%0 Journal Article %1 Lewontin:1964:Genetics:17248194 %A Lewontin, R C %D 1964 %J Genetics %K heterosis hybrid_vigor linkage linked_selection %N 1 %P 49-67 %T The Interaction of Selection and Linkage. I. General Considerations; Heterotic Models %U http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1210557/ %V 49 %X WHILE the theory of the genetic changes in a population due to selection is quite well understood for single loci, our theory for multiple-gene characters is in a rudimentary stage. Most of the formulations for multiple-gene characters are simply extensions of single-locusmodels, extensions which ignore the problem of linkage. There are, however, a few papers in which the role of linkage has been 1956; LEWONTIN investigated for more or less special cases of selection (KIMURA 1962). The results of these investiga- and KOJIMA 1960; BODMER PARSONS and tions were sufficient to show that even for relatively simple cases (two loci, simple symmetrical selective values) linkage might have profound effects on the course of natural selection and, pari passu, natural selection may have major effects on the distribution of coupling and repulsion linkage in a population. The results of the investigations of LEWONTIN KOJIMA(1960) of the two- and locus model can be summarized as follows: (1) If the fitnesses are additive be- tween loci (no epistasis), linkage does not effect the final equilibrium state of the population. (2) If linkage is tighter than the value demanded by the magnitude of the epistasis (the greater the epistasis the greater the value) there may be permanent linkage disequilibrium and alteration of equilibrium gene frequencies. (3) The rate of genetic change with time is affected by the tightness of the link- age. (4)In some cases stable gene frequency equilibria are possible only if link- age is tight enough. Although these conclusions were based only on two-locus model and for selec- tive values of a fairly restricted sort, they point clearly to the importance of taking linkage into account in understanding the changes of gene frequencies in popula- tions. In fact, some experimental results (an example of which will be given below) can be understood only if the interaction of selection and linkage is taken into account. The equations describing the interaction between selection and linkage (see below) do not usually have general literal solutions. It is for this reason that the authors cited above have restricted themselves to relatively simple cases. In view of the interesting findings of those previous papers, however, it is worthwhile to explore the subject more intensively. To do so requires the numerical rather than general literal solutions to the equations, but such numerical solutions apply, obviously, only to the particular parameter values chosen. T o make such a nu merical approach at all useful, it is necessary to cover a variety of models of selection and to vary each model so that an empirical “feel” for general results can be obtained. In this sense, numerical calculations are like experiments: the generality of the results depends upon the variety of conditions of the experiments. In this and the succeeding two papers of this series, three main types of selec- tion are discussed. While these are not completely exhaustive of all possibilities, they represent the main modes of selection in natural and artificial populations. I n this paper I will consider heterotic models, in which heterozygotes at each locus are more fit than homozygotes. In the second paper of the series optimum selection will be examined; that is, selection operating against individuals whose phenotypes deviate from some intermediate optimum. The last paper will deal with unidirectional selection in which an extreme phenotype or genotype is select- ed against. Since the effect of linkage is rather different in these three cases, separate discussions of each are required.

@article{Lewontin:1964:Genetics:17248194, abstract = {WHILE the theory of the genetic changes in a population due to selection is quite well understood for single loci, our theory for multiple-gene characters is in a rudimentary stage. Most of the formulations for multiple-gene characters are simply extensions of single-locusmodels, extensions which ignore the problem of linkage. There are, however, a few papers in which the role of linkage has been 1956; LEWONTIN investigated for more or less special cases of selection (KIMURA 1962). The results of these investiga- and KOJIMA 1960; BODMER PARSONS and tions were sufficient to show that even for relatively simple cases (two loci, simple symmetrical selective values) linkage might have profound effects on the course of natural selection and, pari passu, natural selection may have major effects on the distribution of coupling and repulsion linkage in a population. The results of the investigations of LEWONTIN KOJIMA(1960) of the two- and locus model can be summarized as follows: (1) If the fitnesses are additive be- tween loci (no epistasis), linkage does not effect the final equilibrium state of the population. (2) If linkage is tighter than the value demanded by the magnitude of the epistasis (the greater the epistasis the greater the value) there may be permanent linkage disequilibrium and alteration of equilibrium gene frequencies. (3) The rate of genetic change with time is affected by the tightness of the link- age. (4)In some cases stable gene frequency equilibria are possible only if link- age is tight enough. Although these conclusions were based only on two-locus model and for selec- tive values of a fairly restricted sort, they point clearly to the importance of taking linkage into account in understanding the changes of gene frequencies in popula- tions. In fact, some experimental results (an example of which will be given below) can be understood only if the interaction of selection and linkage is taken into account. The equations describing the interaction between selection and linkage (see below) do not usually have general literal solutions. It is for this reason that the authors cited above have restricted themselves to relatively simple cases. In view of the interesting findings of those previous papers, however, it is worthwhile to explore the subject more intensively. To do so requires the numerical rather than general literal solutions to the equations, but such numerical solutions apply, obviously, only to the particular parameter values chosen. T o make such a nu merical approach at all useful, it is necessary to cover a variety of models of selection and to vary each model so that an empirical “feel” for general results can be obtained. In this sense, numerical calculations are like experiments: the generality of the results depends upon the variety of conditions of the experiments. In this and the succeeding two papers of this series, three main types of selec- tion are discussed. While these are not completely exhaustive of all possibilities, they represent the main modes of selection in natural and artificial populations. I n this paper I will consider heterotic models, in which heterozygotes at each locus are more fit than homozygotes. In the second paper of the series optimum selection will be examined; that is, selection operating against individuals whose phenotypes deviate from some intermediate optimum. The last paper will deal with unidirectional selection in which an extreme phenotype or genotype is select- ed against. Since the effect of linkage is rather different in these three cases, separate discussions of each are required. }, added-at = {2013-07-24T21:50:56.000+0200}, author = {Lewontin, R C}, biburl = {https://www.bibsonomy.org/bibtex/2cf4860f9eeb78c77770813a45819e6d0/peter.ralph}, description = {The Interaction of Selection and Linkage. I. General Considerations; Heterotic Models}, interhash = {f966b8dbfe132c94d017a2e198443fe5}, intrahash = {cf4860f9eeb78c77770813a45819e6d0}, journal = {Genetics}, keywords = {heterosis hybrid_vigor linkage linked_selection}, month = jan, number = 1, pages = {49-67}, pmid = {17248194}, timestamp = {2013-07-24T21:50:56.000+0200}, title = {The Interaction of Selection and Linkage. {I}. General Considerations; Heterotic Models}, url = {http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1210557/}, volume = 49, year = 1964 }