# Chronometric dating and seriation tasks

The Backbone of Archaeological Dating Michael J. O'Brien, R. Lee Lyman of sites and Given the important roles that chronometric methods play in modern arc . Chronometric dating seriation task, Teased with some tasks. Given the important roles that chronometric methods play in modern There are as well two other methods—seriation and cross dating—that deserve special.

This limitation is partly due to a lack of quantitative algorithms that can be used to build deterministic seriation solutions. When the number of assemblages becomes greater than just a handful, the resources required for evaluation of possible permutations easily outstrips available computing capacity. On the other hand, probabilistic approaches to creating seriations offer a computationally manageable alternative but rely upon a compressed description of the data to order assemblages.

This compression removes the ability to use all of the features of our data to fit to the seriation model, obscuring violations of the model, and thus lessens our ability to understand the degree to which the resulting order is chronological, spatial, or a mixture.

Recently, frequency seriation has been reconceived as a general method for studying the structure of cultural transmission through time and across space.

The use of an evolution-based framework renews the potential for seriation but also calls for a computationally feasible algorithm that is capable of producing solutions under varying configurations, without manual trial and error fitting.

Here, we introduce the Iterative Deterministic Seriation Solution IDSS for constructing frequency seriations, an algorithm that dramatically constrains the search for potential valid orders of assemblages. Our initial implementation of IDSS does not solve all the problems of seriation, but begins to moves towards a resolution of a long-standing problem in archaeology while opening up new avenues of research into the study of cultural relatedness.

The results compare favorably to previous analyses but add new details into the structure of cultural transmission of these late prehistoric populations. Frequency seriation is a technique that produces chronological sequences by arranging descriptions of assemblages so that the frequencies of artifact classes jointly form unimodal distributions.

Developed in the early 20th century, frequency seriation played an integral role in the emergence of archaeology as a coherent discipline [ 2 ] and enabled culture historians to construct regional chronologies of prehistory throughout the New World [ 3 — 12 ]. Yet, for the last 50 years, frequency seriation has been largely ignored due to its association with relative chronology and the mistaken belief that radiometric dating techniques have replaced it. While there has been some interest in seriation for disciplines outside of archaeology [ 15 — 18 ], to the extent that methodological development has occurred in archaeology over the last 50 years, the focus has been largely on reducing the method to probabilistic similarity-ordering problems that can be attacked via multivariate statistical methods [ 19 — 23 ].

The roots of frequency seriation, however, stem from a deterministic algorithm that identifies orders on the basis of occurrence and frequency criteria. Recently, deterministic frequency seriation hereafter, DFS received some attention due to the demonstration that the method can be theoretically rationalized using an evolutionary framework.

While the potential of this idea has been long recognized [ 24 — 26 ], the work of Neiman [ 27 ] firmly established an explanatory basis within cultural transmission models for the unimodal distributions that form the core of the frequency seriation algorithm. With these advances, there remains substantial promise for DFS to again become a primary tool for archaeological analyses as it enables researchers to quantitatively track patterns of interaction, define social communities, and trace lineages among past populations, in addition to informing upon chronology.

**What Is A Radiometric Dating?**

In this way, frequency seriation could serve as a key method in the establishment of a fully evolution-based discipline. Despite its potential, the use of DFS as a productive tool for archaeological research remains difficult, and methods for constructing and evaluating solutions are incomplete.

While a handful of assemblages can be seriated using hand manipulation, sorting through all possible orderings for a set of assemblages is neither feasible nor systematic.

When the numbers of assemblages grows, a combinatorial explosion sets in, first visible once 10 or more assemblages are analyzed.

The order of magnitude of numbers involved makes brute force approaches impossible even using modern computing power. This limitation was recognized early in the discipline. When archaeologists became concerned with the quantitative basis of their methods, probabilistic approaches were developed that could construct orders on the basis of similarity scores [ 41 — 49 ].

### Seriation (archaeology) - Wikipedia

With probability-based seriation techniques one is guaranteed to find a solution, but the order produced reflects sources of variability beyond time including the effects of sample size, biased transmission processes and spatial variation [ 1 ].

While one may suspect that the final order is largely chronological, it is not possible to ascertain the degree to which the order represents time or other possible factors. The order of any particular subset of assemblages might be explained as a consequence of several factors: Allowing a computational method to obscure the causal influence of these factors destroys the value that seriation can have in helping disentagle such factors in real data sets.

Here, we introduce a new quantitative seriation algorithm that addresses the computational barrier inherent in DFS while also building upon the logical structure of the original method.

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The algorithm succeeds by iteratively constructing small seriation solutions and then using the successful solutions as the basis for creating larger ones. Significantly, the proposed algorithm produces the entire set of unique valid seriation solutions, and does not stop when a single valid solution has been located. This is important because there are typically a number of valid orderings.

Some are suboptimal solutions because they are subsets of larger, more complete ones. Others are simply valid alternative solutions, which point to the influence of multiple causal factors. By including all valid orders, one can use the distribution of solutions as data regarding the structure of interaction between localities, and thus evidence about past cultural transmission.

Our algorithm also enables statistical assessment of the significance of solutions, given the sample sizes employed. Using an example from the Mississippi River Valley, we demonstrate how the new algorithm provides detailed insight into the temporal and spatial structure of inheritance. Creating a typology frequently is the basis of a seriation.

Errors in typology result in errors in seriation: For example, if a certain design style had two peaks in popularity bimodal distributionthis design style is not appropriate for seriation and its inclusion in the analysis may result in strange results. Some design styles were used for a very long time as the shape constructed was handy and no improvement or ornament was added. Of course, these design styles are not eligible for chronological seriation. For example, knives in early medieval times in Europe are said to show no chronological variation.

In addition to temporal organization, seriation results may reflect assemblage differences in social status, age, sex or those resulting from regional variation or a combination of two or more of these factors. The result is not a chronological sequence due to the selection of types, the ordering seems to start with extremely male hoards and ends with extremely female ones.

Three conditions for chronological seriation[ edit ] Doran and Hodsonp. Regional variation must be kept to a minimum, i. The objects analyzed must all come from a single cultural tradition.

The traits or attributes included in the seriation must depend on cultural aspects rather than on function. Statistical methods[ edit ] Development of seriation methods[ edit ] Nowadays, seriation results are no longer produced manually as in Petrie's times but by appropriate algorithms. Though according to David George KendallPetrie's paper showed already a deep understanding of the mathematics of the seriation problem Quote: In Baxter'sp.

Robinson based his frequency seriation method on a similarity matrix. InKendall proposed the use of multidimensional scaling techniques for seriation problems, and this approach has also been used by some other scientists see Baxterpp. Baxter also presents a review of statistical methods for seriation and a description of these approaches pp.

InDoran and Hodson pp. Correspondence analysis for seriation purposes[ edit ] Today, the most popular seriation method both for contextual and frequency problems is based on correspondence analysis. The sequence of the first axis of a correspondence analysis is considered the best seriation order Shennan[4] p. Using this technique, not only the sequence of the objects but also those of the design styles is established.

Note that external evidence is needed to establish the direction of the sequence calculated, i.

The resulting scatterplot showed the form of a horse-shoe where the graves were arranged on the curve according to their chronological order. Similarly, a mapping of the component scores for the first two axes of the correspondence analysis result will display a parabola if the design styles considered are controlled by one factor only like chronology.

This is called the arch effect by Hill and Gauch Therefore, it is recommended inspecting the scatterplot of the first two axes of correspondence analysis to find out if other factors play a role as well see Examples 2 and 3.

If more than one factor is important, the arch effect may distort the results.

- Seriation (archaeology)

Hill and Gauch presented a method to remove this effect. InGroenen and Poblome adapted the correspondence analysis algorithm to combine seriation with absolute dates and stratigraphic relationships. Small contextual seriation[ edit ] The small example below was inspired by Flinders Petrie's serial ordering of Egyptian pottery as published by Renfrew and Bahnp. Raw data for contextual seriation Result of contextual seriation Another way of presenting the raw data for contextual seriation: For example, consider the first column: A beaker is contained in contexts 1 and 2.

Contextual seriation sorts the design styles and the contexts in such a way that the star symbols are found as close as possible to the diagonal of the table. Of course, for a small examples like this, no computer programs are needed to find the best ordering, but for larger data sets like the graves studied by Petrie they are extremely helpful. Simulated data, seriation and correspondence analysis[ edit ] The data presented in this example was simulated by WinBasp.

Initially 60 contexts called units in WinBasp were created along with 50 types. The contexts were labeled in chronological order by numbers 01 to 60, the types are labeled in the form T to T If a type is represented by one object only this object is not relevant for the chronological sequence as it does not provide a link to another context. Similarly, contexts containing one object only are irrelevant for seriation.

Therefore, the contexts with one or no object and types represented by one object or not at all were eliminated. The resulting raw simulated data consisting of 43 contexts and 34 types are shown on the left.