Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in a evolution reactor, I
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A theory for describing evolution as adaptive walks by a finite population with M walkers (M ≥ 1) on an anisotropic Mt. Fuji-type fitness landscape is presented, from a thermodynamical point of view. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrate that the behavior of these theoretical walkers is almost consistent with the thermodynamical schemes. The major conclusions are as follows: (1) an adaptive walk (=evolution) is driven by an evolutionary force in the direction in which free fitness increases; (2) the expectation of the climbing rate obeys an equation analogous to the Einstein relation in Brownian motion; (3) the standard deviation of the climbing rate is a quantity analogous to the mean thermal energy of a particle, kT (×constant). In addition, on the interpretation that the walkers climb the landscape by absorbing ‘fitness information’ from the surroundings, we succeeded in quantifying the fitness information and formulating a macroscopic scheme from an informational point of view.
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- Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in a evolution reactor, I
Bulletin of Mathematical Biology
Volume 66, Issue 5 , pp 1371-1403
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- 1. Computational Biology Research Center, National Institute of Advanced Industrial Science and Technology, 2-43 Aomi, Koto-ku, Tokyo, 135-0064, Japan
- 2. Department of Functional Materials Science, Saitama University, Saitama, 338-8570, Japan