
Vlad MO, Szedlacsek SE, Pourmand N, CavalliSforza LL, Oefner P, Ross J. . Fisher' s theorems for multivariable, time and spacedependent systems, with applications in population genetics and chemical kinetics. . Proc Natl Acad Sci U S A. , 102, pp. 984853, 2005.
Abstract:
We study different physical, chemical, or biological processes involving replication, transformation, and disappearance processes, as well as transport processes, and assume that the time and space dependence of the species densities are known. We derive two types of Fisher equations. The first type relates the average value of the time derivative of the relative timespecific rates of growth of the different species to the variance of the relative, timespecific rates of growth. A second type relates the average value of the gradient or the divergence of the relative, spacespecific rates of growth to the space correlation matrix of the relative, spacespecific rates of growth. These Fisher equations are exact results, which are independent of the detailed kinetics of the process: they are valid whether the evolution equations are linear or nonlinear, local or nonlocal in space and/or time and can be applied for the study of a large class of physical, chemical, and biological systems described in terms of time and/or spacedependent density fields. We examine the implications of our generalized Fisher relations in population genetics, biochemistry, and chemical kinetics (reactiondiffusion systems). We show that there is a connection between the enhanced (hydrodynamic) transport of mutations induced by population growth and spacespecific rate vectors: the velocity of enhanced transport is proportional to the product of the diffusion coefficient of the species and the space rate vector; this relation is similar to a fluctuationdissipation relation in statistical mechanics.
Keywords:
population genetics,
URL:
http://www.pubmedcentral.gov/picrender.fcgi?artid=1175005&blobtype=pdf
Posted by
Stefan Eugen Szedlacsek
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