Precipitin Tests as a Basis for a Quantitative Phylogeny

In an earlier report1the results of a series of precipitin tests on the sera of certain common Mammalia were given. The degree of reaction as indicated by the titer of the ring tests was expressed as percent of the homologous titers. A new method of using these percent values as a basis for a quantitative phylogeny is here proposed and illustrated.The method involves the calculation of the average values of the reciprocal relationships between pairs of species. These average values (M) constitute the primary data to be used. The values of M together with their probable errors are given in Table I.The least reliable value (dog vs. horse) is still 3.3 times its P.E., and hence the whole series is probably significant. To express these quantitative measures of relationship graphically, it is proposed to use the corresponding 100-M values for the actual distances between the loci of the species. For example, taking dog as the starting point, the distances of the other species from dog are given in the table. The positions of the other species, beef, sheep, pig and horse may then be further defined by their corresponding 100-M values in relation to each other. There will be four 100-M values to be used in establishing the proper locus of each species and all must be so used. The result is shown in Fig. 1, which gives a side view of the spatial arrangement of the loci projected on a plane surface.It should be borne in mind that Fig. 1 shows only the present relationshipsof these 5 species, not their ancestry. The figure does not show time and hence cannot show ancestry. To add the element of time to this geometric figure would require a fourth dimension.