A generalized Fisher equation and its utility in chemical kinetics

Proc Natl Acad Sci U S A. 2010 Jul 20;107(29):12777-81. doi: 10.1073/pnas.1008257107. Epub 2010 Jul 6.


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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.