Section 9 — Population Genetics 



fitness of an individual to be related to its metric 

 value and heterozygosis respectively and there- 

 fore have different consequences on the distri- 

 bution of gene frequencies and the level of 

 heterozygosity at equilibria. Data from a pre- 

 dominantly inbreeding population of barley, 

 however, did not allow a clear choice between 

 these alternative models. It would be particularly 

 significant to find clear evidence for the operation 

 of homeostatic model in this case in view of the 

 probable role of heterozygote advantage in in- 

 breeding populations postulated earlier.* 1 ^ The 

 present study was taken up in order to charac- 

 terize changes in various statistics (mean, inter- 

 family and intra-family variances, fitness, 

 hybridity, linkages) of a population under diffe- 

 rent forms of stabilizing selection. The case of 

 complete selfing was analysed with the use of 

 generation matrices and of mixed mating with 

 the help of numerical work on a digital computer. 

 In the "variable" parameter runs, the selective 

 values and the proportion of selfing were made 

 random variables in turn and the initial values of 

 "fixed" parameters were varied among the paral- 

 lel runs. These results allow a distinction between 

 the consequences of different models and seem 

 to have interesting bearing on the mode of selec- 

 tive changes in inbreeding populations. 



A mathematical study of natural selection in a 

 fluctuating environment was carried out by 

 analytic methods and computer simulation. 

 The average fitness of the population was deter- 

 mined for different genetic systems, and the optim- 

 al genetic system was found for different pattern 

 of environmental heterogeneity. Genetic variance 

 increases the average fitness provided the environ- 

 mental variation is large compared to the tole- 

 rance of individual genotypes, or when the corre- 

 lation between the environments of successive 

 generations exceeds a threshold that depends on 

 the model. If the first condition holds but not 

 the latter, the optimal system has no additive 

 variance but much epistatic and dominance 

 variance. If only the second condition holds, most 

 of the variance will be additive. In a fluctuating 

 environment the average frequency of a heterotic 

 lethal is below its optimal value so that mutation 

 to the lethal may increase fitness. Mutation also 

 reduces the variance of gene frequency and in- 

 creases the correlation between the state of the 

 population and its optimal state. The optimal 

 rate of recombination was also shown to depend 

 on the environmental variance and autocorre- 

 lation. 



1. S. K. Jain and R. W. Allard, Proc. Nat. 

 Acad. Sci. 46, 1373-1378, 1960. 



9.18. On the Theory of Genetic Loads. Howard 

 Levene (New York, U.S.A.). 



Morton, Crow and Muller and Crow have 

 suggested a method of determining whether the 

 genetic load is mainly due to recurrent deleterious 

 mutations or to genes with heterozygous ad- 

 vantage. The method is based on the comparison 

 of individuals from random matings with inbred 

 individuals. A number of restrictive assumptions 

 are made in the derivation of the method, and 

 additional assumptions must be made to apply 

 it to actual data. The effect of relaxing these as- 

 sumptions, and the degree to which valid con- 

 clusions may be drawn from the types of data 

 so far employed will be discussed. The broader 

 implications of the concept of a "genetic load" 

 will also be considered. 



9.20. Linkage in Selection Programmes. A. Robert- 

 son (Edinburgh, Great Britain). 



Linkage is obviously a retarding factor in 

 artificial selection programmes. The extent of 

 this retardation is dependent on several factors 

 between which there may well be important 

 interactions. The population size in the selection 

 programme may well have an effect at intermedi- 

 ate values but not with very large or very small 

 populations. We may expect the effect to be 

 greater (i) when linkages are primarily in repul- 

 sion in the initial population, (ii) when we are 

 concerned to fix a large number of genes, and 

 (iii) when the initial frequencies of these genes 

 are small. Possible interactions between the 

 factors will be discussed theoretically and with 

 reference to results of computer programmes. 

 Finally a selection experiment with Drosopliila, 

 in which crossing-over was suppressed in one 

 series of lines, will be discussed. 



9.19. Optimal Genetic Systems in a Fluctuating 

 Environment. Richard Levins (Rio Liedras, 

 Puerto Rico). 



9.21. Heterosis and Genetic Balance. N. V. Turbin 

 (Minsk, U.S.S.R.). 



At the present time there can be no doubt that 

 the two conflicting concepts of heterosis -the 



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