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The use of D2 implies that the investigator is willing to assume that the character dispersions are at least approximately the same in the two groups. When this is not so D2 is inappropriate, and in such a case a possible alternative is Jardine and Sibson's Normal Information Radius (see Jardine & Sibson, 1971). A number of other possibilities exist for between-group distance or similarity measures. For example, the distance between two groups could be defined as the distance between their closest members, one in each group.
The definition of homology given above has been the subject of considerable dispute. For example, Jardine & Sibson (1971) make the point that the definition is logically circular (since we can only infer phylogeny from the classification made after the comparison of characters) and that it also fails to provide any practical criterion for the determination of homologies. Sneath & Sokal (1973) are also critical of the usual definition of homology and prefer to use the term operational homology which implies resemblance between parts with respect to some set of properties.
For an example of a situation where the city-block metric is the obvious measure of distance to use, consider the comparison of amino acid sequences in homologous proteins. 5 Dissimilarity and distance 37 sequences of the last eight amino acids of cytochrome c from man, dog, and chicken : Man Dog Chicken Tyr Tyr Tyr Leu Leu Leu Lys Lys Lys Lys Lys Asp Ala Ala Ala Thr Thr Thr Asn Lys Ser Glu Glu Lys One way of measuring the distance between any two sequences is simply to count the number of non-matching amino acids.