Guttman, Ruth and Louis Guttman (Department of Psychology, The Hebrew University of Jerusalem, Israel, and The Israel Institute of Applied Social Research, Jerusalem) 1974. Nonmetric analysis of relationships among inbred strains of mice. Syst. Zool. 23: 355-362.-A multidimensional scalogram analysis, MSA-I, shows that 27 inbred mouse strains, classified by thirteen loci, can be represented as points in a two-dimensional space. Five of the loci provide a rectangular coordinate system for partitioning of the space, three a polar, while the remaining ones make little further systematic contribution. The systematic partitionings may suggest theories of the origin of the strains' similarities and differences. [Nonmetric analysis; relationships; inbred mice.] In comparing subgroups of populations of common origin, several different methods have been developed that attempt to estimate degrees of relatedness or of genetic between these populations. Nei (1972) has critically reviewed a number of such methods and proposed a measure of distance based on the identity of genes in local populations within a species. A conceptually more satisfying procedure is that of Taylor (1972) who has used the distribution of alleles at 16 polymorphic loci in 27 inbred strains of mice to produce a two-dimensional plot of these strains on the basis of an eigenvector analysis of their similarity matrix. This plot gives a graphic picture of the relative similarity of the strains based on all the information available, and shows whether a strain is relatively common or distinctive on the basis of the average number of shared alleles with the other 26 strains. The eigenvector method of analysis has, however, at least four limitations, some of them pointed out by Taylor himself. One limitation is the need to calculate similarity coefficients. This involves an arbitrary decision, Taylor's being simply to count the number of shared alleles for each pair of strains. A second limitation is the use of linear (vector) methods for basically qualitative (dichotomous) data. A third is the lack of a clear stopping rule as to how many eigenvectors to use. Finally, the most important limitation may be the loss of information about the individual loci by focusing on the mouse strains alone as points in the derived space. The present paper presents a reanalysis of Taylor's data which avoids these four limitations. The reanalysis plots the 27 strains as points in a two-dimensional space that is not unlike Taylor's approximation, but in which the role of each locus is made explicit for partitioning the space. No similarity coefficients are needed. The analysis is based directly on the observed distributions of alleles over the strains, as given in Taylor's Table 1 (1972, p. 83). The analysis is nonmetric rather than vectorial, as is appropriate for the qualitative nature of the data involved. Of the sixteen polymorphic loci given in Taylor's Table 1, thirteen have been used in this analysis. Each of the three that were omitted (Es-2, Pgm-2, and Ldr-1) had identical alleles in all but one or two strains. The data used in this analysis are given in Table 1. The loci are Es-1:esterase-1; Es-3:esterase-3; Mod-l:NADP malate dehydrogenase-1; Id-i :isocitrate dehydrogenase-1; Gpd-i:autosomal glucose 6-phosphate dehydrogenase-1; Gpi-i glucose phosphate isomerase-i; Pgm-l :phosphoglucomutase-i; Hbb:hemoglobin beta chain; Dip-l:dipeptidase-i; H2:the histocompatibility locus; Hc:serum complement; rd:retinal degeneration; and In:7-12 dimethylbenzanthracene inflammatory response.
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