THE DISTRIBUTION OF GENETIC VARIANCE ACROSS PHENOTYPIC SPACE AND THE RESPONSE TO SELECTION

SummaryEpistasis plays important roles in evolution, for example in the evolution of recombination, but each of the current methods to study epistasis has limitations. Here, we propose a new strategy. If a quantitative trait locus (QTL) affecting a quantitative character has been identified, individuals who have the same genotype at that QTL can be regarded as comprising a subpopulation whose response to selection depends in part on interactions with other loci affecting the character. We define the marginal differences to be the differences in the average phenotypes of individuals with different genotypes of that QTL. We show that the response of the marginal differences to directional selection on the quantitative character depends on epistatic gene interactions. For a model with no interactions, the marginal differences do not differ on average from their starting values once linkage equilibrium has been re-established. If there is directional epistasis, meaning that interactions between the QTL and other loci tend to increase or decrease the character more than under an additive model, then the marginal differences will tend to increase or decrease accordingly when larger values of the character are selected for. We develop a likelihood ratio test for significant changes in the marginal differences and show that it has some power to detect directional epistasis for realistic sample sizes. We also show that epistatic interactions which affect the evolution of the marginal differences do not necessarily result in a substantial epistatic component of the genetic variance.

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Testing limits to adaptation along altitudinal gradients in rainforest Drosophila

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2008.1601 ◽

2009 ◽

Vol 276 (1661) ◽

pp. 1507-1515 ◽

Cited By ~ 52

Author(s):

Jon R Bridle ◽

Sedef Gavaz ◽

W. Jason Kennington

Keyword(s):

Gene Flow ◽

Genetic Variance ◽

Local Density ◽

Theoretical Models ◽

Rate Of Change ◽

Adaptive Divergence ◽

Local Optimum ◽

Response To Selection ◽

Costs And Benefits ◽

The One

Given that evolution can generate rapid and dramatic shifts in the ecological tolerance of a species, what prevents populations adapting to expand into new habitat at the edge of their distributions? Recent population genetic models have focused on the relative costs and benefits of migration between populations. On the one hand, migration may limit adaptive divergence by preventing local populations from matching their local selective optima. On the other hand, migration may also contribute to the genetic variance necessary to allow populations to track these changing optima. Empirical evidence for these contrasting effects of gene flow in natural situations are lacking, largely because it remains difficult to acquire. Here, we develop a way to explore theoretical models by estimating genetic divergence in traits that confer stress resistance along similar ecological gradients in rainforest Drosophila . This approach allows testing for the coupling of clinal divergence with local density, and the effects of genetic variance and the rate of change of the optimum on the response to selection. In support of a swamping effect of migration on phenotypic divergence, our data show no evidence for a cline in stress-related traits where the altitudinal gradient is steep, but significant clinal divergence where it is shallow. However, where clinal divergence is detected, sites showing trait means closer to the presumed local optimum have more genetic variation than sites with trait means distant from their local optimum. This pattern suggests that gene flow also aids a sustained response to selection.

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The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA)

Evolutionary Computation ◽

10.1162/evco.1993.1.4.335 ◽

1993 ◽

Vol 1 (4) ◽

pp. 335-360 ◽

Cited By ~ 158

Author(s):

Heinz Mühlenbein ◽

Dirk Schlierkamp-Voosen

Keyword(s):

Genetic Algorithm ◽

Genetic Variance ◽

Response To Selection ◽

Gene Effects ◽

Fitness Functions ◽

Additive Gene ◽

Regression Techniques ◽

Algorithm Theory ◽

And Control ◽

Theoretical Results

The breeder genetic algorithm (BGA) models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection equation and the concept of heritability can be applied to predict the behavior of the BGA. Selection, recombination, and mutation are analyzed within this framework. It is shown that recombination and mutation are complementary search operators. The theoretical results are obtained under the assumption of additive gene effects. For general fitness landscapes, regression techniques for estimating the heritability are used to analyze and control the BGA. The method of decomposing the genetic variance into an additive and a nonadditive part connects the case of additive fitness functions with the general case.

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Measurement of fleece wettability in sheep and its relationship to susceptibility to fleece rot and blowfly strike

Australian Journal of Agricultural Research ◽

10.1071/ar9820141 ◽

1982 ◽

Vol 33 (1) ◽

pp. 141 ◽

Cited By ~ 1

Author(s):

L Pascoe

Keyword(s):

Genetic Variance ◽

Additive Genetic Variance ◽

Genetic Correlations ◽

Economic Importance ◽

Correlated Response ◽

Response To Selection ◽

Significant Incidence ◽

The Mean ◽

Selection For ◽

The One

Fleece wettability in sheep is a character believed to be related to susceptibility to fleece rot and blowfly strike. The present study was undertaken to investigate that hypothesis and to assess wettability as a possible character for a selection program. Wool samples were taken from two flocks which had been subject to selection for wool quality and resistance to fleece rot and a third flock which was unselected. The wettabilities of about 800 samples were determined. The results were found to be repeatable and the technique was capable of distinguishing between sheep. Some problems of measurement are discussed. In the one flock with a significant incidence of fleece rot, susceptibility to fleece rot was found to be associated with higher wettabilities. The mean wettability and the variance were found to be significantly higher in the unselected flock than in the two selected flocks. The heritability of wettability was estimated in the two selected flocks and was found to be low. It is argued that there is likely to be more additive genetic variance in the unselected flock and that the observed difference in wettability was due to a correlated response to selection for resistance to fleece rot. It is considered that further work on the heritability of wettability and its genetic correlations with other characters of economic importance could be fruitful.

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Asymptotic rates of response from index selection

Animal Science ◽

10.1017/s0003356100032347 ◽

1989 ◽

Vol 49 (2) ◽

pp. 217-227 ◽

Cited By ~ 67

Author(s):

Naomi R. Wray ◽

W. G. Hill

Keyword(s):

Genetic Variance ◽

Additive Genetic Variance ◽

Index Selection ◽

Selection Intensity ◽

Response To Selection ◽

Multiple Trait ◽

Breeding Values ◽

Breeding Programmes ◽

Breeding Schemes ◽

Rate Of Response

ABSTRACTThe reduction in additive genetic variance due to selection is investigated when index selection using family records is practised. A population of infinite size with no accumulation of inbreeding, an infinitesimal model and discrete generations are assumed. After several generations of selection, the additive genetic variance and the rate of response to selection reach an asymptote. A prediction of the asymptotic rate of response is considered to be more appropriate for comparing response from alternative breeding programmes and for comparing predicted and realized response than the response following the first generation of selection that is classically used. Algorithms to calculate asymptotic response rate are presented for selection based on indices which include some or all of the records of an individual, its full- and half-sibs and its parental estimated breeding values. An index using all this information is used to predict response when selection is based on breeding values estimated by using a Best Linear Unbiased Prediction (BLUP) animal model, and predictions agree well with simulation results. The predictions are extended to multiple trait selection.Asymptotic responses are compared with one-generation responses for a variety of alternative breeding schemes differing in population structure, selection intensity and heritability of the trait. Asymptotic responses can be up to one-quarter less than one-generation responses, the difference increasing with selection intensity and accuracy of the index. Between family variance is reduced considerably by selection, perhaps to less than half its original value, so selection indices which do not account for this tend to place too much emphasis on family information. Asymptotic rates of response to selection, using indices including family information for traits not measurable on the individuals available for selection, such as sex limited or post-slaughter traits, are found to be as much as two-fifths less than their expected one-generation responses. Despite this, the ranking of the breeding schemes is not greatly altered when compared by one-generation rather than asymptotic responses, so the one-generation prediction is usually likely to be adequate for determining optimum breeding structure.

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The Equation for Response to Selection and Its Use for Prediction

Evolutionary Computation ◽

10.1162/evco.1997.5.3.303 ◽

1997 ◽

Vol 5 (3) ◽

pp. 303-346 ◽

Cited By ~ 295

Author(s):

Heinz Mühlenbein

Keyword(s):

Genetic Algorithms ◽

Genetic Variance ◽

Additive Genetic Variance ◽

Linkage Equilibrium ◽

Realized Heritability ◽

Response To Selection ◽

Infinite Population ◽

Livestock Breeding ◽

Genotype Frequencies ◽

Tournament Selection

The Breeder Genetic Algorithm (BGA) was designed according to the theories and methods used in the science of livestock breeding. The prediction of a breeding experiment is based on the response to selection (RS) equation. This equation relates the change in a population's fitness to the standard deviation of its fitness, as well as to the parameters selection intensity and realized heritability. In this paper the exact RS equation is derived for proportionate selection given an infinite population in linkage equilibrium. In linkage equilibrium the genotype frequencies are the product of the univariate marginal frequencies. The equation contains Fisher's fundamental theorem of natural selection as an approximation. The theorem shows that the response is approximately equal to the quotient of a quantity called additive genetic variance, VA, and the average fitness. We compare Mendelian two-parent recombination with gene-pool recombination, which belongs to a special class of genetic algorithms that we call univariate marginal distribution (UMD) algorithms. UMD algorithms keep the genotypes in linkage equilibrium. For UMD algorithms, an exact RS equation is proven that can be used for long-term prediction. Empirical and theoretical evidence is provided that indicates that Mendelian two-parent recombination is also mainly exploiting the additive genetic variance. We compute an exact RS equation for binary tournament selection. It shows that the two classical methods for estimating realized heritability—the regression heritability and the heritability in the narrow sense—may give poor estimates. Furthermore, realized heritability for binary tournament selection can be very different from that of proportionate selection. The paper ends with a short survey about methods that extend standard genetic algorithms and UMD algorithms by detecting interacting variables in nonlinear fitness functions and using this information to sample new points.

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Optimal weighting of information in marker-assisted selection

Genetics Research ◽

10.1017/s0016672397002711 ◽

1997 ◽

Vol 69 (2) ◽

pp. 137-144 ◽

Cited By ~ 17

Author(s):

J. C. WHITTAKER ◽

C. S. HALEY ◽

R. THOMPSON

Keyword(s):

Linear Regression ◽

Marker Assisted Selection ◽

Quantitative Traits ◽

Genetic Variance ◽

Cross Validation ◽

Inbred Lines ◽

Response To Selection ◽

Phenotypic Information ◽

Optimal Weighting ◽

Marker Information

In crosses between inbred lines linear regression can be used to estimate marker effects; these marker effects then allow marker-assisted selection (MAS) for quantitative traits. Weighting of marker and phenotypic information in MAS requires estimation of genetic variance associated with the markers: the usual estimators are biased, resulting in too much weight being placed on marker information relative to phenotypic information. In this paper we develop a cross-validation method to remove this bias, and show by simulation that response to selection using this method is almost as high as that achieved using optimal weighting of marker and phenotypic information.

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