The influence of internal fluctuations and external noise on the gene frequency in a haploid population
type: Item
instance of: scholarly article
title: The influence of internal fluctuations and external noise on the gene frequency in a haploid population
zbMATH Open document ID: 0568.92013
DOI: 10.1007/BF02460011
author: Mark F. Schumaker
author: Werner Horsthemke
published in: Bulletin of Mathematical Biology
publication date: 1985-01-01T00:00:00Z
review text: We consider a Markov chain modeling competition between two alleles in a haploid population of constant size and undergoing mutation, selection and Fisher-Wright mating. The Markov chain is rescaled to a diffusion process. We study the interaction of external noise (due to a random selection coefficient) and internal fluctuations (due to mating); the interaction is found to be additive. The stationary probability density displays a critical point. We draw an analogy between the behavior of the probability density at the critical point and the theory of phase transitions; critical exponents are introduced and calculated. We also analyze the effect of external noise on the genetic diversity of the population and on mean first passages times of the gene frequency.
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 60J20
zbMATH DE Number: 3908222
zbMATH Keywords: Markov chain
zbMATH Keywords: competition
zbMATH Keywords: haploid population of constant size
zbMATH Keywords: mutation
zbMATH Keywords: selection
zbMATH Keywords: Fisher-Wright mating
zbMATH Keywords: external noise
zbMATH Keywords: random selection coefficient
zbMATH Keywords: internal fluctuations
zbMATH Keywords: stationary probability density
zbMATH Keywords: critical point
zbMATH Keywords: phase transitions
zbMATH Keywords: critical exponents
zbMATH Keywords: genetic diversity
zbMATH Keywords: mean first passages times of the gene frequency
Wikidata QID: Q52678891
MaRDI profile type: Publication
cites work: Q5518219
cites work: Advanced synergetics. Instability hierarchies of self-organizing systems and devices
cites work: Noise-induced transitions. Theory and applications in physics, chemistry, and biology
cites work: Temporal fluctuations in selection intensities: Case of small population size
full work available at URL: https://doi.org/10.1007/bf02460011
OpenAlex ID: W4237133640
description: scientific article; zbMATH DE number 3908222