scholarly journals "FUNDAMENTAL THEOREM" FOR TWO LOCI

Genetics ◽  
1981 ◽  
Vol 99 (2) ◽  
pp. 365-369
Author(s):  
John R G Turner
Keyword(s):  
Linkage Disequilibrium ◽  
Fundamental Theorem ◽  
Mean Fitness ◽  
Two Parameters ◽  
Change In Mean

ABSTRACT The change in mean fitness for two loci under selection can be described by four terms: (i) the variance of fitness, (ii) a weighted between-gamete covariance, (iii) a function of recombination, linkage disequilibrium and the slope of the surface of mean fitness on disequilibrium, and (iv) a function of these two parameters and the curvature of the surface. Independent derivations of this equation by different methods, although thought at one time to be in disagreement, give algebraically identical results.

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 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 Indirect genetic effects clarify how traits can evolve even when fitness does not

2018 ◽  
Author(s):  
David N. Fisher ◽  
Andrew G. McAdam
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Genetic Effects ◽  
Social Effects ◽  
Indirect Genetic Effects ◽  
The Social ◽  
Mean Fitness ◽  
Related Individuals ◽  
Fundamental Theorems ◽  
Fisher’S Fundamental Theorem

AbstractThere are many situations in nature where we expect traits to evolve but not necessarily for mean fitness to increase. However, these scenarios are hard to reconcile simultaneously with Fisher’s Fundamental Theorem of Natural Selection and the Price identity. The consideration of indirect genetic effects on fitness reconciles these fundamental theorems with the observation that traits sometimes evolve without any adaptation, by explicitly considering the correlated evolution of the social environment, which is a form of transmission bias. While transmission bias in the Price identity is often assumed to be absent, here we show that explicitly considering indirect genetic effects as a form of transmission bias for fitness has several benefits: 1) it makes clear how traits can evolve while mean fitness remains stationary, 2) it reconciles the fundamental theorem of natural selection with the evolution of maladaptation, 3) it explicitly includes density-dependent fitness through negative social effects that depend on the number of interacting conspecifics, and 4) its allows mean fitness to evolve even when direct genetic variance in fitness is zero, if related individuals interact and/or if there is multilevel selection. In summary, considering fitness in the context of indirect genetic effects aligns important theorems of natural selection with many situations observed in nature and provides a useful lens through which we might better understand evolution and adaptation.

scholarly journals SELECTION FOR LINKAGE MODIFICATION II. A RECOMBINATION BALANCE FOR NEUTRAL MODIFIERS

Genetics ◽  
1973 ◽  
Vol 74 (4) ◽  
pp. 713-726
Author(s):  
Marcus W Feldman ◽  
Beverley Balkau
Keyword(s):  
Linkage Disequilibrium ◽  
Gene Locus ◽  
Recombination Fraction ◽  
Neutral Gene ◽  
Mean Fitness ◽  
Selection For ◽  
Relationship Of ◽  
The Relationship

ABSTRACT A stable polymorphic equilibrium may be established at a selectively-neutral gene locus which controls the extent of recombination between two other selected loci. The condition for the existence of the stable polymorphism is analogous to heterozygous advantage. The heterozygote at the modifying locus should produce a recombination fraction allowing the greatest linkage disequilibrium. In the models treated this has the effect of producing the highest mean fitness. The relationship of these findings to general problems of coadaptation is discussed.

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 effects of normalizing and disruptive selection on genes for recombination

1979 ◽  
Vol 33 (2) ◽  
pp. 121-128 ◽  
Author(s):  
J. Maynard Smith
Keyword(s):  
Linkage Disequilibrium ◽  
Adult Population ◽  
Disruptive Selection ◽  
Additive Effects ◽  
Frequency Selection ◽  
Mean Fitness ◽  
The Mean ◽  
Deterministic Simulations ◽  
Selection For ◽  
Large Decline

SUMMARYDeterministic simulations have been carried out of populations under normalizing and disruptive selection for a trait determined by genes with additive effects at six loci. In some simulations a pair of alleles at a seventh locus determined the rate of recombination between the seven loci. Normalizing selection with a single optimum, fixed or fluctuating, invariably led to genetic homozygosity. If the optimum fluctuates widely, the approach to homozygosity may be accompanied by a large decline in the mean fitness of the population. Disruptive selection was simulated by having two ‘niches’ with separate optima and separate density-dependent regulation, but with the adult population mating randomly. If the optima are widely separated, this leads to stable polymorphism. Selection produced linkage disequilibrium, normalizing selection causing repulsion and disruptive selection coupling between + and − alleles. This linkage disequilibrium accelerates the phenotypic response to selection, but delays changes in gene frequency. Selection always favoured alleles for low recombination at the expense of alleles for high recombination.

scholarly journals An inequality from genetics

1986 ◽  
Vol 18 (3) ◽  
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 The dynamics of adapting, unregulated populations and a modified fundamental theorem

2013 ◽  
Vol 10 (78) ◽  
pp. 20120538 ◽  
Author(s):  
James P. O'Dwyer
Keyword(s):  
Fundamental Theorem ◽  
Fitness Landscape ◽  
Analytical Relationship ◽  
Single Mutation ◽  
Adaptive Mutations ◽  
Theoretical Predictions ◽  
Change In The Mean ◽  
Pathogen Populations ◽  
Change In Mean ◽  
Over Time

A population in a novel environment will accumulate adaptive mutations over time, and the dynamics of this process depend on the underlying fitness landscape: the fitness of and mutational distance between possible genotypes in the population. Despite its fundamental importance for understanding the evolution of a population, inferring this landscape from empirical data has been problematic. We develop a theoretical framework to describe the adaptation of a stochastic, asexual, unregulated, polymorphic population undergoing beneficial, neutral and deleterious mutations on a correlated fitness landscape. We generate quantitative predictions for the change in the mean fitness and within-population variance in fitness over time, and find a simple, analytical relationship between the distribution of fitness effects arising from a single mutation, and the change in mean population fitness over time: a variant of Fisher's ‘fundamental theorem’ which explicitly depends on the form of the landscape. Our framework can therefore be thought of in three ways: (i) as a set of theoretical predictions for adaptation in an exponentially growing phase, with applications in pathogen populations, tumours or other unregulated populations; (ii) as an analytically tractable problem to potentially guide theoretical analysis of regulated populations; and (iii) as a basis for developing empirical methods to infer general features of a fitness landscape.

scholarly journals Correlation measures for linkage disequilibrium within and between populations

2009 ◽  
Vol 91 (3) ◽  
pp. 183-192 ◽  
Author(s):  
J. A. SVED
Keyword(s):  
Linkage Disequilibrium ◽  
Steady State ◽  
Local Population ◽  
Primary Data ◽  
Population Subdivision ◽  
Gene Frequencies ◽  
Island Populations ◽  
Correlation Measures ◽  
Two Parameters ◽  
Correlation Statistics

SummaryCorrelation statistics can be used to measure the amount of linkage disequilibrium (LD) between two loci in subdivided populations. Within populations, the square of the correlation of gene frequencies, r2, is a convenient measure of LD. Between populations, the statistic rirj, for populations i and j, measures the relatedness of LD. Recurrence relationships for these two parameters are derived for the island model of population subdivision, under the assumptions of the linked identity-by-descent (LIBD) model in which correlation measures are equated to probability measures. The recurrence relationships closely predict the build-up of r2 and rirj following population subdivision in computer simulations. The LIBD model predicts that a steady state will be reached with r2 equal to 1/[1+4Nec(1+(k−1)ρ)], where k is the number of island populations, Ne is the effective local population (island) size, and ρ measures the ratio of migration (m) to recombination (c) and is equal to m/[c(k−1)+m]. For low values of m/c, ρ=0, and E(r2) is equal to 1/(1+4Nec). For high values of m/c, ρ=1, and E(r2) is equal to 1/(1+4kNec). The value of rirj following separation eventually settles down to a steady state whose expectation, E(rirj), is equal to E(r2) multiplied by ρ. Equations predicting the change in rirj values are applied to the separation of African (Yoruba – YRI) and non-African (European – CEU) populations, using data from Hapmap. The primary data lead to an estimate of separation time of less than 1000 generations if there has been no migration, which is around one-third of minimum current estimates. Ancient rather than recent migration can explain the form of the data.

scholarly journals Joint phenotypes, evolutionary conflict and the fundamental theorem of natural selection

2014 ◽  
Vol 369 (1642) ◽  
pp. 20130423 ◽  
Author(s):  
David C. Queller
Keyword(s):  
Natural Selection ◽  
Species Interactions ◽  
Fundamental Theorem ◽  
Genetic Variance ◽  
Inclusive Fitness ◽  
Evolutionary Conflict ◽  
Mean Fitness ◽  
The Mean ◽  
Multiple Species ◽  
Fisher’S Fundamental Theorem

Multiple organisms can sometimes affect a common phenotype. For example, the portion of a leaf eaten by an insect is a joint phenotype of the plant and insect and the amount of food obtained by an offspring can be a joint trait with its mother. Here, I describe the evolution of joint phenotypes in quantitative genetic terms. A joint phenotype for multiple species evolves as the sum of additive genetic variances in each species, weighted by the selection on each species. Selective conflict between the interactants occurs when selection takes opposite signs on the joint phenotype. The mean fitness of a population changes not just through its own genetic variance but also through the genetic variance for its fitness that resides in other species, an update of Fisher's fundamental theorem of natural selection. Some similar results, using inclusive fitness, apply to within-species interactions. The models provide a framework for understanding evolutionary conflicts at all levels.

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