Calculation of Smith’s Mean Measure of Divergence for Intergroup Comparisons Using Nonmetric Data

Harris, Edward F.; Sjøvold, Torstein

doi:10.26575/daj.v17i3.152

Cited by 96 publications

(67 citation statements)

References 22 publications

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“…The MMD statistic converts a battery of trait frequencies into a nonlinear distance value between group pairs; low values indicate similarity and high values imply dissimilarity (Harris & Sjøvold, ). The MMD was calculated according to the formula in Sjøvold ():

M M D = \frac{1}{r} true {true\sum}_{i = 1}^{r} ({}, {(θ_{1 i} - θ_{2 i})}^{2} - \frac{1}{n_{1 i} + 0.5} - \frac{1}{n_{2 i} + 0.5})

where r is the number of traits used, n 1 i and n 2 i are the numbers of individuals examined for the i th trait in the two groups being compared and Θ 1 i and Θ 2 i are the transformed frequencies of the i th trait in the two groups.…”

Section: Methodsmentioning

confidence: 99%

“…The transformed frequencies were calculated using the Freeman & Tukey () angular transformation to correct for small sample sizes and low (≤0.05) or high (≥0.95) trait frequencies:

θ = \frac{1}{2} \sin^{- 1} ((), 1 - 2 \frac{k}{n + 1}) + \frac{1}{2} \sin^{prefix- 1} ((), 1 - 2 \frac{k + 1}{n + 1})

where k is the count of positive observations for a trait in a sample of size n . MMD distances can be considered significant if they are more than twice their standard deviation (see Harris & Sjøvold, ; formula 12).…”

Section: Methodsmentioning

confidence: 99%

“…The MMD statistic converts a battery of trait frequencies into a nonlinear distance value between group pairs; low values indicate similarity and high values imply dissimilarity (Harris & Sjøvold, 2004). The MMD was calculated according to the formula in Sjøvold (1977):…”

Section: Quantitative Analysismentioning

confidence: 99%

“…where k is the count of positive observations for a trait in a sample of size n. MMD distances can be considered significant if they are more than twice their standard deviation (see Harris & Sjøvold, 2004; formula 12). The nonlinear distance matrix produced by the MMD was then submitted to multidimensional scaling (MDS) to calculate an optimally scaled distance matrix (Irish, 2010).…”

Section: Quantitative Analysismentioning

confidence: 99%

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Evidence for Migration Influx into the Ancient Greek Colony of Metaponto: A Population Genetics Approach Using Dental Nonmetric Traits

Rathmann

Semerari

Harvati

2016

Intl J of Osteoarchaeology

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Ancient Greek colonies were founded by Greek seafarers all along the Mediterranean coast as early as the eighth century bc. Despite extensive archaeological and historical research, the population structure of the inhabitants of Greek colonies and their relationship to indigenous populations are still debated. Here, we perform a biodistance analysis to reconstruct migration and gene flow between the ancient Greek colony of Metaponto (southern Italy) and indigenous groups in the surrounding hinterland (900–250 bc). We collected dental nonmetric trait data of 355 human skeletons from the indigenous Italic sites of Santa Maria d'Anglona, Incoronata and Passo di Giacobbe. This data set is compared with an urban and rural sample of the Greek colony of Metaponto comprising 351 individual dentitions. The R‐matrix approach is used to estimate inter‐population relationships and FST. The resulting kinship coefficients indicate that the three indigenous groups exhibit greater similarity to each other and possess lesser similarity to the two Metapontian samples. Interestingly, the two samples of Metaponto are least similar to each other, although they are geographically very close. The FST estimates confirm this pattern and reveal greater biological variation between the two nearby Metaponto samples (FST = 0.0603) than between the three geographically fairly distant indigenous groups (FST = 0.0389). We conclude that the Greek colony of Metaponto included large numbers of people with diverse geographical origins, whereas the indigenous Italic communities of the surrounding hinterland exhibited high levels of homogeneity and cohesion. Copyright © 2016 John Wiley & Sons, Ltd.

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M M D = \frac{1}{r} true {true\sum}_{i = 1}^{r} ({}, {(θ_{1 i} - θ_{2 i})}^{2} - \frac{1}{n_{1 i} + 0.5} - \frac{1}{n_{2 i} + 0.5})

Section: Methodsmentioning

confidence: 99%

“…The transformed frequencies were calculated using the Freeman & Tukey () angular transformation to correct for small sample sizes and low (≤0.05) or high (≥0.95) trait frequencies:

θ = \frac{1}{2} \sin^{- 1} ((), 1 - 2 \frac{k}{n + 1}) + \frac{1}{2} \sin^{prefix- 1} ((), 1 - 2 \frac{k + 1}{n + 1})

Section: Methodsmentioning

confidence: 99%

“…The MMD statistic converts a battery of trait frequencies into a nonlinear distance value between group pairs; low values indicate similarity and high values imply dissimilarity (Harris & Sjøvold, 2004). The MMD was calculated according to the formula in Sjøvold (1977):…”

Section: Quantitative Analysismentioning

confidence: 99%

Section: Quantitative Analysismentioning

confidence: 99%

See 2 more Smart Citations

Evidence for Migration Influx into the Ancient Greek Colony of Metaponto: A Population Genetics Approach Using Dental Nonmetric Traits

Rathmann

Semerari

Harvati

2016

Intl J of Osteoarchaeology

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“…We surveyed the frequency of appearance of 12 NMTs (Table ) within p3 teeth as illustrated by Suchentrunk (), Suchentrunk and Flux (), and Suchentrunk, Alkon, Willing, and Yom‐Tov (). We then evaluated the affinity of the three taxonomic groups based on the appearance frequency of NMTs using Smith's mean measure of divergence (MMD), adopting Harris and Sjøvold's () approach for calculation. Thus, a statistically significant result can be reported when the MMD is greater than two standard deviations (Sjøvold, ).…”

Section: Methodsmentioning

confidence: 99%

Late Pleistocene hares of the Japanese archipelago: Paleobiogeographic implication at the Last Glacial Maximum

Sawaura

Sawada

Sato

et al. 2018

Intl J of Osteoarchaeology

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The Tsugaru Strait is often referred to as Blakiston's Line in biogeography. Although this strait is thought to have become narrower during the Last Glacial Maximum, it did not close completely to form a land bridge. Sea‐level drawdown associated with cooling nevertheless weakened the influence of the Tsugaru Strait as a barrier to faunal migration. The currently accepted hypothesis is that only some large and highly mobile ungulates were able to migrate to Honshu over this strait to the exclusion of small mammals. However, this remains problematic as very few fossils corroborate this idea, and quantitative identification methods for use with tiny fragments of teeth have not been developed. In this study, we determine which of the species Lepus timidus (now distributed on Hokkaido and to the north) and Lepus brachyurus (now mainly distributed on Honshu, Shikoku, and Kyushu) can accurately be identified within a sample of Late Pleistocene Lepus sp. fossils recently unearthed from the Shitsukari‐Abe cave to the immediate south of the Tsugaru Strait. This is because we are unable to exclude the possibility that these fossils are referable to L. timidus on the basis of site location alone. Thus, utilising images of mandibular third premolar teeth obtained via microcomputed tomography scanning, we report (a) linear measurements, (b) a survey of the frequency of appearance of nonmetric traits, and (c) principal component analysis using landmark methods. The results show that fossil representatives of the genus Lepus can be differentiated from extant L. timidus and closely resemble L. brachyurus. Considering the past allopatric distribution of the 2 species suggested by other studies as well as fossil records around the Tsugaru Strait, this result corroborates the existing hypothesis that only large and highly mobile ungulates were able to navigate the Tsugaru Strait.

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Assessing Dental Nonmetric Variation among Populations

Irish¹

2015

A Companion to Dental Anthropology

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Calculation of Smith’s Mean Measure of Divergence for Intergroup Comparisons Using Nonmetric Data

Cited by 96 publications

References 22 publications

Evidence for Migration Influx into the Ancient Greek Colony of Metaponto: A Population Genetics Approach Using Dental Nonmetric Traits

Evidence for Migration Influx into the Ancient Greek Colony of Metaponto: A Population Genetics Approach Using Dental Nonmetric Traits

Late Pleistocene hares of the Japanese archipelago: Paleobiogeographic implication at the Last Glacial Maximum

Assessing Dental Nonmetric Variation among Populations

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