By A.G. Buckley, J-.L. Goffin

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**Extra resources for Algorithms for Constrained Minimization of Smooth Nonlinear Functions**

**Example text**

2. 2 support the conclusions just given and show that while selection acts so that variation is ultimately destroyed, the times required are usually very long, and are much longer than those required under any blending theory of inheritance. We may therefore often expect to observe considerable genetic polymorphism in populations even though they are subject to directional natural selection. We shall find several uses later for this table and its various generalizations. 2 in increasingly complex conditions, for example inbreeding, the case of different sets of fitnesses in the two sexes.

Since, in the model we consider, changes in gene frequencies are the fundamental components of evolution, the rate of increase of mean fitness can be expected to be related to that component of the total genetic variance which is accounted for by the alleles themselves, that is the additive genetic, or genic, variance. The MFIT is not the FTNS. The Fundamental Theorem in its full generality is deeper, more general and more complex than the MFIT. In particular, it applies in cases when mating is not at random and also when the fitness of any individual depends on his entire genomic make-up, not simply his genetic make-up at one single locus.

27) that the frequency of Al steadily increases towards unity. 28). 28) contains a multiplicative term (1 - x)2. This very slow rate of increase is due to the fact that, once X is close to unity, the frequency of A 2 A 2 , the genotype against which selection is operating, is extremely low. 28) assumes the simple form J X2 t(Xl' X2) = gsx(l - x)} -1 dx. 29) 14 h 1/2 1 1. 2. 2. 2 support the conclusions just given and show that while selection acts so that variation is ultimately destroyed, the times required are usually very long, and are much longer than those required under any blending theory of inheritance.