Mathematics of evolution (Q988048)

Summary: This article tries to provide an overview of the contributions of mathematics to evolutionary theory. From population genetics to the theory of complex networks, going through the theory of stochastic processes, many relevant results about the evolutionary mechanisms driving life have been obtained thanks to their mathematical descriptions. We still cannot say that the theory of evolution is a fully mathematically formulated scientific theory, like Darwin would have liked it to be, but it is unquestionable that we are getting closer and closer to such an achievement. Nowadays we could say that the theoretical studies of evolutionary processes are at least as important as the experimental ones and that, as the opening sentence by Darwin states, it is those that shed light in the darkness. Given the divulgatory nature of this article many interesting topics have been left out. Some of them provide new insights into evolutionary mechanisms and some illustrate further contributions of mathematics to evolutionary theory. Among them we can mention the infinite allele model, which is currently employed in analysing evolutionary divergence of DNA or protein sequences, or the coalescent process, which is an interesting and practical backward formulation of genetic drift. We have not mentioned the important contributions of game theory to evolution either. This theory is currently being used to deal with the problem of the evolutionary emergence of cooperation. Instead, the focus has been on the subject of adaptive landscapes and neutral networks because, in the author's opinion, this is the area where a new reformulation of the evolutionary paradigm can emerge in the following years. Understanding evolution requires, against all expectations, an understanding of the role of genetic drift on neutral networks. And due to the complexity of this problem, it is one of the topics in which mathematics can be our eyes in the dark room that help us fin the black cat that is not there.