realistically the intensity of use fordifferent activity areas and provide a progressionof occupation for a given site. For example, at theWatmough Bay site (45SJ280) (Figure 8), the accumu-

lation rates for individual units result in two lines ofunequal slope. But if the outlier sample of very recentage (and shallow depth) is removed and consideredseparately, then three different periods of occupationappear, each of which accumulated very rapidly (steepslopes on regression lines). The earliest occupation isrepresented by the three samples in Unit 1N, 9W,falling in the range of 380 to 5. The nextoccupation is represented by the three samples fromUnit 0N, 24W, falling in the range of 395–890. Thelast occupation is represented by one sample from thetop of Unit 1N, 9W and suggests that people returnedto the location as recently as 1665–1950. The slopesof the lines are not overlapping but are similar insteepness, suggesting that the settlement pattern forthis site was occupation for short periods of timeduring which abundant material accumulated rapidly.

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Figure 5. 45SJ24, English Camp, Operation D site. Topographic map of the site and location of excavation units, accompanied byaccumulation rate data. Graphs show depth below surface versus 2� calibrated radiocarbon age () for (1) all units and (2) individual units.Slopes of regression equations represent accumulation rates in cm/yr.

Factor 2—Period of time (duration) over which theaccumulation occurredThe period of time over which the accumulationoccurred affects the resolution of the accumulation rate


and the interpretations that follow. The settlementpatterns represented in our sites occurred within thelast 1500 to 2500 years. Because these sites were 200 to300 m wide and 2 m thick the duration of time wasshort compared to the size of the deposits. Forexample, in the case of the English Camp site (45SJ24),Operation D (Figure 5), the duration of time overwhich the deposits accumulated was so short that theregression lines produced from the individual unitaccumulation rate calculations were nearly vertical.Our interpretation of this phenomenon is that peoplearrived at the site and quickly deposited over 2 m ofshell midden within a 500-year period, after which theyleft. Previous to these dating results the interpretationwas that the shell had accumulated over much longerperiods of time (Carlson, 1954, 1960). We can imagine,however, smaller sites occupied over longer periodsthat would require different sampling strategies.

Factor 3—Number of samples datedThe number of samples employed in calculatingaccumulation rates affects both the accuracy of the

rates and the interpretations of the meaning of therates. Obviously the larger the sample of radiocarbondates the more accurate the calculation of the rate.Rates based on only two samples give the impressionthat all the deposits over the entire site accumulatedconstantly, which is probably an oversimplificationof the depositional sequence. In this research, an‘‘adequate’’ sample exists when the addition ofanother data point does not change significantly theregression line. Looking at the San Juan Islands data,the Fisherman Bay site samples are too few todescribe conclusively the type of accumulation. BothEnglish Camp Operations, however, have achievedredundancy. Obviously, as the sample size increases,anomalous samples can be more easily identified.

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Figure 6. 45SJ105, Fossil Bay site. Topographic map of the site and location of excavation units, accompanied by accumulation rate data.Graphs show depth below surface versus 2� calibrated radiocarbon age () for (1) all units and (2) individual units. Slopes of regressionequations represent accumulation rates in cm/yr.

Factor 4—Distribution of samplesThe horizontal and vertical distribution of samplesacross the deposits presented the biggest challengeto our ability to make meaningful interpretations. Ratecalculations and subsequent interpretations are


manipulated easily by selecting datable materials fromclustered or unevenly dispersed locations across thesite. We were constrained to the unit locations chosenby the original excavators. At the Fisherman Bay site(45SJ254) the collection from only one unit containedcharcoal sufficient for dating. At English Camp,Operation A (45SJ24), Stein (1992) excavated in aspecific location of the site to test a hypothesis concern-ing sea level fluctuations and dissolution in the ground-water table. If samples are selected from onlythe deepest deposit or the thickest sequence, then theaccumulation rate will not be representative of theentire site, especially if the site is large and the depositsof variable thickness.

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Figure 7. 45SJ278, Mud Bay site. Topographic map of the site and location of excavation units, accompanied by accumulation rate data.Graphs show depth below surface versus 2� calibrated radiocarbon age () for (1) all units and (2) individual units. Slopes of regressionequations represent accumulation rates in cm/yr.

Factor 5—Target date versus sample dateWe considered at least three problems when assessingthe accuracy of the actual date of deposition (targetdate) as compared to the measured radiocarbon age(sample date): (a) sample mixing in a disturbed area,

(b) downward or upward movement of the sampleafter deposition, and (c) death of the sampled organismbefore it was burned or deposited.

(a) A number of processes mix particles and mayintroduce error into the calculations, includingrodents, worms, roots, frost heaving, liquefaction, andsand volcanoes, as well as house posts, hearths, storagepits, trenches, and burials constructed by occupants ofthe site (Wood & Johnson, 1978). These phenomenacan result in older samples being deposited on top ofyounger samples, thereby creating anomalous dates. AtEnglish Camp, Operation A (Figure 4), sample number310,302fE1#1 has an age range of 1500–1730 ,while samples 310,302fD2#6 and 310,302fD1#1 rangebetween 920 to 1300 . The two lower samples areclearly younger than the sample above them and aretherefore anomalous samples. The charcoal in thisexcavated unit was not translocated through the mid-den because there is too much silt and clay to allowmovement over any distance greater than about 1 cm.A better explanation for the anomalous date is the


discovery of a large pit evident in the profile afterexcavation. English Camp, Operation D (Figure 5),also has anomalous dates, as does the Fossil Bay site(Figure 6). We suspect that such anomalies are morecommon in sites that accumulated rapidly, because theerror within the radiometric dating technique overlapsthe experimental error of the radiocarbon technique,and dumping material quickly moves objects of thesame age over large vertical and horizontal distances.

(b) Many kinds of sites contain interconnected porespaces preserved between the large gravel-sized objects,which allow small objects such as charcoal to betranslocated downward (or upward if groundwater can‘‘float’’ them). These pore spaces can fill with air,water, fine-grained sediment, organic matter, orartifacts, and act as conduits for surface water andground water. The shell middens observed duringexcavation have pores filled with silt and clay that clogthe movement of charcoal along these pathways, elimi-nating this problem in our study. But this problem cancause anomalous dates to appear in the data.

(c) In northwestern North America, trees such asWestern red cedar (Thuja plicata) and Douglas fir(Pseudotsuga menziesii) frequently live for 800 to 1000years. The heartwood from these species cannot giveprecise dates for the cutting event, because it stoppedexchanging carbon with the atmosphere long beforethe tree was cut. To prevent the inadvertent datingof old wood, we selected charcoal from only smalltwigs or branches and from only short-lived treespecies.

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Figure 8. 45SJ280, Watmough Bay site. Topographic map of the site and location of excavation units, accompanied by accumulation rate data.Graphs show depth below surface versus 2� calibrated radiocarbon age () for (1) all units and (2) individual units. Slopes of regressionequations represent accumulation rates in cm/yr.

Factor 6—Conventional C-14 age versus calibrated ageThe calculation of accumulation rates compares theage and depth of two or more samples, and requiresthat these ages exist on a linear time scale. Becauseatmospheric C-14 activity has not remained constant inthe past, conventional (uncalibrated) C-14 ages do notreflect a linear measure of time. The calibration curve isrelatively flat at various times in the past and canproduce many possible age intercepts for a single


sample (see CALIB (Stuiver & Reimer, 1993) andOxCal (Bronk Ramsey, 1995)). This flatness results inidentical 2� calibrated date ranges, which when dividedby the depth, suggest instantaneous (very rapid)deposition. For instance, English Camp, Operation A,a unit accumulation rate of 206 cm/100 years wascalculated for Unit 310,306 (Table 3). This rate is anorder of magnitude larger than any other calculatedrate and thus warrants a closer examination. The ratewas calculated from two samples, one from a depth of104 cm and the other from 135 cm, but with similartwo-sigma intercept. The intercept fell on a flat sectionof the radiocarbon calibration curve and therefore thedates of both samples have to be considered equal.They were roughly 30 cm apart in the same 2�2 mexcavation unit, yet result in the same age. Eventhough the intercept includes a 140-year swing inpossible ages, the most logical interpretation for thisdiscovery is that the layer from which they came wasdeposited as one large dumping event. The layer wascharacterized in field notes as containing abundantwhole shells, with boundaries sloping towards thewater. It was interpreted during excavation as an areadifferent from the rest. Now we suspect it accumulatedrapidly relative to the other units of excavation.

DiscussionWhen analysing these data and after consideringfactors that may influence our interpretations, wecompared calculated accumulation rates to the hypo-thetical models shown in Figure 2. Although thenumerical rate calculations are the most powerfuloutcome of the method offered in this report, com-parisons of these numerical values is difficult. Forexample, in Table 3, 22 unit rates are calculated.Interpreting the significance of those rates requirescomparing them to each other using either a statisticalmethod or ranking system. We chose to create ordinalcategories into which each unit and site accumulationrate could be placed, in this case defined by slow,intermediate, and rapid categories. Defining theboundaries of this ordinal scale on the basis of somescientifically reasoned assumptions is problematic,but we offer an explanation that we believe can bedefended with common sense. In this case, we definecategories by considering sedimentation typical of aNorthwest Coast shell midden.

Slow accumulation occurs at a location wherematerial is being deposited at a rate of less than2 cm/100 years. Most of the sites in this study were notolder than 2000 years, and may be closer to 1000 yearsold. That means that, if we assume the older date, asite where material was constantly accumulating ata rate of 2 cm/100 years would have a thickness of40 cm in 2000 years. Under forested conditions inthe Northwest, the upper 40 cm of the biomantle isconstantly mixed by pedoturbation. Material that

accumulated this slowly is mixed in this process and thecharcoal from such deposits would most likely result inanomalous dates.

Intermediate rates of accumulation in NorthwestCoast shell middens occur where material is depositedat a rate higher than 2 cm/100 years and less than50 cm/100 years. Material accumulating at this ratewould be buried before it was mixed. Bioturbationshould not be an overriding cause for disturbance indeposits that accumulated at this rate.

Rapid accumulation occurs when particles aredeposited at a rate higher than 50 cm/100 years. Over aperiod of 2000 years, a location experiencing thisrate would accumulate a thickness of 1000 cm (10 m),assuming a constant rate of accumulation for the entireperiod. A thickness of 10 m is a rather thick shellmidden, even by Northwest Coast standards, andsuch rapid burial would insure the preservation ofcontextual relationships between sediments and layers.

When using these relative terms (slow, intermediate,and rapid) we find that most sites, calculated using allsamples to obtain the site accumulation rate, fell withinthe category of slow to intermediate accumulation. Yetwhen rates were calculated for individual excavationunits within a site, many rates of accumulationincreased. In other words, rates for smaller excavatedareas turned out to be higher than rates for entire sites.Reading top to bottom from Table 3, rates in cm/100years of 22, 7, 9, 12, 10, 17, 8, 53, 25, 4, 5, 35, 6, 3, 59,15, and 5 were found using excavation unit accumula-tion rate calculations (anomalous rates were left out ofthis list). These rates compared to site accumulationrates 1, 1, 5, 1, 6, 4, and 4 cm/100 years, provide a verydifferent view of Northwest Coast middens. Theassumptions of slow accumulation rates previouslypublished (e.g., Mitchell, 1971; Kidd, 1971) have to bereconsidered, as well as the settlement patterns derivedfrom these assumed rates.

We now realize that these sites and areas defined byindividual excavation units did not always accumulateslowly over long periods of time. In Figures 3–8, onecan easily see that deposition began and endedover discreet and short periods of time, approximately500 years in duration. In the sites we sampled, eacharea within the site accumulated at intermediate orrapid rates (for a period less than 500 years), and inmost cases the duration of accumulation in any givenexcavation unit was short.

For example, at the Cattle Point site (Figure 3), Unit105–110N, 15–20W accumulated at a rate of 21·58cm/100 years, starting about 1500 and halting at1000 . At British Camp, Operation D (Figure 5)the calculated rates for most units was intermediate,occurring over a duration of 500 years. At the FossilBay site (Figure 6) the duration of accumulation of oneunit was less than 500 years, another unit was anoma-lous (inverted dates to depth), and another was over aperiod of 1500 years. At the Mud Bay site (Figure 7)Unit 21N, 2W accumulated over less than 500 years,


while the other unit, with one very old date at thebottom, ranged over 2500 years duration. AtWatmough Bay site (Figure 8) one unit accumulatedquickly starting at 1500 and stopping 1250 years ,while another unit accumulated quickly from 2500 to2000 years with an additional depositional eventcapping the unit dating to the last 300 years.

A close examination of these duration data suggeststhat the accumulations longer than 500 years actuallycan be divided into two periods of accumu-lation. The first was a deposition event (deepest),followed by an unconformity (unseen in the profiles),and overlain by a later period of accumulation. Theunconformities were invisible until this dating projectalerted us to its presence. Because others excavatedmany of these sites, and the notes do not contain thenecessary descriptions to look back and identify anunconformable surface, we can only suggest that themultiple occupation scenario is the best interpretation.

Even though we identified periods of accumulation,separated by unconformities, we have not identifiedthe cause of the accumulation and its cessation.We do not know if a few people deposited largequantities of material, or many people depositedsmall quantities, and we cannot assess the reasons forthe absence of deposition for long stretches of time.We know, however, that these calculations are thefirst step in explaining such episodes and they areabsolutely necessary for the next step to reconstructsettlement patterns.

ConclusionsEstimating the accumulation rates of stratigraphicallycomplex sites has led to erroneous conclusions con-cerning occupation history of single locations as well asregional settlement patterns. When accumulation ratesare calculated using radiometric ages and depths, thecomplexity of occupation history can be empiricallyidentified. Most sites are large and contain a variety ofmaterials dropped by people, rivers, wind, and gravity.These materials were not transported to all areas at thesame time or rate, and this inequality of transport canbe calculated using the method of accumulation ratesforwarded in this report. Archaeologists often think ofaccumulation rates in terms other than quantita-tive expressions. They have been taught to interpretaccumulation rates on the basis of qualitative infor-mation, such as evidence of house building, shellfishprocessing, or pit construction. Instead, the calculationof accumulation rates will provide a quantitativedescription of the depositional environment and willlend even more data for subsequent interpretations ofsettlement patterns.

Individual excavation unit accumulation rates as amethod of calculation are recommended in this studyover the calculation of site (all unit) accumulationrates. The calculation is essentially a statistical analysis

of corrected radiocarbon ages and depths for eachexcavation unit and provides a robust measure ofaccumulation. When the area from which the samplesare collected is small (compared to the site as a whole),then discreet differences appear and can lead tostronger interpretations. Complex archaeological sites,such as shell middens, require that accumulation ratesbe calculated on the scale of the individual unit, whichin turn requires more dated samples.

The accumulation rate calculations performed inthis study demonstrate that shell middens in theSan Juan Islands consist of discreet areas wheredeposits accumulated rapidly over short periods oftime (approximately 500 years) followed by longerperiods of abandonment (approximately 1000 years).We can no longer look at a late Holocene shell middenin the Northwest Coast and say with any certainty thatpeople lived at that location for the last 2000 years.These accumulations rates are much higher thanmost archaeologists previously reconstructed, and thedurations of occupation much shorter. Rather thanthinking of these sites as accumulating slowly overlonger periods and continuously occupied, we now candetermine the actual time of deposition for each area ofthe site.

This study suggests to us three final conclusions.(1) Archaeologists need to ask for funding to dateadequately any site excavated. We dated 82 samples,which admittedly represents a large financial invest-ment, but was still inadequate to date all these sites.The time has come to be responsible and analyse thematerial we remove from the ground using the bestpossible procedures. We have the technology to extractquantifiable information about the past, when pre-viously we were forced to estimate. We should ask forall the funds necessary to perform the appropriateanalyses.

(2) Calibration reflects a statistical level of signifi-cance involving a probability. We cannot stress enoughhow important it is to fight the urge to discuss andreport only measured C-14 ages. These numbers arenot calendar years and their use will continue toconfuse rather than help us decipher the chronology ofthe past. Accumulation rates, in particular, are calcu-lated using the probability and precision offered bycalibrated ages.

(3) Many collections of previously excavated sitescontain samples suitable for calculating accumulationrates. They are not, however, being utilized to theirfullest potential. These collections exist in repositoriesand provide a wealth of information to archaeologistswith appropriate research questions. For regions thathave experienced chronological difficulties, a study thatcalculates accumulation rates using dated samplesfrom archived collections could make significantcontributions.

We conclude with the suggestion that calculatingaccumulation rates is appropriate not only forshell middens, but will be especially helpful to


researchers excavating equally complex sequences suchas found in caves and rockshelters, coastal and alluvialsettings, and older sites where significant post-depositional alterations have complicated the depo-sitional sequence. The time for relative derivations ofaccumulation rates is over.

AcknowledgementsWe would like to thank the Burke Museum of NaturalHistory and Culture and the San Juan Island NationalHistoric Park, National Park Service for access to thecollections and data used in this research. Severalundergraduate and graduate students assisted in up-grading the storage of collections courtesy of aRoyalty Research Fund grant from the University ofWashington, especially Chris Schaefer, Tim Allen,Kate Gallagher, and Betsy Scharf. The authors wish tothank Fraser Neiman for setting us down the correctstatistical path.

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