variety. Corn index numbers, as formulated above, are only directly comparable within a single variety. They may of course just as well be used in judging a dent corn, for example, as for the sweet corn here discussed. The average ear of dent corn will obviously give a different value for the index from that given by the average ear of sweet corn.

Any one familiar with the score cards used in judging corn in the various agricultural shows and fairs in this country will recognize that the corn selection index formula here given combines in one expression quantitative determinations of a majority of the characters which appear on the score card. The index in a way takes the place of the judge. It impartially "cuts for each defect" according to a previously agreed upon system of weights. By the combined use of the index number, scales and measuring tape, unconscious or conscious partiality and bias is inevitably and absolutely taken out of the judging. The selection index idea seems capable, when properly developed to meet the needs of particular cases, of supplying in some measure that thing which has been so long desired in all kinds of stock judging, whether of plants or animals, viz., an absolute base or datum plane.

V. SUMMARY

The purpose of this paper is to call the attention of those interested in breeding operations to the usefulness of what we have called "selection index numbers" in such work. The idea of such index numbers is to combine in a single numerical expression the values of a series of variable characters with regard to all of which the breeder wishes to practise selection at the same time. The analytical expression of this idea is discussed and its adaptability and usefulness are illustrated by examples drawn from poultry and maize breeding. It is shown that selection index numbers form a valuable adjunct to the score card in stock judging.

A CONTRIBUTION TO THE THEORY OF

1

ORTHOGENESIS 1

DR. ALEXANDER G. RUTHVEN

UNIVERSITY OF MICHIGAN MUSEUM

SEVERAL reasons have been given why biological discussion has, for a number of years, ceased to center about the fact of evolution and is now chiefly concerned with the factors, for such is evidently the case: the principal aim of modern biological researches is apparently to throw light upon the question of method. It is now a part of common knowledge that Darwin considered the natural selection of fluctuating variations to be the principal factor in evolution, and some of his successors have gone so far as to see in it a sufficient one; but, while few biologists will probably be disposed to deny that natural selection is an efficient factor in evolution, there seems to be now on hand a sufficient body of data to show that it is far from being the only one. Among other methods that have been emphasized, mutation and orthogenesis may be mentioned, each of which has its adherents, and it is the last named of these that seems to be the principal one concerned in the evolution of a group of snakes that I have recently monographed-the genus Thamnophis (the garter-snakes).3

I will briefly summarize the conditions that prevail in this group:

1. The genus Thamnophis consists of four groups of 1 Read at the Darwinian Celebration of the Michigan Academy of Science, April 1, 1909.

I mention only these three (selection, mutation and orthogenesis), as they appear to me to be the only ones that can be considered to have been dominant methods in the evolution of the forms in the genus that constitutes the basis of this discussion.

* Ruthven, Alexander G., "Variations and Genetic Relationships of the Garter-snakes," Bull. 61, U. S. Nat. Museum.

closely related forms, each group ranging both northward and southward from the Mexican plateau (which is their center of dispersal) into North and Middle America.

2. Each group consists of a series of forms, the ranges of which adjoin and correspond to different geographical regions.

3. The forms of the same group may intergrade or not, but in either case they come in contact where the geographic conditions with which they are associated meet, and the areas of transition in characters correspond to the areas of intermediate environmental conditions. When the forms intergrade the transition in characters takes place gradually in the intermediate region, and where there is apparently no intergrading at present the two forms become most like each other in this region, there being no abrupt changes in characters between two directly related forms.

4. Each group tends to become progressively more dwarfed away from the Mexican plateau, each form usually being more dwarfed than its neighbor toward the center of origin, and less so than the representative whose range adjoins it on the side away from the center.

5. The relative size is correlated with the number of labials and rows of body scales, and these two characters -size and scutellation-constitute the only apparent specific differences, except in the few cases where they are accompanied by differences in color or relative taillength.

6. The amount of dwarfing is not associated with particular geographic regions, but the scutellation and relative size of any form is that of its immediate ancestor plus the dwarfing which it has itself undergone. Thus a dwarf form of one group frequently occurs in the same region with a much less dwarfed representative of another group, the difference in relative size being due to differences in the number of forms between the one in question and the center of origin.

7. The variations in the characters of each form fluctu

ate about a mean, and the transition in characters between the different forms is brought about by a gradual variation of the average type.

Students of evolution problems will recognize in this summary (a) the old story of the association of different forms with different environmental conditions, (b) the so-called definite or determinate evolution, and (c) that the phylogenetic variations are gradual.

It has long been noted that, among animals of the same group, the different forms are generally associated with different environmental conditions. In some cases it seems that these forms may occupy different habitats in the same environment, but in by far the greater number of instances, at least among terrestrial animals, directly related forms inhabit different, but neighboring, geographic areas. That there is some connection between the differentiation of such a group and the diversities of the region it occupies has usually been assumed; at least it is a fact that must be considered in any explanation of evolution. It is explained by natural selection on the assumption that the different conditions in the two regions demand different adaptations on the part of the organism, but this explanation will apparently not hold in the case of the garter-snakes, for there is certainly no advantage in dwarfing per se. It might be assumed (and it would be pure assumption) that this trait is correlated with unperceived adaptative characters, but this would seemingly be trying harder to save the theory of natural selection than to explain the facts. I have pointed out that there is no relation between the amount of dwarfing and particular habitats, but that forms (belonging to different groups) of quite diverse scutellation may occupy the same region. Apparently the conditions in each region do not call for a particular size (as would, it seems to me, be approximately the case if the struggle for existence in each habitat required that the forms become dwarfed), but only act to modify to some extent the invading form, the relative size of the latter being

determined as much by the modifications which the group has previously undergone as by those to which the particular form has been subjected.

I believe that these objections to the operation of selection in the evolution of these forms also argue against De Vries's mutation theory as an explanation, for, while it is easily conceived that mutations may have arisen within the limits of fluctuating variation in each case, we must also assume that the new form pushed into the new environment, or at least now occupies it to the exclusion of immediately related forms, because better fitted for it, which does not seem to be the case. What seems to have actually taken place is that as each group pushed out from the center of origin it became modified each time it encountered a new region of environmental conditions, not by the selection of forms better adapted to the new conditions, but by the modification of the entire section that invaded the new region. This may be tested more thoroughly by an examination of the method of evolution.

Perhaps the most striking characteristic of this genus. is the manner in which evolution has taken place along definite lines. Although the forms frequently have other distinctive characters, they nearly all have this in common that they are more dwarfed than the form from which they have been derived, and there is no case in the genus where a form is larger than its neighbor toward the center of origin. The history of each group has thus been one of progressive dwarfing as it departed from the center of dispersal.

It is too often overlooked by students of evolution that natural selection can cause directed evolution (orthoselection); for in order that it may do so it is only necessary that there be an accruing advantage in the increased development of a character. The characters must thus be utilitarian, however, which is apparently not true in this case. Moreover, it would certainly be taxing the theory to make it account for the continued development