scholarly journals A Faster and More Accurate Algorithm for Calculating Population Genetics Statistics Requiring Sums of Stirling Numbers of the First Kind

2020 ◽  
Vol 10 (11) ◽  
pp. 3959-3967
Author(s):  
Swaine L. Chen ◽  
Nico M. Temme
Keyword(s):  
Population Genetics ◽  
Beta Function ◽  
Neutral Theory ◽  
Stirling Numbers ◽  
Cumulative Distribution ◽  
Direct Estimate ◽  
Theory Of Evolution ◽  
Sampling Formula ◽  
Improve Accuracy ◽  
Analytical Result

Ewen’s sampling formula is a foundational theoretical result that connects probability and number theory with molecular genetics and molecular evolution; it was the analytical result required for testing the neutral theory of evolution, and has since been directly or indirectly utilized in a number of population genetics statistics. Ewen’s sampling formula, in turn, is deeply connected to Stirling numbers of the first kind. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu’s Fs. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed.

scholarly journals A faster and more accurate algorithm for calculating population genetics statistics requiring sums of Stirling numbers of the first kind

2020 ◽  
Author(s):  
Swaine L. Chen ◽  
Nico M. Temme
Keyword(s):  
Population Genetics ◽  
Dna Sequences ◽  
Cumulative Distribution Function ◽  
Beta Function ◽  
Stirling Numbers ◽  
Cumulative Distribution ◽  
Incomplete Beta Function ◽  
Improved Method ◽  
Direct Estimate ◽  
Improve Accuracy

AbstractStirling numbers of the first kind are used in the derivation of several population genetics statistics, which in turn are useful for testing evolutionary hypotheses directly from DNA sequences. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu’s Fs. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed.

Evolution, genetics, and systematics

2017 ◽  
Author(s):  
Francisco J. Ayala ◽  
Camilo J. Cela-Conde
Keyword(s):  
Population Genetics ◽  
Sexual Selection ◽  
Fossil Record ◽  
Life Sciences ◽  
Altruistic Behavior ◽  
Synthetic Theory ◽  
Theory Of Evolution ◽  
Evolution By Natural Selection ◽  
Current Paradigm ◽  
Epigenetic Processes

This chapter starts with the general principles of the theory of evolution by natural selection advanced by Darwin and the Mendelian theory of heredity. Next comes consideration of the “new-Darwinian synthesis” or “synthetic theory,” which integrates both precedents into what has become the current paradigm of the life sciences. Molecular evolution and population genetics follow, including epigenetic processes. Next, special models of selection are considered, such as sexual selection and the models that account for altruistic behavior. After the mechanisms of speciation, the main concepts of systematics are explored, which facilitate understanding of different traits. The chapter finally explores the fundamental concepts of taxonomy and the methods from phenetics to cladistics, that makes it possible to evaluate the diversity of organisms and the methods for dating the fossil record.

GENETIC REPRESENTATION AND GENETIC NEUTRALITY IN GENE EXPRESSION PROGRAMMING

2002 ◽  
Vol 05 (04) ◽  
pp. 389-408 ◽  
Author(s):  
CÂNDIDA FERREIRA
Keyword(s):  
Gene Expression ◽  
Molecular Evolution ◽  
Gene Expression Programming ◽  
Neutral Theory ◽  
Artificial System ◽  
Evolutionary Systems ◽  
Theory Of Evolution ◽  
Coding Regions ◽  
Neutral Mutations

The neutral theory of molecular evolution states that the accumulation of neutral mutations in the genome is fundamental for evolution to occur. The genetic representation of gene expression programming, an artificial genotype/phenotype system, not only allows the existence of non-coding regions in the genome where neutral mutations can accumulate but also allows the controlled manipulation of both the number and the extent of these non-coding regions. Therefore, gene expression programming is an ideal artificial system where the neutral theory of evolution can be tested in order to gain some insights into the workings of artificial evolutionary systems. The results presented in this work show beyond any doubt that the existence of neutral regions in the genome is fundamental for evolution to occur efficiently.

Historical Origins

2021 ◽  
pp. 11-45
Author(s):  
J. Arvid Ågren
Keyword(s):  
Population Genetics ◽  
Group Selection ◽  
Evolutionary Biology ◽  
Natural Theology ◽  
Living World ◽  
Selfish Gene ◽  
Theory Of Evolution ◽  
The Third ◽  
Historical Origins ◽  
The Way

This chapter traces the origins of the gene’s-eye view through three sections of evolutionary biology. The first is adaptationism, the tradition that takes the appearance of design in living world to be the cardinal problem a theory of evolution needs to explain. The chapter shows how this view has been especially prominent in British biology, owing the strong standing of natural theology and the writings of William Paley. The second is the emergence of population genetics during the modern synthesis. Here, the work of R.A. Fisher was particularly important. The third and final section was the levels selection debate and the rejection of group selection. G.C. Williams led the way the way and the origin of the gene’s-eye view culminated with the publication of The Selfish Gene.

scholarly journals Sewall Wright, 21 December 1889 - 3 March 1988

1990 ◽  
Vol 36 ◽  
pp. 567-579 ◽  
Keyword(s):  
Population Genetics ◽  
Evolutionary Biology ◽  
Natural Populations ◽  
Coat Colour ◽  
Balance Theory ◽  
Theory Of Evolution ◽  
Shifting Balance Theory ◽  
Sewall Wright ◽  
Shifting Balance ◽  
Active Research

Sewall Wright's active life spanned the development of genetics from a new discipline when the principles of inheritance were still being elucidated to the technology of recombinant gene construction and insertion. He was one of the major pioneers of population genetics, which gave a quantitative basis to the studies of evolution, of variation in natural populations and of animal and plant breeding. He contributed most significantly to methods and ideas over a long period, indeed his four volume treatise was written long after he formally ‘retired’ and his last paper (211) was published a few days before his death at the age of 98. In the field of population genetics Wright developed the method of path coefficients, which he used to analyse quantitative genetic variation and relationship, but which has been applied to subjects as diverse as economics, the ideas of inbreeding coefficient and F -statistics which form the basis of analysis of population structure, the theory of variation in gene frequency among populations, and the shifting balance theory of evolution, which remains a topic of active research and controversy. Wright contributed to physiological genetics, notably analysis of the inheritance of coat colour in the guinea pig, and in particular the epistatic relationships among the genes involved. There was a critical interplay between his population and physiological work, in that the analysis of finite populations on the one hand and of epistatic interactions on the other are the bases of Wright’s development of the shifting balance theory. A full and enlightening biography of Sewall Wright which traces his influence on evolutionary biology and his interactions with other important workers was published recently (Provine 1986) and shorter appreciations have appeared since his death, notably by Crow (1988), Wright’s long-time colleague. This biography relies heavily on Provine’s volume, and does no more than summarize Wright’s extensive contributions. Many of his important papers have been reprinted recently (1986).

Random partitions in population genetics

1978 ◽  
Vol 361 (1704) ◽  
pp. 1-20 ◽  
Keyword(s):  
Population Genetics ◽  
Genetic Variation ◽  
Charge State ◽  
Characteristic Property ◽  
Large Population ◽  
Recurrent Mutation ◽  
Random Partitions ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
State Models

This paper is concerned with models for the genetic variation of a sample of gametes from a large population. The need for consistency between different sample sizes limits the mathematical possibilities to what are here called ‘partition structures Distinctive among them is the structure described by the Ewens sampling formula, which is shown to enjoy a characteristic property of non-interference between the different alleles. This characterization explains the robustness of the Ewens formula when neither selection nor recurrent mutation is significant, although different structures arise from selective and ‘charge-state’ models

Motoo Kimura. 13 November 1924—13 November 1994

1997 ◽  
Vol 43 ◽  
pp. 255-265 ◽  
Author(s):  
James F. Crow
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Neutral Theory ◽  
Random Chance ◽  
Evolutionary Changes ◽  
Sewall Wright ◽  
Theoretical Population ◽  
Theoretical Population Genetics

Motoo Kimura's research contributions can be divided into two parts. The first is a series of papers on theoretical population genetics, the quality and quantity of which place him as the successor to the great trinity, R.A. Fisher, J.B.S. Haldane and Sewall Wright. The second is his neutral theory, the idea that the bulk of molecular evolutionary changes are driven by mutation and random chance, rather than by natural selection. The neutral theory brought him fame far beyond the confines of population genetics, and has made the name Motoo Kimura well-known to evolutionary biologists. (Motoo is pronounced ‘Mo-toe’, not ‘Mo-two’. By repeating the letter O, Kimura sought to indicate that this syllable was to be protracted. Unfortunately, rather than producing the desired effect, this more often led to mispronunciation.)

Random partitions in population genetics

1978 ◽  
Vol 201 (1143) ◽  
pp. 217-217
Keyword(s):  
Population Genetics ◽  
Genetic Drift ◽  
Mutant Allele ◽  
Constant Factor ◽  
Population Models ◽  
Statistical Equilibrium ◽  
Theoretical Research ◽  
Random Partitions ◽  
Sampling Formula

One of the most striking results of recent theoretical research in population genetics is the sampling formula associated with the name of W. J. Ewens, who enunciated it in 1972, since which time it has been shown to hold for many different population models. This asserts that, if a sample of n gametes is taken from a population, and classified according to the gene at a particular locus, then the probability that there are a 1 alleles represented once in the sample, a 2 represented twice, a 3 thrice, and so on, is given for some positive value of θ by the expression P n (a 1 ,a 2 ..., a n ) = n !/θ(θ+1)...(θ+ n ─1) ∏ n j=1 ﴾θ aj /j aj a j !﴿. Most of the models for which this has been established share three broad features: ( a ) the size of the population is large compared with n , and the expected total number of mutations per generation is moderate (and in fact differs from θ by a constant factor depending on the reproductive mechanism), ( b ) the population is in statistical equilibrium under mutation and genetic drift, with selection at the locus playing a negligible rôle, and ( c ) mutation is non-recurrent, so that every mutant allele is a completely novel one.

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