Summary
The paper discusses some theoretical and practical considerations in the choice of diversity and distance measures or comparing populations in terms of gene frequencies associated with various characteristics. It develops systematic methods for grouping populations by similarity in genetic diversity, apportioning diversity as between and within populations, grouping of populations by similarity in gene frequencies (cluster analysis) and testing consistency of results by using different diversity and distance measures and subsets of data. The methods are illustrated using the data on nine serological and six biochemical characteristics of the Makiritare Indians. They can be used in the analysis of any qualitative data, such as those that arise in sociological research.
This work is supported by the Air Force Office of Scientific Research under Contract F 49629-82-K-001.
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References
Bhattacharya, A.: 1946, A measure of divergence between two multinomial populations. Sankhyā, 7, 401.
Burbea, J. and Rao, C. Radhakrishna: 1982a, On the convexity of some divergence measures based on entropy functions. IEEE Trans. Information Theory, 28, 489–495.
Burbea, J. and Rao, C. Radhakrishna: 1982b, On the convexity of higher order Jensen differences based on entropy functions. IEEE Trans. Information Theory, 28, 961–963.
Cavalli-Sforza, L.L. and Edwards, A.W.: 1967, Phylogenetic analysis models and estimation procedures. Amer.J.Hum.Genet. 19, 234–257.
Chakraborty, R.: 1974, A note on Nei’s measure of gene diversity in a substructural population. Humangenetik, 21, 85–88.
Csiszár, I.: 1967, A class of measures of informativity of observation channels. Periodica Math. Hungar., 2, 191–213.
Gershowitz, H. et.al.: 1980, Gene frequencies and microdifferentiation among Makiritare Indians (Parts I-IV). Amer.J.Hum.Genet., 22, 515–561.
Jorde, L.B.: 1980, The genetic structure of subdivided populations. A review, pp. 135–208, in Current Developments in Anthropological Genetics, Plenum Press, Edited by J.H. Mielke and M.H. Crawford. Karlin, S., Kenett, R. and Bonne-Tamir, B.: 1979, Analysis of biochemical genetic data on Jewish populations. 11. Results and interpretations of heterogeneity indices and distance measures with respect to standard. Amer.J.Hum.Genet., 31 341–365.
Lalouel, Jean-Marc: 1980, Distance analysis and multidimensional scaling, pp. 209–250, in: Current Developments in Anthropological Genetics, Plenum Press, Ed. J.H. Mielke and M.H. Crawford.
Latter, B.D.H. : 1973, Measures of genetic distance between individuals and populations, in Genetic Structure of Populations, pp. 27–39, edited by N.E. Morton., Univ. of Hawaii Press.
Lau, Ka-Sing: 1983, Characterization of Rao’s quadratic entropy. Sankhyā (in press).
Lewontin, R.C.: 1972, The apportionment of human diversity. Evolutionary Biology, 6, 381–398.
Matusita, K. : 1957, Decision rule based on the distance for the classification problem. Ann. Inst. Stat. Math., 8, 67–77.
Morton, N.E.: 1973, Editor., Genetic Structure of Populations. Honolulu: University of Hawaii Press.
Nei, M.: 1973, Analysis of gene diversity in subdivided populations. Proc.Nat.Acad.Sci., 70, 3321–3323.
Nei, M.: 1978, The theory of genetic distance and evolution of human races. Japan J. Human Genet., 23, 341–369.
Rao, C. Radhakrishna: 1971, Taxonomy in anthropology, in: Mathematics in Archaelogical and Historical Sciences, pp. 19–20. Edin. Univ. Press.
Rao, C. Radhakrishna: 1977, Cluster analysis applied to a study of race mixture in human populations, in: Proceedings, Michigan Univ. Symposium, pp. 175–197.
Rao, C. Radhakrishna: 1982a, Diversity and dissimilarity coefficients: a unified approach. Theoret. Pop. Biol., 21, 24–43.
Rao, C. Radhakrishna: 1982b, Diversity: Its measurement, decomposition, apportionment and analysis. Sankhyā 44A, 1–22.
Rao, C. Radhakrishna: 1982c, Gini-Simpson index of diversity: a characterization, generalization and applications. Utilitas Mathematica, 21B, 273–282.
Rao, C. Radhakrishna and Boudreau, R.: 1982, Diversity and cluster analyses of blood group data on some human populations. Tech. Rept. 82–35, Center for Multivariate Analysis, University of Pittsburgh.
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© 1984 D. Reidel Publishing Company
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Rao, C.R. (1984). Use of Diversity and Distance Measures in the Analysis of Qualitative Data. In: Van Vark, G.N., Howells, W.W. (eds) Multivariate Statistical Methods in Physical Anthropology. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6357-3_5
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DOI: https://doi.org/10.1007/978-94-009-6357-3_5
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