June, 1931 



EVOLUTION 



Page seven 



thetical forty-nine individuals. 



We may now consider what would happen in the case of 

 seine kind of creatures, or objects, which did not have the 

 power of multiplication, but which were otherwise similar to 

 the organisms just discussed, and like them could mutate (or 

 in this case we should simply say, "change") . We may sup- 

 pose either that these beings produce just one offspring and 

 then themselves die, or that they are potentially immortal and 

 change directly from one form into another. In either case, 

 if their "mutational" possibilities are the same as those of the 

 multiplying organisms previously considered, then we should 



iliiLiiliililLLlLLiLLlLLLLLLLLLliilLlliLLl 



Diagram 2. 



How a beneficial combination of variations (gi g^) might arise 



without multiplication, and number required. 



have to start with seven of them to get one having 

 a change equivalent to g^. But we should have to be provided 

 with seven already bearing gi in order to obtain one having g2. 

 * Since in the first place only one in seven come to have gi (or 

 its equivalent) , we should have to start with 7 x 7, or 7^, or 

 49, in order to get the required seven having gi (or its equiva- 

 lent) which would in turn yield the one finally having both 

 gi and g2 (or their equivalents) . This is indicated in the dia- 

 gram. (Here, for convenience in examining the diagram, simi- 

 lar types are grouped together, although chance would scatter 

 them indiscriminately. Also, all forms of "equivalent" type 

 are represented as though identical) . 



On comparing these non-multiplying objects with the mul- 

 tiplying ones we then see that, to get a given kind of combina- 

 tion by means of a given incidence of "mutation," we have to 

 start with just as many, in the case of the non-multiplying 

 objects, as, in the case of the others, would have been produced 

 in the end by the entire process of multiplication, if all indi- 

 viduals had multiplied at the rate at which the selected indi- 

 viduals did. One out of this total number hence represents 

 the "chance" that our desired combination could have come 

 about purely fortuitously in any particular individual at the 

 end of the given lapse of time, no matter whether the indi- 

 viduals were of the multiplying kind or not. By the laws of 

 chance, if only a few times this total number are given, this 

 combination, or one equivalent to it in "excellence," is prac- 

 tically certain, under the conditions postulated, to be present in 

 one or more individuals. 

 % Organisms, however, represent many more than two advan- 

 tageous features in combination. By the same reasoning as 

 the above, we may find the chance of obtaining a combmation 

 of three features — gi g2 gs- We may assume again that the 

 g3 change is in itself, at its time of occurrence, about as rare 

 as either gi or g2 alone was: namely, of the frequency of 1 in 

 7. It will then be seen that the gi g2 individual must be al- 

 lowed to go through a period (the third period) of mutation 



and of multiplication times 7, whereupon gj g2 g3 will arise. 

 Further, it is evident that the rate of multiplication of the 

 individuals in the line of descent that gave rise to the gi g2 gg- 

 bearing individual was such as to have given rise to 7 x 7 x 7, 

 or 7 3 or 343 individuals, after this lapse of time, if only all 

 descendants of these ancestors had multiplied at the same rate 

 as they themselves had. In the case of non-multiplying objects, 

 it would have been necessary to start with 7^ or 343 individuals, 

 in order to get a corresponding result — an individual with a 

 rare combination of three advantageous mutually adjusted 

 characters, gi go gs- Generalizing, we may say that if the 

 frequency of an advantageous mutation were 1 in r instead of 

 1 in 7, and the number of steps involved was s instead of 3, 

 the corresponding total number of individuals would be r^. 

 All this is, in fact, only a simple application of a well-known 

 and very elementary mathematical principle applying to the 

 formation of random combinations in general. 



It is not, however, until we apply this little formula to the 

 natural conditions pertaining to our immediate problem that 

 its full significance for us becomes clear. What shall we take 

 as our "r" (the rarity of advantageous, or "organizational" 

 mutations) and what as our "s" (the number of such advan- 

 tageous mutational steps) ? 



Undoubtedly r changes its value radically at different stages 

 in the evolutionary sequence, but it would seem quite con- 

 servative to represent r, in general, as being as small as 100. 

 In other words, it seems likely that at least 100 mutations 

 must usually occur before one occurs of such a special type that 

 it could take part in the improvement of the life-organization. 

 In flies (Drosophila) we find that there are something like 

 ten times as many "lethal" and "semi-lethal" as ordinary vbible 

 mutations, and even among the "visibles," the vast majority 

 reduce vitality or lessen the chances of survival in one or more 

 ways. It is certain that not 1 in 100 detectable mutations is 

 advantageous in flies; in fact, for all we know, the number 

 may be more Uke 1 in 100,000. 



In the case of s there are almost equally wide limits of un- 

 certainty, but again we may arrive at a safe minimum figure. 

 In flies I have shown that there are at least 1,500 different 

 genes, and probably many times that number. There must 

 then have been at least 1,500 different mutations to produce 

 these genes from their predecessors. This figure, however, 

 seems absurdly small in view of the great complication of a 

 fly's anatomy, physiology and developmental processes. It is 

 very likely, then, that there are many more genes than 1,500 

 and that each gene has had a history of numerous mutations, 

 which step by step have differentiated it from one original type 

 of gene. Considering too that man is certainly much more 

 complicated than a fly, we might boldly guess that there may 

 have been a million or more advantageous mutational steps in 

 his ancestry (this would allow, say, 50,000 genes, in each of 

 which, on the average, 20 mutational changes had occurred). 

 Let us first, however, take s for man, at the undoubtedly far 

 too low minimum value of 1,500, and r at 100. 



Our total number rS thus becomes (100) i5oo_ jhat then is 

 the minimum number of individuals we should have to start 

 with, in the case of non-multiplying objects, to arrive, by "pure 

 chance," at one having the complication and perfection of or- 

 ganization of a man. We shall examine later what the size 

 of this number implies. It is also the minimum number which 



