A generalized Fisher equation and its utility in chemical kinetics

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for which the mechanisms and rate coefficients correspond reasonably well to experiments. A bad fit of the GFE can be a sign of high levels of measurement noise; for low or moderate levels of noise, fulfillment of the GFE is not degraded. Hence, the GFE presents a noise threshold that may be used to test the validity of experimental measurements without requiring any additional information. In a different approach information about the system (model) is included in the calculations. In that case, the discrepancy with the GFE can be used as an optimization criterion for the determination of rate coefficients in a given reaction mechanism.

[1]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[2]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[3]  G. W. Snedecor.  Statistical Methods , 1964 .

[4]  R. J. Field.  Limit cycle oscillations in the reversible Oregonator , 1975 .

[5]  Irving R. Epstein,et al.  Systematic design of chemical oscillators. 42. Dynamic behavior in the chlorite-iodide reaction: a simplified mechanism , 1987 .

[6]  T. Nagylaki.  Introduction to Theoretical Population Genetics , 1992 .

[7]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[8]  Christopher W. Wilson,et al.  Genetic algorithms for optimisation of chemical kinetics reaction mechanisms , 2004 .

[9]  B. Frieden.  Science from Fisher Information , 2004 .

[10]  J. Ross,et al.  Fisher's theorems for multivariable, time- and space-dependent systems, with applications in population genetics and chemical kinetics. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Julio R. Banga,et al.  Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems , 2006, BMC Bioinformatics.

[12]  J. Ross.  Determination of complex reaction mechanisms. Analysis of chemical, biological and genetic networks. , 2005, The journal of physical chemistry. A.

[13]  Tibor Csendes,et al.  Extensions of a multistart clustering algorithm for constrained global optimization problems , 2009 .

[14]  Julio R. Banga,et al.  An evolutionary method for complex-process optimization , 2010, Comput. Oper. Res..

[15]  Fisher Information Study in Position and Momentum Spaces for Elementary Chemical Reactions. , 2010, Journal of chemical theory and computation.