Geminate Recombination in the Presence of Scavengers: The New Vision of the Old Problem

A geminate reaction between and reactants affected by the bulk reaction between and scavengers is discussed. The exact solution of the problem obtained recently for randomly walking reactant (excess electron) is compared with the superposition approximation commonly used to interpret experimental data. Distinctions related to the important role of time correlations between geminate and bulk reactions are analyzed. The largest deviations exponentially growing in time are observed for geminate reaction rate in the presence of scavengers. It is shown that superposition approximation can decrease essentially the ultimate probability of geminate recombination. The difference is great enough to lead to qualitatively incorrect description of the experiment even at small concentration of scavengers. This, in turn, may give rise to considerable errors in the determination of geminate pair parameters or, alternatively, to the wrong information about bulk kinetics of electron scavenging.

Random selective advantages of genes and their probabilities of fixation

SUMMARYThe question of what is meant by random fluctuations in selection intensities in a finite population is re-examined. The model presented describes the change in the frequency of a gene in a haploid population of size M. It is assumed that in any generation the adaptive values of A and a are equally likely to be 1 + s: 1 or 1: 1 + s. If s is the selective advantage and x the frequency of gene A, then the first two moments of the change in frequency are found to be m(Δx) = x(1 − x)(1 − 2x) θ/2M andwhere E(s2) = θ/M. The ultimate probability of fixation is computed, showing that variability in selection increases the chance of fixation of a rare gene. A more general form for m(Δx) also is obtained. This form is compared with the equation currently used in describing random fluctuations in selection intensities.

1. On the Average Value of Human Testimony

The author began by some remarks upon the expression or . Where p represents the a priori probability of an event attested by a witness whose veracity, or the ratio of whose true assertions to the number of all his assertions is, v. He observed that U, or the ultimate probability of the asserted fact, depended upon the accuracy of the numerical value given to v, and that men have never such knowledge of their neighbours' antecedents, as to assume this value with anything like an approximation to the truth.