scholarly journals Survival of the frequent at finite population size and mutation rate: bridging the gap between quasispecies and monomorphic regimes with a simple model

2018 ◽  
Author(s):  
Bhavin S. Khatri
Keyword(s):  
Population Size ◽  
Stationary Distribution ◽  
Finite Population ◽  
General Description ◽  
Multiple Alleles ◽  
Intermediate Regime ◽  
Theory Of Evolution ◽  
Predictive Theory ◽  
First Time ◽  
Explicit Derivation

In recent years, there has been increased attention on the non-trivial role that genotype-phenotype maps play in the course of evolution, where natural selection acts on phenotypes, but variation arises at the level of mutations. Understanding such mappings is arguably the next missing piece in a fully predictive theory of evolution. Although there are theoretical descriptions of such mappings for the monomorphic (Nμ ≪ 1) and deterministic or very strong mutation (Nμ ⋙ 1) limit, given by developments of Iwasa’s free fitness and quasispecies theories, respectively, there is no general description for the intermediate regime where Nμ ~ 1. In this paper, we address this by transforming Wright’s well-known stationary distribution of genotypes under selection and mutation to give the probability distribution of phenotypes, assuming a general genotype-phenotype map. The resultant distribution shows that the degeneracies of each phenotype appear by weighting the mutation term; this gives rise to a bias towards phenotypes of larger degeneracy analogous to quasispecies theory, but at finite population size. On the other hand we show that as population size is decreased, again phenotypes of higher degeneracy are favoured, which is a finite mutation description of the effect of sequence entropy in the monomorphic limit. We also for the first time (to the author’s knowledge) provide an explicit derivation of Wright’s stationary distribution of the frequencies of multiple alleles.

scholarly journals A note on the diffusion approximation for the variance of the number of generations until fixation of a neutral mutant gene

1970 ◽  
Vol 15 (2) ◽  
pp. 251-255 ◽  
Author(s):  
P. Narain
Keyword(s):  
Population Size ◽  
General Expression ◽  
Diffusion Approximation ◽  
Finite Population ◽  
Mutant Gene ◽  
Matrix Methods ◽  
Neutral Gene

SUMMARYA general expression is derived for the variance of time to fixation of a neutral gene in a finite population using a diffusion approximation. The results are compared with exact values derived by matrix methods for a population size of 8.

POPULATION DYNAMICS OF SEX-DETERMINING ALLELES IN HONEY BEES AND SELF-INCOMPATIBILITY ALLELES IN PLANTS

Genetics ◽  
1979 ◽  
Vol 91 (3) ◽  
pp. 609-626 ◽  
Author(s):  
Shozo Yokoyama ◽  
Masatoshi Nei
Keyword(s):  
Population Dynamics ◽  
Population Size ◽  
Honey Bee ◽  
Honey Bees ◽  
Finite Population ◽  
Large Population ◽  
Allele Frequencies ◽  
Self Incompatibility ◽  
Overdominant Selection ◽  
Incompatibility Alleles

ABSTRACT Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is l/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from l/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.

scholarly journals Entropic Equilibria Selection of Stationary Extrema in Finite Populations

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 631
Author(s):  
Marc Harper ◽  
Dashiell Fryer
Keyword(s):  
Markov Process ◽  
Population Size ◽  
Mutation Rate ◽  
Stationary Distribution ◽  
Markov Processes ◽  
Local Maxima ◽  
Moran Process ◽  
The Stability ◽  
Definition Of ◽  
Selection Of

We propose the entropy of random Markov trajectories originating and terminating at the same state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation and show that variations in population size, mutation rate, and strength of selection all affect the stability of the stationary extrema.

DIFFUSION OF A POPULATION OF INTERACTING REPLICATORS IN SEQUENCE SPACE

2002 ◽  
Vol 05 (04) ◽  
pp. 457-461 ◽  
Author(s):  
BÄRBEL M. R. STADLER
Keyword(s):  
Simple Model ◽  
Population Size ◽  
Computer Simulations ◽  
Mutation Rate ◽  
Sequence Space ◽  
Finite Population ◽  
Fitness Landscape ◽  
Diffusion Constant ◽  
Sequence Length

We consider a simple model for catalyzed replication. Computer simulations show that a finite population moves in sequence space by diffusion analogous to the behavior of a quasispecies on a flat fitness landscape. The diffusion constant depends linearly on the per position mutation rate and the ratio of sequence length and population size.

The supersession of one rumour by another

1977 ◽  
Vol 14 (1) ◽  
pp. 127-134 ◽  
Author(s):  
G. K. Osei ◽  
J. W. Thompson
Keyword(s):  
Population Size ◽  
Finite Population ◽  
Closed Population ◽  
Asymptotic Case ◽  
Distribution Of The Maximum ◽  
Maximum Value

A model is considered for a situation in which one rumour suppresses another in a closed population. The distribution of the maximum value attained by the proportion spreading the weaker rumour is obtained in the asymptotic case, and this is compared with some actual distributions for finite population size. Closer approximations to the latter distributions are obtained.

Ali Sedad Bey’s (d. 1900), ()

2016 ◽  
Author(s):  
Nazif Muhtaroglu
Keyword(s):  
Nineteenth Century ◽  
Modern Science ◽  
Natural Sciences ◽  
Point Of View ◽  
Natural Phenomena ◽  
Working Mechanism ◽  
Basic Principles ◽  
Theory Of Evolution ◽  
First Time ◽  
Late Ottoman

This chapter presents and evaluates Ali Sedāt’s (d. 1900) Principles of Transformation in the Motion of Particles. In this work, Ali Sedad gives a detailed description of the working mechanism of the whole universe, including topics that range from the interaction of atoms to the emergence of animate bodies and the motion of heavenly bodies. In doing this, he introduces thermodynamics and Darwin’s theory of evolution for the first time to the Turkish-speaking community in a detailed way and discusses the laws behind natural phenomena in a philosophical way. Ali Sedāt’s Principles of Transformation is a unique work introducing the basic principles of the natural sciences in nineteenth-century European circles to the Ottoman world and interpreting them from an Ashʿarite perspective. It shows how an Ashʿarite scholar from the late Ottoman era followed modern science thoroughly but interpreted it critically from its own philosophical point of view.

scholarly journals Stipa glareosa (Poaceae) in the Republic of Buryatia (Russia)

2015 ◽  
Vol 60 (1) ◽  
pp. 75-79 ◽  
Author(s):  
Polina D. Gudkova ◽  
Marcin Nobis ◽  
Aleksandr L. Ebel ◽  
Daba G. Chimitov ◽  
Alla V. Verkhozina
Keyword(s):  
Population Size ◽  
Habitat Preferences ◽  
Distribution Range ◽  
General Distribution ◽  
Northern Limit ◽  
The Republic ◽  
First Time

Abstract Stipa glareosa P. A. Smirn. (sect. Smirnovia Tzvel.) is reported for the first time from the Republic of Buryatia (Russia). Its stations are located at the northern limit of its general distribution range. The taxonomy, distribution and habitat preferences of the species are given, along with its population size at each new locality.

scholarly journals Measures of spatial structure in samples of genotypes for multiallelic loci

1999 ◽  
Vol 73 (3) ◽  
pp. 251-261 ◽  
Author(s):  
B. K. EPPERSON ◽  
Z. HUANG ◽  
T.-Q. LI
Keyword(s):  
Allele Frequencies ◽  
Multiple Alleles ◽  
Sampling Schemes ◽  
Animal Populations ◽  
Wide Range ◽  
Theoretical Population ◽  
Theoretical Population Genetics ◽  
Predicted Values ◽  
Join Count Statistics ◽  
First Time

Various spatial autocorrelation statistics have been widely used both in theoretical population genetics and to study the spatial distribution of diploid genotypes in many plant and animal populations. However, previous simulation studies have considered only diallelic loci. In this paper, we use a large number of space–time simulations to characterize for the first time the parametric and statistical values of Moran's I-statistics for converted individual genotypes as well as for join- count statistics. A wide range of levels of dispersal and numbers of alleles and allele frequencies are modelled and the results reveal the different general effects of each of these factors on these statistics. We also examine the range of appropriate sampling designs and sizes for which predicted values can be interpolated for specific sampling schemes for any given population genetic field survey. Numbers of alleles and allele frequencies each affect some statistics but not others. The results indicate generally low standard deviations. The results also develop precise and efficient methods of estimating gene dispersal, based on the various autocorrelation measures of standing spatial patterns of genetic variation within populations. The results also extend these methods to loci with multiple alleles, typical of those studied through modern molecular methods.

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