The Population Genetics of Selection

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Population Genetics ◽  
Genetic Variation ◽  
Linkage Disequilibrium ◽  
Equilibrium Structure ◽  
Single Locus ◽  
Stabilizing Selection ◽  
Frequency Change ◽  
Single Generation ◽  
Expected Time ◽  
Locus Selection

This chapter examines models of one- and two-locus selection in the absence of drift and mutation. Expressions for the per-generation rate of allele-frequency change and the expected time for a specified amount of change are developed for single-locus models, and their equilibrium structure is examined for those settings where selection retains more than one allele. The presence of selection-generated linkage disequilibrium greatly complicates the extension of single-locus results to two loci, and the chapter examines some of the resulting complications. Finally, it examines the nature of selection on a locus that underlies a trait under selection, and then uses this to develop the breeder's equation for the single-generation response in a trait under selection. One important result is that the loci for a trait under stabilizing selection experience fitness underdominance, and thus trait selection removes, rather than retains, genetic variation.

scholarly journals Pleiotropy and multilocus polymorphisms.

Genetics ◽  
1992 ◽  
Vol 130 (1) ◽  
pp. 223-227
Author(s):  
A Gimelfarb
Keyword(s):  
Genetic Variation ◽  
Linkage Disequilibrium ◽  
Stabilizing Selection ◽  
Additive Genetic Variation ◽  
Very High

Abstract It is demonstrated that systems of two pleiotropically related characters controlled by additive diallelic loci can maintain under Gaussian stabilizing selection a stable polymorphism in more than two loci. It is also shown that such systems may have multiple stable polymorphic equilibria. Stabilizing selection generates negative linkage disequilibrium, as a result of which the equilibrium phenotypic variances are quite low, even though the level of allelic polymorphisms can be very high. Consequently, large amounts of additive genetic variation can be hidden in populations at equilibrium under stabilizing selection on pleiotropically related characters.

Genetic Diversity at a Single Locus Under Viability Selection and Facultative Apomixis: Equilibrium Structure and Deviations from Hardy-Weinberg Frequencies

Genetics ◽  
1998 ◽  
Vol 148 (4) ◽  
pp. 2029-2039
Author(s):  
R Deborah Overath ◽  
Marjorie A Asmussen
Keyword(s):  
Genetic Diversity ◽  
Genetic Variation ◽  
Equilibrium Structure ◽  
Single Locus ◽  
Numerical Analyses ◽  
Mixed Mating ◽  
Viability Selection ◽  
Diallelic Locus ◽  
Facultative Apomixis ◽  
Fixation Indices

Abstract We extensively analyze the maintenance of genetic variation and deviations from Hardy-Weinberg frequencies at a diallelic locus under mixed mating with apomixis and constant viability selection. Analytical proofs show that: (1) at most one polymorphic equilibrium exists, (2) polymorphism requires overdominant or underdominant selection, and (3) a simple, modified overdominance condition is sufficient to maintain genetic variation. In numerical analyses, only overdominant polymorphic equilibria are stable, and these are stable whenever they exist, which happens for ~78% of random fitness and mating parameters. The potential for maintaining both alleles increases with increasing apomixis or outcrossing and decreasing selfing. Simulations also indicate that equilibrium levels of heterozygosity will often be statistically indistinguishable from Hardy-Weinberg frequencies and that adults, not seeds, should usually be censused to maximize detecting deviations. Furthermore, although both censuses more often have an excess rather than a deficit of heterozygotes, analytical sign analyses of the fixation indices prove that, overall, adults are more likely to have an excess and seeds a deficit at equilibrium.

THE TIME REQUIRED FOR ALLELE FREQUENCY CHANGE

2017 ◽  
Vol 58 (3-4) ◽  
pp. 464-473
Author(s):  
TAI-HE FAN ◽  
SHUHAO SUN ◽  
PING-AN HE
Keyword(s):  
Stochastic Process ◽  
Population Genetics ◽  
Allele Frequency ◽  
Evolutionary Theory ◽  
Directional Selection ◽  
Selection Model ◽  
Frequency Change ◽  
Weak Selection ◽  
Expected Time ◽  
Time Required

In evolutionary theory, a key issue in selection theory is the expected time for a given amount of allele frequency change to occur. Crow and Kimura, by assuming weak selection, presented explicit results for several important cases of the directional selection and of the stochastic process. Those results played an important role in the theory of population genetics. In this paper, first we show that the weak selection assumption can be removed from most of the results of Crow and Kimura, and then we generalize those results to the most general selection model. Next, we estimate the errors of the deterministic formulae produced by proving that the deterministic formulae are limits of the corresponding stochastic formulae when the size of the population tends to infinity. Finally, we present a result which removes the restriction of Kimura’s corresponding results for a favourite recessive selection model, and we also observe that the conclusion made by Kimura about the favourite dominant selection might not be correct.

scholarly journals Polygenic selection within a single generation leads to subtle divergence among ecological niches

2020 ◽  
Author(s):  
Moritz A Ehrlich ◽  
Dominique N Wagner ◽  
Marjorie F Oleksiak ◽  
Douglas L Crawford
Keyword(s):  
Genetic Variation ◽  
Allele Frequency ◽  
Local Adaptation ◽  
Ecological Niches ◽  
Frequency Change ◽  
Heterogeneous Environments ◽  
Nucleotide Polymorphisms ◽  
Single Generation ◽  
Frequency Changes ◽  
Polygenic Selection

Abstract Selection on standing genetic variation may be effective enough to allow for adaptation to distinct niche environments within a single generation. Minor allele frequency changes at multiple, redundant loci of small effect can produce remarkable phenotypic shifts. Yet, demonstrating rapid adaptation via polygenic selection in the wild remains challenging. Here we harness natural replicate populations that experience similar selection pressures and harbor high within-, yet negligible among-population genetic variation. Such populations can be found among the teleost Fundulus heteroclitus which inhabits marine estuaries characterized by high environmental heterogeneity. We identify 10,861 single nucleotide polymorphisms in F. heteroclitus that belong to a single, panmictic population yet reside in environmentally distinct niches (one coastal basin and three replicate tidal ponds). By sampling at two time-points within a single generation we quantify both allele frequency change within as well as spatial divergence among niche subpopulations. We observe few individually significant allele frequency changes yet find that the number of moderate changes exceeds the neutral expectation by 10-100%. We find allele frequency changes to be significantly concordant in both direction and magnitude among all niche subpopulations, suggestive of parallel selection. In addition, within-generation allele frequency changes generate subtle but significant divergence among niches, indicative of local adaptation. Although we cannot distinguish between selection and genotype-dependent migration as drivers of within-generation allele frequency changes, the trait/s determining fitness and/or migration likelihood appear to be polygenic. In heterogeneous environments, polygenic selection and polygenic, genotype-dependent migration offer conceivable mechanisms for within-generation, local adaptation to distinct niches.

Maintenance of Quantitative Genetic Variation

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Genetic Variation ◽  
Quantitative Genetics ◽  
Stabilizing Selection ◽  
Quantitative Genetic ◽  
Wide Range

One of the major unresolved issues in quantitative genetics is what accounts for the amount of standing genetic variation in traits. A wide range of models, all reviewed in this chapter, have been proposed, but none fit the data, either giving too much variation or too little apparent stabilizing selection.

scholarly journals A MARKOV PROCESS OF GENE FREQUENCY CHANGE IN A GEOGRAPHICALLY STRUCTURED POPULATION

Genetics ◽  
1974 ◽  
Vol 76 (2) ◽  
pp. 367-377
Author(s):  
Takeo Maruyama
Keyword(s):  
Genetic Variation ◽  
Markov Process ◽  
Diffusion Process ◽  
Gene Frequency ◽  
Transition Probabilities ◽  
Large Population ◽  
Sample Path ◽  
Time Parameter ◽  
Frequency Change ◽  
Structured Population

ABSTRACT A Markov process (chain) of gene frequency change is derived for a geographically-structured model of a population. The population consists of colonies which are connected by migration. Selection operates in each colony independently. It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population. The time parameter is a local random time that is dependent on the sample path. In fact, if the alleles are selectively neutral, the time parameter is exactly equal to the sum of the average local genetic variation appearing in the population, and otherwise they are approximately equal. The Kolmogorov forward and backward equations of the process are obtained. As a limit of large population size, a diffusion process is derived. The transition probabilities of the Markov chain and of the diffusion process are obtained explicitly. Certain quantities of biological interest are shown to be independent of the population structure. The quantities are the fixation probability of a mutant, the sum of the average local genetic variation and the variation summed over the generations in which the gene frequency in the whole population assumes a specified value.

scholarly journals Linkage disequilibrium and genetic variances under mutation-selection balance.

Genetics ◽  
1989 ◽  
Vol 121 (4) ◽  
pp. 857-860 ◽  
Author(s):  
A Hastings
Keyword(s):  
Linkage Disequilibrium ◽  
Mutation Rate ◽  
Genetic Variance ◽  
Harmonic Mean ◽  
Recombination Rates ◽  
Genetic Variances ◽  
Locus Selection

Abstract I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.

scholarly journals Cryptic variation and its manifestation in the Lower Trentonian Rafinesquina lineage (Ordovician, New York State)

1992 ◽  
Vol 6 ◽  
pp. 292-292
Author(s):  
Robert Titus
Keyword(s):  
New York ◽  
Genetic Variation ◽  
Natural Selection ◽  
New York State ◽  
Ecological Factors ◽  
Stabilizing Selection ◽  
Rapid Population Growth ◽  
York State ◽  
Cryptic Variation ◽  
Adaptive Peak

Species populations commonly carry a great deal of genetic variation which is not expressed in individual phenotypes. Cryptic variation can be carried in recessive alleles, in cases of heterosis, or where modifier genes inhibit expression of the hidden trait. Other genetic and ecological factors also allow cryptic variation. Stabilizing selection prevents the expression of hidden traits; normalizing selection weeds out the deviants and canalizing selection suppresses their traits. Together the two keep the species near the top of the adaptive peak. Cryptic variation balances a species' need to be well-adapted to its environment and also for it to maintain a reserve of variation for potential environmental change. Expression of cryptic traits is rare and is usually associated with times of greatly reduced natural selection and rapid population growth, when the lower slopes of the adaptive peak are exposed.A possible example of the manifestation of cryptic traits occurs within the lower Trentonian Rafinesquina lineage of New York State. The two most commonly reported species of the genus have been reappraised in terms of cryptic variation. Extensive collections of Rafinesquina “lennoxensis” reveal far more intergrading morphotypes than had hitherto been recognized. The form which Salmon (1942) described is broadly U-shaped with sulcate margins. It grades into very convex forms as well as sharply-defined or convexly geniculate types. Of great importance, all forms grade into the flat, U-shaped, alate R. trentonensis, which is, by far, the most common and widespread lower Trentonian member of the genus. The R. “lennoxensis” assemblage has a very narrow biostratigraphy, being confined to a few locations in the upper Napanee Limestone. This places it in a quiet, protected, low stress, lagoonal setting behind the barrier shoal facies of the Kings Falls Limestone.The R. “lennoxensis” assemblage does not constitute a natural biologic species; it is reinterpreted as an assemblage of phenodeviants occupying a low stress, low natural selection lagoon facies. All such forms should be included within R. trentonensis. Given the evolutionary plasticity of this genus, extensive cryptic variation is not surprising.

scholarly journals mixIndependR: a R package for statistical independence testing of loci in database of multi-locus genotypes

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Bing Song ◽  
August E. Woerner ◽  
John Planz
Keyword(s):  
Population Genetics ◽  
Linkage Disequilibrium ◽  
Genetic Markers ◽  
Software Package ◽  
Tandem Repeats ◽  
Population Data ◽  
Real Data ◽  
R Package ◽  
Nucleotide Polymorphisms ◽  
Mutual Independence

Abstract Background Multi-locus genotype data are widely used in population genetics and disease studies. In evaluating the utility of multi-locus data, the independence of markers is commonly considered in many genomic assessments. Generally, pairwise non-random associations are tested by linkage disequilibrium; however, the dependence of one panel might be triplet, quartet, or other. Therefore, a compatible and user-friendly software is necessary for testing and assessing the global linkage disequilibrium among mixed genetic data. Results This study describes a software package for testing the mutual independence of mixed genetic datasets. Mutual independence is defined as no non-random associations among all subsets of the tested panel. The new R package “mixIndependR” calculates basic genetic parameters like allele frequency, genotype frequency, heterozygosity, Hardy–Weinberg equilibrium, and linkage disequilibrium (LD) by mutual independence from population data, regardless of the type of markers, such as simple nucleotide polymorphisms, short tandem repeats, insertions and deletions, and any other genetic markers. A novel method of assessing the dependence of mixed genetic panels is developed in this study and functionally analyzed in the software package. By comparing the observed distribution of two common summary statistics (the number of heterozygous loci [K] and the number of share alleles [X]) with their expected distributions under the assumption of mutual independence, the overall independence is tested. Conclusion The package “mixIndependR” is compatible to all categories of genetic markers and detects the overall non-random associations. Compared to pairwise disequilibrium, the approach described herein tends to have higher power, especially when number of markers is large. With this package, more multi-functional or stronger genetic panels can be developed, like mixed panels with different kinds of markers. In population genetics, the package “mixIndependR” makes it possible to discover more about admixture of populations, natural selection, genetic drift, and population demographics, as a more powerful method of detecting LD. Moreover, this new approach can optimize variants selection in disease studies and contribute to panel combination for treatments in multimorbidity. Application of this approach in real data is expected in the future, and this might bring a leap in the field of genetic technology. Availability The R package mixIndependR, is available on the Comprehensive R Archive Network (CRAN) at: https://cran.r-project.org/web/packages/mixIndependR/index.html.

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