26 INTROGRESSIVE HYBRIDIZATION 



same time the chances of producing plants with values close 

 to those of the Fi become greater and greater. 



In the same way we may consider theoretical expectations 

 among the backcrosses. As the numbers of genes affecting a 

 character increase, there is again an exponential increase in 

 the number of possible intermediates but at a lower rate than 

 in the F2. The chances of producing a backcross exactly 

 similar to the recurrent parent also become exponentially 

 less, but again at a lower rate. With 10 genes there is still 

 about 1 chance in 1000 (Ho 24) of obtaining the same gene 

 combination as the original parent. 



It will be noticed that the ratio between the expectation 

 of recovering the parental type in a backcross and in an F2 

 is an exponential one. Since the chances of recovering the 

 parental gene combination in an F2 are ^i^ and in a back- 

 cross are H", the parental type is 2^ times as likely to occur 

 in a backcross as in an F2. Where n equals the number of 

 gene differences, with 5 gene differences, the chances of re- 

 covering the parental type in a backcross are 30 times what 

 they would be in an F2 ; with 10 gene differences they rise to 

 over 1000 times, and with 20 gene differences to over 1,000,- 

 000. Since in species crosses we are dealing with large num- 

 bers of gene differences, this is a significant point. The 

 greater the gene differences between two hybridizing entities, 

 the exponentially greater are the comparative chances of re- 

 assembling the parental gene combination in a backcross. 



The explanation as outlined above is, of course, highly 

 theoretical. It assumes that all genes have equal effects, that 

 none of them are dominant, and that there are no special 

 factors affecting the randomness of segregation, of fertiliza- 

 tion, of gametic survival, and of zygotic survival. All such 

 complications are known, but before we can consider them 

 and their effects we must understand the basic genetics of 

 large numbers of multiple factors. 



From theoretical genetics, therefore, following the argu- 

 ment outUned above and using the basic formulae of Table 

 2, we can expect that with a large number of independent 



