5. Selection and mutation: Consider a very large population of individuals characterize by a ï¬tness parameter f, which is assume to be Gaussian distributed with a mean m an variance 0. The population undergoes cyclic evolution, such that at each cycle: (2') on half of the population with lower fitness f is removed without creating progeny; (it) th remaining half (with f values in the upper half) reproduces before dying; (iii) because ( mutations the f values of the new generation is again Gaussian distributed, with mea value and variance reï¬‚ecting the parents (i.e. coming from the upper half of the origin; Gaussian distribution). (a) Relate the mean mm and variance an of fitness values of the nâ€”th generation to thos of the previous ones (mn_1 and an_1). (b) What happens to the distribution of fitness after many generations?
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