GENETICS: H. S. JENNINGS 
45 
region of New Mexico; and at San Cristobal in still another part of the 
state, N. C. Nelson has excavated a stratified deposit showing four suc- 
cessive layers of different type. It is quite likely that some of the types 
at these three sites will prove to be similar, or even identical, as soon as 
the material can be compared. In this event a chronological frame 
work would be established that may prove capable of extension to ac- 
commodate a considerable part of the prehistoric data from the South- 
west, and to fix distinctive and otherwise undatable local variations of 
ancient culture. The impression that there were at least two principal 
periods in the Southwest, the earlier represented by what are currently 
called Cliff Dweller forms, has of course long been prevalent, but the sup- 
porting evidence has been random. The three present sequential de- 
terminations promise not only definitely to establish but to elaborate the 
older general conviction. 
The findings here discussed will be published in the Anthropological 
Papers of the American Museum of Natural History. 
THE NUMERICAL RESULTS OF DIVERSE SYSTEMS OF 
BREEDING 
By H. S. Jennings 
ZOOLOGICAL LABORATORY, JOHNS HOPKINS UNIVERSITY 
Received by the Academy, December 20, 1915 
When organisms differing with respect to a pair of characters are 
bred for generation after generation, the relative numbers of individuals 
that will show any particular combination of characters in any given 
generation of course depend on the system of mating followed. The 
different classes of individuals may mate at random; or there may be 
assortative mating (dominants with dominants, recessives with re- 
cessives); or dominants alone may be bred; or recessives alone. Or 
again, self fertihzation may prevail; or one of the various possible t3^es 
of inbreeding may be followed. If we represent the two alternative 
characters by A (dominant) and a (recessive), then three types of indi- 
viduals are possible, AA, Aa, and aa. The question here raised is as 
to the relative numbers of each of these three types of individuals after 
any number n of generations of mating, by any of the systems mentioned 
above. This depends of course on the constitution of the parents at 
the beginning, as well as on the system of breeding and the number of 
generations. 
When breeding by a given system is continued for many generations, 
several types of results may be distinguished: 
A. In some cases the proportions of the population having particular 
