Population genetics from an information perspective.

Abstract

Some basic effects of population genetics are derived governing the occurrences of alleles A(i)and genotypes A(i)A(j)among its members. A principle of extreme physical information (EPI) is used. These effects are (1) the equation of genetic change, (2) Fisher's theorem of partial change, (3) a new uncertainty principle, and (4) the monotonic decrease of Fisher information with time, indicating increased disorder for the population. General conditions of population change are allowed: fitness coefficients w(ij)generally changing with time [except in effect (2)], population randomly or non-randomly mating, and a general number of loci present within each chromosome. EPI is a practical tool for deriving probability laws. It is an outgrowth of a physical process that occurs during any act of measurement. Here the measurement is the random observation of a genotype A(i)A(j). This observation is to be used to estimate the time of the observation, called "evolutionary time". The measurement activity incurs errors in the estimated observation time and fitness value of the observed genotype. By the Cramer-Rao inequality, the product of the two uncertainties must exceed unity [effect (3)]. The Fisher information I in data space is postulated to originate in the space of the genotype where it had some generally larger value J. The EPI principle extremizes the loss of information (I--J) with I=1/2 J. The solution gives rise to effects (1) and (2). Finally, it is shown that effect (4) holds when the population approaches an equilibrium state, e.g. for time values greater than a threshold if fitness coefficients w(ij)are constant. EPI provides a common framework for deriving physical laws and laws of population genetics. The new effects (3) and (4) are confirmed through computer simulation.