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This formal comment has been written in response to Brown and Thomas’s article in the current issue of PLoS ONE entitled “The first New Zealanders? An alternative interpretation of the stable isotope data from Wairau Bar”. In their article, Brown and Thomas attempt to reanalyse and re-interpret the stable isotope (δ13C and δ15N) and radiogenic isotope (87Sr/86Sr) data originally presented in Kinaston et al. [1] “The first New Zealanders: patterns of diet and mobility revealed through isotope analysis.” PLoS ONE 8(5): e64580. Brown and Thomas (p. 2) were prompted to undertake their ‘critical review’ of our study as a result of a disagreement with the groupings of burials, and state “ultimately, these divisions introduce bias, which leads to conclusions that we feel are not supported by the available data.”  The criticisms of Brown and Thomas are not valid. There are three major flaws in the analyses and interpretations, and their findings do not add anything meaningful to the interpretations we already presented. The first flaw is a misunderstanding by Brown and Thomas about the differences between the two approaches and the logic of the argument we set out. The second relates to their treatment of stable isotope data, especially their new dietary interpretations. The third pertains to the way they have used the biologically available 87Sr/86Sr baseline (from dog enamel) to interpret the human 87Sr/86Sr ratios and their use of a ranked ordering of the human 87Sr/86Sr ratios. We present our detailed responses in relation to each of these flaws as follows, in addition to comments regarding more minor inconsistencies in their analysis and interpretations.  Brown and Thomas argue that we were wrong in the way they grouped burials at Wairau Bar and thus in the way they constructed analytical units. They attempt to demonstrate this by taking the isotope data from Kinaston et al. and running it through a number of cluster analyses while “treating the isotope data independently from cultural or biological factors” (Brown and Thomas). Brown and Thomas are not able to replicate the existence of Group 1 by clustering the stable isotope values and 87Sr/86Sr ratios and this, they believe, undermines our findings.  This criticism misses the fundamental point of Kinaston et al. Group 1 (Burials 1–7) is an independently defined group based on a range of archaeological and biological factors. The grouping was first introduced as a concept by Duff (page 61 in [2]) who suggested that “…burials 1–7, appear to have been the exclusive resting place of men of superior rank”. The burials 1–7 grouping was further validated by Anderson (Table 9.1 in [3])who grouped all the burials according to the presence or absence of moa eggs, moa bone elements, artefact types, and material used for artefact manufacture. Brown and Thomas dismiss the differences in grave good type and number as simply being a result of taphonomic bias, providing a convenient means to disregard the evidence that is actually available; specifically that “there is a ratio of approximately 5:1 in favor of Group 1 in terms of mean numbers of grave goods” (page 2 in [1]). There are also stratigraphic grounds justifying this treatment of burial groups which were first noted by Owen Wilkes (summarized in [3]). Most recently, Buckley et al. [4] re-evaluated the health indicators of the entire Wairau Bar burial population and discussed the data in reference to these groupings. They found that oral health, which reflects aspects of diet, further reinforces the identification of burials 1–7 as a group.  Thus we. do not need to demonstrate the existence of Group 1; it is already well attested in the literature [3,4]. The logic of our approach is as follows:   There is a group of burials (1–7) at Wairau Bar, which for reasons that include spatial, stratigraphic, material culture and other factors (some of which were outlined in the text and others cited below), have proven to stand out from the others in interesting ways.   Can we add knowledge about the diet and origins of this group through the application of new analytical methods?     Explaining Exploratory versus Confirmatory Analyses To take a data-driven exploratory approach such as cluster analysis, as Brown and Thomas have done, would not have been appropriate in our study because this would address a very different question. They are effectively looking for ‘patterns’ within the data based on isotope values, while we were examining how isotope values were distributed across the population given the already accepted groupings. Data-driven exploratory approaches can be very useful for generating new hypotheses, such as “are there groups”, but are much less useful for examining whether or not the new, in this case the isotope, data are consistent with an existing model. Cluster analysis in its conventional (non-Bayesian) form fails to make direct use of this existing knowledge in the modelling process. In summary, the approach Brown and Thomas used would have been entirely appropriate if we were interested in the question “are there possibly different groups amongst the burials?” but are not at all appropriate for addressing our question about whether Group 1 was distinct from the rest of the sample in terms of diet and origins.  Furthermore, it is important to note that when hierarchical cluster analysis is performed in an agglomerative fashion, there are implications from the choice of linkage method, and different linkage methods can produce very different clusters. With single linkage, there is the well-known problem of observations combining in chains, which can produce ultimately meaningless clusters. Other approaches, including Ward’s linkage as used in Brown and Thomas’s article, are often not stable in the presence of a small number of changes to the data set and, as Blashfield and Aldenderfer (page 450 in [5]) noted,“stability is an important property of any classification in that stable groups are more likely to represent ‘natural’ groups in the data than those which disappear when cases are reordered or a few cases are omitted”. Such problems are especially common in small data sets, as is the case here. We note that Brown and Thomas do not present sensitivity analyses to explore the robustness of their findings.  The hypothesis-driven confirmatory approach that we used is more appropriate for our study because it applies existing knowledge about the burials and how they had been grouped, and then develops hypotheses about those groups in terms of the isotope data. We tested these hypotheses using statistical tests of means, including t-tests and regression models; tests of variances, in particular Levene’s test; and correlations. This approach allowed us to ask the question of interest to us, specifically: Are there differences between the burials in Group 1 and the remainder of the burials (Group 2/3) that cannot be readily attributed to chance?  It is not surprising that the two approaches result in different interpretations of the data as the goals are clearly different. By way of example, suppose we were to perform both a test for difference in means and an exploratory cluster analysis on heights from a sample of individuals suspected to be from two distinct populations which are known to have different mean heights but whose height distributions overlap. It would not be at all surprising if, despite finding that the mean heights for the two groups differed statistically significantly as expected, we also found individuals from the two different populations ended up included in the same clusters. In fact, it would be remarkable if the resulting clusters exactly reflected the underlying populations, especially with a mixture of men and women in the sample. If there was any overlap between the isotope values for the underlying groups, similar issues could readily arise in a cluster analysis of that data also.

Critical Review of Brown and Thomas “The First New Zealanders? An Alternative Interpretation of the Stable Isotope Data from Wairau Bar”