Molecular Evolution Activities
 

This is a comprehensive bibliography (under construction) of primary and secondary sources on the neutral theory of molecular evolution. It currently covers the period 1973-2001.

Author :

Vlad, M. O.;Schonfisch, B.;Mackey, M. C.

Year :

1996

Title :

Fluctuating Poissonian clocks, fractal random processes and dynamical Porter-Thomas distributions: Applications to evolutionary molecular biology, enhanced diffusion and dynamical relaxation

Journal :

Physica Scripta

Volume :

54

Issue :

6

Pages :

581-593

Date :

Dec

Short Title :

Fluctuating Poissonian clocks, fractal random processes and dynamical Porter-Thomas distributions: A

Alternate Journal :

Phys. Scr.

Custom 2 :

ISI:A1996VW63400006

Abstract :

The influence of the memory effects on the Poissonian clocks with fluctuating counting rates is investigated by using the technique of characteristic functionals. A general approach for computing all cumulants of the number of counts is suggested based on an analogy with the theory of rate processes with dynamical disorder. The large time behavior of the cumulants is investigated for stationary random processes with short and long memory, respectively. For short memory in the long run all cumulants increase linearly in time and the averaged stochastic process describing the statistics of the number of counts, although generally non-Poissonian, is non-intermittent and can be used as a clock. For finite long memory described by a stationary fractal random process, even though the cumulants of the number of events increase faster than linearly in time, the fluctuations are still non-intermittent and the averaged random process is also a clock. For infinite memory, however, the fluctuations of the number of counts are intermittent and the averaged random process is not a clock any more. An alternative stochastic approach is developed based on the use of a dynamical analogue of the Porter-Thomas formula; the results are consistent with the first version of the theory. Three applications of the general theory are presented The first application is related to the connection between the Kimura's neutral theory of molecular evolution and the Gillespie's episodic clock for the rate of amino acid substitutions through the evolutionary process. If the fluctuations of the rate of substitution have short memory or long finite memory then Gillespie's episodic clock is consistent with Kimura's theory. Only the infinite memory is not consistent with the neutral hypothesis. The second application is the study of a hopping mechanism for enhanced diffusion A biased random walk is investigated by assuming that the distribution of the number of jumps is given by a Poissonian process with a fluctuating counting rate. If the fluctuations of the counting rate have short memory then the resulting biased diffusion is normal and obeys Einstein's linear equation for the mean square displacement of the moving particle. For long memory the mean square displacement of the moving particle increases faster than linearly in time and the diffusion is enhanced. An alternative approach for a random walk in the velocity space is developed In this case the diffusion process is even more efficient than for a random walk in the real space. The third application is the study of Porter-Thomas relaxation for systems with dynamical disorder. It is shown that for small and moderately long times the relaxation function obeys a scaling law of the negative power law type followed by a fast decaying exponential tail which is determined by the fluctuation dynamics. This type of relaxation behavior is of interest both for nuclear and molecular physics and corresponds to a non- ideal statistical fractal.

Notes :

Times Cited: 0 VW634 PHYS SCR
 -- contributed by John Beatty, March 29, 2002