But when this individual produces germ cells, these genes separate with their respective chromosomes, so that half the eggs or sperms have one gene and half the other. On union of these eggs or sperms with sperms or eggs from another parent of the same generation, or any other similarly constituted, three kinds of progeny will be produced-those with both genes for one character, those with both for the other, and those with one for each. The two former will breed true, while the latter are like their immediate parents. The mathematical probability is that there will be one of each kind having both genes alike to two with unlike genes. Without dominance the ratio is thus 1:2:1 and with dominance 3: 1. These results are obtained for very many characters in all sorts of creatures. In the Andalusian fowl, for instance, where dominance is absent, a white mated with a black will have all blue offspring. These blues will give, with sisterbrother mating, blacks, blues, and whites in the ratio 1:2:1. In the garden pea, a tall plant crossed with a dwarf will produce all tall plants, tall being dominant over dwarf. Selffertilized talls of this generation will give talls and dwarfs in the ratio of 3:1.

But there are many cases where crossing individuals with contrasting characters results in offspring which are intermediate for this character, and which breed approximately true. Such instances as inheritance of size and height, and, in negro-white crosses, of skin colour, will occur to everyone. Here we find that more than one pair of genes is responsible for the character. In some cases there are two or three with dominance absent, and sometimes there are several, perhaps not identical, and often with degrees of dominance. Frequently one gene is responsible for the existence of the character, but many other genes may modify the degree of its expression. This situation results in a greater possible range of combination of genes in the formation of the second generation following a cross of extreme types.

A mathematical presentation of the possibilities is beyond the scope of this paper, but it may be said that for every individual of the extreme types obtained in this generation there would be more and more of each degree approaching

and culminating in an exact blend between the two, the number increasing with the number of genes involved. When there is only one pair of genes with dominance absent, we would get, as already explained, two intermediates for one of each of the extreme types. With three pairs, for instance, for every one of each extreme, we would have thirty approximately and twenty exactly intermediate, in a total of sixtyfour. This distribution of degrees of a character ranging from very few of one extreme up to very many intermediate and down to very few of the opposite extreme gives us a symmetrical curve when frequency of occurrence is plotted against degree of expression of character, which latter, when dominance is absent, represents the number of genes for the character present. This curve is, in mathematical language, a 'normal.' It is outlined by the tops of the columns in figure A.

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A. Diagrams to show the number and frequency of the classes of individuals to be expected from a cross involving Mendelian segregation without dominance. Lower left, one pair of genes concerned; middle, two; upper, three; right, four pairs. After Castle.

When many of these similar or multiple genes are involved, and progenies are not numerous, as in domestic animals for instance, the extremes ver yseldom come out even after many generations, and, when one does appear, it is usually hailed as a curiosity or a reversion to an ancestral type, which

latter in a way it is, although through the regular means of Mendelian inheritance. However, it is possible to obtain these extremes at will even under these conditions. If individuals are chosen each generation for resemblance to an extreme, and bred together, the intermediate point or mode will be shifted, until finally we get all the genes for the character together and we have reached our ideal. As all the genes will then consist altogether of like pairs, germ cells will be all alike, and fertilization can produce nothing different from the parents. In other words, selection will no longer be effective. This goal will be attained in about a dozen generations, although the linkage of genes on the same chromosome will delay the process somewhat. This effect of linkage will be removed eventually, through 'crossing-over', a phenomenon the description of which is beyond the scope of this article. The point is mentioned here as it is probably the cause of the irregularities in the curve in the figure representing the effect of selection in an insect much used in genetics, the fruit fly, Drosophila melanogaster.

2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66
generations.

B. Results of selection for a reduced number of bristles in the fruit fly, Drosophila melanogaster. Selection ineffective beyond the 16th generation. After Payne.

Here, then, we have the mechanism to explain Darwin's variations. Random cross-fertilization such as occurs normally in nature will constantly throw together various assortments of these multiple genes which segregate in egg and sperm formation, and recombine in various ways on fertilization, thus producing fluctuating variations such as Darwin

observed. These breed approximately true because they are normally about intermediate as regards their gene complement. Most species are quite variable and none more so, perhaps, than man. We should therefore expect to find in nature where random cross-mating occurs, that the great mass of a population would be intermediate as regards those characters dependent upon or affected by multiple genes, with smaller and smaller numbers as the extremes are approached. This we find to be the case, and it is sufficient to refer to the human race as an example. The general truth of this statement is obvious, but exact measurements have been made on rather a large scale on such features as height, weight, etc., with surprisingly close conformation to the expected normal

curve.

The real test, of course, lies in selection and close inbreeding for several generations. With whatever creatures this has been tried, a limit has soon been reached beyond which progress is impossible. In this way have been built up our remarkably uniform races of animals and plants. Inherited variations are therefore due to multiple genes in a static situation of segregation and recombination, and not to dynamic, progressive, indefinite change. There are other variations, too, which are due solely to the environment and which are not inherited. In the case of plants these might be caused by differences in soil, shade, etc., and in man by such factors as different educational influences.

Darwinism, therefore, insofar as it refers to variations, appears to be a mistaken idea. Forms of life do not constantly change by slow degrees indefinitely. There is possible, however, the production of a profound change in the complexion of a species through selection and inbreeding. Natural selection is not sufficiently severe nor accompanied by close enough inbreeding ordinarily to prevent the existence of great masses of intermediate forms, as described above. Moreover, the well-known vigour of hybrids will give the intermediates an advantage in the struggle for existence. But a pronounced change in the environment may shift the mode in one or the other direction; or the influence of man on plants and animals, and of civilization on him, may equally produce marked results

in favouring various degrees of expression of characters affected or produced by multiple genes. Thus have arisen our breeds of animals and plants, although mutations, which will presently be described, have been effective here also.

The effect of our state of civilization on the human race is a matter of profound interest. There is abundant evidence to show that people of ability (which certainly is caused by many hereditary factors or genes) are marrying late in life and having few children, while those more deficient in intelligence are contributing far more largely to the population of the future. Under a system of equal opportunities for all, persons of ability are being removed from the ranks of the prolific under-intelligent as fast as they arise, and are changed to the status of those who, to say the least, are barely holding their own numerically from generation to generation. It is a melancholy fact that if Harvard had to depend for students entirely on the descendants of its graduates it would long ago have had to close its doors. And so we find that the normal conditions are becoming changed and the human population, instead of remaining from generation to generation preponderantly average with equal small proportions of those of extreme low and extreme high ability, is showing rapid increase in those of lower intelligence and is probably not increasing at all in those of high ability.

The results of mental tests performed during the war on 1,700,000 American soldiers who probably represent that nation fairly well, may at least be regarded as an indication of the situation in modern civilized countries: 4.5% were of very superior intelligence, 9% superior, 16.5% high average, 25% average, 20% low average, 15% inferior, 10% very inferior. Thus we see that 45% are below average and only 30% above. This process of selection may justly be regarded as having been in operation for relatively few generations, but already the balance is shifted to a marked extent. This change is well known to political economists, although perhaps the true cause is not widely realized. So that while we have here to do only with the principles of heredity and not with continuous evolution, profound effects may thus be produced within limits.