HEREDITY 203 



chromosomes (in which case they are said to be hnked) these probabilities 

 are altered, roughly in proportion to the relative distance bervveen the two 

 pairs of factors on the chromosomes. This distance determines how often 

 the factors may assort at all, the assortment approaching a random one 

 as the relative distance increases. 



(3) The type of mating. When a population consists of various sorts of 

 individuals, there will be, of course, various sorts of mating possible. The 

 kinds and proportions of germ cells available for fertilization in any 

 particular mating will depend upon the genetic composition of the indi- 

 viduals involved in the mating. Mass matings in a population may be at 

 random or may be assortative (that is, certain types of mating tending to 

 occur to the exclusion of others). The probabilities for various kinds of 

 offspring depends among other things on the type of mating. 



(4) The freqiievcies, in the population, of the genes concerned. The 

 two members of a pair of factors may be equally distributed in a popula- 

 tion, or one may be common and the other rare. The relative proportions 

 can be determined by the use of certain mathematical technics, and are 

 of importance wherever mass matings are concerned. Moreover, the fre- 

 quencies of the two members of a pair of factors may have reached an 

 equilibrium in the population, or they may not yet have done so. This too 

 may be deduced by special methods. Gene frequencies and equilibria be- 

 come of especial importance in the modern analysis of human pedigrees, 

 and will be further discussed later in this paper. 



(5) The union of the germ cells. Fertilizations normally occur at ran- 

 dom, that is, any sperm has an opportunity equal to that of any other sperm 

 of fertilizing a particular tgo^; conversely, an tg^ has a probability equal 

 to that of any other available tg^ of being fertilized by a particular sperm. 

 Here again, however, exceptions occur, and cases of selective fertiliza- 

 tion are known. In such cases the probabilities are of course shifted. 



(6) The ijiter action of factors, during development, zvith each other 

 and with the environment, residting in observable characters (phenotypes). 

 The characters finally produced and the proportions in which they are 

 produced will depend upon this and the preceding five phenomena. These 

 phenomena, serially taking place from generation to generation in specific 

 environments, give rise to the phenotypic expressions of characters in 

 definite ratios, from the analysis of which the laws of heredity have been 

 deduced. 



The type of inheritance involved in any particular case, the number 

 of pairs of factors concerned, the mode of interaction and other relevant 

 conclusions have long been determined from the study of the phenotypic 

 ratios derived from specific types of mating. The classical genetic analyses 

 of animals and plants have necessitated the scrutiny of at least three gen- 

 erations (parents, F^ and Fg). Often additional generations (back-crosses, 

 F3, etc.) have been required. As long as such planned matings were readily 



