69 Chapter IV ANALYTICAL METHODS Most studies of biological distance using cranial data rely upon the analysis of either metric or nonmetric data. As discussed earlier, metric analyses usually result in greater precision while the use of nonmetric traits can sometimes be more effective in special cases, such as when one is examining differences between very closely related groups. An ideal approach to a study of this nature might be the use of a mixed-data model incorporating both types of data, such as the mulitvariate model of Anderson & Pemberton (1985) or the mixed-data model proposed by de Leon & Carrièrre (2005), both of which produce a generalized Mahalanobis distance matrix using nominal, ordinal and continuous variables. For this study, however, one of the goals is to carry out both types of analysis as a test of the use of discrete traits in a study involving small sample sizes and extensive post-mortem damage to the skeletal materials at the critical test site – a common problem in archaeology. Therefore, separate analyses of metric and of discrete traits were carried out. Analysis of Metric Traits Trait Correlation For the purposes of this study, the craniometric traits Maximum Cranial Breadth, Maximum Cranial Length, Nasal Height and Nasal Breadth seemed most likely to be 70 significant because of reported differences in previous cranial studies done on California populations, and because of informal observations of a difference in physical type made by Bennyhoff (1968, 1986) and Wiberg (1984). If Bennyhoff’s hypothesis is correct, then the populations from the Berkeley Pattern sites (CA-SCL-137, CA-SCL-674 and the flexed burials at CA-ALA-343) should demonstrate rounder smaller skull shapes and wider noses than all of the other sites. The materials from the Meganos aspect at CAALA-343 should demonstrate larger longer skull shapes and narrower noses. The population from the Early Horizon Central Valley Site (CA-SJO-091) should demonstrate the greatest similarity to the Meganos Aspect at CA-ALA-343; and the materials from the Late Horizon Central Valley sites (CA-SAC-117 and CA-SJO-105) should show some tendency toward homogenization of these two types, but should still be more similar to the Meganos type than the Berkeley Pattern type. In order to facilitate the analysis of craniometric traits, the data sets selected from six sites of interest were organized into seven test cases: (A) CA-SJO-091: a site possibly ancestral to the “Meganos” people, and related to both the Plains Miwok and the Northern Yokuts; (B) CA-SAC-117: a site associated with the Plains Miwok; (C) CA-SJO-105: a site linked to the Northern Yokuts; (D) CA-ALA-343e: a component of the Middle Period site characterized by extended burial positions and Meganos-type grave goods; (E) CA-ALA-343f: a component of the same Middle Period site characterized by flexed burial positions and Berkeley Pattern traits; 71 (F) CA-SCL-137: a site characterized by Berkeley Pattern traits; (G) CA-SCL-674: a site characterized by Berkeley Pattern traits. Since Bennyhoff’s hypothesis is based on observations concerning a difference in overall head shape and nasal dimensions, a multivariate statistical analysis of the craniometric data from all six sites should provide the clearest evidence of biological distance between the groups in question. However, at CA-ALA-343, the only site that clearly demonstrates the “Meganos” traits in question, and for which good skeletal data were available, the burials were greatly disturbed by a number of taphonomic processes, including the use of bulldozers in clearing the site for new construction. As a result, only six intact skulls were recovered from a site with a total of nearly 400 burials. The bulk of the measurements in this dataset were taken from fragments, making it impossible to use either cranial indices or chords in this analysis. In addition, the vast majority of the measurements taken from such fragments came from flexed burials. Only a handful of useable measurements came from the extended “Meganos” type burials. Worse yet, the cranial structures that suffered the most damage were those of greatest interest in this case, the thinner bones associated with the nasal opening. As a first step, the datasets were entered into Excel spreadsheets. For bilateral traits, only data recorded for the left side was used. Konigsberg (1990) recommends a random selection from both the right and left sides in order to avoid bias as well as distortions caused by unilateral expression of such traits. However, this approach was not practical when combining data collected under four different standards. For some 72 sites, such as CA-SCL-137, only the left-side data were available. Therefore, in the interests of consistency, left-side data were selected for all sites. The sole exception was CA-ALA-343e, where right-side data for maximum ramus height were used instead of left. Right-side data for this particular trait included seven data points, while left-side data included only three. In this instance, maximizing the data set was deemed more important than consistency, especially when the difference in means between right and left-side data for this site amounted to a single millimeter. Once entered, the metric data for each of the 14 traits and seven test groups was subjected to an ANOVA at the 0.05 significance level. This was done in order to determine which traits show significance and which are marginal in comparing the seven cases (Zar 1996). For this test, the null hypothesis assumes the variance seen is not significant. The traits surviving the ANOVA were then subjected to a Student’s t-Test, in order to determine whether differences in means between the seven test cases are significant. As recommended by Zar (1996) for analyses of data sets with equal variance, but unequal sample sizes, a Two-Tailed test was used since the ranges and means revealed by the ANOVA test indicated roughly equal levels of variance for all seven cases, while the number of data points available for each test case varied between three and 46. Traits showing significant differences can then be used to calculate a minimum R matrix as described by Relethford, Crawford & Blangero (1997) in a study of Irish populations following the Great Potato Famine. The R matrix calculates a centroid for 73 each trait, and then determines the differences between each pair of measurements and the centroid. The means of these differences for each test case generate measures of covariance called eigenvectors. The eigenvectors are then combined for all of the traits, providing a Mahalanobis (D2) estimate of the genetic distances between sample groups. The R matrix can also be used to calculate genetic differentiation (FST) by examining the variance of each mean. In this model, when variances are greater than expected for groups of similar size, the result indicates higher rates of gene flow between the groups in question. Principal components analysis can then be used to extract the first two eigenvectors of the scaled R matrix and identify the major factors affecting the outcome of these calculations. Analysis of Nonmetric Traits Trait Elimination As a first step in the analysis of discrete traits, it was necessary to deal with the large number of missing data points in the seven data sets. Missing data points can easily be ignored in a metric analysis, but not in a binary data set (Sharma 1995). Mahalanobis calculations, in particular, are subject to inflation when missing data points are included in the data set (Sharma 1995, Shaw 2003). Missing points can distort the outcome enough to render the results completely unreliable. It is, therefore, recommended that the number of missing data points be reduced to zero, if at all possible. For all of the test cases, the number of missing data points could be minimized by eliminating traits for which missing data points formed the largest percentage of the 74 scoring totals. For this reason, the following traits were eliminated from further analysis: Condylar Canal patent; Infraorbital Voramen present; Lesser Accessory Palatine Foramina present; Parietal Notch bone present; Asterionic Bone present; and Os Lambda present. Two other traits, Os Bregma and Metopism, were eliminated for lack of differential power, in that both were absent or very nearly absent in all instances in all seven test cases. While the complete absence of a trait may be useful in differentiating these populations from others, it will provide no help in separating these test cases from each other. For four of the test cases, CA-SJO-091, CA-SAC-117, CA-SJO-105 and CASCL-674, the complete elimination of missing data points could be accomplished by deleting all burials that included missing data points for the remaining traits: Supraorbital Foramen present; Parietal Foramen present; Mastoid Foramen present; Zygomatico-Facial Foramina present; Lamboid Ossicle(s) present; and Coronal Ossicle(s) present. The data on discrete traits for CA-SCL-137, however, were available only as a list of trait ratios, expressed as the number of occurrences over the number of nonoccurrences for each of the fourteen traits in question, then converted to percentages. The original scoring sheets are not available, either at the Phoebe Hearst Museum or at the Northwest Information Center. In the absence of data individualized by burial, it is not possible to eliminate individual burials with missing data points. 75 In addition, the data for both test cases from CA-ALA-343 came largely from fragments, which means that any list of trait occurrences linked to the actual burial for which occurrence/non-occurrence was recorded necessarily generates large numbers of missing data points. For the non-Meganos aspect at CA-ALA-343, sufficient datapoints are available to use the same elimination process as in the Central Valley sites and the Santa Clara site at CA-SCL-674. For the Meganos aspect, however, elimination reduced the dataset to a level at which comparative analysis becomes untenable. Therefore, it was decided to subject the data from two test cases, CA-ALA-343e, and CA-SCL-137, to logistic regression. Logistic Regression Regression is a mathematical method of predicting the value of individual data points where: (1) some data points are missing; or (2) where data have been compressed to produce a smaller sample size, so that average trait frequencies can be maintained in the process (Hosmer & Lemeshow 2000). Logistic regression is a variation of ordinary regression that can be applied to binary values representing the occurrence or non-occurrence of an outcome event, in this case the occurrence or non-occurrence of a discrete cranial trait. The outcome event is usually coded as 1 or 0, respectively, on data sheets. In essence, logistic regression fits binary (i.e., presence/absence) data to a special s-shaped curve by taking the linear regression (Hosmer & Lemeshow 2000), which could produce any y-value between minus infinity and plus infinity, and transforming that yvalue, using the function: 76 p = Exp(y) / ( 1 + Exp(y) ) This function produces p-values between 0 (as y approaches minus infinity) and 1 (as y approaches plus infinity). The result is a non-linear regression better suited than ordinary regression to the variance seen in biological samples. Logistic regression also produces Odds Ratios associated with each predictor value (p). The odds of an event taking place are defined as the probability of the occurrence of an outcome event divided by the probability of the non-occurrence of that event. The odds ratio for a predictor yields the relative amount by which the probability of the outcome increases (Odds Ratio > 1.0) or decreases (Odds Ratio < 1.0) when the value of the predictor value (p) is increased by 1.0 units. This means the Odds Ratio can predict the value of a data point not present in the original dataset with a known level of confidence. Using logistic regression to fill in missing data points, however, is a questionable procedure, especially for smaller data sets (Hosmer & Lemeshow 2000), and its overuse would render further analysis pointless. Therefore, in the test case CA-SCL-137, where the available data has only been published as ratios of presence/absence for discrete traits, it was decided to reduce the data set by roughly one third, from 30 to 22. This approach maintains the ratios of absence/presence data for those traits which were recorded for all or most of the total number of burials while, at the same time, it eliminates all but one of the missing data points for other traits that were more often recorded as indeterminate due to the absence of, or damage affecting the related bony structure. Scores for the presence/absence of a Supraorbital Foramen, for example, were recorded for all 30 77 burials at this site, while presence/absence data for a Mastoid Foramen were recorded for 27 burials. Scores for Zygomatico-Facial Foramina, on the other hand, were only recorded for 21burials. Subjecting these data to logistic regression reduced the presence/absence data for Supraorbital Foramen from 16 present out of 30 burials (16/30) to 12 present out of 22 burials (12/22). The presence/absence data for Mastoid Foramen was reduced from 24/27 to 19/22. The presence/absence data for Zygomatico-Facial Foramina, on the other hand, was changed from 16/21 to 16/22. Thus logistic regression ensures the ratios of trait occurrence in the reduced data set remain the same as in the unaltered data set and ‘fills in’ only that one missing data point (for Zygomatico-Facial Foramina). Used in this fashion, logistic regression maximizes the usable data set but should not expand the trait occurrence data beyond levels justified by the limited information available at this site. The dataset for discrete traits at CA-SCL-137 was, therefore, converted from that listed in Appendix 3F to the data listed below, in Table 4. Using the same logistic regression process as above, the dataset for discrete traits from CA-ALA-343e was also converted, from that listed in Appendix 3D to the data listed below in Table 5. However, as mentioned earlier, the data set for the Meganos Aspect at CA-ALA-343e consisted almost entirely of data scored from fragments. Therefore, the total number of instances was reduced to 11 from 24, which served to eliminate most missing data points. Then logistic regression was used to maintain trait frequencies while assigning data to artificial data points not linked to specific burials. This resulted in the extrapolation of an additional 12 data points, or roughly one fifth of 78 Table 4. Binary Datapoints For CA-SCL-137 After Logistic Regression Data Points 137-1 137-2 137-3 137-4 137-5 137-6 137-7 137-8 137-9 137-10 137-11 137-12 137-13 137-14 137-15 137-16 137-17 137-18 137-19 137-20 137-21 137-22 Supraorb. Foramen 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 Parietal Foramen 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 Mastoid Foramen 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Zygomat. Foramina 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Lambdoid Coronal Ossicle Ossicle 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Table 5. Binary Datapoints For CA-ALA-343e After Logistic Regression Data Points 343e-1 343e-2 343e-3 343e-4 343e-5 343e-6 343e-7 343e-8 343e-9 343e-10 343e-11 Supraorb. Foramen 1 1 1 1 1 1 1 1 0 0 0 Parietal Foramen 1 1 1 1 1 1 1 0 0 0 0 Mastoid Foramen 1 1 1 1 1 1 1 1 0 0 0 Zygomat. Foramina 1 1 0 0 0 0 0 0 0 0 0 Lambdoid Coronal Ossicle Ossicle 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 79 the total (66), and an outcome which almost certainly expands the data set beyond levels justified by the limited information available from this test case. However, all of those 12 inferred data points are concentrated in scores for three traits: Parietal Foramen, Lambdoid Ossicle(s) and Coronal Ossicle(s). For the remaining three traits, Supraorbital Foramen, Mastoid Foramen and Zygomatico-Facial Foramina, no additional data points were produced. This difference became a factor in later analytical decisions concerning Mahalanobis calculations. Trait Correlation The 14 discrete traits originally selected for this part of the study were drawn from the list of 30 nonmetric traits compiled by Buikstra and Ubelaker (1994), which demonstrate the least amount of pair-wise correlation among Native American populations. Because of this general lack of correlation, Buikstra & Ubelaker consider these the discrete traits most likely to be useful in evaluating the biological distance between populations and subpopulations. Nevertheless, following trait elimination on other grounds (see above, p. 79), pairwise correlation was tested, using a Pearson Correlation Coefficient (Zar 1996), and the resulting correlation coefficients (R) were then used to compute a standard error for the correlations. Then a Student’s t-Test was used to test for pair-wise correlations at the 0.01 significance level (see Tables 6 and 7 for results). The significance level was set at the more stringent level of 0.01 to minimize the risk of producing a strong correlation by chance because of the small sample sizes used in this study (Zar 1996). 80 Table 6. Pearson’s Correlation Coefficient (R) for Five Traits Trait Parietal foramen Mastoid foramen Zygo. foramina Lambdoid ossicle Coronal ossicle Supraorb. Foramen 0.0424 0.1907 0.0041 -0.0443 0.0542 Parietal Foramen Mastoid Foramen Zygomat. Foramina Lambdoid Ossicle 0.1907 0.0041 -0.0443 0.0542 0.1652 0.0990 0.0101 -0.0464 -0.0307 0.3105 Table 7. Student’s t-Test, Two-tailed (p-values) Trait Parietal foramen Mastoid foramen Zygo foramina Lambdoid osssicle Coronal ossicle Supraorb. Foramen 0.0102 0.0460 0.9661 0.6460 0.5736 Parietal Foramen Mastoid Foramen Zygomat. Foramina 0.0460 0.9661 0.6459 0.5736 0.0689 0.3035 0.9166 0.6287 0.7206 Lambdoid Ossicle 0.0008 As can be seen in Table 6, there is a detectable correlation between the traits supraorbital foramen and parietal foramen, barely larger than the cut-off point of 0.01. There is also a slight correlation between the traits Parietal Foramen and Mastoid Foramen. For this reason, the trait Parietal Foramen was eliminated from further analysis. There is also a significant correlation in the occurrence of the Lambdoid and Coronal Ossicles. For this reason, one of these two traits must be eliminated from further analysis. There are slightly more data available for Coronal Ossicles in the critical test case CA-ALA-343e. Therefore Lambdoid Ossicle(s) were eliminated from further analysis. Then, since scoring for Coronal Ossicle(s) includes all of the remaining 81 additional data points (four) generated by logistic regression for CA-ALA-343e, this trait was also eliminated. The remaining three traits, Supraorbital Foramen, Mastoid Foramen and Zygomatico-Facial Foramina, did not demonstrate correlation at the 0.01 level, and as their scores included no data points generated by purely mathematical means, further analysis was limited to these three traits. Sex Correlation The surviving traits (Supraorbital Foramen, Mastoid Foramen and ZygomaticoFacial Foramina) were then tested for correlation with sex, using Pearson’s Correlation Coefficient (Zar 1996). The data from the Santa Clara site at CA-SCL-137 could not be included, since nonmetric trait data from this site were expressed as occurrence frequencies rather than scores linked to individual burials. Since the burials included a preponderance of females (12 out of 15), a sex-linked expression bias for any of the discrete traits selected for this study could affect the outcome of later analysis. However, as discussed earlier in comparing Metric and Nonmetric Analysis, the sex-linked biases reported by Jantz (1970), Schultz (1923) and Comas (1942) applied mainly to sutural traits such as the presence of bregmatic ossicles and the persistance of metopism. Since sutural traits have all been eliminated from this study, the effects of any such hypothetical bias in a single and rather small test case should be limited. Data for the other six test cases was pooled, and pair-wise correlation with sex was tested for each trait, again using Pearson’s Correlation Coefficient (Zar 1996). The resulting correlation coefficients (R) were then used to compute a standard error for the 82 correlations, and a Student’s t-Test was used to test for pair-wise correlations at the 0.01 significance level (see Table 8 for results). Using either the one- or two-tailed p-values, no correlation was found between sex and trait expression for any of the three traits which will be used for the remainder of the analysis. Elimination of missing data points and of correlated traits resulted in the reduction of the data set to the sample sizes shown in Table 9: Table 8. Pearson’s Correlation Coefficient (R) for Three Traits Trait Pearson’s coefficient p-value, two-tailed p-value, one-tailed Supraorb. Foramen Mastoid foramen Zygomat. Foramina -0.0824 0.0488 -0.0511 0.2608 0.5425 0.5212 0.1304 0.2713 0.2606 Table 9. Final Nonmetric Sample Sizes Test Case CA-SJO-091 CA-SAC-117 CA-SJO-105 CA-ALA-343e CA-ALA-343f CA-SCL-137 CA-SCL-674 Data Points 18 21 24 11 29 22 23 Tetrachoric Correlation Matrix Tetrachoric correlation is a mathematical variation of the R matrix described above, in the section on Analysis of Metric Traits. Like the R matrix, tetrachoric 83 correlation calculates for each test case the means of the differences between each pair of data points and the centroid for each trait, producing a form of Pearson’s Coefficient of Correlation. These coefficients are then used to generate measures of covariance called eigenvectors. The eigenvectors are then combined for all of the traits, providing a Mahalanobis (D2) estimate of the genetic distances between sample groups. Tetrachoric correlation is the approach used when the variables are not continuous (i.e., measurements) but dichotomies, commonly presence/absence data like those used here to score the occurrence of discrete cranial traits. In order to assess biological distances between the seven test cases, the scores for the remaining three traits were used to create a contingency table (Chen & Popovich 2002). This was done by calculating the tetrachoric correlation coefficient for each possible pair of test cases. The calculation does this by generating a Pearson productmoment correlation coefficient between hypothetical row and column variables (with Normal distributions). These coefficients would reproduce the observed contingency table if they were divided into two categories in the appropriate proportions. In general, x is the value at which the distribution is calculated, and r (an integer ≥ 1) represents the degrees of freedom parameter for the t-distribution. The r value can be selected to yield results with one or two modes, allowing calculation of either the one or two-tailed form of the Student’s t-Test. The algorithm then returns the probability density function for the t-distribution, calculating: 84 The program used for this purpose was a quantitative computer software program in Fortran 95 written by Dr. Lyle Konigsberg and provided to the author courtesy of the Anthropology Department at the University of Tennessee. The program was run on the SilverFrost statistical analysis software package available at http://www.download.com/Silverfrost-FTN95/3000-2069_4-10491439.html. As stated above, the software first generates a tetrachoric correlation matrix and then uses those coefficients to generate eigenvectors for each trait and sample site. These eigenvectors describe the covariance of the test cases from the centerpoint of the whole and result in a D2 matrix of Mahalanobis distances. The Mahalanobis distance (Chen & Popovich 2002) is a measurement of the similarity or dissimilarity of an unknown sample set to a known one, ranging upward from zero (identity). It differs from Euclidean distance in that it takes into account the correlations within the data set. It is also scale-invariant, meaning the distances produced are not dependent on the scale of measurements. It is equally useful for metric and nonmetric data. Formally, the Mahalanobis distance from a group of values with mean and covariance matrix Σ for a multivariate vector is defined as: Mahalanobis distance can also be defined as a measure of dissimilarity between two random vectors and of the same distribution with the covariance matrix Σ : 85 If the covariance matrix is the identity matrix, the Mahalanobis distance reduces to the Euclidean distance, which is considered a linear estimate of relative biological distance (Chen & Popovich 2002). A Mahalanobis distance is smaller between sample populations that are more closely related than others, and larger between sample populations that are not as closely related. Principal Components Analysis The D2 matrix generated by Dr. Konigsberg’s program was then subjected to a Principal Components Analysis (PCA). PCA is a vector space transform (Shaw 2003) used to reduce multidimensional data sets to a smaller number of dimensions for ease of analysis. It generates a table in which the rows are the observed raw indicator variables (in this case, eigenvectors based on the original presence/absence data), and the columns are the extracted factors (or latent variables) that explain as much of the variance as possible. The cells in this table contain factor loadings, and the meanings of the factors are then induced by seeing which variables are most heavily loaded on which factors. PCA, then, will help identify the principal axes underlying the biological distances measured by the tetrachoric correlation matrix. The PCA was accomplished using the Ecodist computer software package compiled by Goslee & Urban (2007) for use with the open-source Linux-based statistical analysis system known as Cran R. Ecodist was designed for use in analyses of similarity in ecological data, including species presence/absence data, continuous variables and 86 spatial measures (Goslee & Urban 2007). It is, therefore, easily adapted to the analysis of discrete cranial traits. Cran R consists of a language (Dalgaard 2002) plus an on-line run-time environment with graphics, a debugger, access to certain system functions, and the ability to run programs stored in script files. Once the principal factors were extracted, the columns of the eigenvector matrix and the eigenvalue matrix were resorted in order of decreasing eigenvalue (Shaw 2003). Then the cumulative content for each eigenvector was calculated. This allows easy visualization of the relative importance of each factor by means of plotting a scree chart, which takes its name from the general profile of scree at the bottom of a cliff. When ordered eigenvalues are plotted against the number of factors in this fashion, a line connecting their peak values will show a break in slope between the principal factors and lesser factors. On the basis of the scree chart, a subset of the principal eigenvectors was selected to serve as basis vectors, and the resulting factor loadings were examined for possible correlations with the biological groupings suggested by Bennyhoff’s (1986) hypothesis about the Meganos Intrusion. 87 Chapter V RESULTS Results for Metric Traits Unfortunately, only one cranial trait and two mandibular traits survived the preliminary ANOVA tests of significance: Minimum Frontal Breadth, Minimum Ramus Breadth and Maximum Ramus Height. Minimum Frontal Breadth is directly related to the size and shape of the cranial vault, but the two mandibular traits are unlikely to be helpful in evaluating these differences in the overall shape of the cranial vault, and even less helpful regarding the size of the nasal opening. In all other cases, the ANOVA failed for lack of sufficient data points for one of the seven test cases. In all tests but one, the Meganos component of the Santa Clara site designated CA-ALA-343e was the case with insufficient data points. The results of the ANOVA tests for Minimum Frontal Breadth, Minimum Ramus Breadth and Maximum Ramus Height are summarized below, in Tables 10, 11 and 12: Table 10. ANOVA results for Minimum Frontal Breadth. Source of Variation Between Error Total Sum of Squares 3368.0 4106.0 7474.0 Degrees of Freedom 6 115 121 Mean Squares 561.3 35.71 F 15.72 The probability of the resulting F (15.72), assuming the null hypothesis, is less than 0.0001. Therefore, Minimal Frontal Breadth should be considered significant as a means of separating the seven test cases. 88 Table 11. ANOVA results for Minimum Ramus Breadth. Source of Variation Between Error Total Sum of Squares 492.3 1665.0 2158.0 Mean Squares 82.04 10.54 d.f. 6 158 164 F 7.783 The probability of the resulting F (7.783), assuming the null hypothesis, is less than 0.0001. Therefore, Minimum Ramus Breadth should be considered significant as a means of separating the seven test cases. Table 12. ANOVA results for Maximum Ramus Height. Source of Variation Between Error Total Sum of Squares 1357.0 5811.0 7168.0 d.f. 6 128 134 Mean Squares 226.2 45.40 F 4.984 The probability of the resulting F (4.984), assuming the null hypothesis, is less than 0.0001. Therefore, Maximum Ramus Height should also be considered significant as a means of separating the seven test cases. The ranges and means for all three traits are shown below in Figures 16, 17 and 18. The ranges and means shown in Figure 16 seem to support the Bennyhoff hypothesis, with the widest faces found at the possibly ancestral site at CA-SJO-091 and the narrowest linked to the non-Meganos site at CA-SCL-137. The possibly descendant sites at CA-SAC-117 and CA-SJO-105 appear to be more closely associated with the ancestral site than either of the Santa Clara sites. The Meganos Aspect at CA-ALA-343e appears 89 Figure 16. Ranges and Means, Minimum Frontal Breadth (in mm.) for all sites. SJO 091 SAC 117 SJO 105 ALA 343e ALA 343f SCL 137 SCL 674 Figure 17. Ranges and Means, Minimum Ramus Breadth (in mm.) for all sites. SJO 091 SAC 117 SJO 105 ALA 343e ALA 343f SCL 137 SCL 674 90 Figure 18. Ranges and Means, Maximum Ramus Height (in mm.) for all sites. SJO 091 SAC 117 SJO 105 ALA 343e ALA 343f SCL 137 SCL 674 to be intermediate between the three Central Valley sites and the non-Meganos Aspect at the same site. As shown in Figure 16, the non-Meganos Aspect at CA-ALA-343f appears to match up more closely with the two Santa Clara sites that are definitely non-Meganos. However, a Student’s t-Test shows far less significance in the means for these three traits (Minimum Bifrontal Breadth, Minimum Ramus Breadth, and Maximum Ramus Height). As recommended by Zar (1996) for analyses of data sets with equal variance but unequal sample sizes, a Two-Tailed test was used. The ranges and means revealed by the ANOVA test indicate roughly equal levels of variance for all seven cases, but the number of data points available for each test case varies between 3 and 46. In general, differences in the means should be considered significant if the resulting probability (p) 91 falls below 0.05. Traits should be considered marginal if p is larger than 0.05. The results of the Two-Tailed test for Minimum Frontal Breadth are shown in Table 13. Table 13. Two-Tailed P Values for Minimum Frontal Breadth Sites SAC117 SJO105 ALA343e ALA343f SCL137 SCL674 SJO091 0.0014 <0.0001 0.0021 <0.0001 <0.0001 <0.0001 SAC117 SJO105 ALA343e ALA343f SCL137 <0.0001 0.0578 0.2895 <0.0001 0.0022 0.4556 0.0046 <0.0001 0.0035 0.4676 0.0578 0.4561 0.2895 0.9428 0.2303 The differences in means between the Central Valley sites and the Santa Clara sites are significant. The differences between the Meganos and non-Meganos cases at CA-ALA-343, however, show no statistical significance. The Meganos Aspect does show significant differences when compared to the ancestral site at CA-SJO-091 and significant differences when compared to the Plains Miwok site at CA-SAC-117, but there is no significant difference compared to the Yokuts site at CA-SJO-105. The nonMeganos Aspect at CA-ALA-343 is most comparable to the Santa Clara site at CA-SCL674, while its differences from the possibly ancestral site at CA-SJO-091 are extremely significant, and its differences from the Yokuts site at CA-SJO-105 are very significant. The non-Meganos aspect, however, does not show significant difference when compared to the Plains Miwok site at CA-SAC-117. These results are suggestive, then, but inconclusive. The biological distances between the seven test cases are further muddled when a Student’s T-Test is applied to the two mandibular traits, with results shown below in Tables 14 and 15. 92 Table 14. Two-Tailed P Values for Minimum Ramus Breadth Sites SAC117 SJO105 ALA343e ALA343f SCL137 SCL674 SJO091 <0.0001 <0.0001 0.0022 <0.0001 <0.0001 <0.0001 SAC117 SJO105 0.3727 0.6906 0.9332 0.3188 0.2609 0.3086 0.2920 0.7159 0.8271 ALA343e ALA343f 0.3679 0.3202 0.1068 0.3202 0.1068 SCL137 0.8358 For Minimum Ramus Breadth, the difference in means is significant for the possibly ancestral site at CA-SJO-091 when compared to all other cases except for the Meganos Aspect at CA-ALA-343, where the difference is smaller but still significant. All of the other six cases fall into similar ranges and their means show no significant differences when compared with each other. Table 15. Two-Tailed P Values for Maximum Ramus Height Sites SAC117 SJO105 ALA343e ALA343f SCL137 SCL674 SJO091 0.0285 0.0012 0.3983 0.0089 0.9933 0.5893 SAC117 SJO105 ALA343e ALA343f SCL137 0.6978 0.0450 0.9218 0.0567 0.0155 0.0128 0.8036 0.0061 0.0002 0.1006 0.4449 0.5894 0.0392 0.0006 0.6614 For Maximum Ramus Height, the difference in means is significant between the three Central Valley sites and between the Central Valley sites and the Meganos Aspect at CA-ALA-343. The difference in means is significant between the Santa Clara site at CA-SCL-674 and the Yokuts site at CA-SJO-105 as well as the non-Meganos Aspect at 93 CA-ALA-343. The mean for the non-Meganos Aspect at CA-ALA-343 is also significant compared to the non-Meganos site at CA-SCL-137. Ramus heights for the Meganos Aspect at CA-ALA-343 show the widest range of values despite the small size of the data set (7), and the highest mean of all the sites. While these differences may be useful in separating some groups, their meaning within the larger scheme of the Bennyhoff hypothesis is unclear and somewhat contradictory when combined with the other two traits. At this point, further analysis was deemed unlikely to generate useful results in a multivariate analysis. Therefore, Dr. J. Relethford’s (2008) R matrix software was not applied. While the results of the ANOVAs and t-Tests are somewhat suggestive, the data set is far too limited to allow a complete analysis, particularly when the results for the only surviving cranial trait, Minimum Frontal Breadth, are based on only three data points in the critical test case, CA-ALA-343e. With more data points from other posited Meganos sites, it should be possible to obtain a more definitive answer concerning the biological distance between Meganos component burials and those from other test cases. Clarity concerning these relationships could then help support or refute the objective reality of the Meganos Intrusion. At present, however, craniometric analysis cannot provide a conclusive result. Results For Nonmetric Traits Application of Dr. L. Konigsberg’s Fortran 95 software to the scores for the surviving three nonmetric traits, Supraorbital Foramen, Mastoid Foramen and 94 Zygomatico-Facial Foramina, produced the tetrachoric correlation matrix seen below in Table 16. Table 16. Tetrachoric Correlation Matrix TRAIT Supraorbital Foramen Mastoid Foramen ZygomaticoFacial Foramina Supraorbital Foramen Mastoid Foramen ZygomaticoFacial Foramina 1.00000 0.13816 -0.03990 0.13816 1.00000 0.08483 -0.03990 0.08483 1.00000 From the tetrachoric correlation matrix, a secondary matrix of threshold traits was derived, seen below in Table 17. The figures for these threshold traits are eigenvectors describing the distance from the data’s centroid for each trait and test case. Table 17. Eigenvectors for Threshold Traits in Each Test Case Test Case CA-SJO-091 CA-SAC-117 CA-SJO-105 CA-ALA-343e CA-ALA-343f CA-SCL-137 CA-SCL-674 Supraorbital Foramen 1.22064 1.28155 0.64067 0.52440 0.00000 0.05972 0.11419 Mastoid Foramen ZygomaticoFacial Foramina 1.59335 1.64498 1.35974 0.52440 -0.56595 1.06757 -1.33518 -0.58946 -0.38532 -0.51194 -0.84162 -1.46537 0.87614 -1.09680 The eigenvectors show that the centroid for the trait Supraorbital Foramen is located in the non-Meganos Aspect at CA-ALA-343f. The most similar site for this particular trait is the Berkeley Pattern site at CA-SCL-137, and the next most similar is 95 the other Santa Clara site, CA-SCL-674. The Meganos component at the same site, CAALA-343e, and the Yokuts site at CA-SJO-105 show intermediate distance. The other two Central Valley sites, the proto-Miwok site at CA-SJO-091, and the Northern Miwok site at CA-SAC-117, show the greatest distance. The eigenvectors for the trait Mastoid Foramen show the three Central Valley sites as roughly equidistant from a centroid located between the two components at CAALA-343. The Santa Clara site at CA-SCL-137 shows intermediate distance from the centroid, and in the same direction as the Central Valley sites. The other Santa Clara site, at CA-SCL-674, shows roughly the same distance from the centroid as the Central Valley sites but in the opposite direction. The eigenvectors for the trait Zygomatico-Facial Foramina indicate a centroid located between the Santa Clara site at CA-SCL-137 and all of the other sites, with the non-Meganos Aspect at CA-ALA-343f showing the greatest distance. By means of the Ecodist software package, these eigenvectors were then used to generate a D2 matrix. This matrix, shown in Table 18, shows Mahalanobis distances for each pair of test cases. Table 18. D2 Matrix of Mahalanobis Distances For Nonmetric Traits Sites SAC117 SJO091 SJO105 ALA343e ALA343f SCL137 SCL674 SAC117 0.00000 0.21695 0.60426 1.21902 2.46673 1.90157 3.02768 SJO091 SJO105 ALA343e ALA343f SCL137 SCL674 0.00000 0.68435 1.33473 2.59986 1.80058 3.11679 0.00000 0.87491 2.12453 1.52285 2.72413 0.00000 1.27977 1.82193 1.86902 0.00000 2.74939 0.91741 0.00000 3.00238 0.00000 96 When resorted in order of increasing distance, Table 19 was generated (see below). Not surprisingly, the smallest distances are those between the Central Valley sites. The ancestral population at the proto-Miwok site, CA-SJO-091, shows the least biological distance from the Middle/Late Period site, CA-SAC-117, whose population has long been considered directly descendant. The next smallest distance is between the ancestral site and its other probable descendant, the Yokuts site at CA-SJO-105. Table 19. Mahalanobis Distances in Order of Decreasing Similarity Site 1 Site 2 Biol. Dist. SJO091 SJO105 SJO105 ALA343e SCL674 ALA343e ALA343e ALA343e SCL137 SCL137 SCL137 SCL674 SCL137 ALA343f ALA343f ALA343f SCL674 SCL137 SCL674 SCL674 SCL674 SAC117 SAC117 SJO091 SJO105 ALA343f SAC117 ALA343f SJO091 SJO105 SJO091 ALA343e ALA343e SAC117 SJO105 SAC117 SJO091 SJO105 ALA343f SCL137 SJO091 SAC117 0.21695 0.60426 0.68435 0.87491 0.91741 1.21902 1.27977 1.33473 1.52285 1.80058 1.82193 1.86902 1.90157 2.12453 2.46673 2.59986 2.72413 2.74939 3.00238 3.02768 3.11679 97 The Yokuts site at CA-SJO-105, however, appears to be almost equidistant from both the posited proto-Miwoks (CA-SAC-117) and their contemporaries at the Northern Miwok site, CA-SAC-117. This is consistent with known archaeological data for this region and makes sense if the Proto-Miwoks divided into two or more descent groups, one of whom remained nearby, experiencing similar environmental pressures, while the other moved into a new environment and then, possibly, returned to the general area. The next closest association is between the Meganos Aspect at CA-ALA-343e and the Yokuts site, CA-SJO-105. If Bennyhoff’s (1986) hypothesis is correct, and the Meganos people were indeed the descendants of the proto-Miwoks, then this outcome suggests the Meganos may have become the ancestors of the Yokuts rather than the Northern Miwoks. This outcome is also what might be expected if limited gene flow was reestablished between the descent groups, slightly reducing the biological distance that had developed between them. The next closest association is between the non-Meganos component at CA-ALA343f and the somewhat earlier Berkeley Pattern site at CA-SCL-674. This, too, matches predictions based on Bennyhoff’s hypothesis, indicating a biological distance nearly as short as that between the Miwok descent groups in the Central Valley. The next three distances indicate the Meganos component at CA-ALA-343e is almost equidistant from the ancestral proto-Miwok site (CA-SJO-091), the descendant Northern Miwok site (CA-SAC-117), and the non-Meganos component at the same site, CA-ALA-343f. An outcome like this might result from more extensive gene flow taking place between the populations forming the two components at CA-ALA-343. If 98 Bennyhoff was correct, then the two populations were in close contact for approximately two hundred years, so gene flow would be a logical development. The South San Jose site, CA-SCL-137, shows an intermediate biological distance from all of the Central Valley sites and the Meganos component at CA-ALA-343e, as well as the Berkeley Pattern site at CA-SCL-674. It shows the greatest distance from the non-Meganos component at CA-ALA-343, indicating this population was distinct from all others included in this study. The non-Meganos Aspect at CA-ALA-343f demonstrates substantial biological distance from all off the Central Valley sites, again matching what would be predicted by Bennyhoff’s hypothesis. The largest biological distances are between the Berkeley Pattern site at Rubino, CA-SCL-674, and the Central Valley sites. The largest of all is between the Early/Middle Rubino site (CA-SCL-674) and the proto-Miwok site at CA-SJO-091. This, too, is what would be expected of a Hokan-speaking group that had not yet experienced any substantial contact with the ancestors of the Miwoks, the Yokuts and, according to these results, the Meganos people. Outcome of Principal Components Analysis The Principal Components Analysis (PCA) included in Ecodist software was used to examine the D2 matrix from the previous section, and to generate the eigenvalues shown in Table 20. 99 Table 20. Eigenvalues for Principal Components Factor 1 2 3 4 5 6 7 Total Eigenvalues 9.18357e+00 2.42792e+00 3.33651e+-01 4.37738e+-06 1.00132e+-15 0.00000e+00 0.00000e+00 20.3267 Proportion Percentage 0.451799 45.12% 0.119445 11.94% 0.164144 16.41% 0.215351 21.54% 0.049261 4.93% 0.000000 0.00% 0.000000 0.00% 1.000000 100% When the eigenvalues were resorted in order of descending magnitude, the result was Table 21. Table 21. Cumulative Importance of Principal Components Statistical Factor Analysis Factor Eigenvalue 1 4 3 2 5 6 7 9.18357 4.37738 3.33651 2.42792 1.00132 0.00000 0.00000 Eigenvalues Extraction: Principal Components % of total Variance 45.1799 21.5351 16.4144 11.9445 4.9261 0.00000 0.00000 Cumulative Eigenvalue 9.18357 13.56095 16.89746 19.32538 20.3267 20.3267 20.3267 Cumulative % 45.1799 66.7150 83.1294 95.0739 100.0000 100.0000 100.0000 According to these results, nearly half of the variance in the data is explained by Principal Component 1, which is twice that explained by the next largest component, and so on (Shaw 2003). A complete factor analysis requires the deletion of the smallest components and recalculation of the surviving eigenvectors in order to search for underlying structure in the data. As mentioned earlier, one way to select components for 100 Figure 19. Scree Chart of Principal Components 10 9 8 7 6 5 4 3 2 1 0 PC 1 PC 4 Others 1 4 3 2 5 6 7 deletion is to plot a scree chart of the eigenvalues against the number of factors and look for a break in the slope of the line connecting the peaks of the columns. The scree chart for this analysis is shown in Figure 19. In this case, the break in slope occurs at the second column, indicating the eigenvectors should be reduced to two components, PC 1 and PC 4. Between them, these two eigenvectors explain two thirds of the variance seen in the data. Principal Component 1 seems likely to be a reflection of gene flow between these prehistoric populations. Figure 20 shows the result of plotting PC 1 against the seven test cases. The plot shows icons which can be connected to one another to form a fairly smooth S-shaped curve linking the ancestral Miwok site (CA-SJO-91) to its two descendant sites (CA-SAC-117 and CA-SJO-105) and then to the Meganos Aspect at CA-ALA-343e. A sharper rise in slope leads to the non-Meganos Aspect at CA-ALA343f, and then to the Rubino site at CA-SCL-674. The division between the Central 101 Valley/Meganos test cases and the non-Meganos/Rubino test cases is apparent. The other Santa Clara site at CA-SCL-137 is clearly an outlier not directly related to any of the other groups. Principal Component 1, then, provides a graphic depiction of the biological distances seen in the D2 Matrix discussed earlier. The sloping s-curved line that might connect six of these test cases can best be explained by a scenario in which two very different populations came into contact and experienced homogenization, some of which was retained by one of the descendant groups (the Yokuts site at CA-SJO-105). In any case, the division between the Meganos and non-Meganos Aspects at CA-ALA-343 is evident. Figure 20. Eigenvectors – Principal Component 1 SJO 091 SAC 117 SJO 105 ALA 343e ALA 343f SCL 137 SCL 674 102 Figure 21. Eigenvectors – Principal Component 4 SJO 091 SAC 117 SJO 105 ALA 343e ALA 343f SCL 137 SCL 674 Principal Component 4 affects the matrix about half as much as Principal Component 1. As plotted in Figure 21, a sloping v-shaped line can be drawn connecting six out of seven test cases. Here, however, the outlier is CA-SAC-117, the Late Period Northern Miwok site. The two test cases at CA-ALA-343 are most similar, and distinct from two other groupings – the outlier far below the centroid and the remaining four sites at or well above it. What biological or environmental factor is reflected in this axis is debatable, but the centrality of the Santa Clara site at CA-SCL-137 for Principal Component 4 is the opposite of its outlier position along Principal Component 1. Here, CA-SCL-137 lies on the central axis of the eigenvectors, suggesting the basis of this axis may be the difference between this outlier site and all of the other test cases, or the 103 underlying cause of that difference, e.g., diet, climate, disease, heritability or some other factor. When the remaining components are removed, a plot of Principal Component I vs. Principal Component 4 (see Figure 22) reveals a new grouping: the Meganos Aspect and the non-Meganos Aspect at CA-ALA-343 lie along a horizontal axis intermediate between two extremes, one being the Rubino site at CA-SCL-674, and the other being the three Central Valley sites and the other Santa Clara site at CA-SCL-137. The Meganos Aspect is closer to the Central Valley sites and the non-Meganos Aspect is closer to the Rubino site. This underlying structure, then, appears to depict the Figure 22. Principal Components 1 and 4. ○ SJO091 SAC117 x ALA343e ALA343f + SJO105 SCL137 SCL674 104 zone of biological contact between two very distinct population groups. The possible meaning of this result will be discussed in conjunction with modern tribal identities in the Conclusions section. 105 Chapter VI CONCLUSIONS The purpose of this study was two-fold: (1) to examine cranial data from archaeological sites relevant to the so-called ‘Meganos Intrusion’ first described by Bennyhoff (1986) and determine whether the differences in physical type reported by several observers are reflected in measures of biological distance; and (2) to compare and contrast the utility of analyses based on metric vs. nonmetric traits in attempting to verify or refute Bennyhoff’s hypothesis. Part 1. Evidence of The Meganos Intrusion Because of reported differences in previous cranial studies done on California populations, and because of informal observations of a difference in physical type made by Bennyhoff (1968, 1986) and Wiberg (1984), metric traits (Maximum Cranial Breadth, Basion-Prosthion Length, Nasal Height and Nasal Breadth, in particular) were originally deemed most likely to be significant in attempting to verify or refute the biological reality of the Meganos Intrusion. If Bennyhoff’s hypothesis were correct, then populations from the Berkeley Pattern sites should have demonstrated rounder smaller skull shapes and wider noses than all of the other sites; the materials from the Meganos and Central Valley sites should demonstrate larger longer skull shapes and narrower noses. In addition: 106 (1) The population from the Early Horizon Central Valley Site (CA-SJO-091) should demonstrate the greatest similarity to the Meganos site (CA-ALA-343e). (2) The materials from the Late Horizon Central Valley sites should show some tendency toward homogenization of trait patterns characterizing the Early populations at the proto-Miwok site (CA-SJO-091) and the Berkeley Pattern sites (CA-SCL-137 and CA-SCL-674). (3) The Meganos physical type should be more similar to the Central Valley sites, early and late (CA-SJO-091, CA-SAC-117 and CA-SJO-105) than to the Berkeley Pattern type at the Santa Clara sites (CA-SCL-137 and CA-SCL-674). From Craniometric Traits An attempt to test the three predictions listed above using metric traits produced inconclusive results. In large part, this is the result of limited data sets. No craniometric data were available for the two Contra Costa sites considered ‘type’ sites for the Meganos people, and the only Meganos site for which cranial data were available had major problems with post-mortem damage to the skeletal materials. The damage was so extensive that only six intact skulls were recovered from 224 burials (Marshall 2002) during the most recent excavation there. The bulk of the data that was recovered came from fragments. In addition, the cranial data for the seven test cases was collected and scored under several sets of standards, so that the number of traits that were directly comparable and were recorded for all seven test cases was limited to approximately half of those most likely to be useful in a study of this kind. 107 As a result of these and other problems, only three out of 14 metric traits survived the initial ANOVA tests of their significance. All four of the traits originally considered mostly likely to differentiate the test cases (Maximum Cranial Breadth, Basion-Prosthion Length, Nasal Height and Nasal Breadth) failed to survive the initial ANOVA tests. Only one surviving cranial trait, Minimum Frontal Breadth, is directly related to the predictions made on the basis of Bennyhoff’s hypothesis: the populations with the widest faces should be those from the Central Valley sites and the Meganos component, while those with the widest noses should be those from the Santa Clara sites and the nonMeganos component at CA-ALA-343. A Student’s t-Test showed some indications that these predictions were confirmed in the case of this particular cranial trait, but the critical portion (from the Meganos component denoted CA-ALA-343e) was based on only three data points. The other two traits surviving the initial ANOVA tests were mandibular traits, Minimum Ramus Breadth and Maximum Ramus Height. These mandibular traits showed contradictory trends that did not confirm or refute the predictions made on the basis of head size and shape. Minimum Ramus Breadth showed no consistent trend at all. Maximum Ramus Height showed no significant differences between any of the sites, except for the separation of the ancestral site at CA-SJO-091 from all of the other test cases. Therefore, a multivariate analysis of the three surviving metric traits (Minimum Frontal Breadth, Minimum Ramus Breadth and Maximum Ramus Height) was abandoned. 108 From Nonmetric Traits The analysis of nonmetric traits was carried out successfully by severely limiting the number of traits and data points used in generating a tetrachoric correlation analysis. Fortunately, tetrachoric correlation can tolerate small sample sizes and tends to generate more precision in the Mahalanobis distances it produces as fewer traits are included in the data set (Chen & Popovich 2002). As a result, the analysis generated a D2 matrix of Mahalanobis distances which matches up almost perfectly with the predictions made on the basis of Bennyhoff’s (1986) hypothesis. Those points that do not match up can be readily explained by: (1) lack of gene flow in some circumstances, and (2) by reverse gene flow in others. The first prediction made was that the population from the Early Horizon Central Valley Site (CA-SJO-091) would demonstrate the greatest similarity to the Meganos site (CA-ALA-343e). Analysis shows that the population from CA-SJO-091 did not demonstrate the greatest similarity to the Meganos Aspect at CA-ALA-343e, but did show a small relative distance. In this analysis, the population at the ancestral site at CASJO-091 was most similar to the Northern Miwoks already believed to be their direct descendants at CA-SAC-117. The descendant population at the Yokuts site (CA-SJO105) actually showed the smallest biological distance from the Meganos Aspect, an outcome which makes sense if the Meganos people did originate in the Central Valley, then migrated westward and shared some genes with the resident Hokan speakers in the East and South Bay. Then, when the Meganos people returned to their original domain, they became the Yokuts. Resuming intimate contact with the population which did not 109 migrate would have resulted in a new homogenization process that reduced the biological distance between the Yokuts and their cousins. The same process would have increased the biological distance between the later (Hokan-homogenized) Meganos people and their direct descendants – the Yokuts. In any case, the Northern Miwoks at CA-SAC-117 might be a descendant group of the proto-Miwoks, represented by CA-SJO-091, who did not migrate west and experienced much less gene flow with unrelated groups who were part of the Berkeley Pattern. The Northern Miwoks would also have experienced far less change in the selection pressures exerted by a very similar environment. The second prediction was that materials from the Late Horizon Central Valley sites (CA-SAC-117 and CA-SJO-105) would show some tendency toward homogenization of trait patterns characterizing the Early populations at the proto-Miwok site (CA-SJO-091) and the Berkeley Pattern sites (CA-SCL-137 and CA-SCL-674). Analysis indicates that the materials from only one of the Late Horizon Central Valley sites (CA-SJO-105) showed the predicted tendency toward homogenization of trait patterns characterizing the Early populations at the proto-Miwok site (CA-SJO-091) and the Berkeley Pattern site, CA-SCL-674. The Northern Miwok site at CA-SAC-117 shows little sign of gene flow in this direction or, as mentioned above, of differing environmental selection pressures. The Yokuts site, however, is clearly intermediate between the Meganos Aspect at CA-ALA-343e and the other Central Valley sites. The third prediction stated that the Meganos physical type should be more similar to that seen at the Central Valley sites, early and late (CA-SJO-091, CA-SAC-117 and 110 CA-SJO-105) than to the Berkeley Pattern type at the Santa Clara sites (CA-SCL-137 and CA-SCL-674). Analysis shows that the Meganos physical type seen at CA-ALA-343e is indeed more similar to the Central Valley sites, early and late (CA-SJO-091, CA-SAC-117 and CA-SJO-105) than it is to the Berkeley Pattern type at the Rubino site, CA-SCL-674. The other Santa Clara site, CA-SCL-137, appears to be an outlier relative to all of the other groups, and its relationship to the Meganos/non-Meganos arc is unclear. It seems most likely this Berkeley Pattern group did not interact with the Meganos People in a way that contributed to the trait patterns characteristic of any of their probable descendants. This group also seems unrelated to the other Berkeley Pattern group at Rubino, despite the short geographic distance between the sites. Whether this is because the group at CA-SCL-137 was entirely displaced or because their movements took a different direction cannot be discerned from the data sets available for these test cases. Possibly, this group interacted instead with the Costanoans, the Esselen or even the Patwin, the other Penutian-speaking group who moved in from the north and displaced the Meganos in turn. The Patwin are believed to have introduced the bow and arrow to the Bay Area, tipping the balance of power and forcing the Meganos to retreat back into the Central Valley. Other groups were also strongly affected by their arrival. A follow-up study of biological distance between those groups, along the lines of the current analysis, might be able to delineate those relationships. 111 As a whole, however, it is clear that there is a discernable difference in trait patterns between the Meganos and non-Meganos components of the population at CAALA-343. The nature of that difference does appear to reflect the biological relationships described by Bennyhoff’s (1986) hypothesis. This study, therefore, does lend support to the biological reality of the Meganos Intrusion. Part II. Metric vs. Nonmetric Analytical Techniques The utility of metric analysis is often limited by small sample sizes, and by postmortem damage to skeletal remains. This is particularly true of rural and suburban sites in California, where many archaeological sites are only discovered in the process of plowing fields or bulldozing land for new construction. At the site most critical to the present study, CA-ALA-343, this was certainly true. The damage done to the skeletal materials is the chief reason why the analysis of metric traits failed in this instance, producing results that are inconclusive but somewhat suggestive. A similar situation resulted from a previous attempt to run a comparative analysis of long bone metrics (Marshall 2002), a study which failed for the very same reasons. The methods used here for the analysis of nonmetric traits, however, are wellsuited to small sample sizes and to the use of small numbers of traits. The success of tetrachoric correlation matrices in the analysis of discrete traits, particularly when the metric analysis reached no useful conclusion, is a clear indication of the value of this approach. The developing trend toward a combined-model metric and nonmetric approach, such as that recommended by De Leon and Carrièrre (2005), suggests that nonmetric traits are rapidly becoming part of a wider approach to bioarchaeological 112 problems that may be able to combine the precision of craniometrics with the adaptability of nonmetric analysis.