Long-term rhythms in the development of Hawaiian social

stratiﬁcation

Thomas S. Dye

University of Hawai‘iatM



anoa, 735 Bishop St., Suite 315, Honolulu, HI 96813, USA

article info

Article history:

Received 27 February 2016

Received in revised form

12 May 2016

Accepted 13 May 2016

Keywords:

Time-series analysis

Hawai‘i

Bayesian calibration

Social change

Joint posteriors

abstract

The tempo plot, a statistical graphic designed for the archaeological study of rhythms of the long term

that embodies a theory of archaeological evidence for the occurrence of events, is introduced. The

graphic summarizes the tempo of change in the occurrence of archaeological events using the model

states generated by the Markov Chain Monte Carlo routine at the heart of Bayesian calibration software.

Tempo plots are applied to the archaeological record of Hawai‘i to expose rhythms of i) tradition in taro

pond-ﬁeld construction, ii) innovation in temple construction, and iii) fashion in the harvest of branch

coral for use as a religious offering. Rhythms of the long term identify a hitherto unrecognized trans-

formation of religious practice in Hawai‘i, establish temporal coincidence in temple construction in

leeward sections of Maui and Hawai‘i Islands previously described as regionally idiosyncratic, suggest

shallow temporal limits to the use of the direct historical approach in Hawai‘i, and disclose processes at

work in the politic al economy recorded at the time of western Contact.

1. Introduction

Many of the rhythms of life in contact-era Hawai‘i are well

known. The cyclical rhythms imposed by naturedthe daily routine

and the seasonal rounddand those imposed by society as status

transformations through the life cycle are recorded in Hawaiian

traditions and imprinted on modern practices (Chun, 2011; Malo,

1996; Pukui et al., 2001; Handy and Pukui, 1972). Less well

known are rhythms of the long term, the working out of multi-

generational projects of labor and innovation whose details typi-

cally fall outside the scope of Hawaiian traditional accounts, but

whose remains characterize the archaeological record of Hawai‘i.

Like their shorter-term counterparts, rhythms of the long term can

reﬂect cyclical processes or instead be linear, a rhythm theorized to

reﬂect processes of inter-group alliance (Lefebvre, 2004). The study

of rhythms of the long term in Hawai‘i thus complements the long-

standing anthropological investigation into the development of

Hawaiian social complexity, which arguably created “states” or

“archaic states” prior to the advent of sustained Western contact in

CE 1778 (Hommon, 2013, 1976; Kirch, 2010a).

Three factors have slowed archaeological study of rhythms of

the long term in Hawai‘i. Foremost among these is Hawaiian

archaeology’s struggle to establish accurate and precise chronology

(Dye, 2015), which is slowly being resolved by more frequent

application of chronometric hygiene (Dye, 2000; Spriggs and

Anderson, 1993) and Bayesian calibration (Athens et al., 2014;

Dye, 2011). A second factor, closely related to the ﬁrst, is an incli-

nation among Hawaiian archaeologists faced with an uncertain and

changing chronology to privilege social scientiﬁc explanations over

historical ones (Trigger, 1989). Recent book-length treatments of

social stratiﬁcation in Hawai‘i that take a social scientiﬁc stance

posit universal cultural traits, then illustrate them with in-

terpretations of a selective body of oral traditions kept by the

Kamehameha dynasty, which ruled a uniﬁed Hawaiian kingdom

through most of the nineteenth century (Hommon, 2013; Kirch,

2010b). A third factor has to do with the limited tools available to

archaeologists who wish to measure rhythms of the long term. The

“mainstay of time-series analysis of archaeological trends”

(Williams, 2012, 578) is the summed calibrated probability distri-

bution (SCPD). Archaeological practice has shown that interpreta-

tion of an SCPD is complicated by several factors: i) there are

different ways to construct an SCPD that yield different results

(Weninger et al., 2011); ii) their formal statistical meaning is the

probability of the data of one of the events chosen at random,

rather than the probability of the event itself; iii) as typically con-

structed, an SCPD lacks an estimate of uncertainty (cf. Steele, 2010);

iv) much of the structure is due to the

C calibration curve; v) very

E-mail address: tsd@tsdye.com.

Contents lists available at ScienceDirect

Journal of Archaeological Science

journal homepage: http://www.elsevier.com/locate/jas

http://dx.doi.org/10.1016/j.jas.2016.05.006

Journal of Archaeological Science 71 (2016) 1e9

large sample sizes are needed to detect changing frequencies of

events, assuming a Poisson distribution of counts; and vi) the SCPD,

as it is typically constructed, works directly with the dated events

and not with target events of interest (Bayliss et al., 2007; Chiverrell

et al., 2011; Culleton, 2008; Wood, 2015). These factors have

contributed to recommendations that SCPD’s be used in concert

with other measures to check for errors and guide interpretation

(e.g., Williams, 2012).

This paper describes the tempo plot, a statistical graphic

designed for the archaeological study of rhythms of the long term. A

tempo plot summarizes the joint posterior distribution of events

speciﬁed in a chronological model using output from the Markov

Chain Monte Carlo (MCMC) routine at the heart of Bayesian cali-

bration software. It is applied to four chronological data sets from

Hawai‘i that have been calibrated with chronological models that

distinguish dated, reference, and target events (Dean, 1978). Three

distinct trajectories are identiﬁed in the resulting tempo plots and,

as described below, these are interpreted as representing tradition,

innovation, and fashion. Together, the tempo plots measure with

archaeological materials rhythms of long term history in Hawai‘i.

They identify a hitherto unrecognized transformation of religious

practice, establish temporal coincidence in temple construction in

leeward sections of Maui and Hawai‘i Islands, suggest temporal

limits to the use of the direct historical approach in Hawaiian

archaeology, and expose developmental processes in the political

economy recorded at the time of western Contact.

2. Methods and materials

The tempo plot makes use of the raw data produced by the

MCMC procedure at the heart of Bayesian calibration software,

which repeatedly generates parameter values that satisfy the con-

straints speciﬁed by a chronological model. The chronological

model sets out what is known about the relative ages of dated,

reference, and target events (Dean, 1978). This information is

typically drawn from stratigraphic observations, but the model is

general and information on relative ages can come from any source,

including expert opinion, interpretations of oral traditions, etc. The

model-building step is important for the tempo plot because the

events it intends to summarize must all be speciﬁed in the chro-

nological model.

Each call to the MCMC routine produces a set of values that

represent one valid instance of the chronological model. In the

course of a typical calibration, the MCMC routine produces several

hundred thousand of these valid instances, which in the case of a

successful calibration might be thought of as having explored the

state space of the chronological model. The marginal posterior for

an individual event summarizes the several hundred thousand

values assigned to it by the MCMC routine during the calibration

process. A histogram of these values yields the calibrated age

graphic familiar to archaeologists and produced by all of the cali-

bration software applications. In addition to this standard graphic,

calibration software applications also provide ways to investigate

the joint distributions of two events, either by estimating the hiatus

between them or by calculating the probability that one is older

than the other. In these cases, the software compares the several

hundred thousand values assigned to the two values by the MCMC

routine to calculate the appropriate statistic. When more than two

events are of interest, then some applications will calculate an

SCPD, which yields a rather poor estimate of event density. How-

ever, for practical reasons, the software applications do not provide

general sets of tools with which to investigate joint posteriors.

Access to the raw MCMC values is needed for these more special-

ized analyses.

For many years, the Bayesian calibration software applications

popular among archaeologists used the MCMC results internally,

but did not report them. This meant that it was effectively impos-

sible to carry out specialized analyses of three or more joint pos-

teriors. In 2009, the OxCal software package added a function,

MCMC_sample, to write out raw MCMC values, and a similar facility

was added to the BCal software (Buck et al., 1999) sometime later.

Raw MCMC values can also be accessed with the open-source

Chronomodel application (Lanos et al., 2015). These de-

velopments make it possible to investigate arbitrarily complex re-

lations among events speciﬁed in a chronological model.

The tempo plot is one example of a tool designed to investigate

the joint posteriors of multiple events in a chronological model (see

Steele, 2010, for a use of raw MCMC output to estimate event

density). For each instance generated by the MCMC routine, the

tempo plot calculates the cumulative frequency of speciﬁed events

by calculating how many events took place before each date in a

speciﬁed range of dates. The results for each date are then sum-

marized by ﬁnding the mean and standard deviation. The tempo

plot is constructed by plotting three lines, one connecting the

means for each date to show the central tendency of the tempo, and

two others connecting the standard deviations younger and older

than the mean to indicate the dispersion of the data. An R software

routine for calculating the joint posteriors for a tempo plot using

the raw MCMC output from OxCal is presented in the Supporting

Information.

Tempo plots are calculated and constructed for four chrono-

logical data sets from Hawai‘i, including i) estimates of 16 taro

pond-ﬁeld construction events on Moloka‘i, O‘ahu, and Hawai‘i

based on

C dates; ii) estimates of 11 temple construction dates in

the rain-fed agricultural region of Kohala, Hawai‘i based on

dates; iii) estimates of 11 temple construction dates in the rain-fed

agricultural region of Kahikinui, Maui based on

230

Th dates; and iv)

estimates of 46 branch coral harvest events at Kahikinui, Maui

based on

230

Th dates (see Fig. 1).

2.1. Taro pond-ﬁeld construction events

Taro (Colocasia esculenta), a Hawaiian staple native to India and

mainland Southeast Asia and possibly domesticated in the western

Paciﬁc(Coates et al., 1988), was widely cultivated in pond-ﬁelds in

Hawai‘i(Ladefoged et al., 2010). Irrigated facilities for taro pro-

duction are found throughout the Paciﬁc, where they contrast with

rain-fed cultivation of crops such as yams and sweet potatoes

(Barrau, 1965; Kirch, 1994; Spriggs et al., 2012). In Hawai‘i, the

pond-ﬁeld system has been characterized as “a set of artiﬁcially

leveled planting surfaces designed to impound water, sharing a

single water source, and forming a hydraulic unit for the purposes

of irrigation” (Kirch, 1977, 252). Individual pond-ﬁelds are located

in intermittent stream beds, on taluvial slopes, and most commonly

on alluvial terraces where they impound water with an earthen

bund typically faced with a veneer of stones (Earle, 1980; Kirch,

1977; Ladefoged et al., 2010).

Archaeologists in Hawai‘i have dated materials with which to

estimate the construction dates of 16 taro pond-ﬁelds on three

islands. In each case, the dated material was collected from a

context beneath the base of the pond-ﬁeld bund facing. Thus, the

reference event, which is deposition of the dated material at the

collection location, has a disjunct association with the target event,

which is construction of the pond-ﬁeld bund. A disjunct association

ensures that the hiatus between the dated event and reference

eventdthe in-built age that is always present (Waterbolk, 1971)d

lacks the potential to confound the relationship between reference

and target events (Fig. 2).

The ﬁrst project to collect dating material in disjunct association

with the pond-ﬁeld construction event recovered and dated a piece

T.S. Dye / Journal of Archaeological Science 71 (2016) 1e92

of unidentiﬁed charcoal from alluvium underlying a pond-ﬁeld soil

exposed in a stream cut in Anahulu Valley, O‘ahu (Spriggs and

Kirch, 1992, 123). The strategy of isolating charcoal strati-

graphically inferior to a pond-ﬁeld was later applied routinely at

Wailau Valley, Moloka‘i(McElroy, 2012) and in H



alawa Gulch on

Hawai‘i Island (McCoy et al., 2013) where excavations adjacent to

pond-ﬁeld bunds took care to collect materials from beneath a

basal facing stone of the bund and identiﬁed short-lived materials

for dating.

The chronological model used to estimate the age of the pond-

ﬁeld construction event in each case establishes a dry phase that

pre-dates construction of the pond-ﬁeld (Supporting Information).

The dry phase is deﬁned by an early boundary,

dry

, and a late

boundary,

dry

, from which one or more

C dates were determined

on materials collected below the pond-ﬁeld,

dry

. In addition,

dry

is constrained to be later than the date Polynesians discovered and

settled Hawai‘i(Athens et al., 2014). The chronological model can

be expressed algebraically as follows:

pre

post

(1)

dry

(2)

pre

dry

(3)

where: i)

pre

and

pre

are the early and late boundaries of the pre-

Polynesian phase, respectively; ii)

pre

represents the true ages of

the reference events for

C dates conﬁdently assigned to the pre-

discovery phase, which in each case is deposition of the dated

material; iii)

post

and

post

are the early and late boundaries of the

post-discovery phase, respectively; iv)

post

represents the true

ages of the reference events for

C dates conﬁdently assigned to

the post-discovery phase, which in each case is deposition of the

dated material; v) > means “is older than”; and vi)

pre

and

post

represent the date of Polynesian discovery.

The best estimates for the pond-ﬁeld construction dates are the

marginal posterior densities for

dry

(Fig. 3).

2.2. Temple construction events

Two recent investigations provide data on the tempo of temple

construction in leeward locations where rain-fed cultivation of

sweet potatoes was the dominant crop.

Excavations at eleven temples in the leeward Kohala ﬁeld sys-

tem collected short-lived wood charcoal from contexts beneath the

basal stones of the temple structures (McCoy et al., 2011). Here, the

reference event, which is deposition of the dated material at its

collection location, is in disjunct association with the target event,

which is construction of the temple’s stone architectural elements.

The

C dates were subsequently calibrated with a chronological

model similar to the one used for the taro pond-ﬁeld construction

events, which considers the reference event in each case to be a

terminus post quem for temple construction (Dye, 2012). Like the

construction of taro pond-ﬁelds, the temple construction events

are constrained to be later than Polynesian discovery of Hawai‘i, but

Fig. 1. The Hawaiian Islands, showing territorial divisions of the islands and places mentioned in the text.

Fig. 2. Associations and discontinuities in archaeological dating identiﬁed by Dean

(1978). Arrows point from a younger event to an older event. E

¼ target event;

¼ reference event; E

¼ dated event. Note that direct, disparate, and disjunct as-

sociations are distinguished by the relationship of the reference and target events. The

dated event is drawn lower than the target event for the disparate association to

emphasize the possibility that temporal relationships might be confounded due to in-

built age and residuality.

T.S. Dye / Journal of Archaeological Science 71 (2016) 1e9 3

in this case there is the additional constraint that the temple must

have been built before the overthrow of the traditional Hawaiian

religion in 1819 (Kamakau, 1992,219e228). This chronological

model uses (1) and

prelkfs

> AD 1819 (4)

pre

prelkfs

(5)

where: i)

prelkfs

and

prelkfs

are the beginning and end of the pre-

construction phase; and ii)

prelkfs

are the calendar ages of the

date reference events, which in each case is deposition of the dated

material. In this model, the best estimate of the temple construc-

tion date is

prelkfs

(Supporting Information). The Bayesian cali-

bration yields construction date estimates ranging from the early

sixteenth to the early nineteenth century (Fig. 4).

The second project, in the dry Kahikinui lands on Maui Island,

collected and dated pieces of branch coral from architectural ﬁll

contexts at 11 temples identiﬁed by the excavator as “architectur-

ally integral” (Kirch et al., 2015). Here, there is a direct association

between the reference event and the target event, which in both

cases is construction of the architectural element from which the

dated branch coral was collected. The branch coral pieces were

dated with the

230

Th method, which yields precise age de-

terminations with typical errors of less than a decade. A Bayesian

model designed to estimate temple construction dates in Kahikinui

is slightly different than the one used to calibrate the

C dates from

beneath the temples in the leeward Kohala ﬁeld system

(Supporting Information). Because the branch coral pieces were

harvested, they must all be younger than the colonization event.

The model includes (1) and

prekahikinui

> AD 1819 (6)

pre

prekahikinui

(7)

where: i)

prekahikinui

and

prekahikinui

are the beginning and end

of the pre-construction phase; and ii)

prekahikinui

are the calendar

ages of the

230

Th dated reference events, which in each case is

deposition of the branch coral. In this model, the best estimate of

the temple construction date is

prekahikinui

. The Bayesian cali-

bration yields estimates that start in the mid-sixteenth century and

run to the early nineteenth century (Fig. 5).

2.3. Branch coral harvest events

Forty-six

230

Th dates on branch coral pieces chosen for dating to

minimize the hiatus between coral death and harvest (Fig. 6)have

been reported for Maui Island (Kirch et al., 2015, Table 1). The dates

provide a high resolution record of branch coral harvest associated

with ritual offerings on temples from Kahikinui and Kaup



o districts

of Maui Island (Supporting Information). The dates range from CE

1099 ± 8 to CE 1794 ± 4, with most falling between the mid-

sixteenth to seventeenth centuries.

3. Results

Tempo plots for the pond-ﬁeld construction events, coral har-

vests, and temple construction events at the leeward Kohala ﬁeld

system and Kahikinui are shown in Fig. 7. The tempo plot indicates

that pond-ﬁeld construction began early and that new pond-ﬁelds

were added steadily well into the historic period. In contrast,

branch coral harvest on Maui starts early, is practiced frequently

from CE 1550 to 1700, and then declines. The sigmoidal shape of the

branch coral harvest tempo plot contrasts strongly with the linear

shape of pond-ﬁeld construction tempo plot. Finally, construction

of temple foundations in the leeward Kohala ﬁeld system and at

Kahikinui starts latedafter sweet potato was introduced to Eastern

Polynesia from South America (Green, 2005; Yen, 1974), transferred

to Hawai‘i sometime before CE 1290e1430 (Ladefoged et al., 2005),

and procedures for its optimal production were developed (Kagawa

and Vitousek, 2012)dand expands rapidly until the overthrow of

the traditional religion in 1819, when temple construction stopped

throughout the islands.

Fig. 3. Construction date estimates for 16 taro pond-ﬁelds on Moloka‘i (M), O‘ahu (O), and Hawai‘i (H) Islands.

T.S. Dye / Journal of Archaeological Science 71 (2016) 1e94

Uncertainty in the estimates shown in Fig. 7 is directly tied to

sample size and to the underlying uncertainty of the age de-

terminations. This can be seen most clearly in the tempo plot of

branch coral harvest, which summarizes 46 event estimates with

standard deviations mostly less than 10 years. The irregular shape

of the tempo plot of the Kahikinui temple foundations compared to

the smooth tempo plot of the leeward Kohala temple foundations is

due to the relative precision of the

230

Th dates from Kahikinui.

4. Discussion

The tempo plot was designed to contribute to an historical

interpretation of the Hawaiian archaeological past. Like the historic

turn in the human sciences that developed in response to the

universalizing goals of social scientiﬁc research (McDonald, 1996,

1), historicism in Hawaiian archaeology is developing in response

to the neo-evolutionary approach that has dominated Hawaiian

Fig. 4. Construction date estimates for 11 temples in the leeward Kohala ﬁeld system. Source:Dye (2012, 1204).

Fig. 5. Construction date estimates for 11 Kahikinui temples.

T.S. Dye / Journal of Archaeological Science 71 (2016) 1e9 5

archaeology since the rise of the New Archaeology in the 1960’s and

1970’s(Trigger, 1989). The tempo plot is designed to encourage the

acquisition and interpretation of ﬁne-grained chronologies of

change as an antidote to the fuzzy archaeological chronologies

produced by the neo-evolutionists, a circumstance that has argu-

ably led to over-interpretation of traditional historical accounts

(Dye, 2014).

Central to the tempo plot is the event, which is speciﬁed

precisely with a Bayesian chronological model. The event has been

widely disparaged in social scientiﬁc research as idiographic or

unimportant, but historicism’s local scope and embrace of contin-

gency has renewed interest in the analysis and interpretation of

events. There are two main lines of event-based research. Historical

sociologists have a long history of compiling and interpreting event

catalogs to explain social change during times of unrest (Tilly, 2008,

46e54). More recently in anthropology, Marshall Sahlins has

theorized the event as the unit of practice responsible for gener-

ating social change, using historical case studies from Hawai‘i and

Fiji (Sahlins, 1981, 1985, 1991). Sahlins’ ideas have been elaborated

by the political scientist William H. Sewell, Jr (Sewell, 2005) and

this analytic framework is being explored by archaeologists, most of

whom are interested in how material events articulate with the

ideal notion of structure at the center of Sahlins’ and Sewell’s work

(Beck Jr. et al., 2007; Bolender, 2010). In contrast to these studies,

which theorize the role of events in particular pasts, the tempo plot

embodies a theory of the evidence, based on the distinctions

among dated, reference, and target events (Dean, 1978).

Application of the tempo plot to Hawaiian archaeological data

has implications for previous research results and presents an op-

portunity for an interpretation of the long-term rhythms of Ha-

waiian history.

4.1. Implications for previous research

The theory of the evidence embodied in the tempo plot is

important because dating evidence is often misinterpreted in Ha-

waiian archaeology. For example, dates collected from beneath

pond-ﬁeld bunds have sometimes been interpreted as if they

represent vegetation clearance immediately preceding construc-

tion (e.g., McElroy, 2012, 138), but all that can be said with conﬁ-

dence is that materials beneath the bund face are older than the

pond-ﬁeld construction event; the magnitude of the disjunction

can’t be estimated conﬁdently given the evidence. Nevertheless,

the dates from the Wailau pond-ﬁeld systems were calibrated ab-

sent the constraints of a stratigraphic model and the resulting age

estimatesdfor the growth of plants in the region prior to pond-

ﬁeld constructiondhave been interpreted as estimates of con-

struction events (e.g., Kirch, 2010a

, 145). This tactic potentially

yields age estimates for pond-ﬁeld construction that are too old

because there is no guarantee that dated materials are not much

older than the construction event.

Similarly, the tempo plot for temple foundation construction in

the leeward Kohala ﬁeld system can be compared to an ad hoc

interpretation of the dating evidence that postulated an early

chronology that dated two construction events to CE 1474e1522,

four to CE 1522e1647, four to CE 1647e1680, and one subsequent to

CE 1680 (McCoy et al., 2011, 935e936). The conclusion that 10 of the

11 temple foundations were constructed before CE 1680 contrasts

strongly with the tempo plot, which indicates 2e4 construction

events by that time. The decline of temple construction postulated

by the ad hoc chronology, in which only one temple was built be-

tween CE 1680 and 1819, is contraindicated by the tempo plot,

which shows that the pace of temple construction quickened dur-

ing this period.

The theory of the evidence embodied in the tempo plot has

several implications for the chronology of temple construction at

Kahikinui. The Kahikinui dating projects pioneered the

230

Th dating

of branch coral from Hawaiian archaeological sites (Kirch and

Sharp, 2005; Kirch et al., 2015). The lure of

230

Th dating is its pre-

cision; the standard deviation of age estimates is typically less than

a decade and often less than ﬁve years. However, the interpretation

of the initial

230

Th results by Kirch and Sharp (2005) was widely

criticized because seven of the eight dated branch coral pieces were

Fig. 6. A model of potential discontinuities in the process by which branch coral is

introduced to the archaeological record. The nodes indicate events starting with the

death of the branch coral, through its harvest, and deposition at a temple, either as an

offering or a component of the architectural ﬁll. The numbered arcs represent potential

hiatuses in the process. See the text for a full discussion.

Fig. 7. Tempo plots of pond-ﬁeld construction, temple construction at Kahikinui and

the leeward Kohala ﬁeld system, and coral harvest events plotted with 1 s.d. conﬁ-

dence intervals.

T.S. Dye / Journal of Archaeological Science 71 (2016) 1e96

collected from surface contexts that post-date the temple con-

struction event by an unknown interval (Dye, 2010; Kolb, 2006;

Weisler et al., 2005).

Subsequently, another 40

230

Th dates were processed, mostly

from surface contexts but also including 18 from “architecturally

integral” contexts in disjunct association with the construction

event (Fig. 6). The model Kirch et al. (2015) use to interpret these

dates stipulates that a long discontinuity between coral death and

harvest (Fig. 6, hiatus 1) is implausible at Kahikinui where the high

energy marine environment purportedly thins standing dead

corals; this stipulation can be extended to low energy marine en-

vironments because dead coral becomes encrusted with algae fairly

rapidly, and algae encrusted pieces would not be selected for

230

dating. Thus, the dating protocol for selecting pristine coral pieces

ensures that a discontinuity between coral death and harvest is

minimized. Kirch et al. (2015, 171) go on to argue that similarities in

the age distributions of the surface and architecturally integral

corals support a model in which discontinuities between the har-

vest event and deposit of the coral at the temple (Fig. 6, hiatuses 2a

and 2b), discontinuities due to re-deposition of coral offerings

(Fig. 6 , hiatuses 3a and 3b), and discontinuities due to re-deposition

of corals in ﬁll material (Fig. 6, hiatuses 4a and 4b) are also

negligible.

Kirch et al. (2015,172e173) note that a model in which freshly

harvested corals are deposited on or in newly-built temples does

not ﬁt the dating results from KOU temple where: i) a difference of

nearly 300 years separates two architecturally integral coral pieces,

indicating a discontinuity between coral harvest and deposition in

the ﬁll (Fig. 6, hiatuses 2a, 3a, and/or 4a); and ii) ages of surface

corals range over 145 years, indicating a discontinuity between

coral harvest and deposition of offerings (Fig. 6, hiatuses 2b, 3b,

and/or 4b). The poor ﬁt of data to model is treated as an exception

that “demonstrates the complications that can arise with complex,

monumental architecture on a site used over an extended time

period” (Kirch et al., 2015, 173).

However, the KOU site is not the only exception to the model. Six

of the nine other smaller temples from which multiple corals were

dated yielded discontinuities. At the WF-AUW-359 and KIP-330

temples surface corals indicate discontinuities of about 75 and

125 years. At the AUW-9 temple, one of the architecturally integral

dates is 20 years older than the other three, and at LUA-29 two

architecturally integral corals that a site plan (Kirch et al., 2015,173)

shows were part of the smaller, southwest enclosure yielded dates

about 45 years apart. These temples indicate discontinuities be-

tween coral harvest and deposition in the ﬁll (Fig. 6, hiatuses 2a, 3a,

and/or 4a). At the KIP-273 and KIP-306 temples, surface coral is

20e40 years older than architecturally integral coral (Fig. 6, hia-

tuses 2b, 3b, and/or 4b). In these smaller temples, discontinuities

have cumulative effects ca. 20e125 years, an order of magnitude

greater than the

230

Th measurement errors. If the KOU temple is not

exceptional, then the cumulative effect of discontinuities is two

orders of magnitude greater than the

230

Th measurement errors.

Evidence for “a major phase of temple construction in Kahikinui

beginning ca. CE 1550 and continuing until ca. CE 1700” (Kirch et al.,

2015, 166) is not apparent in Fig. 7, which indicates that temple

construction began in the late sixteenth century and continued

steadily through the seventeenth, eighteenth, and early nineteenth

centuries. The purported surge in temple construction in the

sixteenth and seventeenth centuries appears to be an artifact of an

ad hoc method that ignores potential discontinuities in the pro-

cesses by which branch coral is introduced to the archaeological

record (Fig. 6) and that estimates construction events with dispa-

rate target events (Fig. 2). When a plausible theory of the evidence

is applied, there is no credible evidence for a quickening tempo of

temple construction associated with the rulers Pi‘ilani, Kiha-a-

Pi‘ilani, and Kamalalawalu, whom tradition credits with unifying

the districts of the island, a crucial step in state formation (Kirch

et al., 2015, 174).

The theory of the evidence embodied by the tempo plot in-

dicates that

230

Th dates on pieces of branch coral are, instead,

associated with the coral harvest event, when the living or recently

dead coral piece was broken off from the rest of the colony and

removed from the sea. This association is interesting for several

reasons. First, given that the dated corals were selected to minimize

the effect of a discontinuity between coral death and harvest (Fig. 6,

hiatus 1), and thus conﬁdently date human activity, the oldest

dated coral, KOU CS-5a, which yielded an estimate of CE 1099 ± 8,

indicates that Polynesians were in Hawai‘i around the start of the

12th century, about a century earlier than a recent colonization

date estimate (Wilmshurst et al., 2011). Second, at the other end of

the distribution, the youngest branch coral date, KOU-CS-2, on a

piece of coral collected from the surface of the KOU temple, yielded

an age estimate of CE 1794 ± 4. This age estimate indicates that the

practice of harvesting branch coral for deposition at temples

continued to within about a generation of the overthrow of the

traditional religion in 1819, albeit at a much reduced frequency and

likely reduced importance. Third, the tempo plots indicate that the

century and a half when branch coral harvesting was regularly

practiceddfrom the mid sixteenth century to the turn of the

eighteenth centurydcoincides with the early stages of temple

expansion at Kahikinui and the leeward Kohala ﬁeld system. Later

stages in the process of temple expansion were carried out at a time

when branch coral harvesting had declined. When Hawaiian tra-

ditions were recorded in the early nineteenth century, the practice

of depositing branch coral as an offering within the temple was no

longer remembered, but corals were still collected and placed

outside the temple (Malo, 1996, 92, 256). This suggests that reli-

gious practice at the time when Pi‘ilani, Kiha-a-Pi‘ilani, and

Kamalalawalu were unifying the island was one in which the har-

vest of branch coral offerings was important, but that this changed

around the turn of the eighteenth century. Regardless of the precise

nature of the transformation, which might be discovered through

additional archaeological inquiry, the decline of branch coral har-

vest indicates a temporal limit to application of the direct historical

approach to the interpretation of Hawaiian temples. In this case, the

direct historical approach might be useful back to around the

beginning of the eighteenth century, but is problematic for earlier

times.

4.2. Long-term rhythms in Hawaiian history

Tempo plots for taro pond-ﬁeld construction, harvest of branch

coral, and temple construction in rain-fed agricultural regions take

on three different patterns or shapes indicative of distinct rhythms

of the long term. The tempo plot for taro pond-ﬁeld construction

starts early and rises steadily through the sequence. This shape is

indicative of a tradition in much the same sense as this term was

deﬁned by American archaeologists in the 1950’s, as “a (primarily)

temporal continuity represented by persistent conﬁgurations in

single technologies or other systems of related forms” (Willey and

Phillips, 1958, 37). If taro pond-ﬁelds can be considered a single

technology and the long-term practice of their construction a

“persistent conﬁguration,” then the label can be seen to have a

more or less consistent application from the culture-historical

framework of the mid twentieth century through to the practice

and event based framework advocated here. Persistence of the taro

pond-ﬁeld construction tradition implies an extension of cyclical

rhythm in Hawaiian practice, where the impetus for pond-ﬁeld

construction arises at semi-regular intervals to create space for

the cyclical production of taro at the center of Hawaiian practice.

T.S. Dye / Journal of Archaeological Science 71 (2016) 1e9 7

Labeling this pattern a “tradition” ﬁts well with Hawaiian tradi-

tional accounts, which give great value to taro cultivation and

consider the plant a genealogical ancestor of the Hawaiian people.

In contrast to the steadily rising shape of the tempo plot for taro

pond-ﬁeld construction, branch coral harvest starts early, persists

at a low level for several centuries, then rises sharply before

becoming once again infrequent. The shape of this tempo plot is

indicative of a fashion, a practice that comes into and then goes out

of style. Plotted in a different way, the data on branch coral harvest

would produce a battleship-shaped curve indicative of a stylistic, as

opposed to a functional, trait (Dunnell, 1978). Because the rela-

tionship between an offering and its meaning in the ritual is

essentially arbitrary, harvest of branch coral for use in temples is a

prime candidate for a stylistic attribute in this evolutionary sense.

Finally, tempo plots for temple construction at Kahikinui and the

leeward Kohala ﬁeld system exemplify a third pattern. Both plots

start late and rise strongly until CE 1819, when the traditional

religion was overthrown and temple construction ceased. Their late

start and consistent practice over brief spans are indicative of in-

novations, linear rhythms imposed on the more cyclical rhythms of

local life. When Cook arrived in the late eighteenth century, tem-

ples were used by high status men to feast on pork, a food by that

time denied to women and others (Kirch, 2001). Linear rhythms

such as these are “determined by the forms of alliance that human

groups give themselves” (Lefebvre, 2004, 100). In this case, simi-

larities in tempo plots for temple construction on opposite sides of

the ‘Alenuihaha channel reﬂect the quickening pace of marriage

alliances between elite families of Hawai‘i and Maui (Graves et al.,

2010) and a corresponding increase in demand for pigs that

might be used in gift exchanges central to alliance creation and

maintenance (Dye, 2014).

5. Conclusions

Tempo plots are a potentially useful tool for archaeologists

interested in the time-series analysis of trends, and are easily

constructed from the raw MCMC output of Bayesian calibration

software. They provide a framework consisting of a chronological

model, the established methodology of Bayesian calibration, and a

simple descriptive statistical graphic that reveals the rhythm of

events in the long term. The graphic appears able to distinguish at

least three different rhythms. The cyclical rhythms of pond-ﬁeld

construction and use can be characterized as a tradition with

deep roots in Hawaiian culture that was established early and

practiced steadily into the modern era. In contrast, the linear

rhythm of temple construction in the rain-fed agricultural ﬁelds of

leeward Maui and Hawai‘i Islands can be characterized as an

innovation that began late in the traditional Hawaiian period and

continued until the overthrow of the traditional religion in 1819.

This long-term rhythm of temple construction can be divided into

an early period of about a century and a half when it was the fashion

to harvest branch coral and either offer it at temples or incorporate

it in the structural ﬁll, and a later period when branch coral harvest

fell out of fashion in the century leading up to 1819.

Tempo plots shed some light on the development of Contact-era

political economy, which has been investigated primarily by ar-

chaeologists working within a neo-evolutionary framework,

resulting in two recent book-length treatments, both of which rely

heavily on traditional historical accounts and less so on strictly

archaeological data. One of these accounts hypothesizes an early

development of “archaic states” in the seventeenth century (Kirch,

2010a), while the other favors a later development of “states” in the

eighteenth century (Hommon, 2013). Although it is unlikely that

the timing of “archaic state” or “state” formation will be deter-

mined with conﬁdence from the archaeological record, because the

state is an abstract notion that leaves no direct traces, the long-term

rhythms of temple construction and branch coral harvest cast

doubt on the hypothesis of early development. In particular, reli-

gious practices that supported the political aspirations of Hawaiian

kings (Valeri, 1985) developed their Contact era form in the eigh-

teenth century, sometime after harvest of branch coral for temple

offerings went out of fashion.

Analysis of archaeological events with tempo plots encourages

the archaeologist to move beyond the stadial view of cultural

development proposed by neo-evolutionary theory and invites the

theorist to hypothesize state formation as a process with an

archaeological expression, rather than as an event that might be

inferred from traditional accounts (Routledge, 2014). From the

perspective of an historical approach to Hawaiian archaeology,

rhythms of the long-term revealed by the tempo plot, including the

cyclical rhythms of tradition and the linear rhythms of fashion and

innovation, can be interpreted as diachronic strands that contribute

to a multi-stranded cable of explanation, an explanatory form that

distinguished early modern science from the scholastic tradition it

eventually replaced (Peirce, 1868) and is favored by at least one

philosopher who has thought deeply about archaeological expla-

nation (Wylie, 1989).

Acknowledgments

The author thanks: Caitlin Buck for pointing out how joint

posteriors might be used instead of SCPD’s, and for reviewing an

early draft of the R code included in the Supporting Information;

Derek Hamilton for help reﬁning the chronological model for

Polynesian discovery of Hawai‘i; Jeffrey Pantaleo for the opportu-

nity to develop tempo plots in the context of an integrated cultural

resources management plan; Cynthia Hunter for information on

changes to the appearance of branch coral after death; Ray Kidd for

supplying a bibliographic reference in response to a post on the

OxCal mailing list; Andrew Millard for a post on the OxCal mailing

list that helped summarize the statistical drawbacks of SCPD’s;

Christopher Bronk Ramsey for implementation details of the OxCal

MCMC_sample function; Tim Rieth, Rob Hommon, H. David Tuggle,

Jim Bayman, Alex Morrison, and especially Patrick McCoy for

commenting on an early rough draft of the paper and for general

encouragement; and three anonymous reviewers for several

helpful suggestions.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://

dx.doi.org/10.1016/j.jas.2016.05.006.

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