DARWIN-WALLACE CENTENARY— DE BEER 347 
confers survival value from the very start of the improvement. But 
when both these functions have been achieved in the same eye a 
mechanism is produced, as E. N. Willmer has indicated, in which the 
visual elements are differentially sensitive to light of different wave- 
lengths, and this is the basis of color vision. The emergence of color 
vision as an unexpected “bonus” resulting from the perfection of two 
other functions is a concrete example of the principle to which Lloyd 
Morgan applied the term “emergent evolution.” 
It has also been objected that natural selection is a difficult concept 
to apply to the evolution of very complex adaptations involving co- 
ordinated variations either in one and the same organism, or even in 
two different organisms. It is not necessary to go far afield to find 
examples of this, for in all animals with separate sexes and internal 
fertilization there has been a separate yet harmonious evolution of the 
reproductive organs in the two sexes. It has been supposed that such 
situations argued so high a degree of “mathematical improbability” 
that they could not be explained as a result of natural selection, which 
was, very erroneously, called “chance.” To this objection there are 
several answers. 
In the first place, those who invoke mathematical improbability 
against natural selection can be refuted out of their own mouths. 
Muller has estimated that on the existing knowledge of the percentage 
of mutations that are beneficial, and a reasoned estimate of the number 
of mutations that would be necessary to convert an amoeba into a 
horse, based on the average magnitude of the effects of mutations, the 
number of mutations required on the basis of chance alone, if there 
were no natural selection, would be of the order of one thousand raised 
to the power of one million. This impossible and meaningless figure 
serves to illustrate the power of natural selection in collecting favorable 
mutations and minimizing waste of variation, for horses do exist and 
they have evolved. 
It is worth while to study the question of improbability more closely. 
As Fisher has pointed out, improbability has a different aspect when 
considered from time before or time after the event. The probability 
that any man alive today will have sons, grandsons, and successive 
descendants in the male line uninterruptedly for one hundred genera- 
tions is infinitesimally small. Yet every man today is the living 
proof that this contingency, so highly improbable as it may have 
seemed one hundred generations ago, has nevertheless occurred. 
Similarly, the effects of natural selection are the reverse of chance 
when considered ex post facto; they are rigorously determined, and 
what they have done is to channel random variations into adaptive 
directions and thereby simulate the appearance of purposive change. 
This is why natural selection has been paradoxically defined as “a 
