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Briefings in Bioinformatics Advance Access published online on February 3, 2006
Briefings in Bioinformatics, doi:10.1093/bib/bbk006
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© The Author 2006. Published by Oxford University Press. For Permissions, please email: journals.permissions@oxfordjournals.org
Received July 15, 2005
Accepted November 24, 2005

Original Article

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

Artem S. Novozhilov, Georgy P. Karev, and Eugene V. Koonin *

* To whom correspondence should be addressed.
Eugene V. Koonin, E-mail: koonin{at}ncbi.nlm.nih.gov


  Abstract

In this review, we discuss 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 and 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. We conclude that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological processes, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.

Keywords: mathematical modeling; genome evolution; birth-and-death process; Moran model; horizontal gene transfer; tumorigenesis.

Artem Novozhilov is a post-doctoral Fellow at the National Center for Biotechnology Information of the National Institutes of Health in Bethesda, Maryland. He works on mathematical modeling of evolution at different levels. He received his PhD from Moscow State University of Communication Means.

Georgy Karev is a Research Scientist at the National Center for Biotechnology Information of the National Institutes of Health in Bethesda, Maryland. His research is focused on mathematical modeling in biology. Main research interests include modeling of genome evolution, dynamics of heterogeneous populations and communities (demographic models, forest ecosystems), bifurcation approach to modeling complex biological system (epidemiological models, cancer modeling, neuron firing model), structural individual-based models, stochastic theory of populations. He received his PhD in Mathematics from the Institute of Electronic Engineering in Moscow, Russia, and Dr. Sci. degree in Biophysics from the Institute of Biophysics, Krasnoyarsk, Russia.

Eugene V. Koonin is a Senior Investigator and Group Leader at the National Center for Biotechnology Information of the National Institutes of Health in Bethesda, Maryland. His research interests include all aspects of comparative and evolutionary genomics, in particular, mathematical modeling of genome evolution and evolutionary systems biology. He received his PhD in Molecular Biology from the Department of Biology of Moscow State University (then USSR).


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