On rare mutation, chaos and Darwin’s theory - Ganikhodjaev, Nasir; Saburov, Mansoor (Revelation and Science, IIUM, 2014)
According to the Holy Quran, the evolution of life is the result of divine will and divine guidance. One of the key elements of natural selection is that offspring sometimes vary from their parents. For instance, a yellow buttery may have a black offspring. This kind of variation and mutation, though rare, tends to occur in all species. Over a long period of time, the cumulative effect of such mutations leads to an entirely new specie. Evolution describes the change in genetic material of a population of organisms through successive generations. In this paper we consider the evolution operator, namely quadratic stochastic operators, that naturally occurs to describe the transmission of a trait from parents to their offspring. This operator describes evolutionary dynamics of the considered population. The long run behavior of evolution operator plays an important role in many applied problems. We consider Mendelian inheritance for a single gene with three alleles and assuming that prior to the formation of the new generation each gene has the possibility to mutate, that is, to change into a gene of the other kind, and show that the rare mutation can transform regular dynamical system into chaotic one. As corollary we have that evolutionary operator with rare mutation of alleles contradict to Darwin’s evolution theory on genetic level.