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1- Effects of Linkage on Selection in Heterotic -1- EFFECTS OF LINKAGE ON SELECTION IN HETEROTIC SYSTEMS And EFFECTS OF LINKAGE ON SELECTION FOR AN INTERMEDIATE Dr. Richard C. Lewontin Dept. of Zoology University of Chicago -2- (Summary of 2 talks) c EFFECTS OF LINKAGE ON SELECTION IN HETEROTIC SYSTEMS and EFFECTS OF LINq(AGEON SELECTION FCR AN INTERMEDIATE There have been two strains of thought about the importance of linkage in the dynamics of genetic change in population. One has held that recombi- nation will eventually iron out all correlation between genes at different loci, so that over the long run linkage does not matter. The other, notably that of Fisher and Mather_ has held that linked complexes accumulate under the influence of natural selection. Over the past few years, a number of studies have been carried out treating by exact methods the problem of linkage and selection. These studies have included various models of selection and varying numbers of loci from 2 to 36. The results cannot easily be summarized in a simple elegant statement, but are rather complex. In general, e pistatie interactions between genes are necessary before any effect of linkage on the outcome of selection can be expected. The stronger the epistasis, the greater the value of recombination may be and still show some effect on the outcome of selection. If epistasis is strong enough, and for example in selection for an intermediate optimum, even genes on different chromosomes will be correlated in their gametic distribution. The following thirteen points summarize our present findings on the effect of linkage: -3- i) If linkage is tight enough, gametic frequencies are affected by linkage even though gene frequencies may not be. 2) Linkage has an effect on equilibrium gametic frequencies only if there is non_additivity among the fitness effects at different loci. 3) Tight linkage may produce stable equilibrium of intermediate gene frequency where none would exist without linkage. 2) Linkage, if it is too tight, may destroy the stability of a gene frequency equilibrium. 5) Linkage increases the mean fitness of the equilibrium population. 6) The equilibrium allelic frequencies are generally altered by linkage. 7) There may be alternative stable equilibrium for a given linkage value. 8) Even genes on different chromosomes may be out of random combination at equilibrium. 9) Multiple locus systems show cumulative effects of linkage along the chromosome. 10) Genes closer to the center of a linkage group are more strongly correlated than those at the ends. ll) Optimum deviation models generate enough epistasis to cuase profound effects of linkage. 12) Quadratic optimum models always generate repulsion equilibria. 13) The effect of linkage in quadratic optimum models is to increase the genetic variance and decrease the deviation of the population mean from the optimum. i - 4 - References W. F. Bodmer and P. A_ Parsons, "Linkage and recombination in evolution,.. Adv. Genet., Vol. ll (1962), pp. 1-99. J. Felsenstein, "The effect of linkage on directional selection,'.Genetics, Vol. 52 (1965), pp_ 3_9-363o J. B. S. Haldmne, "The selection of double heterozygotes,,,J. Genet., Vol. 58 (1962), pp. 125-128. M. Kimura, "A model efa genetic system which leads to closer linkage by natural selection," Evolution, Vol. lO (1956), pp. 278-287. , "Attainment of a quasi-linkage equilibrium when gene frequencies are changing by natural selection, Genetics, Vol. 52 (1965), pp. 875-890 M. Kojima and T. Kelleher, "Changes of mean fitness in random mating population when epistasis and linkage are present," Genetics, Vol. 46 (1961), pp. 527-52( K. KoJima and H. E. Schaffer, "Accumulation of epistatic gene complexes," Evolution, Vol. 18 (1962), pp. 127-129. R. C. Lewontin, "The interaction of selection and linkage. I. General consideration; heterotic models," Genetics, Vol. 29 (196_), pp. 29-67. ______., "The interaction of selection and linkage. II. Optimum models," Genetics, Vol. 50 (1962), pp. 757-782. ..... , "The role of linkage in natural selection,'.Genetics Today, New York, Macmillan, 1964, Vol. 2, pp. 517-525. R. C. Lewontin and K_ Kojima, "The evolutionary dynamics of complex polymorphisms,,, Evolution, Volo 14 (1960), pp_ h58-h72. I DR. RICHARD LEWONTIN - "EFFECTS OF LINKAGE ON SELECTION IN HETEROTIC SYSTEMS" J G. E, DICKERSON: Does decrease in fitness with increase in recombination mean natural selection for tighter linkage? L_4ONTIN: Yes, this is the effect predicted by Fisher in "The Genetical Theory of Natural Selection.,, A particularly special case of this _as worked out by Kimura (Evolution_ 10, 278-287). G. E. E[CK_RSON: Does linkage affect validity of Wright's inbreeding coefficients in estimating from pedigree the expected increase in homozygosity relative to that in some base generation? (As published by J. Gill in GENETICS based on computer simulation studies). LEWONTIN: I am a little embarrassedby this question. I share with most people the belief that in the absence of selection, linkage can have no effect whatsoever on the rate of approach to homozygosity at an individual locus. The question of proof hardly seems to arise since the probability argument on which the rate of increase of homozygotes is calculated in no way involves reference to other loci. Unless there is a hidden assumption that no one has been intelligent enough to see, and that is always possible, then Gill must be incorrect. The only suggestion I can make is that there are numerous ways in which a computer program can be in error and some of them are very subtle. One is that random number generations can produce correlations with unusual cycle lengths and the other is that subtle errors in Program writing will result in correlation between successively chosen gametes that are I _ meant to be independent. Since I do not have Gill's program I cannot make a more exact statement. DR. RICHARD LEWONTIN - "EFFECTS OF LINKAGE ON SELECTION FOR AN INTERMEDIATE" G. E. DICKERSON: What genetic conditions most certainly lead to equilibrium gene frequencies at important proportions of loci? Primarily overdominance loci? Or combination with intermediate optimum? L_4ONTIN: The intermediate optimum alone does not usually lead to equilibrium gene frequencies at large numbers of loci. The quadratic devia- tions model can lead to equilibrium with the appropriate dominance values as shown by Kojima (PNAS, hS, 989-993). Moreover, tight linksge increases the possibility of stable equilibrium so that almost any values of dominance will do ($ingh and Lewontin (PN_S, 56, 13h5-1348). However, the gene fre- quencies at equilibrium are very close to fixation and the maximum amount of genetic variance that can be preserved by this model is .75 a2. Other optimum models do not lead to stable equilibrium. In general, overdominance is the ohly well-demonstrated method of maintaining intermediate equal gene frequencies, although frequency dependent selection can also do so. H. ALPLANALP: How important is epistatic variation due to the optimum model in causing regression of means of selected populations after relaxation of selection? LEWOI_TIN: Dr. Griffing can answer this question better than I can, but I doubt that there is much regression of means after relaxation of selection in the optimum model since there is not a great deal of effect on the mean by linkage in this model. There is, of course, some, as I demonstrated in the talk. J J. L. LUSH: If we grant that selection coefficients are rarely as large as .02 for traits, or as large as .O1 for single genes, what then is the role of recombination? That is, can such low selection coefficients keep the gametic array more tbmn a tiny bit away from its random composition? LEWONTIN: The answer to this question depends on how closely linked the genes concerned are. I would say that ordinary selection coefficients are probably not important in maintaining non-randomness of the gametic array except for genes that are very close together on the chromosomes. Thus, there will probably be important non-random effects over very short stretches of the linkage map, but not much for genes that are say five centimorgans apart, and probably not a great deal for those more than one unit apart. W. E. ELLS: Do you consider the concentration of about 85% of the genes of the chicken in six large chromosomes to have any special implications for the selection procedures employed by the poultry breeder? LEWONTIN: This question can only be answered when we know the length of the linkage maps of the six large chromosomes. Many organisms have few chromosomes but a great deal of recombination because the chiasma frequency is very high on every chromosome. The restriction to six large chromosomes is not in itself a cause of tight linkage. In fact, if chromosomes get small enough there may be no recombination within them but only assortment between them. This appears to be the case for the so-called microchromosome in Drosophila. It represents about one-sixtieth of the total genetic material but has no crossing over at all. J J. L. LUSH: Just a comment on the history of genetics - Detlefsen at the A.A.A.S. neeting in 1923 announced experiments in which by selection he had succeeded in tightening or loosening the linkage in Drosophila. Does this have priority over Fisher's thesis that selection for a trait would tighten or loosen the linkage between the genes affecting it? LEWONTIN: I am not sure but I think that Detlefsen,s experiment was directly on the linkage value itself, whereas Fisher's hypothesis concerned changes in linkage value as a result of fitness differences at the major loci concerned, rather than by selection directly for lower recombination. Of course, Detlefsen,s experiment did show that there was genetic variance for linkage value. G.
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