scholarly journals THE EVOLUTION OF ONE- AND TWO-LOCUS SYSTEMS. II

Genetics ◽  
1977 ◽  
Vol 85 (2) ◽  
pp. 347-354
Author(s):  
Thomas Nagylaki
Keyword(s):  
Continuous Time ◽  
Initial Period ◽  
Natural Populations ◽  
Weak Selection ◽  
Total Change ◽  
Linkage Disequilibria ◽  
Mean Fitness ◽  
Monoecious Population ◽  
Change In Mean ◽  
Age Independent

ABSTRACT Weak selection in a monoecious population is studied in two multiallelic panmictic models. In the first, a single locus is considered with continuous time and age-independent fertilities and mortalities. If the fertilities of the various matings and the genotypic mortalities may be expressed with an error at most of the second order in s (i.e., O(s  2)), where s is the intensity of selection, as sums of terms corresponding to the different genotypes and alleles, respectively, then after several generations the deviations from Hardy-Weinberg proportions are of O(s  2). In the second model, two loci are treated with discrete nonoverlapping generations. It is shown that if the epistatic parameters are of O(s2), then after several generations the linkage disequilibria are reduced to O(s  2). Assuming only weak selection, it is proved that in both models, after several generations, the total change in mean fitness is generally positive. It is likely that the exclusion of the initial period is usually unnecessary in natural populations. Exceptions are discussed.

scholarly journals An Exactly Solved Model for Mutation, Recombination and Selection

2003 ◽  
Vol 55 (1) ◽  
pp. 3-41 ◽  
Author(s):  
Michael Baake ◽  
Ellen Baake
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Sufficient Criterion ◽  
Linkage Disequilibria ◽  
Additive Type ◽  
Mean Fitness ◽  
The Mean ◽  
Necessary And Sufficient ◽  
Independent Mutation ◽  
Selection Of

AbstractIt is well known that rather generalmutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from.Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of Möbius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.

scholarly journals The strength of the selection barrier between populations

2000 ◽  
Vol 76 (2) ◽  
pp. 179-185 ◽  
Author(s):  
KONSTANTIN V. PYLKOV ◽  
LEV A. ZHIVOTOVSKY ◽  
FREDDY BUGGE CHRISTIANSEN
Keyword(s):  
Small Parameter ◽  
Genetic Difference ◽  
Weak Selection ◽  
Approximate Analytical Expression ◽  
Epistatic Interactions ◽  
Linkage Disequilibria ◽  
Donor Population ◽  
Mean Fitness ◽  
Two Populations

Genetic differences among populations exposed to selection form barriers against genetic exchange by mortality among hybrids. The strength of such a selection barrier, with which one (recipient) population reacts against immigration from another (donor) population, may be measured as the cumulative mean fitness of hybrids and their descendants relative to the fitness of the recipient population. Previous work analysed a case of weak selection with pairwise epistatic interactions by assuming small genetic distance between two populations in contact. The present study allows large genetic difference between the donor and recipient populations and considers weak multilocus selection with arbitrary epistatic interactions between two or more linked loci. An approximate analytical expression for the barrier strength is obtained as an expansion in which the strength of selection plays the role of a small parameter. It is shown that allele frequencies and gametic linkage disequilibria contribute in different ways to the strength of the selection barrier.

scholarly journals THE EVOLUTION OF ONE- AND TWO-LOCUS SYSTEMS

Genetics ◽  
1976 ◽  
Vol 83 (3) ◽  
pp. 583-600
Author(s):  
Thomas Nagylaki
Keyword(s):  
Continuous Time ◽  
Time Derivative ◽  
Second Order ◽  
Rate Of Change ◽  
Evolutionary Significance ◽  
Multiple Alleles ◽  
Mean Fitness ◽  
The Mean ◽  
Change In Mean ◽  
Continuous Time Models

ABSTRACT Assuming age-independent fertilities and mortalities and random mating, continuous-time models for a monoecious population are investigated for weak selection. A single locus with multiple alleles and two alleles at each of two loci are considered. A slow-selection analysis of diallelic and multiallelic two-locus models with discrete nonoverlapping generations is also presented. The selective differences may be functions of genotypic frequencies, but their rate of change due to their explicit dependence on time (if any) must be at most of the second order in s, (i.e., O(s  2)), where s is the intensity of natural selection. Then, after several generations have elapsed, in the continuous time models the time-derivative of the deviations from Hardy-Weinberg proportions is of O(s  2), and in the two-locus models the rate of change of the linkage disequilibrium is of O(s  2). It follows that, if the rate of change of the genotypic fitnesses is smaller than second order in s (i.e., o(s  2)), then to O(s  2) the rate of change of the mean fitness of the population is equal to the genic variance. For a fixed value of s, however, no matter how small, the genic variance may occasionally be smaller in absolute value than the (possibly negative) lower order terms in the change in fitness, and hence the mean fitness may decrease. This happens if the allelic frequencies are changing extremely slowly, and hence occurs often very close to equilibrium. Some new expressions are derived for the change in mean fitness. It is shown that, with an error of O(s), the genotypic frequencies evolve as if the population were in Hardy-Weinberg proportions and linkage equilibrium. Thus, at least for the deterministic behavior of one and two loci, deviations from random combination appear to have very little evolutionary significance.

scholarly journals The quantitative genetics of fitness in a wild bird population

2021 ◽  
Author(s):  
Maria Moiron ◽  
Anne Charmantier ◽  
Sandra Bouwhuis
Keyword(s):  
Reproductive Success ◽  
Genetic Variance ◽  
Evolutionary Ecology ◽  
Additive Genetic Variance ◽  
Natural Populations ◽  
Common Tern ◽  
Adult Survival ◽  
Lifetime Fitness ◽  
Mean Fitness ◽  
Change In Mean

Additive genetic variance in fitness equals the change in mean fitness due to selection. It is a prerequisite for adaptation, as a trait must be genetically correlated with fitness in order to evolve. Despite its relevance, additive genetic variance in fitness has not often been estimated in wild populations. Here, we investigate additive genetic variance in lifetime fitness, as well as its underlying components, in common terns (Sterna hirundo). Using a series of animal models applied to 28 years of data comprising ca. 6000 pedigreed individuals, we find nominally zero additive genetic variance in the Zero-inflated component of lifetime fitness, and low but unreliable variance in the Poisson component. We also find low but likely nonzero additive genetic variance in adult annual reproductive success, but not in survival. As such, our study (i) suggests heritable variance in common tern fitness to result mostly from heritable variance in reproductive success, rather than in early-life or adult survival, (ii) shows how studying the genetic architecture of fitness in natural populations remains challenging, and (iii) highlights the importance of maintaining long-term individual-based studies such that a major research aim in evolutionary ecology will come within better reach in the next decade.

scholarly journals GENETIC LOAD IN NATURAL POPULATIONS: IS IT COMPATIBLE WITH THE HYPOTHESIS THAT MANY POLYMORPHISMS ARE MAINTAINED BY NATURAL SELECTION?

Genetics ◽  
1974 ◽  
Vol 77 (3) ◽  
pp. 569-589
Author(s):  
Martin L Tracey ◽  
Francisco J Ayala
Keyword(s):  
Drosophila Melanogaster ◽  
Natural Selection ◽  
Natural Population ◽  
Natural Populations ◽  
Genetic Load ◽  
Structural Genes ◽  
Invertebrate Species ◽  
Average Proportion ◽  
Mean Fitness ◽  
The Mean

ABSTRACT Recent studies of genetically controlled enzyme variation lead to an estimation that at least 30 to 60% of the structural genes are polymorphic in natural populations of many vertebrate and invertebrate species. Some authors have argued that a substantial proportion of these polymorphisms cannot be maintained by natural selection because this would result in an unbearable genetic load. If many polymorphisms are maintained by heterotic natural selection, individuals with much greater than average proportion of homozygous loci should have very low fitness. We have measured in Drosophila melanogaster the fitness of flies homozygous for a complete chromosome relative to normal wild flies. A total of 37 chromosomes from a natural population have been tested using 92 experimental populations. The mean fitness of homozygous flies is 0.12 for second chromosomes, and 0.13 for third chromosomes. These estimates are compatible with the hypothesis that many (more than one thousand) loci are maintained by heterotic selection in natural populations of D. melanogaster.

scholarly journals Joint Linkage and Linkage Disequilibrium Mapping in Natural Populations

Genetics ◽  
2001 ◽  
Vol 157 (2) ◽  
pp. 899-909
Author(s):  
Rongling Wu ◽  
Zhao-Bang Zeng
Keyword(s):  
Linkage Disequilibrium ◽  
Complex Traits ◽  
Positional Cloning ◽  
Genome Structure ◽  
Natural Populations ◽  
Linkage Disequilibrium Mapping ◽  
Linkage Disequilibria ◽  
Time Simulation ◽  
New Strategy ◽  
Fisher Scoring Algorithm

Abstract A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.

scholarly journals Naturally occurring variation in the restriction map of the amy region of Drosophila melanogaster.

Genetics ◽  
1988 ◽  
Vol 119 (3) ◽  
pp. 619-629
Author(s):  
C H Langley ◽  
A E Shrimpton ◽  
T Yamazaki ◽  
N Miyashita ◽  
Y Matsuo ◽  
...  
Keyword(s):  
Drosophila Melanogaster ◽  
Restriction Site ◽  
Natural Populations ◽  
Alpha Amylase ◽  
Low Frequencies ◽  
Linkage Disequilibria ◽  
Restriction Sites ◽  
Site Variation ◽  
Transcriptional Units ◽  
Polymorphic Restriction

Abstract The restriction maps of 85 alleles of the Amy region of Drosophila melanogaster from natural populations were surveyed. A subset of these were also scored for allozyme phenotype and adult enzyme activity of alpha-amylase. Large insertions were found in 12% of the alleles in a 15-kb region surrounding the two transcriptional units of the duplicated Amy locus. The low frequencies at which each of these large insertions were found are consistent with earlier reports of variation in other loci. Four small deletions were found in the region 5' to the Amy genes. Each was also rare in the population. Restriction site variation provided an estimate of per nucleotide heterozygosity of 0.006. Several statistically significant linkage disequilibria were observed between four polymorphic restriction sites and the allozymes. Adult alpha-amylase activity was correlated with the allozymes and with the polymorphism at one restriction site close to the transcriptional units.

scholarly journals Fluctuating selection: the perpetual renewal of adaptation in variable environments

2010 ◽  
Vol 365 (1537) ◽  
pp. 87-97 ◽  
Author(s):  
Graham Bell
Keyword(s):  
Natural Selection ◽  
Evolutionary Biology ◽  
Natural Populations ◽  
Phenotypic Variance ◽  
Weak Selection ◽  
Fluctuating Selection ◽  
Environmental Variance ◽  
Strong Selection ◽  
Genomic Studies ◽  
Over Time

Darwin insisted that evolutionary change occurs very slowly over long periods of time, and this gradualist view was accepted by his supporters and incorporated into the infinitesimal model of quantitative genetics developed by R. A. Fisher and others. It dominated the first century of evolutionary biology, but has been challenged in more recent years both by field surveys demonstrating strong selection in natural populations and by quantitative trait loci and genomic studies, indicating that adaptation is often attributable to mutations in a few genes. The prevalence of strong selection seems inconsistent, however, with the high heritability often observed in natural populations, and with the claim that the amount of morphological change in contemporary and fossil lineages is independent of elapsed time. I argue that these discrepancies are resolved by realistic accounts of environmental and evolutionary changes. First, the physical and biotic environment varies on all time-scales, leading to an indefinite increase in environmental variance over time. Secondly, the intensity and direction of natural selection are also likely to fluctuate over time, leading to an indefinite increase in phenotypic variance in any given evolving lineage. Finally, detailed long-term studies of selection in natural populations demonstrate that selection often changes in direction. I conclude that the traditional gradualist scheme of weak selection acting on polygenic variation should be supplemented by the view that adaptation is often based on oligogenic variation exposed to commonplace, strong, fluctuating natural selection.

scholarly journals An inequality from genetics

1986 ◽  
Vol 18 (03) ◽  
pp. 860-861
Author(s):  
E. Seneta
Keyword(s):  
Lower Bound ◽  
Stability Structure ◽  
Mean Fitness ◽  
Change In Mean

A class of fitness matrices whose parameters may be varied to give differing stability structure is shown by Chebyshev&s covariance inequality to possess a variance lower bound for the change in mean fitness.

scholarly journals Genetic differentiation of neutral markers and quantitative traits in predominantly selfing metapopulations: confronting theory and experiments with Arabidopsis thaliana

2006 ◽  
Vol 87 (1) ◽  
pp. 1-12 ◽  
Author(s):  
EMMANUELLE PORCHER ◽  
TATIANA GIRAUD ◽  
CLAIRE LAVIGNE
Keyword(s):  
Arabidopsis Thaliana ◽  
Genetic Differentiation ◽  
Quantitative Traits ◽  
Natural Populations ◽  
Additive Model ◽  
Linkage Disequilibria ◽  
Large Populations ◽  
Selfing Species ◽  
Theory And Experiments

The comparison of the genetic differentiation of quantitative traits (QST) and molecular markers (FST) can inform on the strength and spatial heterogeneity of selection in natural populations, provided that markers behave neutrally. However, selection may influence the behaviour of markers in selfing species with strong linkage disequilibria among loci, therefore invalidating this test of detection of selection. We address this issue by monitoring the genetic differentiation of five microsatellite loci (FST) and nine quantitative traits (QST) in experimental metapopulations of the predominantly selfing species Arabidopsis thaliana, that evolved during eight generations. Metapopulations differed with respect to population size and selection heterogeneity. In large populations, the genetic differentiation of neutral microsatellites was much larger under heterogeneous selection than under uniform selection. Using simulations, we show that this influence of selection heterogeneity on FST can be attributable to initial linkage disequilibria among loci, creating stronger genetic differentiation of QTL than expected under a simple additive model with no initial linkage. We found no significant differences between FST and QST regardless of selection heterogeneity, despite a demonstrated effect of selection on QST values. Additional data are required to validate the role of mating system and linkage disequilibria in the joint evolution of neutral and selected genetic differentiation, but our results suggest that FST/QST comparisons can be conservative tests to detect selection in selfing species.

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