NATURAL SELECTION 221 



of ascertaining how far these are to be considered representative. 

 Now that temperature is known to affect the mutation-rate, 

 the actual numerical value of the observed rate must be 

 received with added caution. But there are more serious 

 difficulties. It is admitted that mutations may be easily 

 passed over, so that the observed rates can be only minimum 

 values. On the other hand, at any given moment there can 

 be only a limited number of directions in which profitable 

 mutations can occur, and it is the frequency of these rare 

 mutations that most interest us. Now statistical methods 

 are not well fitted for dealing with very rare occurrences. On 

 this point an interesting article by Bridgman (1932) on the 

 application of statistics to thermodynamics may be consulted. 

 He comes to a conclusion that appears relevant to the present 

 discussion. ' In order to establish with sufficient probability 

 that the actual physical system has those properties which are 

 assumed in estimating the frequency of rare occurrences, it is 

 necessary to make a number of observations so great that the 

 probability is good that the rare occurrence has already been 

 observed.' It would seem likely that the occurrence of muta- 

 tions in desired directions would be rare enough to make it 

 impossible to estimate their frequency apart from direct 

 observation. 



Probably the most important contribution from the mathe- 

 matical evolutionists is the basic contention that the known 

 mutation-rates are insufficient to account for evolutionary 

 change, if they are unaccompanied by a selective process. 

 It had been for a long time felt by some authors, who were 

 inclined to discount the value of Natural Selection, that a 

 mutation which conferred no advantage on its possessor (or 

 was not correlated with an advantageous mutation) would 

 have little chance of surviving the normal incidence of elimina- 

 tion. Fisher {I.e. p. 20) has stated this difficulty clearly. He 

 points out that, as the mutation-rate in Drosophila is of the 

 order of 1 : 100,000, ' a lapse of time of the order of 100,000 

 generations would be required to produce an important change 

 in Drosophila ' at the known rate. Thus, ' for mutations 

 (alone) to dominate the trend of evolution, it is necessary to 

 postulate mutation-rates immensely greater than those which 

 are known to occur and of an order of magnitude incompatible 

 with- particulate inheritance.' There is thus held to be a 



