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Bioinformatics 2005 21(Suppl 3):iii12-iii19; doi:10.1093/bioinformatics/bti1202
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Published by Oxford University Press 2005

Modeling genome evolution with a diffusion approximation of a birth-and-death process

Georgy P. Karev 1, Faina S. Berezovskaya 2 and Eugene V. Koonin 1,*

1National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health Bethesda, MD 20894, USA
2Department of Mathematics, Howard University 2400 Sixth Street, Washington, DC 20059, USA

*To whom correspondence should be addressed.

Motivation: In our previous studies, we developed discrete-space birth, death and innovation models (BDIMs) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and model parameters that provide for the evolution of these distributions within a realistic time frame have been identified. However, extracting the temporal dynamics of genome evolution from discrete-space BDIM was not technically feasible. We were interested in obtaining dynamic portraits of the genome evolution process by developing a diffusion approximation of BDIM.

Results: The diffusion version of BDIM belongs to a class of continuous-state models whose dynamics is described by the Fokker–Plank equation and the stationary solution could be any specified Pareto function. The diffusion models have time-dependent solutions of a special kind, namely, generalized self-similar solutions, which describe the transition from one stationary distribution of the system to another; this provides for the possibility of examining the temporal dynamics of genome evolution. Analysis of the generalized self-similar solutions of the diffusion BDIM reveals a biphasic curve of genome growth in which the initial, relatively short, self-accelerating phase is followed by a prolonged phase of slow deceleration. This evolutionary dynamics was observed both when genome growth started from zero and proceeded via innovation (a potential model of primordial evolution), and when evolution proceeded from one stationary state to another. In biological terms, this regime of evolution can be tentatively interpreted as a punctuated-equilibrium-like phenomenon whereby evolutionary transitions are accompanied by rapid gene amplification and innovation, followed by slow relaxation to a new stationary state.

Contact: koonin{at}ncbi.nlm.nih.gov

Received on May 31, 2005; accepted on July 27, 2005

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