Alba Regia. Annales Musei Stephani Regis. – Alba Regia. A Szent István Király Múzeum Évkönyve. 30. 2000 – Szent István Király Múzeum közleményei: C sorozat (2001)

Tanulmányok – Abhandlungen - Finnegan, M. –Éry Kinga: Biological distance among six population samples excavated in the environs around Székesfehérvár, Hungary, as derived by non-metric trait variation. p. 61–76.

MMD. As such, these populations must be viewed as different samples drawn from the same population, and should not be further analyzed at this level. In order to reduce these population samples, which logically are different samples of the same population, we have used the distances presented in Table 7 and the statistical package of Rohlf et al. (1974) to generate a general distance phenogram, a bivariate plot and a phenogram of cophenetic relationships in order to help us determine how the samples should be pooled. The statistic used is a sequential agglomerative, hierarchical cluster analysis where the unweighted pair-group method using arithmetic averages was used. We decided that the lowest values were to be considered for similarity. The phenogram which resulted is presented in Figure 1. Cophenetic values for each element in the matrix were generated and compared to the original matrix for congruence (Sokal-Sneathl963). The bivariate scatter diagram shown in Figure 2 was developed by comparing elements of the first matrix plotted against corresponding elements of the cophenetic matrix. The phenogram of the cophenetic matrix is presented in Figure 3 and in comparing this to Figure 1, we see little distortion in the groupings based on cluster analysis techniques. This gives us additional confidence in the original matrix, and the correlation between the original and cophenetic matrices is 0.804. The significance of the cophenetic relationships which also shows the integrity of this plot has been determined by Derish-Sokal (1988) to be in the neighborhood of 0.85 in order to be highly significant. We have not attained this level in this particular plot. While the groupings of the phenogram presented in Figure 1 meet our expectation, the correlation itself is not highly significant which probably reflects the number of population pairings from the matrix in Table 7 which are also not significant. In order to adjust for the lack of significance seen in the matrix of Table 7, and in order to heighten the cophenetic correlation, we decided to group a number of population samples into higher groupings. As such, Tác (GorsiumHerculia) and Dunaújváros-Csetény were coalesced as one sample, which can be justified in that the MMD between these two samples was not significant, suggesting they were different samples from the same larger population. Similarly, samples Csákvár and Dunaújváros-Táborkerület (Intercisa) were also coalesced into one sample. These reductions are supported in Figure 1, particularly for the reductions of Csákvár and Dunaújváros-Táborkerület (In terei sa); less so for the reduction between Tác (Gorsium-Herculia) and Dunaújváros-Csetény which join later in the phenogram (Figure 1) at a relatively low, insignificant, level (0.010 from Table 7). The new populations can be called Tác (GorsiumHerculia)-Dunaújváros-Csetény that is made up of populations Tác (Gorsium-Herculia) and Dunaújváros-Csetény. The other new grouping, Csákvár (Floriana)-DunaújvárosTáborkerület (Intercisa) is the coalescence of samples Csákvár (Floriana) and Dunaújváros-Táborkerület (Intercisa). Once these samples were brought together, the trait frequencies and sample sizes were re-established for each trait in each new sample. These are presented in Table 8 and 9 respectively. Theta transformations were again conducted and the Grewal-Smith statistic was utilized in developing new MMD's (Finnegan 1972). The resultant distance matrix is presented in Table 10. The figures underwritten in italics are estimates of the variance and note that in this case, all of the samples are significant at or above the .05 level with one sample generating significance at the .01 level. In this case, our reduction of samples, making larger population samples, appears to be correct. Again, the MMD's from this Table were submitted to TAXON and MXCOMP, which develops a phenogram (Figure 4) based on the raw data, creates the cophenetic matrix with resultant phenogram (Figure 6) and generates another bivariate scatter diagram (Figure 5). The results from the sample reduction are quite evident in Table 10 and Figures 4, 5 and 6. In Figure 4, the arbitrary line of significance shows that, in pairs, all samples are now significantly different. Table 10 shows all sample pair MMD's to be significant at or above the .05 level and the new resultant cophenetic correlation is now 0.902 which is highly significant based on the criteria ofSokal-Derish(1988). The small number of samples which remain in the analysis do not cluster into groups. Rather, they join into one large grouping at nearly equal intervals with Tác (GorsiumHerculia)-Dunaújváros-Csetény joining Csákvár (Floriana)-Dunaújváros-Táborkerület (Intercisa) at the 0.007 level. Sample Rácalmás joins this group at a level of 0.0145 and then sample Sárbogárd joins the group at a level of 0.0257. This suggests relatively equal placement of these three samples in the total matrix. DISCUSSION The mean measure of divergence (MMD) seen in Tables 7 and 10, with resulting phenograms, Figure 4 and 6, should be taken as group data with each population joining at roughly equal intervals. In Figure 1, a somewhat arbitrary line can be drawn at 0.0120, which is the level of lowest significant difference as seen in Table 7. In the phenogram in Figure 1, a number of populations are grouped to the right side or below the arbitrary significance level in that phenogram. As a result, some samples were coalesced into larger samples which we felt depicted single populations. 64