Reply to: Craniofacial morphology does not support a pre-contact Carib “invasion” of the northern Caribbean

We are pleased that our research has generated a much-needed dialogue on the prehistory of the Caribbean and appreciate the opportunity to address the misunderstandings reflected in comments by Giovas and colleagues1. Five issues are addressed: (1) misuse of non-metric multidimensional scaling analysis (NMMDS); (2) their erroneous representation of our use of ethnohistoric accounts and archaeological data; (3) their conflation of biology and “ethnicity”; (4) sample size; (5) chronology; and we begin by reiterating the project goal. Our initial objective was to determine whether the pre-Columbian communities of The Bahamas originated in Hispaniola or Cuba using facial morphology (Keegan and Hofman2), based on previously observed significant differences between those islands (Ross and Ubelaker3). The clusters were derived using a Mahalanobis or generalized distance matrix, a function of the group means and the pooled variances and covariances (Afifi and Clark4), computed using the Principal Components Analysis (PCA), a dimension reducing technique, derived from the craniofacial anatomical landmarks (e.g., coordinate data).

1. We reiterate the importance of the tests we used for craniofacial analyses. We analyzed facial shape and size using coordinate data and geometric morphometrics (GMM) including male and female individuals based on valid statistical methods. We used accepted methods to study population history, movements, and biological distances (agglomerative hierarchical cluster, spatial analyses, etc.; see Sneath and Sokal 5 ). The approach we contribute is the application of a population structure perspective (Sneath and Sokal 5 ) coupled with an archaeological and historical context-providing a more holistic lens. In response, Giovas et al. offer a figure of non-metric multidimensional scaling analysis (NMMDS), an ordination method, which is simply a means to visualize and graphically illustrate the Mahalanobis distance matrix published in our study. With this plot, they contest the results of our in-depth population study. NMMDS is an exploratory analysis often used in conjunction with clustering methods to quickly visualize the distance matrix (JMP multivariate methods, Neves et al. 6 , Stynder and Ackermann 7 ; Lessa 8 ; von Cramon-Taubadel et al. 9 ). Their figure does not equate to the hierarchical average linkage cluster analysis we conducted (see original paper for details). In addition, they misinterpret our generalized distance (a classic measure of biological distance, Pietrusewsky 10 ) by using NMMDS, which is a dimension reducing technique (e.g., concerned with finding a low dimension from high dimensional data such as coordinate data, Härdle and Simar 11 ). Principal component analysis or PCA is the preferred dimension reducing technique in GMM that was applied in our original study. Generalized (Mahalanobis) distance is used to test whether group centroids are significantly different  and is used to examine the patterning of phenetic (morphometric) affinities and not to reduce the dimensionality of the data.
Notably, MDS can obscure the underlying phenetic affinities, especially when assessing interspecific relationships and they may not disclose finer divisions that are biologically significant (Sneath and Sokal 5 , Neves et al. 6 , Lessa 8 ). To illustrate this, we reproduced the non-metric multidimensional scaling analysis in JMP 14.3 using the Waern links as a visual check of the actual and predicted proximities (JMP multivariate methods, Waern 15 , Fig. 1). Figure 1 shows that non-metric MDS is not a good representation of the proximities based on the links between the Cuban and Yucatan samples because they stretch across the plot to the other samples and by the unconnected link for Florida and Panama to the rest of the groups. We further tested this using a  Fig. 2) that shows that it is not a good representation of group similarities as the underlying assumption NMMDS is that there is a monotonic relationship (i.e., increase in distance from the most to the least similar pair) between the actual and predicted values and the Shepard diagram is non-monotonic. A good representation would be indicated by the points falling on the x = y line (red line). The reported r 2 value of 0.76 for the non-metric MDS further demonstrates that this is not a good fit to explain the amount of variation within the data (Fig. 2). These procedural statistical tests demonstrate that their MDS plot does not accurately represent our data and that the assumptions used in their NMMDS test to produce their results and interpret their findings (such as the number of dimensions or starting location) may be erroneous. Further, in our original manuscript, we established that there was a lack of spatial autocorrelation for shape and a non-monotonic pattern for centroid size supporting the inappropriateness of using NMMDS for our data (see Figure 7 in our original paper).
In conclusion, the non-metric MDS plot presented by Giovas et al. 1 does not accurately capture the clusters created by our thorough population structure approach that included multivariate, cluster, and spatial analyses, and does not pass the non-metric MDS visual Waern and Shepard proximity checks. Thus, their statistical critique is based on inappropriate methods and procedures, and in our view should be rejected. 2. The morphological data provide a new way to conceptualize the Indigenous communities of the northern Caribbean. It was only after the craniofacial clusters were generated that we recognized the common material culture shared by the Hispaniola/Jamaica/Bahamas (HJB) cluster was Meillacoid pottery. The HJB cluster encompasses the region in which Meillacoid series pottery predominates (Keegan and Hofman 2 ). Rouse 16 derived Meillacoid style pottery from an Ostionoid tradition based largely on the red paste observed near Ft. Liberté, Haiti, where he conducted his primary fieldwork (Rouse 17 ). He further concluded that the incised designs reflected the copying of motifs on Archaic Age stone bowls. We are not convinced that Meillacoid developed from an Ostionoid tradition. Meillacoid pottery appeared suddenly in Hispaniola as a full-blown complex of motifs created through a combination of incision, punctation, appliqué, and modeling. These motifs are far more complicated than could be achieved by simply copying Archaic designs, and they are fully represented in pottery series from western South America, including "Carib" (Lathrap 18 ) and Valdivia (Meggar et al. 19 ).
Outside Ft. Liberté, the paste has a much darker color (fired in a reducing as opposed to the oxidizing environment), and there is little evidence for a transition from Ostionoid to Meillacoid, especially in Jamaica At issue is why a coherent ceramic assemblage that shares an abundance of modes with western South America suddenly appeared in Hispaniola. We proposed a migration from western Venezuela, whose timing coincides with the expansion of Caribs in that area, which is based on phenotypic characteristics that clustered in HJB. This migration could have involved a large-scale population expansion or the infiltration of smaller numbers of men (Lathrap 18 ; Schmidt 26 ). We chose to call them Carib based on Spanish accounts of "Caribs" in the Greater Antilles and the Bahamas. Guinea pigs were mentioned only to highlight their geographical origins and the timing of their introduction coincident with our proposed migration; any further inference is limited by the small sample size. 3. Giovas and colleagues 1 conflate biology and culture (see Crellin and Harris 27 ), and compound their error by claiming filiation between present-day Kalinago and Garifuna and the Meillacoid "Caribs" of HJB. Garifuna is an Afro-indigenous group that was not present before the Trans-Atlantic Slave Trade. We made no claims concerning language or "ethnicity. " The name "Carib" has been used in so many ways that it seems to create endless confusion. Columbus mentioned "Caribs" while sailing through the Bahamas and along the north coasts of Cuba and Hispaniola during his first voyage (Dunn and Kelley 28 ). Other Spanish chroniclers continued to do likewise (Keegan 29 ). Giovas et al. acknowledge the substantial differences between the cultures of the Greater Antilles and those of the southern Lesser Antilles, yet they insist that Columbus must have been describing the inhabitants of the southern Lesser Antilles, who were living over 1500 km away. He wasn't 2 .
We included a discussion of previous accounts by early chroniclers to draw attention to the long-neglected subject of Caribs in the Greater Antilles. Further, they continue to argue that we used our analysis to support "ethnic" distinctiveness and reiterate that this is a misrepresentation of the original work. They refer to the individuals used in our study as "specimens", which shows a lack of sensitivity for the decedents. This is a community collaborative project whereby archaeological research and excavations have been approved and provided by present-day community members in the Bahamas to elucidate the prehistory of the Caribbean. They also claim that we are harming contemporary populations of the Lesser Antilles whilst we only examined prehistoric biological variation in the Western Antilles with no living descendants. If anything, associating the Island Carib with the pejorative attitudes of the Spanish, who were writing about completely different Indigenous communities may be more harmful. 4. We agree that sample size is an issue for island archaeologists, particularly for those who work in coastal environments, such as the Caribbean (Erlandson and Fitzpatrick 30 ; Ross and Cunningham 31 ), which is why such few studies have been reported from this region before but contend that the samples we have and use are a valid depiction of biological (i.e., genetic) similarity. Sample size was limited by the number of human   36 ). Our study includes New World individuals after initial settlement, within relevant geographic areas, and thus, our time and spatial frame to explore the underlying population structure are appropriate (Ross and Ubelaker 11 ).
In conclusion, we collected for the first time 3D measurements of Lucayan facial morphology and compared these individuals to established datasets from the circum-Caribbean. Using standard methods, we observed clustering that identified a significant relationship among individuals living in Hispaniola, Jamaica, and The Bahamas. The material culture shared by these individuals is represented by Meillacoid pottery. The results highlight a connection between western Venezuela and the Antilles that demands further investigation.