Non-metric data

Formulae used in calculation of genetic distances

1)    Freeman Tukey transformation

        theta (θ)  =  (0.5*arcsin(1-(2*k)/(N+1)))+(0.5*arcsin((1-(2*k+1))/(N+1)))

    where k is the number of teeth showing the trait and N is the number of teeth observed

2)    Anscombe transformation

        theta (θ) = arcsin[1-(2*(k+0.375)/(N+0.75))]

3)    mean measure of divergence

        (MMD) = 1/r*Σ[(θ₁-θ₂)²-V]

    where r is the number of traits analyzed and

4)    V = (1/(N₁+0.5))+(1/(N₂+0.5))

5)    the variance of the MMD = 2/r²*Σ(V²)

6)    Z = √(2*S)-√((2*r)-1) where S = Σ[(θ₁-θ₂)²/V]

7)    degree of isolation

        DI = MMD-(σ*2)

    An MMD value that is more than twice its standard deviation, is significant at c. .05:  thus a positive DI value is significant.

NON-METRIC TABLE 1. Freeman Tukey transformation theta values used for Figure 9 in Jackes & Lubell (in press).

Key
V1 talus, anterior facet double
V2 calcaneus, anterior middle facet double
V3 mandibular M2, four cusps only
V4 mandibular M1, ml/bd contact cusp; pattern.
V5 mandibular M2, ml/bd contact cusp pattern
V6 mandibular M3, ml/bd contact cusp pattern
V7 left humerus, septal aperture patent
V8 maxillary M1, positive Carabelli's trait
p = frequency of observation
n = total sample examined

NON-METRIC TABLE 2. Freeman-Tukey transformation theta values used for PRINTED FIGURE 3a.
The data for Casa da Moura are from the 1989 analysis of dentitions still in place in bone, as are the data for Feteira.

Key
V1 mandibular right M2, 4 cusps only.
V2 mandibular left M1 code 1, y pattern (ml meets db).
V3 mandibular left M2 code 1, +pattern.
V4 maxillary right M2, 3 cusps only.
V5 maxillary right M1, Carabelli's slight/pronounced tubercle (not pit).
V6 mandibular right M3 'X' pattern code 3.
V7 maxillary left M3, at least 4 cusps.
V8 maxillary right M3, positive Carabelli's trait.
p = frequency of observation.
n = total sample examined.

	p	n	theta
Casa da Moura
V1	24	41	-0.167
V2	11	17	-0.282
V3	5	22	0.550
V4	12	35	0.311
V5	2	29	0.988
V6	11	26	0.149
V7	7	16	0.118
V8	0	10	1.265
Furninha
V1	6	8	-0.464
V2	9	9	-1.249
V3	8	19	0.151
V4	1	7	0.686
V5	2	6	0.293
V6	1	2	0.000
V7	1	1	-0.785
V8	0	4	1.107
Fontainhas
V1	8	8	-1.231
V2	0	1	0.785
V3	1	7	0.686
V4	3	6	0.000
V5	0	5	1.150
V6	6	8	-0.464
V7	2	3	-0.262
V8	0	3	1.047
Moita do Sebastião
V1	25	26	-1.101
V2	8	8	-1.231
V3	3	20	0.732
V4	7	18	0.212
V5	3	30	0.887
V6	7	14	0.000
V7	9	13	-0.366
V8	0	20	1.351
Cabeço da Arruda
V1	27	27	-1.381
V2	8	8	-1.231
V3	4	17	0.525
V4	10	21	0.046
V5	0	30	1.390
V6	3	12	0.482
V7	10	15	-0.319
V8	0	22	1.361
Melides (Zambujal)
V1	12	17	-0.400
V2	3	6	0.000
V3	5	9	-0.101
V4	0	6	1.183
V5	2	5	0.170
V6	4	8	0.000
V7	2	4	0.000
V8	0	4	1.107
Feteira
V1	5	5	-1.150
V2	1	3	0.262
V3	2	4	0.000
V4	0	8	1.231
V5	0	7	1.209
V6	3	3	-1.047
V7	2	3	-0.262
V8	0	4	1.107
Grimsby
V1	10	30	0.329
V2	29	33	-0.827
V3	7	32	0.577
V4	0	53	1.434
V5	3	50	1.042
V6	11	25	0.116
V7	15	27	-0.107
V8	0	30	1.390
Glen Williams
V1	1	19	1.024
V2	35	40	-0.822
V3	4	15	0.454
V4	1	11	0.857
V5	0	29	1.387
V6	12	14	-0.733
V7	3	5	-0.170
V8	1	5	0.535
Maurice
V1	7	36	0.637
V2	20	26	-0.546
V3	11	29	0.236
V4	5	34	0.756
V5	0	43	1.419
V6	17	18	-1.009
V7	7	10	-0.374
V8	0	11	1.278

NON-METRIC TABLE 3. Matrix used for PRINTED FIGURE 3a derived from MMD analysis of Freeman-Tukey transformation theta values;
above diagonal is DI, below diagonal is Z. Positive values above the diagonal are significantly different.

	Casa da Moura	Furninha	Fontainhas	Moita	Arruda	Melides	Feteira	Grimsby	Glen Williams	Maurice
Casa da Moura	-.-	-0.2878	-0.2617	0.0389	0.1431	-0.1550	-0.0322	0.0754	0.1582	0.1456
Furninha	1.1742	-.-	-0.1729	-0.4500	-0.2543	-0.5131	-0.2923	-0.2550	-0.0927	-0.1056
Fontainhas	1.2788	1.4087	-.-	-0.0986	-0.0156	-0.2642	-0.6384	0.3530	0.4026	0.1760
Moita	2.7433	0.4920	-0.0507	-.-	-0.1714	0.1103	0.0677	0.2939	0.5272	0.4430
Arruda	4.5415	1.8705	0.7271	-0.0865	-.-	0.3244	0.2338	0.4800	0.7947	0.6969
Melides	0.9068	0.1393	1.7028	2.8890	4.3049	-.-	-0.3863	-0.0458	0.1886	0.1386
Feteira	2.0776	1.3206	0.1454	2.0463	2.7833	0.3299	-.-	0.1507	0.2170	-0.0158
Grimsby	4.5429	1.7179	4.4390	6.3384	8.5248	2.0587	2.4994	-.-	0.0525	0.1175
Glen Williams	4.7254	3.0869	4.8877	7.6357	9.1749	4.5367	3.4412	2.6639	-.-	-0.1742
Maurice	4.7841	2.7109	4.2724	7.9056	9.6291	3.8962	2.3647	4.0940	-0.2593	-.-

NON-METRIC TABLE 4. Anscombe transformation theta values used for PRINTED FIGURE 3b .
The data for Casa da Moura molars are from the 1989 analysis of dentitions still in place in bone.

Key
V1 mandibular right M2, 4 cusps only.
V2 mandibular left M1, y pattern (ml meets db).
V3 mandibular left M2, + pattern.
V4 maxillary right M2, 3 cusps only.
V5 maxillary right M1, Carabelli's; slight/pronounced tubercle (not pit).
V6 maxillary left M2, positive Carabelli's trait.
V7 mandibular left P4, with more than 2 lingual cusps.
p = frequency of observation.
n = total sample examined.

NON-METRIC TABLE 5. Matrix used for PRINTED FIGURE 3B derived from MMD analysis of Anscombe transformation theta values;
above diagonal is DI, below diagonal is Z. Positive values above the diagonal are significantly different.

	Casa da Moura	Moita	Arruda	Grimsby	Glen Williams	Kleinburg
Casa da Moura	-.-	0.0694	0.1500	0.1355	0.1391	0.3429
Moita	2.8556	-.-	-0.1522	0.3843	0.5803	0.7874
Arruda	4.2059	0.3356	-.-	0.5580	0.7053	0.9175
Grimsby	4.8618	6.7970	8.6130	-.-	0.0084	0.1312
Glen Williams	4.0312	7.4826	8.2650	2.1405	-.-	-0.0074
Kleinburg	9.9025	13.0301	14.6276	5.5342	1.7432	-.-

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