Can Genomic Selection problems be solved?
77
probability. As the number of minor mutations increases - the individual mutation effects become less and less significant, and the efficacy of selection for each one moves toward zero. This problem is alluded to by Kimuna (1983). I have demonstrated this problem mathematically in Appendix 2, and the results are shown in Figures 6a-c. Each time we add another trait that needs to be selected for, the maximum selective pressure that can be applied to each trait individually must decline. As the number of traits undergoing selection increases, selection efficiency for each trait rapidly approaches zero, and the time to achieve any selective goal approaches infinity. According to my calculations (see Appendix 2), for a population such as our own, the maximal number of mutations which could be selected simultaneously is approximately 700. Kimura (1983, p.30) alludes to the same problem, and although he does not show his calculations he states that only 138 sites can undergo selection simultaneously, even for a population with very intense total selection pressure (50% elimination), and minimal selective elimination per trait (c = 0.01). Trying to select simultaneously against more than several hundred mutations should clearly lead to complete cessation of all selective progress. Yet even in a small human population, millions of new mutations are arising every generation, and must be eliminated! In the big picture, we really need to be selecting against billions, not hundreds, of mutations. Even in the very limited case of selecting for just a few hundred genetic loci, although it is theoretically possible to do this, it is noteworthy to point out that such highly diluted selection per trait greatly affects the rate of selective progress – which essentially grinds to a standstill. As the number of loci under selection increases, the rate of selective progress (per trait) slows very rapidly, approaching zero. The resulting rate of genetic change would be glacial at best - requiring