Goodness of fit tests for random multigraph models.

Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribution. Tests are performed using goodness of fit measures between the edge multiplicity sequence of an observed multigraph, and the expected one according to a simple or composite hypothesis. Test statistics of Pearson type and of likelihood ratio type are used, and the expected values of the Pearson statistic under the different models are derived. Test performances based on simulations indicate that even for small number of edges, the null distributions of both statistics are well approximated by their asymptotic χ2-distribution. The non-null distributions of the test statistics can be well approximated by proposed adjusted χ2-distributions used for power approximations. The influence of RSM on both test statistics is substantial for small number of edges and implies a shift of their distributions towards smaller values compared to what holds true for the null distributions under IEA. Two applications on social networks are included to illustrate how the tests can guide in the analysis of social structure.

A Framework for Reconstructing Archaeological Networks Using Exponential Random Graph Models.

Reconstructing ties between archaeological contexts may contribute to explain and describe a variety of past social phenomena. Several models have been formulated to infer the structure of such archaeological networks. The applicability of these models in diverse archaeological contexts is limited by the restricted set of assumptions that fully determine the mathematical formulation of the models and are often articulated on a dyadic basis. Here, we present a general framework in which we combine exponential random graph models with archaeological substantiations of mechanisms that may be responsible for network formation. This framework may be applied to infer the structure of ancient networks in a large variety of archaeological settings. We use data collected over a set of sites in the Caribbean during the period AD 100-400 to illustrate the steps to obtain a network reconstruction.

Reconstructing Archaeological Networks with Structural Holes.

Model-based reconstruction is an approach to infer network structures where they cannot be observed. For archaeological networks, several models based on assumptions concerning distance among sites, site size, or costs and benefits have been proposed to infer missing ties. Since these assumptions are formulated at a dyadic level, they do not provide means to express dependencies among ties and therefore include less plausible network scenarios. In this paper we investigate the use of network models that explicitly incorporate tie dependence. In particular, we consider exponential random graph models, and show how they can be applied to reconstruct networks coherent with Burt's arguments on closure and structural holes (Burt 2001). The approach is illustrated on data from the Middle Bronze Age in the Aegean.

Investigating human geographic origins using dual-isotope (87Sr/86Sr, δ18O) assignment approaches.

Substantial progress in the application of multiple isotope analyses has greatly improved the ability to identify nonlocal individuals amongst archaeological populations over the past decades. More recently the development of large scale models of spatial isotopic variation (isoscapes) has contributed to improved geographic assignments of human and animal origins. Persistent challenges remain, however, in the accurate identification of individual geographic origins from skeletal isotope data in studies of human (and animal) migration and provenance. In an attempt to develop and test more standardized and quantitative approaches to geographic assignment of individual origins using isotopic data two methods, combining 87Sr/86Sr and δ18O isoscapes, are examined for the Circum-Caribbean region: 1) an Interval approach using a defined range of fixed isotopic variation per location; and 2) a Likelihood assignment approach using univariate and bivariate probability density functions. These two methods are tested with enamel isotope data from a modern sample of known origin from Caracas, Venezuela and further explored with two archaeological samples of unknown origin recovered from Cuba and Trinidad. The results emphasize both the potential and limitation of the different approaches. Validation tests on the known origin sample exclude most areas of the Circum-Caribbean region and correctly highlight Caracas as a possible place of origin with both approaches. The positive validation results clearly demonstrate the overall efficacy of a dual-isotope approach to geoprovenance. The accuracy and precision of geographic assignments may be further improved by better understanding of the relationships between environmental and biological isotope variation; continued development and refinement of relevant isoscapes; and the eventual incorporation of a broader array of isotope proxy data.

Nation Building and Social Signaling in Southern Ontario: A.D. 1350-1650.

Pottery is a mainstay of archaeological analysis worldwide. Often, high proportions of the pottery recovered from a given site are decorated in some manner. In northern Iroquoia, late pre-contact pottery and early contact decoration commonly occur on collars-thick bands of clay that encircle a pot and extend several centimeters down from the lip. These decorations constitute signals that conveyed information about a pot's user(s). In southern Ontario the period A.D. 1350 to 1650 witnessed substantial changes in socio-political and settlement systems that included population movement, coalescence of formerly separate communities into large villages and towns, waxing and waning of regional strife, the formation of nations, and finally the development of three confederacies that each occupied distinct, constricted areas. Social network analysis demonstrates that signaling practices changed to reflect these regional patterns. Networks become more consolidated through time ultimately resulting in a "small world" network with small degrees of separation between sites reflecting the integration of communities within and between the three confederacies.