CHAPTER I I 



SPECIFICITY 



The reactions between the gametes exhibit a high, but not total, 

 degree of specificity, whether the reaction is fertihzation or the 

 agglutination of spermatozoa by egg water. Quite apart from en- 

 vironmental barriers in nature, we can, for example, be virtually 

 certain that bull spermatozoa will be unable to fertilize or even 

 activate a rabbit egg. In modern language, p, the probability 

 of a successful sperm-egg collision (i.e. one which achieves 

 fertilization), or a, the sperm-egg interaction rate, will be ex- 

 tremely low in such a case ; p will not be zero and might be made 

 appreciably greater than zero by appropriate treatment of the egg. 

 One such treatment, which has been extensively but empirically 

 used in effecting cross-fertilization, is to have an abnormally large 

 number of heterologous spermatozoa round the eggs in question. 

 The probabilistic analysis of fertilization, discussed in chapter 9, 

 Polyspermy, explains why, but not how, an increase in sperm 

 density improves the chances of cross-fertilization. Equ. (2) in 

 chapter 9 can be written in the approximate form 



u = exp(— Tra^ncpt) . , (4) 



where u = proportion of unfertilized eggs in a suspension allowed 

 to interact with spermatozoa, density n, for a known time t ; 

 a = egg radius; c = mean speed of the spermatozoa; and p = 

 probability of a successful collision. 



We can make u smaller, i.e. increase the number of fertilized 

 eggs, by any of the following operations : 



(i) Increase c. In general, this is extremely difficult, if not im- 

 possible, to do, though it is conceivable that Loeb's method of 

 improving cross-fertilization, which involved making the sea 

 water more alkaline (1903), worked partly in this way. Sea-urchin 

 spermatozoa sometimes become more active in alkaline sea water. 



(2) Increase t. Although this can always be done to a certain 

 extent, the fertilizing life span of spermatozoa is limited, and so is 

 the life of the unfertilized egg. In any case, the technique of known 

 sperm-egg interaction times was only developed in 1950 and, at the 



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