Section 9 — Population Genetics 



systems associated with the problem at hand have 

 been developed and a fairly general computer 

 program has been written for the high speed 

 computer IBM 1620. The experiment consisted 

 of three levels of selection intensity, eight levels 

 of linkage condition, four replicates and three 

 dominance models, no dominance, complete 

 dominance and over-dominance. Each combi- 

 nation of the levels of the five factors was sub- 

 jected to 15 generations of selection with an 

 arbitrary initial population in linkage equili- 

 brium. The chief interest of the study was the 

 progressive changes in mean and variance of the 

 phenotypes at each generation. The statistical 

 analyses consisted of fitting a quadratic regres- 

 sion to the curves to evaluate the rate of genetic- 

 gain per generation. Analysis of variance proce- 

 dure was adopted to gain information on the 

 main effects and particularly the interaction 

 of linkage and selection. Results showed that 

 there was a strong indication of presence of inter- 

 action under no dominance model. No significant 

 interaction was detected for the other models. 

 The optimum combinations for the maximum 

 selection gain per generation were determined 

 under all models. A full account of the study will 

 be published in Biometrics. 



9.15. The Theoretical Study of Gene Flow between 

 Sub-species, using a Digital Computer. J. L. 



Crosby (Durham, Great Britain). 



The representation of plant or animal popu- 

 lations by abstract models within an electronic 

 computer allows the theoretical investigation of 

 evolutionary systems which are too complex for 

 mathematical treatment. 



One problem which has been studied in this 

 way concerns gene flow between two related sub- 

 species which come together again and interbreed, 

 after a period of genetical divergence during 

 geographical isolation. It has long been held that 

 where such genetical divergence is great, there 

 should be selection of factors tending to inhibit 

 interbreeding (and thus accelerate speciation), 

 although the theoretical demonstration of the 

 course of such selection is not easy. 



The present series of experiments has consider- 

 ed one aspect of this problem — the selection of 

 pre-fertilization barriers to interbreeding in 

 plants. The example chosen was that of flowering 

 season in two sub-species which flower simul- 

 taneously and interbreed, with partial sterility of 

 the hybrids. Slight differences in the time of 

 flowering arise in the first place by random 

 fluctuations, but where the hybrid sterility is high 

 enough these differences become subject to 



selection; eventually, the flowering periods of the 

 two sub-species hardly coincide, and at the same 

 time each becomes shorter in duration. Inter- 

 breeding is thus very greatly reduced, and gene 

 flow between the two sub-species is almost 

 eliminated; there has thus been a significant step 

 in the direction of speciation. 



The problem of the selection of post-fertiliza- 

 tion barriers to gene flow is a much more difficult 

 one, but it is certainly amenable to the same 

 kind of theoretical treatment. 



9.16. Biometrical Parameters of Self-fertilizing 

 Diploid Populations. Dewey L. Harris 

 (Ames, U.S.A.). 



The mechanism of inheritance in diploid 

 populations is examined for the situation where 

 all reproduction is by self-fertilization. This 

 study suggests certain parameters for a general 

 representation of the means, variances and 

 covariances involved. Letting M( k ) represent the 

 population mean in generation k and letting 

 Co\(k;r,s) represent the covariance of the rth 

 generation progeny means of generation k 

 individuals with the sth generation means of the 

 same individuals, we have 



n 1 



\xfc)= Z (5 -v) 



X - 2kx 

 and 



n n-xiz n-w n-w 



Cov(Ar; r, s) 



A'12 = w= X\ 

 w X, W 



Xl2 X 2 = X 12 



where n is the total number of segregating loci 

 which influence the quantitative trait under consi- 

 deration and Qxuv and u are the basic parameters 



u 



of this parametrization. The meaning of these 

 parameters and their relation to the types of gene 

 action occurring in the population is discussed. 

 The relation of this parametrization to those 

 previously suggested by Horner and by Kemp- 

 thorne is indicated. The implications to these 

 results to the design of experiments for the 

 selection of genetically superior material in such 

 populations is emphasized. 



9.17. A Theoretical Study of Population Changes 

 Under Stabilizing Selection. S. K. Jain and 

 R. W. Allard (Davis, U.S.A.). 



The "intermediate optimum" and the "homeo- 

 static" models of stabilizing selection require 





148 



