The basic science and mathematics of random mutation and natural selection

Abstract

The mutation and natural selection phenomenon can and often does cause the failure of antimicrobial, herbicidal, pesticide and cancer treatments selection pressures. This phenomenon operates in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures. The mathematical behavior of mutation and selection is derived using the principles given by probability theory. The derivation of the equations describing the mutation and selection phenomenon is carried out in the context of an empirical example.

The mathematics of random mutation and natural selection for multiple simultaneous selection pressures and the evolution of antimicrobial drug resistance

“…This effectively would convert the combination therapy into sequential therapy where the remaining effective drug would only require the population to evolve to that single drug (a process describe in Ref. ). Then the process of beneficial mutation followed by amplification of the beneficial mutation cycle evolution of drug resistance could be followed by the population without the second drug disrupting the amplification process.…”

“…In reference , ‘The Basic Science and Mathematics of Random Mutation and Natural Selection’, the governing equation describing the evolution of drug resistance to a single targeted selection pressure is derived. This equation shows that in order for a lineage in a population to evolve resistance to that targeted selection pressure, it must do so by a cycle of beneficial mutation followed by amplification of that mutation by repeated replications over generations in order for the probability to improve that another beneficial mutation will occur on some member of that lineage to improve fitness.…”

“…There are two fundamental differences in Haldane's and Kimura's models used to model the mathematics of the evolutionary process when compared with reference . The first difference is a physical difference.…”

“…A simple analogy can be used to compare Haldane's and Kimura's approach with the model presented in reference . The analogy for Haldane's and Kimura's model consists of taking a deck of cards.…”

“…In Ref. , the mathematics was derived showing how a lineage in a population can accumulate beneficial mutations to adapt to a single selection pressure targeting a single genetic locus. However, when the lineage is subjected to only a single targeted selection pressure at a time, these beneficial mutations do not have to occur simultaneously in a single replication in order to improve fitness.…”