- Email: [email protected]
Selection Limit
1794
S e l e c t io n L i m i t
generation according to their fitness. Assume that the number of offspring of individual j is Xj and the mean number is m. Hence the relative fitness of the individual is Xj/m, and the selection differential in fitness is j Xj Xj =2 VX =2 . This is called the index of opportunity for selection. As the standardpdeviation p of fitness is VX =, it follows that i VX =. This shows that, of course, selection can occur only if there is variability in fitness. Whether selection on fitness, or indeed any other trait, is effective depends then on it having additive genetic variance. Selection intensity is not used to define the magnitude of stabilizing selection, i.e., whereby selection acts mainly to reduce variance in fitness.
Further Reading
Cameron ND (1997) Selection Indices and Prediction of Genetic Merit in Animal Breeding. Wallingford, UK: CAB International.
Reference
Falconer DS and Mackay TFC (1996) Introduction to Quantitative Genetics, 4th edn. Harlow, UK: Longman.
See also: Artificial Selection; Heritability
Selection Limit W G Hill Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1445
In long-term selection experiments for quantitative traits it has often been found that after many generations of selection, a plateau or selection limit has been reached at which there appears to be little or no response despite continued selection. The limit can be explained by fixation of all useful genetic variation or by counteracting effects, for example, natural selection opposing the artificial selection. It is usually hard to be sure a limit actually has been reached because of sampling due to small numbers of individuals and environmental differences among generations. Even so there are some clear cases (e.g., F. W. Robertson, 1955) where limits have been reached. There are others in which, despite selection for over 50 generations, limits appear not to have been obtained. An example is the Illinois corn experiment for increased oil content, in which response has continued for a century. In the low line, however, little response has occurred in recent generations, but the mean is so near zero there is little opportunity for further change (see graph in the article on Artificial Selection).
A selection limit will occur if a population has run out of useful variation. This is inevitable if there is essentially no phenotypic variation (as for low oil content in the Illinois corn oil experiment). More generally the limit can occur if additive genetic variation is exhausted, i.e., the selected line becomes homozygous for all genes which were segregating in the base and which increase the trait in the desired direction. Residual nonadditive genetic variation can remain at such a limit if the favorable genes are dominant and reach high frequency or if there is overdominance. The magnitude of the response to the limit in relation to the genetic variation in the base population depends on the numbers of genes affecting the trait and on the distribution of their effects. If very few loci which influenced the trait were segregating in the base population, such that individuals with the extreme genotype were present in it, albeit at low frequency, the limit would not be outside the initial range of the population. Usually, however, it is far outside the initial range, i.e., the total response is many phenotypic standard deviations. An estimate of the number (n) of genes affecting a trait, Wright's effective number, can be obtained by comparing the range (R high±low divergence) achieved to the additive genetic variation (VA) in the base population or in an F2 cross of high and low lines, as n R2/8VA. As a population under selection is necessarily of finite size, desirable genes may be lost by chance, particularly those with a small effect on the trait and particularly if selection is weak and the population size is small. The limit to artificial selection then depends on the probability of fixation of the favorable genes. In a theory of limits to artificial selection, A. Robertson (1966) showed that the fixation probability is proportional to the product of effective population size (Ne), selection intensity (i), the effect of the gene on the trait relative to the phenotypic standard deviation, and its degree of dominance. Prediction of the actual limit to selection is not, however, possible without (usually) unknown information on the distribution of gene effects and frequencies in the base population, but nevertheless there are some practical consequences of the theory. In particular there is a trade-off between short- and long-term response, for the initial response is proportional to the selection intensity, whereas the limit is proportional to Nei, and is maximized if only one-half of the population is selected. Similarly, use of relatives' information in a selection index reduces the limit because relatives are coselected, and so Ne is reduced more than the accuracy of selection is increased. Fixation is not the only cause of selection limits. In theory, limits can occur if there are overdominant
S el e c t i o n Te c h ni q ue s 1795 loci or if most of the variance is due to recessive genes, when inbreeding would lead to reduction in performance. More importantly, perhaps, because selected populations become extreme for the trait under selection, but also show correlated responses in other traits, it is to be expected that natural selection opposes artificial selection such that a limit occurs at the balance between these opposing forces. Evidence comes from experiments in which the population mean at the limit falls when either selection in the opposite direction (reversed selection) has been practiced or the population has been maintained without selection (relaxed selection). Natural selection may be a consequence solely of the shift in mean of the correlated traits subject to stabilizing selection, or of increases in frequency of specific genes with effect on the trait under selection but also pleiotropic effects upon fitness. (Extreme examples found are genes that have a large effect on the trait as a heterozygote, but are lethal as a homozygote.) As new variation in quantitative traits arises by mutation, limits cannot happen as a consequence of running out of variation unless there are so few possible loci and useful alleles at them that all were present at the outset or appeared during the selection process. It is therefore likely that fixation cannot account exclusively for limits, and other factors such as natural selection have to be invoked. All `limits' may therefore be transient, and renewed responses expected and explained by mutations or, perhaps, by recombination among haplotypes with balanced repulsion for useful genes. Nevertheless, in selection experiments for competitive fitness in bacteria for which responses must derive from mutation, Lenski and colleagues (Lenski and Travisano, 1994) found plateaus in response after thousands of generations of selection.
Further Reading
Falconer DS and Mackay TFC (1996) Introduction to Quantitative Genetics, 4th edn. Harlow, UK: Longman. Hill WG and Caballero A (1992) Artificial selection experiments. Annual Review of Systematics and Ecology 23: 287± 310.
References
Lenski RE and Travisano M (1994) Proceedings of the National Academy of Sciences, USA 91: 6808±6814. Robertson A (1966) A theory of limits in artificial selection. Proceedings of the Royal Society of London B 153: 234±249. Robertson FW (1955) Cold Spring Harbor Symposia in Quantitative Biology 20: 166±177.
See also: Additive Genetic Variance; Artificial Selection; Heritability; Selective Breeding
Selection Pressure M Tracey Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1164
Selection, either natural or artificial, involves unequal reproduction among various genetic types. Consider the old example of selection for longer necks in giraffes. In times of scarce browse, the giraffes able to reach the tops of trees would eat more and have more progeny. To the extent that their longer necks and legs were genetically determined we would expect to see taller progeny who would, in turn have taller progeny. There is a point of diminishing returns in this type of selection as the giraffe population becomes taller and taller in response to the hunt for nutrition higher and higher in the trees. Eventually the competition for browse is just as intense at the tops of the trees as it was at other levels. The effectiveness of selection in changing giraffe height genotypes over generations is selection pressure. Selection pressure depends primarily on the selection differential (see Selection Differential, Selection Intensity) and the amount of genetic variation in the selected population (see Heritability). Consider genetic resistance to pathogens (see Sickle Cell Anemia) in which any differential reproduction among genotypes, the selection differential, takes place only in the presence of the pathogen and magnitude of the reproductive advantage depends on the prevalence of the pathogen. In this example the selection pressure will depend on the prevalence of the pathogen; there are no genotypic differences in the absence of the pathogen and as the disease becomes more common the reproductive differences among the genotypes become more important in altering the reproductive success of different genotypes. See also: Branch Migration; Heritability; Selection Differential; Sickle Cell Anemia
Selection Techniques I Schildkraut Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1165
Selection techniques are used by geneticists to isolate mutations. The techniques involve the process of isolating cells with a mutant phenotype by choosing conditions that favor the survival of the mutant
S e l e c t io n L i m i t
generation according to their fitness. Assume that the number of offspring of individual j is Xj and the mean number is m. Hence the relative fitness of the individual is Xj/m, and the selection differential in fitness is j Xj Xj =2 VX =2 . This is called the index of opportunity for selection. As the standardpdeviation p of fitness is VX =, it follows that i VX =. This shows that, of course, selection can occur only if there is variability in fitness. Whether selection on fitness, or indeed any other trait, is effective depends then on it having additive genetic variance. Selection intensity is not used to define the magnitude of stabilizing selection, i.e., whereby selection acts mainly to reduce variance in fitness.
Further Reading
Cameron ND (1997) Selection Indices and Prediction of Genetic Merit in Animal Breeding. Wallingford, UK: CAB International.
Reference
Falconer DS and Mackay TFC (1996) Introduction to Quantitative Genetics, 4th edn. Harlow, UK: Longman.
See also: Artificial Selection; Heritability
Selection Limit W G Hill Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1445
In long-term selection experiments for quantitative traits it has often been found that after many generations of selection, a plateau or selection limit has been reached at which there appears to be little or no response despite continued selection. The limit can be explained by fixation of all useful genetic variation or by counteracting effects, for example, natural selection opposing the artificial selection. It is usually hard to be sure a limit actually has been reached because of sampling due to small numbers of individuals and environmental differences among generations. Even so there are some clear cases (e.g., F. W. Robertson, 1955) where limits have been reached. There are others in which, despite selection for over 50 generations, limits appear not to have been obtained. An example is the Illinois corn experiment for increased oil content, in which response has continued for a century. In the low line, however, little response has occurred in recent generations, but the mean is so near zero there is little opportunity for further change (see graph in the article on Artificial Selection).
A selection limit will occur if a population has run out of useful variation. This is inevitable if there is essentially no phenotypic variation (as for low oil content in the Illinois corn oil experiment). More generally the limit can occur if additive genetic variation is exhausted, i.e., the selected line becomes homozygous for all genes which were segregating in the base and which increase the trait in the desired direction. Residual nonadditive genetic variation can remain at such a limit if the favorable genes are dominant and reach high frequency or if there is overdominance. The magnitude of the response to the limit in relation to the genetic variation in the base population depends on the numbers of genes affecting the trait and on the distribution of their effects. If very few loci which influenced the trait were segregating in the base population, such that individuals with the extreme genotype were present in it, albeit at low frequency, the limit would not be outside the initial range of the population. Usually, however, it is far outside the initial range, i.e., the total response is many phenotypic standard deviations. An estimate of the number (n) of genes affecting a trait, Wright's effective number, can be obtained by comparing the range (R high±low divergence) achieved to the additive genetic variation (VA) in the base population or in an F2 cross of high and low lines, as n R2/8VA. As a population under selection is necessarily of finite size, desirable genes may be lost by chance, particularly those with a small effect on the trait and particularly if selection is weak and the population size is small. The limit to artificial selection then depends on the probability of fixation of the favorable genes. In a theory of limits to artificial selection, A. Robertson (1966) showed that the fixation probability is proportional to the product of effective population size (Ne), selection intensity (i), the effect of the gene on the trait relative to the phenotypic standard deviation, and its degree of dominance. Prediction of the actual limit to selection is not, however, possible without (usually) unknown information on the distribution of gene effects and frequencies in the base population, but nevertheless there are some practical consequences of the theory. In particular there is a trade-off between short- and long-term response, for the initial response is proportional to the selection intensity, whereas the limit is proportional to Nei, and is maximized if only one-half of the population is selected. Similarly, use of relatives' information in a selection index reduces the limit because relatives are coselected, and so Ne is reduced more than the accuracy of selection is increased. Fixation is not the only cause of selection limits. In theory, limits can occur if there are overdominant
S el e c t i o n Te c h ni q ue s 1795 loci or if most of the variance is due to recessive genes, when inbreeding would lead to reduction in performance. More importantly, perhaps, because selected populations become extreme for the trait under selection, but also show correlated responses in other traits, it is to be expected that natural selection opposes artificial selection such that a limit occurs at the balance between these opposing forces. Evidence comes from experiments in which the population mean at the limit falls when either selection in the opposite direction (reversed selection) has been practiced or the population has been maintained without selection (relaxed selection). Natural selection may be a consequence solely of the shift in mean of the correlated traits subject to stabilizing selection, or of increases in frequency of specific genes with effect on the trait under selection but also pleiotropic effects upon fitness. (Extreme examples found are genes that have a large effect on the trait as a heterozygote, but are lethal as a homozygote.) As new variation in quantitative traits arises by mutation, limits cannot happen as a consequence of running out of variation unless there are so few possible loci and useful alleles at them that all were present at the outset or appeared during the selection process. It is therefore likely that fixation cannot account exclusively for limits, and other factors such as natural selection have to be invoked. All `limits' may therefore be transient, and renewed responses expected and explained by mutations or, perhaps, by recombination among haplotypes with balanced repulsion for useful genes. Nevertheless, in selection experiments for competitive fitness in bacteria for which responses must derive from mutation, Lenski and colleagues (Lenski and Travisano, 1994) found plateaus in response after thousands of generations of selection.
Further Reading
Falconer DS and Mackay TFC (1996) Introduction to Quantitative Genetics, 4th edn. Harlow, UK: Longman. Hill WG and Caballero A (1992) Artificial selection experiments. Annual Review of Systematics and Ecology 23: 287± 310.
References
Lenski RE and Travisano M (1994) Proceedings of the National Academy of Sciences, USA 91: 6808±6814. Robertson A (1966) A theory of limits in artificial selection. Proceedings of the Royal Society of London B 153: 234±249. Robertson FW (1955) Cold Spring Harbor Symposia in Quantitative Biology 20: 166±177.
See also: Additive Genetic Variance; Artificial Selection; Heritability; Selective Breeding
Selection Pressure M Tracey Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1164
Selection, either natural or artificial, involves unequal reproduction among various genetic types. Consider the old example of selection for longer necks in giraffes. In times of scarce browse, the giraffes able to reach the tops of trees would eat more and have more progeny. To the extent that their longer necks and legs were genetically determined we would expect to see taller progeny who would, in turn have taller progeny. There is a point of diminishing returns in this type of selection as the giraffe population becomes taller and taller in response to the hunt for nutrition higher and higher in the trees. Eventually the competition for browse is just as intense at the tops of the trees as it was at other levels. The effectiveness of selection in changing giraffe height genotypes over generations is selection pressure. Selection pressure depends primarily on the selection differential (see Selection Differential, Selection Intensity) and the amount of genetic variation in the selected population (see Heritability). Consider genetic resistance to pathogens (see Sickle Cell Anemia) in which any differential reproduction among genotypes, the selection differential, takes place only in the presence of the pathogen and magnitude of the reproductive advantage depends on the prevalence of the pathogen. In this example the selection pressure will depend on the prevalence of the pathogen; there are no genotypic differences in the absence of the pathogen and as the disease becomes more common the reproductive differences among the genotypes become more important in altering the reproductive success of different genotypes. See also: Branch Migration; Heritability; Selection Differential; Sickle Cell Anemia
Selection Techniques I Schildkraut Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1165
Selection techniques are used by geneticists to isolate mutations. The techniques involve the process of isolating cells with a mutant phenotype by choosing conditions that favor the survival of the mutant