The three indexes were compared to determine their relative efficiency in making genetic progress. This rate of progress is proportionate to the size of the correlation between genotypes of the selected animals and their indexes. The second and third indexes were 8.8 and 11.3 percent, respectively, more efficient than the first. Since the time and effort expended in keeping records is but a small fraction of the total labor connected with a breeding program, the second index would probably be preferable to the first in most cases. The third might also be chosen over the second, since genetic progress could be increased a little more through its use, and the extra labor would be only that of computing and using the litter averages from data already available.

The progress that could be made by using the three indexes studied by Hazel was 36.3, 39.5, and 40.4 percent, respectively, of that which could have been made by a perfect index, or one in which the phenotype, or appearance of the animal, was a perfect measure of the genotype, or genetic make-up, of the animal. The loss is due to the confusing effects of environment, dominance of one gene over its pair-mate, so that the recessive member of the pair is not evident in the phenotype, and epistasis, or interaction of genes, all of which can make phenotypes unlike genotypes.

A selection index for Rambouillet sheep has been developed at the Western Sheep Breeding Laboratory at Dubois, Idaho, based on the same principles as those outlined for swine indexes. These traits have been included: Face covering (F), length of staple (L), weaning weight (W), type score (T), condition score (C), and neck-fold score (N). The completed index (I) is as follows:

I=-75— (15 X F) + (7 X L) + W+ (0.4 X T) + (7 X C) — (11 X N)

The constant of 75 is added to insure that the index will be positive and average around 100. Corrections for various factors, like twinning, age of dam, and inbreeding, may be made directly on the index, using suitable correction constants. The completed index varies from about 70 to 150 for individual lambs in the Rambouillet flock at Dubois, with an average of about 110. The value of the index may be estimated by comparing the progress when the index was used with that before it was available. Progress was roughly determined by combining the selection differentials for the various traits after each was weighted by its heritability and its economic importance. Over-all progress from selection at weaning age was increased in the range of 20 to 50 percent by the use of the index.

The breeding merit of an animal may be estimated in various ways, including the merits of its ancestors, the animal's own characteristics and performance, the merit of collateral relatives, such as sibs (brothers and/ or sisters) and half sibs, and the merit of its off spring.

The last is usually called the progeny test. Much has been written concerning its accuracy, compared to that of other methods that might give indirect measures of breeding merit. From the standpoint of rate of genetic progress, factors other than relative accuracy must be considered. The most important of these factors are the age at which progeny tests may be obtained and the rate of reproduction. The longer interval between generations that results from use of the progeny test tends to offset the advantage gained by more accurate selection, and may actually reduce the annual rate of improvement.

The relative merits of progeny testing and other methods of selection have been studied by G. E. Dickerson and Dr. Hazel. This is an intricate problem requiring detailed mathematical studies in order to obtain a solution. They considered a number of traits in various species, and concluded that the possibilities of increasing progress by a regular plan for use of progeny-tested sires are limited to certain kinds of livestock and to certain traits. The reasons therefor are outlined here:

1. The less the interval between generations is increased by progeny testing, the more likely it is that progeny testing will increase progress. This is illustrated by an example contrasting the results of selecting for weanling and yearling traits in sheep. Use of the best ram tested the year before on an optimum portion (60 to 70 percent) of the ewes increased progress by about 4 percent for weaning traits, but reduced it for yearling traits, as compared with progress to be expected from use of only the two best yearling rams each year. The only difference between these two examples is that 1 year is required to obtain progeny-test information on weanling traits, while 2 years are required for yearling traits.

2. When the rate of reproduction is low, progeny testing of sires is more likely to increase progress. The resulting increase in genetic superiority of parents tends to be larger, relative to the increase in age of parents, when there is less opportunity for early culling, particularly among females. For example, progeny testing affects progress more favorably for yearling traits in sheep than for growth rate in swine. Obviously, a much higher proportion of the female offspring must be retained in order to maintain the population in sheep than in swine.