The thesis mainly introduces Darwin's biological evolution and the research of biological evolvement, especially on microcosmic level, by the research of the simple asexual populations building the ideal theory model. This passage is focus on the description of Eigen's quasispecies model and its solution. After that we got when the species exceed the threshold of value, they will become random distribution. That is to say, when the species'error exceeds the threshold of value, it will die out. We call this the threshold of value as the error threshold. The body can be divided into 4 parts:The first part introduce Darwin's biological evolvement and set up the ideal model-- quasispecies model; The second part tells us the accurate solution of Eigen and the perturbation approximately among the minor situation. The third part mainly discusses the direct and complementary (plus-minus) replication between low-dimensional and high-dimensional, and make an analogy between the error threshold and statistics. Finally, we get the important conclusion that the error threshold will translate toward the bigger direction.
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