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EFFECTS OF LINKAGE ON SELECTION IN HETEROTIC SYSTEMS

And

EFFECTS OF LINKAGE ON SELECTION FOR AN INTERMEDIATE

Dr. Richard C. Lewontin Dept. of Zoology -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 . 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

, 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 ,.. Adv. Genet., Vol. ll (1962), pp. 1-99.

J. Felsenstein, "The effect of linkage on directional selection,'., 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, , 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 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 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. E. DICKERSON: _at portion of loci have you found segregating in D. pseudoobscura for electrophoretically detected loci?

LE_ONTIN: We have found about one-third of the loci segregating in

this species and this agrees with some fragmentary data on man and some data

on another species of Drosophila studied by Johnson, Richardson, and KoJima

in Texas. The complete analysis of the D. pseudoobscura population is given

in the papers of Hubby and Lewontin (Genetics, 5l_,577-59_, 595-609).

G.E.DICEERSON: Last year Dr. Crenshaw and Dr. Pimentel presented

evidence of cyclical changes in direction of selection under competition models

(that is genetic-environmental interaction) as the basis for fluctuating

or equilibrium? Do you have a comment on this phenomenon as it might be related to linkage? -9-

L_IVONTIN: I do not believe this phenomenon is an important source

of equilibrium but it may be. What it amounts to is frequency dependent selection

in which the fitness of a genotype increases as the genotype becomes rarer.

As a result, there may be stable equilibrium and at the equilibrium point

there is actually no fitness difference among the genotypes. However, if

they deviate from equilibrium, fitness differences appear. I have not inves-

tigated the effects of linkage on such frequency dependent systems, but it

is pretty clear what will happen. Since at equilibrium there are no fitness

differences or virtually4 none, then after the population reaches gene frequency

equilibrium it will proceed to become randomized in respect to linkage equilibrium.