Biological applications of the theory of birth-and-death processes.pdfVIP

Biological applications of the theory of birth-and-death processes Artem S. Novozhilov, Georgy P. Karev, and Eugene V. Koonin* National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894 *To whom correspondence should be addressed. Email koonin@ Abstract In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer, and somatic evolution of cancers. We further describe how empirical data, e.g., distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. It is concluded that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological process, are going to be an indispensable mathematical tool for the burgeoning field of systems biology. 2 Introduction Mathematics has long been intertwined with the biological sciences. The importance of mathematical approaches in many areas of biology is obvious but it is less appreciated that biological questions have stimulated the emergence of a variety of new directions in mathematics. Among many others, the areas of mathematics fully or partially developed in response to demands of biology include branching processes, traveling wave solutions of reaction-diffusion systems, Tur