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Towards Radiocarbon Chronology of the Inca State

Anna Adamska (1)
ul. Waliców 20/410
00-851 Warszawa, Poland.
Adam Michczynski
Gliwice Radiocarbon Laboratory
Institute of Physics
Silesian Technical University
ul. Krzywoustego 2
44-100 Gliwice, Poland.


Summary

This paper is intended to consider a problem of possibility of applying the C-14 method application to establish the Inca state chronology. We attempted to find out the time intervals of Inca Imperial Phase and Inca Preimperial Phase and to make rough estimation of time intervals corresponding to periods, when succeeding rulers of The Inca Empire reigned. To this end we applied the composite probability distribution of calibrated radiocarbon dates. Obtained results seems to confirm time intervals established basing on the chronicles.


Introduction

The Inca State chronology, existing till now and widely accepted, was established on the grounds of the historical sources, particularly on the chronicles of Pedro Cieza de Leon (“El Señorio del los Incas” and “La Cronica del Perú”), Juan de Betanzos (“Summa y narración de los Incas”), Bartolome de las Casas (“Apologetica Historia”), and Miguel Cabello de Valboa (“Miscelanea Antarctica”). However this chronology is still an object of controversies between the scholars. The reasons are:
– on the one hand the Inca did not leave us any written sources on this matter.
– on the other hand the signification of the information contained in the chronicles is not clear and univocal.

These controversies may by solved only by independent archaeological methods. In this paper we consider a possibility of application of C-14 method to establish the Inca state chronology.


Chronology of the Inca State

The equivocality of historical sources resulted in the rise of two general chronological conceptions, so called schools. The first one, called historical, treats the information contained in the chronicles, particularly in the Miguel Cabello de Valboa, as a record of Inca history. Assuming that it is complete, the list of Kings cited in them is so consistent that it can be considered to be a good approximation of the Inca past. The scholars belonging to this school agree that Inca history divides into two phases: preimperial (local) and imperial. From it they derived two chronological models. The first one (elaborated by J.H. Rowe) assumed that in the Inca Kingdom was a monarchy, so the rulers form the list of succeding Kings (see Appendix 2). According to the second model, called diarchical, Cuzco was governed simultaneously by two dynasties: one of the Hurin and other of the Hanan Cuzco (see Appendix 2). As a result, the length of the preimperial phase would be shorter by a half in comparison with the first model. However, lack of a sufficient number of ethnological evidences does not permit us to declare in favour of one of these conceptions and it is reasonable to leave the problem of diarchy opened.

The second school, called anthropological (elaborated by R.T. Zuidema, author of the second models cited above), treats the whole Inca history presented in the chronicles up to the Spanish conquest as a myth (Zuidema 1964; 1982). According to it, the chronology should be established independently by archaeology and its methods.

The most widely accepted version of Inca chronology locates the beginnings of their state about 1200 AD (J.H. Rowe 1945; 1963). From 1200 to 1438 AD the Incas were a small tribe, who lived in the neighbourhood of Cuzco. This period is called Preimperial Phase. The Imperial Phase began with the reign of Pachakuti Inca Yupanqui – ca 1438 AD and terminated in 1537–1539 AD with Manco Inca withdrawal to Vilcabamba. This period is commonly considered to be the end of Inca Empire because by then, the whole Inca administration functioned, although the Spaniards controlled the greater part of the empire. Pachacuti Inca Yupanqui spread his empire over the highlands from lake Titicaca in the south to approximately the Junin lake in the north. About 1463 AD, as it is supposed, his son – Topa Inca Yupanqui – was given the command of the army and invaded the area from Quito northwards to Pacacamac in the Central coast of Peru, including the states Cajamarca and Chimu. When Topa Inca came to the throne, he carried on the territorial expansion untill his death about 1493 AD, submitting the west part of contemporary Bolivia, north-west Argentina and Chile and fixing the southern boundary of empire on the Maule (Maipo) river. His successor – Huayna Capac (1493–1528) conquered the northern part of Ecuadorian highlands from Quito to Ancasmayo river. Huascar Inca and Atahuallpa – sons of Huayna Capac – incorporated only small territories (Huascar – Pasto region, Atahuallpa – Chachapoyas).


State of archaeological investigations

The archaeological investigations have been conduced in all Tawantinsuyu territory, but the degree of their advance is different in particular countries that formed ancient Inca Empire. In Ecuador there is a small number of radiocarbon dates coming from Inca sites with good established stratigraphy, because the information comprised in the chronicles has been considered to be sufficient to solve chronological problems. From the territory of Chile, Bolivia and Argentina derive some radiocarbon dates but in general, the investigations are little advanced. Only in Peru the state of archaeological research that includes the application of C-14 method is satisfactory.

It is important to point that a great part of excavations in the Inca sites is focused on the Imperial Phase, because the cultural markers of this phase, contrary to the preimperial one, are well defined. J. H. Rowe indeed set forth the conception to identify the Killke culture with the Inca Preimperial Phase, but there is a lack of sufficient archaeological research with enough good stratigraphy, which could confirm or deny. This theory was built basing on stratigraphy of Sacsayhuaman, one of the most famous Inca sites. In the main site, the Killke ceramic was found under surface level, where it occurred, mixed with Inca classic one. The Killke culture differs from others only in ceramics, whose shapes are intermediate between Tiahuanaco and Inca. However, the architecture pertained to this culture is constructed in the pirca technique. These arguments in our opinion do not seem to be sufficient enough to identify it with Inca Preimperial Phase. We do not know after all, whether main culture belongs in fact to Inca or to another tribe group, living in Cuzco area at the same time. Consequently, if radiocarbon dates come from architecture built in the pirca technique we can doubt if they pertain to Inca or another group. To assume attitude towards this question we need more archaeological research with good stratigraphy.

Moreover it is worth pointing, that the archaeologists writing about cultural attachment of the site “Inca” mean by this “Inca Imperial Phase”, so it is difficult to establish chronology for earlier phase basing on this information only. Besides, we do not know exactly when the artefacts features, characteristics for Inca imperial phase appeared, which would be important for the estimation of radiocarbon dates attachment on the turn of Preimperial Phase.

Another problem is the attachment of a concrete territory to The Inca Empire, basing only on archaeological evidence, because the presence of Inca material could indicate the Inca occupation as well as being a result of trade with an independent tribe. Moreover there are no visual changes in Inca artefacts during the period of expansion, what makes it difficult to distinguish the reign of successive rulers.

Despite these problems we decided to assume in our analysis that the appearance of the artefacts characteristic for Imperial Phase started in beginnings of this phase and the presence of the Inca material indicates their occupation of a precise territory.


Problems of interpretation of calibrated radiocarbon dates

One of the basis of the radiocarbon dating is the fundamental hypothesis that the concentration of 14C at biosphere has remained constant during the past 100,000 years. However, with the increase of the accuracy of dating, it was realised that this hypothesis is not precisely true, and concentration of 14C has been variable during the past. Systematic studies of discrepancies between radiocarbon and calendar dates, based on accurate radiocarbon determinations in dendrochronologically dated tree-ring samples have led to publication of numerous versions of calibration curves and tables. Finally, the high precision calibration curves, accepted by the participants of the 12th International Radiocarbon Conference in Trondheim in 1985, have been published. Since then, the conversion of radiocarbon dates to calendar time-scale has become possible. In 1993 the new, corrected version of calibration curve was published in the special number of the journal “Radiocarbon” (Fig.1). However, practical application of those high-precision calibration curves is not simple. The correspondence between conventional radiocarbon dates and calendar ages is not univocal because of numerous wiggles of calibration curve and in consequence there are several values of calendar age corresponding to a given radiocarbon date. In order to overcome the difficulties caused by multiple intercepts with calibration curve the concept of probabilistic calibration of radiocarbon dates was introduced and developed together with a set of appropriate computer procedures for performing this calibration.

Probabilistic character of a result of radiocarbon measurement is integrally relevant to the nature of radioactive material decay. Due to this nature and random variation during measurement process several concurrent analyses produce statistical spread of obtained radiocarbon dates. The radiocarbon age expressed as a mean and standard error is a convenient summary of this statistical spread assumed to be Gaussian distribution (with familiar “bell-shape”). The idea of probabilistic calibration consists of making a transformation of initial probability distribution of conventional radiocarbon age into final probability distribution of calendar age. After conversion of likelihood distribution of radiocarbon age, using calibration curve, to appropriate probability distribution of calendar age we can obtain various shapes of the latter. The simplest example we may obtain is likelihood distribution of calendar age looking like Gaussian distribution. A more complex example we may obtain is presented in Figure 2. After performing the calibration procedure with e.g. radiocarbon date 710±55 BP (from Pumamarca site) we obtain two clearly separated modes (peaks). We can assume, that we have obtained two possible calendar dates with probability given by the area under each peak. The base for such interpretation is the nature of calibration curve (samples with different calendar dates may give the same result of radiocarbon measurement – same radiocarbon age). In our example we obtained the date about 1290 AD with likelihood 65% and the date about 1370 with likelihood 35%. Unfortunately it is impossible to choose which of them is the real age of sample using radiocarbon data only, but we may do it by using extra information.


Analysis of the gathered dates

Radiocarbon dates analysed below are divided, according to their provenience, into two parts: dates from architecture and dates from artefacts. The dates derive from Peru (43) Chile (2), Argentina (1) and Ecuador (2). All dates were calibrated using the Gliwice Calibration Program GdCALIB ver.6.0 (Pazdur & Michczyñska 1989). The calibration curves used for the calculation were taken from “Radiocarbon” – “Calibration 1993” (Stuiver, Long and Kra, 1993). We decided to calibrate the dates without correction for systematic age difference between northern and southern hemisphere, which was estimated to be about 40 years (Vogel et al., 1993). The value of this correction was obtained for wood samples from South Africa (latitude between 25°S and 35°S). In our opinion that this value may be not valid for almost strictly equatorial region. Figure 3 shows probability distributions obtained as a result of the calibration, whereas a short analysis of these distributions together with analysis of archaeological context are presented below (Table 1, Table 2).


Results

The aim of our work was, to assign length of the Inca Preimperial and Imperial Phase, as well as the length of periods of succeeding Inca rulers reign, by using calibrated radiocarbon dates. The shape of calibration curve concerning XIII-XVI century (Fig. 1.) is satisfactory to make considerations on the Inca State chronology.

The dates from all groups were calibrated using the Gliwice Calibration Program GdCALIB ver.6.0 (Pazdur & Michczynska 1989). The calibration curves used for the calculation were taken from “Radiocarbon” – “Calibration 1993” (Stuiver, Long and Kra, 1993). We calibrated dates without correction for systematic age difference between northern and southern hemisphere. (2) Furthermore all dates were calibrated with analysed interval ±3s wide.

At first we intended to estimate the time-limits of Preimperial Phase and Imperial Phase. Consequently we created two groups of dates. The first group contains dates from samples collected from archaeological context, which can be recognised as Inca Imperial Phase. The dates from samples, which assumably represent Inca Preimperial Phase are included into the second group. We made efforts to assign each date to appropriate group in accordance with archaeological information. Unfortunately a few dates came from the samples which archaeological context was not satisfactorly defined. In spite of this we decided to include these samples to one of the main groups basing on their radiocarbon age. The list of dates derived from two groups is presented in Table 3.

Unfortunately, the analysis of particular calibrated radiocarbon dates did not give expected results because of their low accuracy (Adamska, 1991). Therefore we decided to apply a composite probability distribution (very useful tool in this type of analysis) for all of the dates collected in this paper. Composite probability distribution is obtained simply by summarising the probability distribution of calendar age of samples, belonging to the analysed phase or culture. The likelihood distribution constructed this way gives us information about limits of investigated period.

Figure 4 (the narrowest 95% confidence intervals of the dates included to analysis) shows a visible division of connected radiocarbon dates on two groups. The limit between them is ca. 1440 AD, what is in accordance with historical sources, which locates the beginnings of the Inca Imperial phase in 1438 AD.

The composite probability distributions of calibrated radiocarbon dates for Preimperial and Imperial Phase, obtained as results of calibration of groups presented in Table 3, are shown in Figure 5. The distribution for Preimperial Phase has a shape with highest part between approx. 1275–1425 AD. This part has distinct, steep edges. Two peaks on the top of distribution are caused most likely by the fact, that the calibration curve has wiggles for values of calendar age from interval ca. 1300–1400 AD (the calibration curve is broken up and down there). It is not a straightforward task to decide, which parameters or features of distribution would give the best information about real time-limits of analysed phase. Table 5 shows confidence intervals we consider, that may give good image of reality. There are 68% confidence interval (corresponds with ±1s interval of radiocarbon date), 50% confidence interval, which conforms to conception of the floruit of culture (Ottaway, 1973; Aitchison et al., 1991) and the narrowest 68% confidence interval. The last one gives us intervals of the highest values of probability, which corresponds with ±1s interval of radiocarbon date. After analysis of probability distribution, we may assume, however, that the edges of the highest part correspond very well with limits of Preimperial Phase. Therefore, the best estimation of these limits would be the narrowest 68% confidence interval. We should lay emphasis on good agreement between all intervals for Inca Preimperial Phase presented in Table 5. At the end it would be worth pointing that this group of radiocarbon dates is composed among others of the dates coming from sites with Killke ceramics and architecture built in pirce technique, so it may confirm J.H. Rowe conception.

Interpretation of cumulative probability distribution obtained for dates representing Inca Imperial Phase is more sophisticated. The distribution has three, almost separated peaks with maxima at ca 1325 AD, 1440 AD and 1600 AD, where the second (central) peak is statistically the most important (Fig. 5). This complicated shape of probability distribution is caused by a wiggles of calibration curve, which occur for values of calendar years 1300–1400 AD and 1475–1650 AD (see Fig. 1). Therefore, we have here an example of the same problem as we described above (Fig. 2) – we can assume that we found three possible locations of interval representing Inca Imperial Phase. But we know from reliable historical sources, that the last bastion of the Inca State – Vilcabamba – fell in 1572, so the third peak (ca 1600 AD) falls in colonial period and it can not conform to Inca Imperial Phase. Basing on these irrefutable facts we may remove the third peak from the area our interest. Because the first peak falls rather in Preimperial Phase (and its importance is a little), we may expect, that only the second (central) peak corresponds with Imperial Phase. Consequently an edges of this peak may be assumed as conforming to limits of Inca Imperial Phase.

Table 5 shows 50% confidence interval, 68% confidence interval and the narrowest 68% confidence interval for discussed likelihood distribution. However these intervals apply to whole distribution, whereas the central peak only gives us interesting information. 50% and 68% confidence intervals are therefore inadequate to our purpose. But we may quite well estimate the limits of Inca Imperial Phase using this part of the narrowest 68% confidence interval, which refer to the second peak i.e. 1401–1518 AD.

We attempted to make a rough estimation of the time-intervals corresponding to periods, when succeeding rulers of the Inca Empire had been in authority. Because there do not exist any simple markers, which could indicate each of rulers, we reached a decision, that all dates from territories incorporated by succeeding Incas would be included to one group. Therefore we created four groups of dates listed in Table 4.

Figure 6 shows the composite probability distributions obtained as results of calibration of groups presented in Table 4. Group D was excluded from analysis, because it was composed of two, probably aberrant dates only. Table 6 presents 50% confidence interval, 68% confidence interval and the narrowest 68% confidence interval for these distributions. Unfortunately, we are not able to distinguish, basing on obtained distributions, between periods of succeeding Inca reign. It is mainly due to a too small accuracy of radiocarbon dates included to analysis.


Final remarks

We would like to lay emphasis on fact, that our paper is the first attempt to establish of the Inca state chronology basing on complex analysis of radiocarbon dates, therefore the limits of periods we obtained do not claim to be decisive. Particularly the systematic age difference between northern and southern hemisphere is one of the reasons for doubts. As we mentioned above, the analysis taking into account the correction for age difference, gives intervals presented in Table 5 and 6 shifted about 20–25 years. Therefore we have to assume, that the limits of periods are definite with an accuracy ca 20 years. The intervals obtained with the correction are even in better accordance with historical sources than intervals calculated without the correction. Moreover we realise, that increase of quantity of radiocarbon dates related to well-defined archaeological context and included to the analysis would make the results more reliable. For all that we are of opinion, that from presented results we may draw following conclusions:
– The obtained limits of Inca Imperial Phase seem to confirm limits, which were based on historical sources (the chronicles).
– Inca Preimperial Phase seems to be by our estimation about 120–150 years long.

Results described above clearly show, that the analysis of calibrated radiocarbon dates may be an useful tool for investigation of controversial problems relating to Inca state chronology.


ACKNOWLEDGEMENTS: We are really grateful to J.L.Hollowell, who rendered significant part of archaeological data accessible to us. We would like also to express our appreciation to Mariusz Ziólkowski for intellectual and financial support and his patience.


NOTES
1 Anna Adamska is a graduate of Department of History, Warsaw University. Analysis of archaeological context of radiocarbon dates concerning the Inca State and initial study of probability distributions obtained after calibration were a subject of her master’s thesis.

2 The composite probability distributions obtained by calibration with this correction do not differ considerable from the distributions presented in this paper, so all conclusions would leave unchanged even though the calculation are carried out with the correction. Limits of confidence intervals presented in Table 5 and Table 6 would be shifted in this instance from ca 5 to ca 25 years in the direction of younger dates.


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TABLE 1. Analysis of dates from architecture.

DATES FROM ARCHITECTURE
SI-6987
710±50 BP
Pumamarca, dep. Cuzco, Peru.The sample was collected from wooden lintel of the door. After calibration we obtained two almost separated, equally probable peaks with max. ca 1275 AD and 1375 AD. In A.Kendall opinion this structure belongs to Preinca Phase (Hollowell, personal communication).
BM-924
695±59 BP
Choquepuquio, dep. Cuzco, Peru. The sample was collected from wooden girder of the wall. Lucre and Killke ceramic was found in the same layer. After calibration we obtained two peaks – with max. at 1300 AD (more probable) and 1375 AD – both in accordance with archaeological context (Kendall, 1976; Burleigh et al., 1977; Ziólkowski et al., 1994).
SI-6988A
660±50 BP
Pumamarca, dep. Cuzco, Peru. The sample derived from wooden lintel. After calibration we obtained two peaks – 1300 AD and 1375 AD with similar probability, both indicating Preimperial Phase (Hollowell, personal communication).
UCLA-1676M
660±60 BP
Ancasmarca, dep. Cuzco, Peru. The sample was collected from unknown archaeological context. After calibration we obtained two peaks – 1300 AD and 1375 AD with equal probability – indicating Preimperial Phase (Kendall, 1976; Ziólkowski et al., 1994).
SI-6988B
645±45 BP
Pumamarca, dep. Cuzco, Peru. The sample derived from burned house constructed in the pirca technique. After calibration we obtained two peaks – narrower peak with max. at ca 1300 AD and wider one with max. at ca 1375 AD – both indicating Preimperial Phase (Hollowell, personal communication).
SI-6990
640±55 BP
Kachiquata, dep. Cuzco, Peru. The sample was collected from wooden lintel of building constructed in the pirca technique. This house is situated near the quarry from which derived the material used in construction of Ollantaytambo was extracted. According to explorer (J.L.Hollowell) this building could have been a guardian house. After calibration we obtained two peaks: first peak at ca 1310 AD and second – more wider one – at ca 1360–1380 AD. Lack of more detailed archaeological context (including artefacts) does not permit to declare definitively, which phase the sample belong to (Hollowell, personal communication).
Gx-6833
535±125 BP
Farfan, dep. La Libertad, Peru. The sample derived from store-house, called audiencia – the structure characteristic for Chimu culture. The archaeological comment indicates Inca-Chimu period. After calibration we obtained two significant peaks with max. at 1350 AD and 1425 AD. The second peak is more probable. It might indicate the early Imperial Phase, but it may be also a result of commercial contacts with the Incas, before their expansion. This date was calibrated with 2s calibration range (Keatinge, Conrad, 1983, Ziólkowski et al., 1994).
SI-6989
515±50 BP
Intihuatana, dep. Cuzco, Peru. The sample derived from wooden lintel of house, which was constructed in the pirca technique. In accordance with the opinion of J.L.Hollowell, this structure may be assigned to Pachakuti Inca Yupanqui period. After calibration we obtained two peaks: 1325 AD and 1425 AD. The last one is more probable (Hollowell, personal communication).
BM-930
482±91 BP
Ancasmarca, dep. Cuzco, Peru. The sample was collected from unknown archaeological context. After calibration we obtained three peaks – 1325 AD, 1440 AD (the most probable) and 1610 AD (Kendall, 1976; Burleigh et al., 1977; Ziólkowski et al., 1994).
WIS-1939
480±60 BP
Cerro Azul, dep. Lima, Peru. The sample derived from mud-walled compound. In accordance with the archaeological comment, this site was abandoned following Inca conquest. After calibration we obtained three peaks – 1325 AD, 1440 AD and 1610 AD. The second peak is significantly more probable than the other ones (Marcus, 1987; Steventon, Kutzball, 1985; Ziólkowski et al., 1994).
UCLA-1676D
475±60 BP
Canamarca, dep. Cuzco, Peru. The sample was collected from trapezoidal niche. After calibration we obtained three peaks: 1325 AD, 1440 AD and 1610 AD. Only the second peak is important, what is in accordance with archaeological context (characteristic for Imperial Phase, trapezoidal niche; lack of colonial material) (Kendall, 1976; Ziólkowski et al., 1994).
SI-6991A
470±70 BP
Ollantaytambo, dep. Cuzco, Peru. The sample was collected from wooden lintel of window. The house was built in the pirca technique. After calibration we obtained three peaks – ca. 1340 AD, 1440 AD and 1610 AD. The second peak is significantly more probable than the other ones (Hollowell, personal communication).
Gx-6829
450±120 BP
Farfan, dep. La Libertad, Peru. The sample derived from wooden post found in adobe wall. This site was occupied in Imperial-Chimu and Chimu-Inca periods. After calibration we obtained three peaks at 1325 AD, 1440 AD and 1625 AD. The second and third peaks have similar probability, whereas the first one is significantly less probable. Therefore the second peak seems to be relevant to the context, however lack of information about existence of cultural markers (e.g. Chimu, Inca or colonial ceramic) does not permit to solve this problem definitively. This date was calibrated with 2s calibration range (Keatinge, Conrad, 1983, Ziólkowski et al., 1994).
BM-925
425±67 BP
Canaraccay, dep. Cuzco, Peru. The sample was collected from niche lintel made of plaiting cane. After calibration we obtained two peaks: 1475 AD and 1610 AD. The first peak is statistically more significant than the second one and seems to be relevant to archaeological context (there is not information about existence of any colonial material) (Kendall, 1976; Burleigh et al., 1977; Ziólkowski et al., 1994).
UCLA-1676B
415±60 BP
Tunasmocco, dep. Cuzco, Peru. The sample derived from window lintel of Inca structure. After calibration we obtained two peaks – 1450 AD and 1610 AD. The first peak is more probable and seems to be relevant with archaeological context (Inca structure, lack of colonial material) (Kendall, 1976; Ziólkowski et al., 1994).
SI-6991B
390±100 BP
Ollantaytambo, dep. Cuzco, Peru. The sample was collected from a hearth situated in Fortress in association with non-Inca brown ceramic. After calibration we obtained two peaks: 1475 AD and 1610 AD with equal probability. This date was calibrated with 2s calibration range (Hollowell, personal communication).
ISGS-545
370±80 BP
Qata Casallacta, dep. Cuzco, Peru. The sample derived from layer connected with the floor of Inca structure. After calibration we obtained two peaks at ca 1500 AD and 1610 AD with equal probability. Lack of colonial material indicates rather Inca Imperial Phase than colonial period. This date was calibrated with 2s calibration range (Li Liu et al., 1986; Ziólkowski et al., 1994).
Beta-22437
370±60 BP
San Antonio, dep. Moquegua, Peru. The sample was collected from Structure 20 in association with Inca pottery. After calibration we obtained two peaks – 1500 AD and 1600 AD with equal probability. This date was calibrated with 2s calibration range (Stanish, Rice, 1989; Conrad, Webster, 1989; Ziólkowski et al., 1994).
UCLA-1676A
365±60 BP
Patallacta, dep. Cuzco, Peru. The sample derived from window lintel of Inca structure. After calibration we obtained two peaks – 1500 AD and 1610 AD with equal probability. Lack of colonial material indicates rather Inca Imperial Phase than colonial period (Kendall, 1976; Ziólkowski et al., 1994).
UCLA-1676K
365±60 BP
Yucay, dep. Cuzco, Peru. The sample was collected from window lintel if Inca structure. After calibration we obtained two peaks: 1500 AD and 1610 AD with equal probability. Lack of colonial material suggest Inca Imperial Phase (Kendall, 1976; Ziólkowski et al., 1994).
BM-929
307±41 BP
Urco, dep. Cuzco, Peru. The sample derived from niche of the building on the rock. After calibration we obtained two peaks: 1530 AD and 1650 AD with equal probability. Lack of information about existence of colonial material indicates rather Inca Imperial Phase than colonial period (Kendall, 1976; Burleigh et al., 1977; Ziólkowski et al., 1994).
BM-931
294±54
Ollantaytambo, dep. Cuzco, Peru. The sample derived from window lintel of Inca building. After calibration we obtained two peaks – at ca 1530 AD and ca 1650 AD. The first peak seems to be in accordance with archaeological context (lack of colonial material, information that the sample comes from Inca house – Inca Imperial Phase). This date was calibrated with 2s calibration range (Kendall, 1976; Burleigh et al., 1977; Ziólkowski et al., 1994).


TABLE 2. Analysis of dates from artefacts.

DATES FROM ARTEFACTS
L-123b
900±150 BP
Pachacamac, dep. Lima, Peru. The sample was collected from rubbish in association with Inca ceramic, situated out of the Templo del Sol. The probability distribution obtained as a result of calibration is very flat, what is a consequence of small precision of the date (50% confidence interval of this date: 1038–1213 AD). Additionally the archaeological context is unclear, so it is possible that the sample derived from layer with mixed material or the rubbish could be utilised during long period. Concluding, this date indicates rather Preimperial than Imperial Phase (Ravines, Alvarez Sauri, 1967; Ravines,1982; Ziólkowski et al., 1994).
Hv-350
740±50 BP
Cancay, dep. Lima, Peru. The sample was collected from Inca mummy bundle. After calibration we obtained two peaks: 1280 AD and 1375 AD. The first peak is statistically more significant (Geyh, Schneekloth, 1964; Ziólkowski et al., 1994).
I-1479
700±120 BP
Chilca, dep. Lima, Peru. The sample derived from layer, which Inca ceramic was found in together with Post-Tiahuanaco textiles (Tambo II). After calibration we obtained two wide peaks at 1280 AD and 1370 AD with equal probability (Ravines, Alvarez Sauri, 1967; Ravines, 1982; Ziólkowski et al., 1994).
CSIC-322
690±80 BP
Inga Pirca, prov. Canar, Ecuador. The sample was collected from house F in association with Inca pottery, but there was mixed material in this layer. After calibration we obtained two peaks – 1300 AD and 1370 AD (Ravines, Alvarez Sauri, 1967; Ravines,1982; Fresco, 1984; Alcina, Franch, 1981; Ziólkowski et al., 1994).
P-1846
630±40 BP
Quebrada Honda, dep. Arequipa, Peru. The sample was collected from level with Inca ceramic, however not far from this site Nazca terraces were found. The probability distribution of calibrated age has three peaks – at ca. 1310 AD, 1350 AD and 1380 AD with equal probability. It seems that this date comes from mixed context, but theoretically it could be a result of early contact with Inca State (Ravines, Alvarez Sauri, 1967; Ravines, 1982; Lawn, 1974; Ziólkowski et al., 1994).
UCLA-2538A
595±105 BP
Machu Picchu, dep. Cuzco, Peru. The sample was collected from Citadel ruins. According to the historical sources this structure was built during Pachakuti Inca Yupanqui and Top Inca Yupanqui reign. After calibration we obtained two peaks: 1325 AD and 1400 AD with equal probability (Berger et al., 1988; Ziólkowski et al., 1994).
Tx-2006
580±100 BP
Huancayo Alto, dep. Lima, Peru. The sample derived from unknown archaeological context, but Inca architecture and ceramic occurred in this site. After calibration we obtained two peaks – 1325 AD and 1400 AD with equal probability (Vlastro et al., 1978; Ziólkowski et al., 1994).
Gak-108
554±70 BP
Churajon, dep. Arequipa, Peru. The sample was collected from unknown archaeological context. This site was occupied during Inca Period. After calibration we obtained two peaks at ca. 1325 AD and 1410 AD. The second peak is statistically more probable (Ravines, Alvarez Sauri, 1967; Ravines, 1982; Ziólkowski et al., 1994).
CSIC-335
550±60 BP
Inga Pirca, prov. Canar, Ecuador. The sample was collected from area near the Inca building. From archaeological comment appear that Inca pottery mixed with local one were found on surface. After calibration we obtained two peaks – 1325 AD and 1410 AD (statistically more probable) (Ravines, Alvarez Sauri, 1967; Ravines,1982; Fresco, 1984; Alcina, Franch, 1981; Ziólkowski et al., 1994).
Tk-93
530±80 BP
Ancash, dep. Lima, Peru. The sample was collected from textiles and gourd debris, found in a tomb. According to investigator’s comment main grave pertained to Inca culture. After calibration we obtained three peaks: 1340 AD, 1412 AD and 1620 AD. The second peak is the most probable and refers to archaeological context (Inca grave, lack of colonial material) (Kobayash et al., 1974; Ziólkowski et al., 1994).
WIS-1937
520±70 BP
Cerro Azul, dep. Lima, Peru. The sample derived from pile of corn-cob, which was left when building was abandoned following Inca conquest. After calibration we obtained two peaks – 1330 AD and 1420 AD. The second peak is more probable (Marcus, 1987; Steventon, Kutzball, 1985; Ziólkowski et al., 1994) .
UCTL-281
510±60 BP
Cerro Grande Compania, Chile. The sample derived from Inca Fortress, where Inca Imperial and Inca Local ceramic were found. After calibration we obtained peaks at ca. 1330 AD and 1430 AD. The second peak i statistically more significant (Dillehay, 1992).
L-123C
500±120 BP
Pachacamac, dep. Lima, Peru. The sample was collected from llama skin. The Inca ceramic was found in the same layer. After calibration we obtained three peaks: 1325 AD, 1425 AD (statistically the most probable) and 1610 AD. This date was calibrated with 2s calibration range (Ravines, Alvarez Sauri, 1967; Ravines, 1982; Ziólkowski et al., 1994).
Tk-193
500±70 BP
La Pampa, dep. Ancash, Peru. The sample was collected from the inside of arrybalus in Inca Local style. After calibration we obtained three peaks: 1325 AD, 1435 AD (statistically the most probable) and 1610 AD (Kobayash et al., 1974; Ziólkowski et al., 1994).
I-1482
485±70 BP
La Centinela, dep. Lima, Peru. The sample derived from level with Inca-Cuzco ceramic. After calibration we obtained three peaks – 1325 AD, 1440 AD (the most probable) and 1610 AD. This date was calibrated with 2s calibration range (Engel, 1966; Ziólkowski et al., 1994).
MC-2352
480±70 BP
Patamarca, dep. Junin, Peru. The sample derived from level with Inca pottery. After calibration we obtained three peaks with max. at ca. 1325 D, 1430 AD and 1610 AD. The second peak is statistically the most significant (the third is negligible), what is in accordance with archaeological comment (presence of Inca ceramic, lack of colonial material) (Bonnier, Rozenberg, 1982; Ziólkowski et al., 1994).
UGa-4662
475±65 BP
Santa Barbara, dep. Cajamarca, Peru. The sample derived from site with store-house system, called colqa. After calibration we obtained three peaks , but only the second peak – 1440 AD is statistically important (Chiswell, 1986; Ziólkowski et al., 1994).
UCTL-229
460±45 BP
Cerro Grande, de la Compania, Chile. The sample was collected from Inca fortress, where Inca Cuzco and Inca Local ceramic were found. After calibration we obtained two peaks – 1440 AD and 1610 AD, but the second peak is statistically unimportant (Dillehay, 1992).
WIS-1936
420±70 BP
Cerro Azul, dep. Lima, Peru. The sample was collected from a pit with maize. The site was abandoned following Inca conquest during Pachakuti Inca Yupanqui reign. After calibration we obtained two peaks: 1460 AD and 1610 AD with equal probability. The site description would indicate the first peak, because there is any evidence of presence of colonial material (Marcus, 1987; Steventon, Kutzball, 1985; Ziólkowski et al., 1994).
I-1476
400±100 BP
Rupashca Wasi, dep. Lima, Peru. The sample was collected from layer with Inca and Local brown ceramic. After calibration we obtained two peaks – 1450 AD and 1610 AD with equal probability. This date was calibrated with 2s calibration range (Ravines, Alvarez Sauri, 1967; Ravines,1982; Ziólkowski et al., 1994).
UGa-4661
395±75 BP
Santa Barbara, dep. Cajamarca, Peru. The sample was collected from unknown archaeological context but there were storehouse – qolqa in this state. After calibration we obtained two peaks at ca. 1460 AD and 1610 AD with equal probability. Lack of colonial material and presence of typical for Inca Imperial Phase storehouse (qolqa) would indicate the first peak (Chiswell, 1986; Ziólkowski et al., 1994).
UCLA-2538F
390±40 BP
Machu Picchu, dep. Cuzco, Peru. The sample derive from Citadel ruins (61–70 cm level) where Inca Imperial ceramic were found. After calibration we obtained two peaks – 1470 AD (more probable) and 1610 AD (Berger et al., 1988; Ziólkowski et al., 1994).
UCLA-2538E
380±40 BP
Machu Picchu, dep. Cuzco, Peru. The sample derive from Citadel ruins (61–70 cm level) where Inca Imperial ceramic were found. After calibration we obtained two peaks – 1470 AD and 1610 AD with equal probability (Berger et al., 1988; Ziólkowski et al., 1994).
KN-2622
350±50 BP
Quebrada de Moca, dep. Arequipa, Peru. The sample was collected from passage between two houses, not far from the Inca road. After calibration we obtained two peaks – 1500 AD and 1625 AD with equal probability (Trimborn, 1988; Ziólkowski et al., 1994).
AC-0331
350±50 BP
Cerro Mercedario, prov. San Juan, Argentina. The sample derived from partially burned wood collected from a room, where Inca ceramic were found. After calibration we obtained two peaks 1500 AD and 1600 AD with equal probability. This date was calibrated with 2s calibration range (Alberto, Angiolini, 1985).
HAM-621
300±80 BP
Quebrada de la Vaca, dep. Arequipa, Peru. The sample was collected from storehouse – qolqa (No 7). The probability distribution obtained in consequence of calibration is very flat and gives the same value of probability for interval 1450–1650 AD. This date was calibrated with 2s calibration range (Trimborn, 1988; Ziólkowski et al., 1994).


TABLE 3. List of radiocarbon dates representing Inca Imperial Phase and Inca Preimperial Phase included to analysis.

IMPERIAL PHASE
No.
Sample name
lab. code
C-14 age
conv. y BP
1 Patayacta Urubamba UCLA-1676a 365±60
2 Tunasmocco UCLA-1676b 415±60
3 Canamarca UCLA-1676d 475±60
4 Yucay UCLA-1676k 365±60
5 Canaracay BM-925 425±67
6 Urco J BM-929 307±41
7 Ancas Marca BM -930 482±91
8 Patamarca MC-2852 480±70
9 La Pampa TK-198 500±70
10 Quebrada de Moca KN-2622 350±50
11 Ollantaytambo SI-6991A 470±70
12 Ancon TK-93 530±80
13 Cerro Santa Barbara UGa-4661 395±75
14 Cerro Santa Barbara UGa-4662 475±65
15 Cerro Azul WIS-1936 420±70
16 Cerro Azul WIS-1939 480±60
17 Machu Picchu UCLA-2538e 380±40
18 Machu Picchu UCLA-2538a 595±105
19 Machu Picchu UCLA-2538f 390±40
20 Cerro Grande UCTL-281 510±60
21 Cerro Grande UCTL-229 460±45
22 Huancayo Alto TX-2006 580±100
23 Batan Grande Beta-2591 450±60
24 Cerro Azul WIS-1987 520±70
PREIMPERIAL PHASE
No.
Sample name
lab. code
C-14 age
conv. y BP
1 Ancas Marca UCLA-1676m 660±60
2 Choquepuquio BM-924 695±59
3 Chilca I-1479 700±120
4 Quebrada Honda P-1846 630±40
5 Pumamarca SI-6987 710±55
6 Pumamarca SI-6988a 660±50
7 Pumamarca SI-6988b 645±45
8 Kachiqhata SI-6990 640±50
9 Inithuatana SI-6989 515±50
10 Pacachamac L-123b 900±150
11 Chancay Hv-350 740±50


TABLE 4. List of radiocarbon dates obtained from territories incorporated by succeeding rulers of The Inca Empire.

GROUP A: DATES FROM CUZCO REGION AND TERRITORIES INCORPORATED BY INCA PACHACUTI
No.
Sample name
lab. code
C-14 age
conv. y BP
1 Machu Picchu UCLA-2538e 380±40
2 Machu Picchu UCLA-2538a 595±105
3 Machu Picchu UCLA-2538f 390±40
4 Huancayo Alto TX-2006 580±100
5 Chancay Hv-350 740±50
6 Patayacta Urubamba UCLA-1676a 365±60
7 Tunasmocco UCLA-1676b 415±60
8 Canamarca UCLA-1676d 475±60
9 Yucay UCLA-1676k 365±60
10 Ancas Marca UCLA-1676m 660±60
11 Choquepuquio BM-924 695±59
12 Canaracay BM-925 425±67
13 Urco J BM-929 307±41
14 Ancas Marca BM-930 482±91
15 Ollantaytambo SI-6991A 470±70
16 Pumamarca SI-6987 710±55
17 Pumamarca SI-6988a 660±50
18 Pumamarca SI-6988b 645±45
19 Kachiqhata SI-6990 640±50
20 Inithuatana SI-6989 515±50
21 Patamarca MC-2351 480±70
GROUP B: DATES FROM TERRITORIES INCORPORATED BY TOPA INCA DURING REIGN INCA PACHACUTI
No.
Sample name
lab. code
C-14 age
conv. y BP
1 Pacachamac L-123b 900±150
2 Cerro Santa Barbara UGa-4661 395±75
3 Cerro Santa Barbara UGa-4662 475±65
4 Batan Grande Beta-2591 450±60
5 Chilca I-1479 700±120
6 Ancon TK-93 530±80
7 La Pampa TK-193 500±70
GROUP C: DATES FROM TERRITORIES INCORPORATED BY TOPA INCA
No.
Sample name
lab. code
C-14 age
conv. y BP
1 Cerro Azul WIS-1936 420±70
2 Cerro Azul WIS-1939 480±60
3 Cerro Grande UCTL-281 510±60
4 Cerro Grande UCTL-229 460±45
5 Cerro Azul WIS-1987 520±70
6 Churajon GaK-108 554±70
7 Quebrada de Moca KN-2622 350±50
8 Quebrada Honda P-1846 630±40
GROUP D: DATES FROM TERRITORIES INCORPORATED BY HUAYNA CAPAC
No.
Sample name
lab. code
C-14 age
conv. y BP
1 Inga Pirca CSIC-322 690±80
2 Inga Pirca CSIC-335 550±60


TABLE 5. Confidence intervals for composite probability distributions obtained as result of calibration of dates representing Inca Imperial Phase and Inca Preimperial Phase. The narrowest 68% confidence interval for Inca Imperial Phase is divided into two parts. In brackets the probability of each part of interval is placed.

 
50% confidence
interval
[calendar years AD]
60% confidence
interval
[calendar years AD]
68% confidence
interval (narrowest)
[calendar years AD]
Inca Preimperial Phase 1288 - 1373 1262 - 1387 1280 - 1396
Inca Imperial Phase 1425 - 1552 1406 - 1590 1401 - 1518 (54%)
1578 - 1624 (14%)


TABLE 6. Confidence intervals for composite probability distributions obtained as result of calibration of groups presented in Table 4. The narrowest 68% confidence intervals are divided into two or three parts. In brackets the probability of each part of interval is placed.

 
50% confidence
interval
[calendar years AD]
60% confidence
interval
[calendar years AD]
68% confidence
interval (narrowest)
[calendar years AD]
GROUP A 1345 - 1513 1313 - 1569 1283 - 1498 (66%)
1604 - 1613 (2%)
GROUP B 1325 - 1478 1247 - 1523 1306 - 1364 (11%)
1375 - 1518 (49%)
1579 - 1624 (8%)
GROUP C 1390 - 1484 1352 - 1537 1308 - 1358 (15%)
1381 - 1485 (53%)


APPENDIX 1. The list of Kings (by Miguel Cabello de Valboa)

1. Manco Capac 945–1006 AD
2. Sinchi Roca 1006–1083 AD
3. Lloque Yupanqui 1083–1161 AD
4. Maita Capac 1161–1226 AD
5. Capac Yupanqui 1226–1306 AD
6. Inca Roca 1306–1356 AD
7. Yahuar Huacac 1356–1386 AD
8. Viracocha Inca 1386–1438 AD
9. Pachacuti Inca Yupanqui 1438–1471 AD
10. Topa Inca Yupanqui 1471–1493 AD
11. Huayna Capac 1493–1528 AD
12. Huascar Inca 1528–1532 AD
13. Atahuallpa 1532–1533 AD
14. Manco Inca 1533–1545 AD


APPENDIX 2. A Chronological Models

1st MODEL – MONARCHY
2nd MODEL – DIARCHY
 
The Hanan Cuzco Dynasty
The Hurin Cuzco Dynasty
Manco Capac
Manco Capac
Sinchi Roca
Inca Roca
Sinchi Roca
Lloque Yupanqui
Yahuar Huacac
Lloque Yupanqui
Maita Capac
Viracocha Inca
Maita Capac
Capac Yupanqui
Pachacuti Inca Yupanqui
Capac Yupanqui
Inca Roca
Topa Inca Yupanqui
Yahuar Huacac
Huayna Capac
Viracocha Inca
Huascar Inca
Pachacuti Inca Yupanqui
Atahuallpa
Topa Inca Yupanqui
   
Huayna Capac
   
Huascar Inca
   
Atahuallpa
   
Manco Inca
   

Figure 1
Figure 2
Figure 3A-E
Figure 4
Figure 5
Figure 6