FURTHER DATA ON THE OVERDOMINANCE BRUCE WALLACE. Received December 8, 1962

Transcription

1 FURTHER DATA ON THE OVERDOMINANCE OF INDUCED MUTATIONS BRUCE WALLACE Department of Plant Breeding, Cornell Uniuersity, Ithaca, New York Received December 8, 1962 ONE of the greatest challenges facing population genetics is the evaluation of the role of overdominance in the determination of fitness. Were overdominance nonexistent, normal individuals would be those fortunate enough to possess an entire complement of normal genes. If mutant genes were completely recessive, individuals possessing at least one normal allele at each locus would be normal in viability; if dominance of the normal alleles were incomplete, the genetic dite would be restricted to only those individuals homozygous for normal alleles at every locus. In either case, alleles with deleterious effects on fitness would be found in Mendelian populations primarily as the result of mutation pressure. On the other hand, to whatever extent overdominance exists, a number of seemingly deleterious alleles will be maintained in populations by natural selection. Normal individuals in this case will be those which, for loci at which alleles exhibiting overdominant effects exist, are heterozygous for two appropriate alleles rather than homozygous for either one alone. An array of appropriate alleles at each of many loci precludes the identification of one genotype as the normal genotype; an array of genotypes must be regarded as normal under these circumstances. That instances of overdominance exist, especially in relation to a trait as complex as fitness, is generally conceded. It is also generally admitted that overdominance need not be exhibited by genes at every locus, by all alleles at any one locus, nor by any one heterozygous combination under all conditions. The problem at issue is the importance of heterotic gene interactions in the maintenance of the adaptive norm of a species or a population, and the frequency of occurrence of overdominant effects at various gene loci. In a series of papers (WALLACE 1957, 1958, 1959) I have presented an argument and experimental results which promise to aid in solving this problem. The argument is exceedingly simple; the experimental test, as so often happens, is more difficult. The argument can be summarized as follows: In the absence of overdominance, the alleles occupying a great majority of loci (99 percent or more) on any chromosome in a large Mendelian population will be normal alleles (A, B, C, D,...). The viability of individuals homozygous for such a 1 This is contribution #434, Department of Plant Breeding, Cornel1 University. Work reported here has been done under Contract No. AT-(30-1)-2139, U. S. Atomic Energy Commission. Genetics 48: 63iL651 May 1963

2 634 B. WALLACE chromosome is subnormal only as the consequence of homozygosis for deleterious genes at a small minority of loci. If one were to compare the viability of such individuals with that of individuals homozygous for the same chromosome but heterozygous for mutant genes newly induced in one but not in the other of the pair of chromosomes, one would expect to find that the carriers of the original genotype have the higher viability. This expectation is not limited solely to the mean viability of an array of new mutant genes; one does not expect to find exidence that any of the new heterozygotes exceeds the original homozygotes in viability. This prediction can be made because virtually all loci in the homozygotes would be occupied by normal alleles; because mutations induced at random would, as a consequence, affect these alleles; and because the newly induced deleterious alleles, to whatever extent they affect heterozygous individuals, would decrease the viability of their carriers. The above prediction was based upon the hypothesis that overdominance is nonexistent. If we assume, to the contrary, that overdominance does exist, predictions become impossible. This is so because we do not know (1) the proportion of loci at which overdominance might occur, (2) the proportion of alleles at a given locus which exhibit overdominance in heterozygous condition, and (3) the increase in fitness which would result from overdominance in any given instance. It can only be said that any mutation affecting one but not the other of two alleles, and occurring in an individual which in the absence of the change would have been homozygous, leads to heterozygosity at that locus. Further, the probability that the newly induced mutation, present in heterozygous condition, will enhance fitness (or a component of fitness amenable to experimental study) is a function of the proportion of loci at which overdominance may occur and of the average proportion of alleles per locus which are capable of exhibiting overdominance in combination with the original, unaltered allele. In order for overdominance to be detectable, the proportion of loci and of heterotic alleles must be sufficiently great to give an increase in mean fitness or an increase in variance which can in turn be related to an increase in fitness (BURDICK and MUKAI 1958), The experimental evidence (see WALLACE, Zoc. cit.) showed that the average viability of otherwise homozygous (second chromosome; Drosophila melanogaster) individuals heterozygous for mutations induced by 500r (1,000r in some experiments) was apparently higher than that of the control, homozygous individuals. However, MULLER and FALK (1961) and FALK (1959, 1961) have discussed the problem of dominance versus overdominance, and have presented results of experiments which appear to contradict those which we obtained. Under these circumstances it seems advisable to present a summary of the results obtained in a new series of experiments, even though they are incomplete at this time. The description of techniques and discussion of the data will be brief. We shall attempt to indicate only the broad outlines of the situation as it appears now, and the bearing of improved procedures on questions left unanswered in the earlier work.

3 OVERDOMINANCE 635 MATERIAL AND METHODS The data described below have been obtained, as the earlier work, through studies of the second chromosome in Drosophila melanogaster. The breeding procedures are sufficiently similar to those used in the earlier experiments SO that they need not be described in detail (see WALLACE 1958 or 1959). The differences between the earlier and present experiments are as follows: (1) In the present study we are using six different chromosomes, two from each of three different populations. The populations are (a) our own experimental population #3 (EX) which was the control population for experiments done at Cold Spring Harbor (WALLACE 1956), (b) flies collected in a market in New Orleans, Louisiana (NO), and (c) flies captured in Riverside, California (RC). A seventh chromosome obtained from South Africa (CA) is used in certain crosses. (2) Instead of the single X-ray dose (500r) that was used for most of the earlier studies, we now employ three levels of radiation: 250r, and 2250r. It would be better to say four levels since the control for the present study is treated as Or; this represents an improvement over the earlier procedure. (3) The experiments reported previously dealt primarily with the viability effects of new mutations in an otherwise homozygous (second chromosome) background; only a single experiment dealt with heterozygous wild-type individuals. In the present study wild-type flies of three categories are under study. First, there are flies (HOMO) that are homozygous for one or the other of the six chromosomes, or homozygous for that chromosome but heterozygous for mutations induced by one of the three radiation exposures (250r, 750r, or 2250r). This part of the experiment is directly comparable to the earlier studies but extends the results to a comparative study of three radiation levels. A comparison of chromosomes of diverse origins (one from experimental and two from natural populations), as well as a comparison of the two chromosomes from each of these populations, will be possible eventually. Second, since we have two chromosomes from each of three populations, it has been possible to study mutations in heterozygous backgrounds; these we call intra-population heterozygotes (INTRA) because the two chromosomes involved have been obtained from the same geographic locality or population. The use of chromosomes from three localities will eventually offer an opportunity to compare the effects of mutations on heterozygous genotypes of diverse origins. Finally, the seventh chromosome (CA) from South Africa allows us to study inter-population heterozygotes (INTER); these heterozygotes carry any one of the other six chromosomes and the one from Africa. These three types of combinations (HOMO, INTRA, and INTER) have been chosen because they represent a series of genotypes with progressively smaller proportions of homozygous loci. The exact proportions of loci that are heterozygous cannot be measured. In intra-population heterozygotes, though, this proportion must be larger than in homozygotes and, because of allelism through descent, it should be smaller than that in chromosomal combinations involving material from widely separated geographic localities.

4 636 B. WALLACE These three kinds of chromosomal combinations should be affected to a virtually identical extent by new mutations if within the species, D. melanogaster, there exists but a single normal allele at each locus. However, should the results obtained by the study of homozygotes (the HOMO category) refute the model which denies overdominance (as the earlier results seemed to do), then we would make the following prediction: Intra- and inter-population heterozygotes should not react to new mutations as homozygotes do. If overdominance is at all common, heterozygotes should carry different alleles at a great many loci. Mutations artificially induced at these loci, and present in heterozygous condition in the X-rayed material, would not increase the proportion of heterozygous loci; they would simply substitute randomly induced mutant alleles for alleles accumulated previously under the guidance of natural selection. Consequently, we would expect radiation-induced mutations in heterozygous condition to be deleterious when induced in a heterozygous background, even though they may not be unconditionally deleterious when induced in homozygotes. Because of the greater proportion of heterozygous loci in inter-population heterozygotes, we might expect the deleterious effect of random mutations to be more pronounced in this combination than in the intra-population heterozygotes. The weakness of this last statement lies in the fact that different alleles within the same population may have been selected in relation to one another (are co-adapted), whereas this is not true in the case of alleles involved in inter-population heterozygotes. In our studies we have two types of inter-population heterozygotes. The first type consists of wild-type flies described above that carry the CA chromosome and another which is either EX, NO, or RC. The second type consists of the mutant flies heterozygous for the laboratory chromosome (CyL) and a wild-type EX, NO, RC, or CA chromosome. It is unlikely that the CyL chromosome is closely related in origin to any of the wild-type chromosomes we are using; hence our use of inter-population in reference to these flies. (4) The breeding program of the present experiment represents an improvement over the earlier ones. The final cross, the one which gives rise to the CyL/Pm. CyL/f, Pm/+, and +/+ flies that are counted (and which in theory should appear in equal proportions) is unchanged; the female parents in this cross are CyL/+, the males. I m/+. Furthermore, the relative viabilities are still determined by the relative frequencies of the different genotypes; the relative viability of the CyL/Pm flies is regarded as 1.OOO. One person generally counts 48 bottles in each weekly experiment, four bottles of each genotype (HOMO, INTRA, INTER) and dose (Or, 250r, 750r, and 2250r) combination. The CyL/+ parental females of all 48 cultures are of one sort and are collected from the same set of culture bottles. There is no radiation involved in the ancestry of these females. The Pm/+ males bring into the final cross wild-type chromosomes that have been exposed to either Or, 250r, 750r, or 2250r. Pm/+ males carrying chromosoma identical (except for radiation effects) to those of the CyL/+ females give rise to HOMO cultures; those carrying the other chromosome from the same population as that carried by the CyL/+ females give rise to INTRA cultures;

5 OVERDOMINANCE 637 while those carrying the CA chromosome give rise to INTER cultures. The CA chromosome is never carried by the parental CyL/+ females of the last cross. Usually three persons perform these crosses, and so the chromosomes of the three localities are distributed among them at random each week. The choice as to which of the two chromosomes of a given locality will be used in setting up cultures for the CyL/+ virgin females (and, hence in determining whether the HOMO genotype will be EXJEX, or EX,/EX,, for example j is also randomized. (The NO chromosomes constitute an exception to this rule; males homozygous for one of these chromosomes tended to be sterile. Eventually this particular chromosome was replaced by another. j Finally, the cultures are coded at the time the parents are introduced into the bottles; the different types of cultures (HOMO-Or, HOMO-250r, HOMO-750r,..., INTER-750r, and INTER-2250r) are randomized within the code so that one culture of each type falls within cultures numbered l to 12, 13 to 24,25 to 36, and 37 to 48. During the counting no prolonged interruptions are allowed to occur within sets of twelve bottles; if one worker assists another in making counts, this person must count a complete set of twelve bottles. One consequence of this breeding system should be emphasized: HOMO and INTRA cultures are extremely similar insofar as suppressors of mutant phenotypes, meiotic drive, and other sources of experimental errors are concerned. Using the EX chromosomes as an example, we see that in one half of the weekly experiments CyL/EX, females are used as parents of the final cultures while in the other half CyL/EX, females are used. In any week the same females are used as parents for INTRA as for HOMO cultures (in fact. for INTER, too). For the HOMO cultures, of course, the male parents are PmIEX,, or PmJEX, and carry the very same chromosome as the CyL/+ females. In the case of INTRA cultures, the experiments are also divided evenly between Pm/EX, and Pm/EX, males except that Pm/EXl males are used in these experiments when the females are CyL/EX, while the males are Pm/EX, when the females are CyL/EXl. Because of randomization, half of both HOMO and INTRA cultures in the long run arise from CyL/EX, and half from CyL/EX, females; similarly, the parental males for both HOMO and INTRA cultures are Pm/EX, in one half of the weekly experiments, and Pm/EX, in the other half. RESULTS The material available consists of 8,189 cultures with nearly two and a half million flies. This may appear to be a very substantial quantity of data; in reality this is not so. Our aim is to analyze six chromosomes in three types of combinations under four levels of radiation (counting the control as Or), There are 72 categories to be studied (6 ~3 ~ 4 so ) there are just over 100 cultures per category. For this reason (and because a complete statistical analysis has not yet been made), we regard these data as preliminary. The first five tables present data based upon the grand totals of flies observed in all cultures. These are data of the sort one obtains simply by maintaining a running summary of the results of weekly experiments.

6 638 B. WALLACE TABLE 1 The relative viabilities of CyL/+. Pm/+, and +/+ flies in cultures consolidated according to the genotype (HOMO = homozygotes, INTRA = intra-population heterozygotes, and INTER = inter-population heterozygotes) of the +/+ class Genotype CYL/+ Pm/+ +/+ n HOMO INTRA INTER Radiation effects are ignored in this consolidation. Avg gives the average number of flies per culture; n is the number of cultures tested. In Table 1 radiation effects have been ignored while the data have been summarized by categories of wild-type flies-homo, INTRA, and INTER. In this table we are interested primarily in three things: (1) The relative viabilities of CyL/+ flies in HOMO and INTRA cultures are similar (identical!) as expected because in each case the observed viability is the average of CyL/S flies carrying EX, NO, and RC chromosomes. CyL/+ flies of the INTER category carry the CA chromosome exclusively; they need not, and indeed do not, have the same viability as flies of the same sort in the preceding two categories. (2) The Pm/f flies of all types of cultures are also similar in viability as expected. The greatest deviation is in the INTRA category but, as we saw earlier, there was some nonrandomness in these cultures because of the sterility associated with one of the chromosomes from New Orleans; it is this sterility that is responsible for the smaller number of test cultures in the INTRA than in the HOMO and INTER categories. (3) The viability of wild-type flies increases steadily with increasing heterozygosity; this, too, is expected. The data summarized in Table 1 agree with obvious expectations; this encourages us to believe that the technique is satisfactory. A further point of encouragement comes from the increase in the numbers of flies per culture observed in categories of increasingly heterozygous wild-type flies. Since it is the wild-type class which differs systematically in viability in the three types of cultures, one expects to find that this class is primarily responsible for changes in the average number of flies per culture. This expectation is borne out by the summary presented in Table 2. An increase in the average number of wild-type flies is observed from HOMO, to INTRA, to INTER; a partially compensatory decrease TABLE 2 The average number of CyL/Pm, CyL/+, Pm/+, and +/+ flies per culture in cultures grouped as in Table i Genotype CyL/Pm CYL/+ Pm/+ +/+ - HOMO INTRA INTER

7 OVERDOMINANCE 639 occurs in the numbers of flies of the other three genotypes; there is also a slight increase in numbers of CyL/+ flies in INTER cultures. All these are changes predictable from the information in Table 1. In Table 3 the data have been summarized by radiation exposure while the categories HOMO, INTRA, and INTER have been ignored. The overall impression from this table is one of uniformity. In the case of Pm/+ flies, we expect the viabilities at various levels of radiation to be the same because regardless of the indicated radiation exposure, Pm/+ flies carry nonirradiated wild-type chromosomes received from their CyL/+ mothers. The four viabilities listed for these flies are in fact quite similar. The viabilities of CyL/+ flies also appear to be similar but, taking the data at face value, it seems that a decrease in viability is associated with increased exposure. In Table 5 we have given the regression of the viabilities of these flies on radiation dose (where 250r equals one arbitrary unit) ; the slope of the regression (-.0009) is more than twice its error, but with only two degrees of freedom this observation is not statistically significant. A discussion of the wild-type class is postponed for the moment. From the data given in Table 3 it appears that radiation has affected these flies scarcely at all; in fact, the viabilities listed appear to be even more similar than those of the Pm/+ flies which are not expected to differ. We saw earlier, though, that there is reason to expect radiation to have contrasting effects on the viabilities of homozygotes and heterozygotes; the apparent absence of an effect of radiation on viability may arise from these opposing tendencies. Finally, we may note in Table 3 that the average number of flies per culture decreases with increasing exposure (the regression of number on dose measured in arbitrary units is *.050; P<.05). In Table 4 we have listed the average number of flies of each of the four genotypes-cyl/pm, CyL/+, Pm/+, and +/+-for different levels of radiation. The decrease noted in the overall average is shared by the individual genotypes. One purpose for stressing the numbers of flies in the experimental cultures is to show that no great environmental differences existed in cultures representing the different radiation levels; the maximum mean difference observed is 2.5 flies, somewhat less than one percent of the total average culture size. TABLE 3 The relatiue Viabilities of CyL/+, Pm/+, and +/+ flies in cultures consolidated according to radiution exposure Dose CYL/+ Pm/+ +/+ AVF( n Or r r r w The effects of the various wild-type genotypes are masked in this consolidation. Radiation was given to the wild-type chromosomes of CyL/+ and to one of the wild-type chromosomes of +/+ flies; Pm/+ flies do not caq irradiated wild-type chromosomes m any case.

8 ~ ~ ~ ~ 640 B. WALLACE TABLE 4 The average numbers of CyL/F, CyL/+, Pm/+, and +/+ flies per culture in cultures grouped as in Table 3 Dose CyL/Pm CYW+ Pm/+ +/+ -~ Or Or r r Data summarized in respect both to radiation exposure and to genotype are given in Table 5. The figures shown for CyL/+ and Pm/+ are the same as those on Table 3; those for HOMO, INTRA and INTER were combined in the earlier table. In Table 5 we see that the CyL/+ flies give the closest approach to a significant effect of radiation; there is an apparent decrease in the viability of these flies associated with increased levels of radiation to which the wild-type chromosome was exposed. The only other interesting feature of the data shown in Table 5 is that the regressions are all negative with the exception of that of the HOMO category; the latter has the largest absolute value and it is positive. Since this and all subsequent analyses are based on the same original data it may not be unexpected, but we will find this contrast between HOMO and various heterozygotes repeatedly. At no time, however, will the observed differences be shown to be statistically significant; they surely are not in Table 5. Until now our discussion has dealt with various aspects of the grand totals of flies counted in all experiments; first these totals have been consolidated in one way, then in another. Now we will turn to a preliminary analysis in which we restrict ourselves to differences observed between the viabilities of different kinds of flies within the work done by individual persons in each week s experiment. An analysis of this sort avoids the variability that exists between individuals and between experiments done at different times. The cultures counted by one person TABLE 5 The relative viabilities of CyL/f, HOMO, INTRA, and INTER flies carrying wi2d-type chromosomes exposed to various levels of radiation Genotype Or 250r 750r 2250r b* b t P CYL/ OOM 2.25.I5 Pm/ WO4, >.50 HOMO f.0016.mi INTRA >.501 INTER OM2, >.50 ~~ The wild-type chromosomes carried by Pm/+ flies are not exposed to radiation in any case. These viabilities are based on the grand totals of flies observed in 82 weekly experiments. * Regression slope relative to dose where Or, 250r, 7Wr, and 2250r are measured as 0, 1, 3, and 9.

9 OVERDOMINANCE 64 1 within one of the weekly experiments are as comparable as cultures can be under existing conditions; consequently, differences between the viabilities of the different flies in this analysis represent differences between paired observations. In Table 6 we have presented results obtained from the signs of these differences only, the actual magnitudes of the differences are not involved in this table. To understand Table 6 we must recall that for CyL/+, HOMO, INTRA, and INTER flies, each person has counted flies in cultures in which the wild-type chromosomes were exposed to Or, 250r, 750r, and 2250r. From the viabilities noted at each of these four levels we can calculate six differences: 250r - Or, 750r - Or, 2250r - Or, 750r - 250r, 2250r - 250r, and 2250r - 750r. (Note that the lower radiation level is always subtracted from the higher.) If the irradiation of the wild-type chromosome has no effect on viability, the four levels could assume any one of 24 possible rank orders: ,l-2-4-3, , ,..., ; the probability of assuming any one of these ranks would be 1/24. Now, each of these rank orders gives a certain number of positive and negative differences among the six we can compute; for instance, if the radiation level increases from left to right, the rank orders listed above give six positive differences, five positive and one negative, five positive and one negative, four positive and two negative,..., six negative differences. Given that each rank order is equally likely, one can calculate an expected frequency for sets of six differences containing six, five, four, three, two, one, and zero that are positive. These expectations have been given in Table 6 in the form of cumulative frequencies together with the observed cumulative distributions for CyL/+, Pn/+, HOMO, INTRA, and INTER flies. The values for Pm/+ are very close to the expected ones-now higher, now lower-as one might have anticipated; since the wild-type chromosomes in these flies are not irradiated the rank order should be a matter of chance. The CyL/+ flies, too, have values much like the expected ones, a very slight deficiency of plus signs or an excess of minus signs but nothing striking. In the case of the wild-type flies, we find that the HOMO category is distinguished by a consistent excess of plus signs and a corresponding deficiency of minus signs. TABLE 6 Differences in the uiability of flies carrying chromosomes exposed to different leuels of radiation analyzed within the individual weekly experiments of each worker No. of +'s n CYL/ Pm/ HOMO Q INTRA INTER Expected For explanation see text.

10 ~~ ~~~ 642 B. WALLACE The INTER category has the opposite characteristics, while the INTRA are intermediate. Despite the consistency of the data of Table 6 and their agreement, at least in the case of the Pm/+ and wild-type classes, with expectation, the trends suggested are not statistically significant. Listed below are the mean number of positive differences for each of the genotypes; obviously none are significantly different from the expected value, 3: HOMO 3.13.ll INTRA 3.02 *.11 EXPECTED Pm/ f.065 CYL/ f.065 INTER ll In Table 7 we consider additional data based on the differences in viability described in the preceding paragraphs. The magnitudes of these differences have now been taken into account. In this table, however, we have treated all differences for a given category or genotype as equivalent and have combined them into a single average difference; we have assumed, that is, that 250r - Or, 2250r - Or, and r, for example, give equivalent differences. Once more we see that the only mean difference with a positive sign is that for HOMO flies; all the others have average differences that are negative. If the mean differences observed for CyL/f, INTRA, and INTER heterozygotes are combined, their combined average difference approaches statistical significance (P =.03). Flies with the more heavily irradiated chromosomes appear to have lower viabilities. The combined average differs, too, from the average observed in the case of the HOMO category (P =.03) as if the latter do not show the same response to radiation. TABLE 7 The average effect of radiation of Wild-type chromosomes upon the viability of their CyL/+, HOMO, INTRA, and INTER carriers Genotype CYL/+ --.OM pm/ HOMO +.OOQl INTRA INTER Combined heterozygotes* HOMO vs combined heterozygotes sa'.0031, n t P I The Pm/+ flies carry only nonirradiated chromosomes. In this table 2 represents the average difference in viability observed between groups receiving different levels of radiation (that is, 250r - Or, 750r - Or,..., 2250r - 750r have been treated as equivalent differences), n equals the number of observations upon which 2 is based, while say t, and P represent the standard error of * CyL/ +, INTRA, and INTER. x/sr. and the probability of observing this deviation by chance.

11 OVERDOMINANCE 643 DISCUSSION In view of their preliminary nature, a brief discussion of the data presented in the seven tables will suffice. In the absence of overdominance, the viability effects of irradiated chromosomes in heterozygous condition would be expected to be deleterious regardless of the genotype in which they are tested. If overdominance exists, we expect new mutations induced in an otherwise homozygous background to have viability effects less deleterious on the average than those of the same sorts of mutations tested in heterozygous background. Indeed, earlier experiments (WALLACE 1957, 1958, 1959) indicated that the mean viability of some homozygotes may be improved by the introduction of heterozygosis for random mutations. The present experiments suggest, as expected, that new mutations in heterozygous condition lower the viability of already heterozygous individuals. That is, if a locus is already heterozygous for two different naturally occurring and, hence, preselected alleles, the substitution of a randomly induced allele for one of these is on the average detrimental. The experiments suggest further, however, that the reactions of homozygous and heterozygotes to these newly induced mutations are different; the deleterious effects of the new mutations are almost certainly smaller in HOMO flies than in heterozygotes. In fact, the viability effects of the new mutations in the HOMO category have been consistemtly positive in sign, a result agreeing with that of our earlier experiments. Thus, the results reported here support the existence, rather than the absence, of overdominance. MULLER and FALK (1961) and FALK (1959, 1961) disagree with the above conclusions. Since the papers by MULLER and FALK and by FALK were published concurrently, references will be made by page and line, thus: (page: line). First, to clear up some misunderstandings. FALK (1959) ascribes to us a suggestion that heterozygosity differs in principle from homozygosity, and is usually associated with superior viability. There is no a priori basis for assuming that heterozygosity is usually associated with superior viability; this point was discussed in the introduction to the present paper. FALK adds that a corollary to this suggestion would be that irradiation given to an isogenic line would be beneficial on the average rather than detrimental. This is not a corollary. The argument we have advanced suggests that viability may under certain circumstances be enhanced by a change from a,/a, to a,/a, where a, represents a randomly induced mutation and a, represents an allele of the sort retained by natural selection in large populations; isogenicity in itself is not enough (see WALLACE 1957). It is true that we did observe that newly induced mutations in heterozygous condition, on the average, appeared to increase viability of individuals homozygous for a chromosome obtained from a large population; prior to the empirical observations, there was certainly no basis for predicting that this would be the average effect of the induced mutations. A misunderstanding of a related nature arises when MULLER and FALK (730:21) argue that the viability effects of single mutations in our earlier experiments appear to be large enough to be detected in a heterozygous back-

12 644 B. WALLACE ground. This argument misses the point. In heterozygotes (according to the model based on overdominance) a large proportion of loci will be occupied by two different alleles, a, a7 for example; a random mutation might change the genotype at such a locus to u,/a,. Radiatioii in this case leads to the replacement of a preselected allele (a7) by a randomly induced one (a,). The fact that a,/a, may represent an improvement over a,/u, does not mean that a,/a, will represent an improvement over ai/u7 as well. On the contrary, under these circumstances we expect (and found in the experiments just described) that random mutations are detrimental to viability. (We may note in passing that the calculations made by MULLER and FALK would have led to a bimodal distribution curve for the viabilities of irradiated material; the absence of bimodality suggests that 500r induces more mutations than they calculated, each with a smaller effect on viability. See BATEMAN 1959). Two further misunderstandings may also be cleared up at this point. According to MULLER and FALK (729: 7), WALLACE and DOBZHANSKY believe that the high proportion of deleterious alleles found to exist in populations is most reasonably explained by the selective superiority of individuals heterozygous for two different forms of such alleles The cited quotation is from WALLACE (1958. p. 554) where we find the following sentence: LA high proportion of such deleterious alleles is most reasonably explained by the selective superiority... The term deleterious was enclosed in quotation marks in the original sentence because the alleles under discussion are not deleterious in the usual sense (lethals, semilethals, obvious subvitals, etc.) but are alleles that would pass for normal were it not for the fact that they lead to even higher viabilities in heterozygous than in homozygous condition; an effect of this sort has been confirmed in a subsequent analysis (WALLACE and DOBZHANSKY 1962). The second point concerns the effect of radiation on populations (759:37). (WALLACE and DOBZHANSKY ( 1959) have suggested that mutation may serve a useful function by feeding back into a population alleles which have been lost by chance but which nevertheless have a slight advantage in heterozygous condition. FALK apparently interprets this suggestion to mean that the immediate effect of mutation would then be to increase fitness and that the higher the mutation rate, the better. Mutation could give a direct beneficial effect only if random mutations were closer to hypothetical equilibrium gene-frequencies than the frequencies actually established within the population. Situations of this sort may exist. but a directly beneficial action of mutation was not implied by the original suggestion of WALLACE and DOBZHANSKY. A number of comments in the papers by MULLER and FALK are directed at mitters of technique, ours and their own. One such comment (730: 37) mentions the possibility of undetected crossovers and misclassifications occurring if chromosomes under investigation are passed in many replications through females heterozygous for genetically marked chromosomes with inverted segments. This remark has little bearing on our experiments. In terms of generations, there is but a single generation per experiment in which the chromosomes under investigation pass through females where crossing-over is possible. Granted that there

13 OVERDOMINANCE 645 is a finite chance of error (crossing-over, for example) in this generation, MULLER and FALK have failed to show why this error should affect one series of cultures and not the other; the control, for example, and not the experimental. In fact, most of the points they have made are of the same sort; they raise possibilities that do not explain any systematic difference between control and irradiated cultures. Thus (750: 15), misclassification of Plum is suggested as a possible source of error despite the fact that two generations in which correctly identified Pm/C males have been used as parents have intervened before the final counts. Further, to avoid distortions in the frequency of Pm/+ flies, we must assume, too, that CyL/Pm is equally often misclassified as CyL/+. This is highly unlikely; at no time has a mating of CyL/+ male x CyL/Pm females proven to be CyL/Pm male x CyL/Pm females. Nor do the CyL/Pm flies in our stock bottle ever appear to be CyL/+ as if a suppressor of Plum were in this stock. Later (730: 23) the possibility of a segregation-distorter is mentioned; again there is no explanation (the word capricious is scarcely an explanation) why, even in the unlikely case that a factor of this sort were present, a segregation-distorter should result in a systematic deviation of control and irradiated cultures. Finally, FALK (730:29) asks why only two of six experiments gave results statistically significant in themselves; the reason is, obviously, that the error variance of one sixth of all observations is six times as large as that of the final error variance. Since the results of the combined experiments were d=-.0150, st=.0047, it can be seen that the s,=.o115 expected for experiments one sixth as large would ordinarily obscure a difference of the observed size. We turn now to a consideration of the MULLER-FALK experiments. There is no information given about the source of the prototype chromosome ( 731 : 1 ). The argument we have presented concerns alleles of the sort maintained by selection in large populations (see WALLACE 1957, 1958). The chromosome used by MULLER and FALK appears to have come from a laboratory stock-culture. In reference to their mating scheme, it would first appear (731: 40) that a great advantage is to be found in the genetic similarity of marked and unmarked flies in the MULLER-FALK experiments; however, this advantage disappears ( 732: 4) when it develops that, despite the similarity, a control series is needed to evaluate the slight dissimilarity that does exist. Thus, except for the absence (732: 18) of two additional classes (which I find useful) their procedure is much like the CyL-Pm technique. MULER and FALK have utilized a radiation technique (732: 21 and following lines) quite different from ours, the exposure of spermatogonia to 24,000r in fractionated doses rather than an exposure of mature sperm to relatively low total doses. This type of exposure has the advantage of inducing fewer gross chromosomal aberrations per point mutation than an exposure of mature sperm. It suffers, as I see it, from our present inability to evaluate accurately its genetic effects in terms of the more standard treatment. In one estimate (733:4) this technique was said to be eightfold as effective as 500r given to sperm; in a second (749:27), sevenfold. In attempting to reconcile the results of their ex-

14 646 B. WALLACE periments and ours, the factor seven is treated as if it has no error; there are apparently no published data by which the reliability of this estimate can be judged. (The abstract by MEYER, EHRLICH, and MULLER 1959, merely describes the technique and gives no quantitative data on the results of irradiating spermatagonia with 24,000r.) Certain features of the experimental procedure used by MULLER and FALK strike us as undesirable. Test vials, for example, were apparently set up in a haphazard rather than a randomized fasion (740: 18 and 740:41 j ; thus we have no knowledge concerning the order in which control and experimental vials were counted despite the fact that the final counts must have taken considerable time. Furthermore, there is no mention made of coding the vials. The latter point is especially important because contaminated vials could not be detected (741: 22 j but, nevertheless, vials suspected of being contaminated were discarded (741: 20). Here, too, one would like to know if second-generation flies form any part of the suspected contamination since in the treated series the class under investigation would suffer greatly from homozygosis for induced lethals (748:25) and other deleterious mutations. In the past, we have carried on experiments in vials, but the technique was abandoned (WALLACE 1960) because many flies were lost in the culture medium; consequently, we were not sure just what the final ratios measured. Using crosses of CyL/Pm virgin females and Basc males, eighteen vials were set up and counted under the conditions described by MULLER and FALK (740: 28). On the 27th and 30th days we found that the medium in every vial contained large numbers of wings and other remains of drowned flies. The total number of adults surviving until the 30th day seemed to have little bearing on the number that emerged. This fact was confirmed by counting the flies in one of the two vials on the 19th day (113 flies) and periodically thereafter until the 30th day (167 flies in all) ; the other vial which appeared similar by inspection on the 19th day yielded a total of only 61 flies in the two counts made on the 27th and 30th days, fewer flies in all than it presumably contained on the 19th day. In view of the accidental loss of flies occurring in 27 and 30 day old vials, it is difficult to understand the importance of discarding cultures with small numbers. If the numbers are small because of loss after emergence, the vials involved do not differ fundamentally from the others, they have simply lost more flies. If, on the other hand, the small numbers result from small numbers of developing larvae (and, thus, represent a considerable reduction in competition for food ) the problem of second generation becomes especially important, for presumably the degree of crowding determines to a large extent the generation time in these cultures. One of the points we wanted especially to determine was to what extent the frequencies of different classes of flies within a culture may be correlated with culture size. There was a correlation of +.08 (not significant in an experiment involving only 18 vials) between the frequency of CyL/f and culture size, and another, significant, correlation of between frequency of males per culture and culture size. Such correlations can be important in evaluating the viability

15 OVERDOMINANCE 647 effects of radiation if the control and experimental cultures differ systematically in the numbers of flies they contain (WALLACE 1958). The data presented by FALK have been examined to see if the treated and untreated cultures are really comparable. In his Table 1 we find that in three of four comparisons treated lines have lower frequencies (=viabilities) than the untreated controls. These results are based on the averages of frequencies. If one calculates the same frequencies using the total flies given in his table, one finds a systematic improvement in the relative viability of the treated lines, as shown in Table 8. A systematic shift that occurs between averages of frequencies and frequencies based on total numbers can only mean that frequencies and numbers of flies per vial are correlated in some manner. The implication of this shift cannot be evaluated on the basis of available information. We may note, though, that the calculation based on totals reverses the average effect emphasized in the original calculation. The average numbers of flies per culture cannot be computed for the material included in FALK S Table 1 because the numbers of cultures are not listed. However, from his Table 2 one can reconstruct that in experiments 42, 43, and 44 there were 734 treated cultures and 568 untreated ones. From his Table 3 the combined totals listed under Females I and Males appear to give the total flies counted in these three experiments; using the 30-day totals for experiments 42 and 43 as well as the totals for experiment 44, we find that the average number of flies per culture in the treated series of these three expermients was 81.9 while in the untreated it was The control cultures are about 4.4 percent larger on the average than the treated ones. When one considers that the viability differences under investigation are small and that relative viability appears to be related to culture size, a difference of 4 to 5 percent in mean culture size seems unduly large. Consideration must be given, too, to some of the theoretical arguments presented by MULLER and FALK. When they claim (738: 15 and 747: 12) for example, that hemizygous males are less heterozygous than heterozygous females (and, hence, are presumably equal to females homozygous for the X-chromosomes), it is pertinent to point out that the between-sib variations in sterno- TABLE 8 Relative viability of treated and untreated flies, recomputed from Table 1 of FALK 1961 Average of frequencies Average based on totals Treated (T) Untreated (U) T/U Treated (T) Untreated (U) T/U,491,493,996, ,988 Average , , Average 1.007

16 648 B. WALLACE pleural bristle numbers of males and of females heterozygous for two different X chromosomes are equal and are smaller than that of corresponding homozygous females (WALLACE, unpublished). Hemizygous males are comparable in this respect not to homozygous females but to heterozygous ones (see too KERR and KERR 1952, and DA CUNHA 1953). An extended discussion on the dominance of subvital genes (749: 23) attempts to show that slightly deleterious mutations are more dominant than lethals and, hence, that these mutations cannot then be overdominant. The first reference cited is MULLER (1950a), who argued that natural selection should be relatively ineffective in perfecting the dominance of normal alleles in reference to nearly normal mutant forms and, hence. that mutant genes with less extreme effects would tend to show more dominance than lethals and near-lethals. And yet, he argued simultaneously ( 1950b) that detrimentals and visibles may show considerably lower dominance... than lethals; for all lethals, no matter how strong their action, are assumed to be only as strong as those which just succeed in causing 100 percent of deaths... In the second argument, MULLER concluded that if five percent is a maximum value for the average dominance of lethals then the average dominance of detrimentals and visibles is probably lower than five percent. A second citation given in support of the greater dominance of slightly deleterious as opposed to lethal mutations is GREENBERG and CROW (1960). In their summary, GREENBERG and CROW say These results imply that either (1) mutants with small effects occur with no greater frequency than lethals, or (2) they have more dominance than lethals and hence are eliminated relatively more rapidly as heterozygotes (italics ours). Furthermore, these authors point out ( 1960, p ) that their mathematical approach does not distinguish between multiple alleles with overdominance and deleterious genes for which hs is a constant (that is. dominance inversely proportional to the deleterious effect of the mutant gene). WALLACE and DOBZHANSKY (1962) have reexamined the material published by DOBZHANSKY, KRIMBAS, and KRIMBAS 1960) and have concluded that this material does in fact distinguish between the two alternatives and that it supports the former (MULLER and FALK also refer briefly to the material of DOBZHANSKY, KRIMBAS, and KRIMBAS 175 l : 241 ). The results of a study of mutations in yeast (JAMES 1960) are also cited in support of the greater dominance of slightly deleterious genes, a citation that once more rules out the possibility of an effect... of lines heterozygous for non-lethals (749: 14). In this study JAMES restricted his attention to mutant genes with detectably deleterious effects on growth rate; subsequently, M~~LLER and JAMES (1961) have tested randomly induced mutations. In the latter study the growth rate of one line was enhanced, another lessened, and a third unaffected by these random mutations. MULLER and JAMES emphasize that epistatic interactions must be important in determining this variety of results in their material. We can agree with this. The precise relation of their work to our own remains unclear, however. since in our use of the term overdominance we do

17 OVERDOMINANCE 649 not exclude epistatic interactions; that is, just as dominance is subject to epistatic modification, so is overdominance. The final point we want to make regarding the studies of MULLER and FALK is that their results are negative. The genetic model they favor is the only one that leads to a testable hypothesis (radiation induced mutations are in an overwhelming majority detrimental in their effects on viability), but this is not the hypothesis they have subjected to test. Instead, they have chosen to assume that estimates of viability are linear with radiation exposure through 24,00Or, that 24,000r given to spermatogonia has exactly seven times the effect of 500r given to sperm, and that their material and their experimental procedures are the same as ours. They assumed all this and then tested, and rejected, the hypothesis that their results and ours are the same. It is our opinion that this series of assumptions has been made to test the wrong hypothesis. The question is very simple: Have MULLER and FALK demonstrated that newly induced mutations in heterozygous condition lower the viability of individuals carrying them, as the genetic model they favor predicts? The answer is that they have not. The above critique of the papers of MULLER and FALK should not obscure several important areas of agreement of which I will list two. The first is that the immediate effect of increased mutation on the fitness of a population is debilitating. Here we agree despite our different views of the genetic structure of populations. Whether a population consists essentially of homozygotes (as MULLER and FALK claim), or whether the population is an array of complex heterozygotes (as we suppose), or whether a combination of both makes up its basic structure, random mutations are almost surely inferior in fitness to preselected genes. The second area of agreement is that the experimental tests we are employing yield information relevant to the question under discussion. In this respect we would both reject the beneficial mutation hypothesis some have suggested as a more palatable explanation than overdominance for an increase in viability caused by mutations in heterozygous condition. When the trait in question is yield, as it often is in plant and animal breeding, one can sometimes postulate that there exist positive and negative genes in about equal frequencies. In the case of fitness or viability this is quite unlikely, Each beneficial mutation one postulates requires an explanation: Why was there a less beneficial gene variant at that locus in the original material? If beneficial mutations were common, the great challenge facing population genetics would not be an evaluation of overdominance as we stated in the introduction, but rather an explanation of the amazing inefficiency of natural selection. Addendum : Subsequent to the preparation of this manuscript, the final experiments of this study have been completed; the data now available for analysis are nearly one half again as extensive as those included in the foregoing analysis. To await an analysis of these data, even to an extent comparable only to that of the present analysis, would be inappropriate. The grand summary of all data leads to the same conclusion as that expressed here: The HOMO category reacts differently (and more favorably) to newly induced mutations than do INTRA,

18 650 B. WALLACE INTER, and CyL/+. This fact becomes especially clear if Pm/+ rather than CyL/Pm flies are chosen as the standard for comparison. SUMMARY A preliminary analysis has been presented of the viability effects of new mutations in heterozygous condition in three sorts of second-chromosome backgrounds: homozygous for chromosomes obtained from large populations, heterozygous for two chromosomes obtained from the same population, and heterozygous for two chromosomes obtained from widely separated populations. The data (although quite extensive) are inconclusive, but in several types of analyses are consistent with the following suggestion: If ai and aj are two of many alleles at the a locus retained in a large population under the influence of natural selecion, and if a, is a newly induced allele, the order of viability of the different genotypes is ai/aj>ai/a, >ai/ai on the average. Contrarxr evidence presented by MULLER and FALK is discussed. BATEMAN, A. J., 1959 Biol. 1: 17C180. LITERATURE CITED The viability of near-normal irradiated chromosomes. Intern. Radiation BURDICK, A. B., and T. MUKAI, 1958 Experimental consideration of the genetic effect of low doses of irradiation on viability in Drosophila melanogaster. Proc. Second U. N. Intern. Conf. Peaceful Uses Atomic Energy, Geneva 22 : CUNHA, A. B. DA, 1953 Chromosomal inversions with sex-limited effects. Nature 172: 815. DOBZHANSKY, TH., C. KRIMBAS, and M. G. KRIMBAS, 1960 Genetics of natural populations. XXIX. Is the genetic load in Drosophila pseudoobscura a mutational or a balanced load? Genetics 45: FALK, R., 1959 Viability of Drosophila heterozygous for irradiated chromosomes. Science 130: Are induced mutations in Drosophila overdominant? 11. Experimental results. Genetics 46: GREENBERG, R. and J. F. CROW, 1960 A comparison of the effect of lethal and detrimental chromosomes from Drosophila populations. Genetics 45 : JAMES, A. P., 1960 The spectrum of seventy of mutant effects. 11. Heterozygous effects in yeast. Genetics 45: KERR, W. E., and L. S. KERR, 1952 Concealed variability in the X-chromosome of Drosophila melanogaster. Am. Naturalist 86 : MEYER, H. U., E. EHRLICH, and H. J. MULLER, 1959 Tolerance of gonia1 cells of Drosophila melanogaster for heavy X-ray doses divided into installments. (Abstr.) Genetics 44: MULLER, ILSE and A. P. JAMES, 1961 The influence of genetic background on the frequency and the direction of radiation-induced mutations affecting a quantitative character. Genetics 46:

19 OVERDOMINANCE 65 1 MULLER, H. J., 1950a Our load of mutations. Am. J. Human Genet. 2: b Radiation damage to the genetic material. Am. Scientist 38: 33-59, 126, MULLER, H. J. and R. FALK, '1961 Are induced mutations in Drosophial overdominant? I. Experimental design. Genetics 46 : WALLACE, B., 1956 Studies on irradiated populations of Drosophila melanogaster. J. Genet. 54: The effect of heterozygosity for new mutations on viability in Drosophial melanogaster: a preliminary report. Proc. Natl. Acad. Sci. U. S. 43 : The average effect of radiation-induced mutations on viability in Drosophila melanogaster. Evolution 12: The role of heterozygosity in Drosophila populations. Proc. 10th Intern. Cong. Genet. 1: Heterotic mutations. Molecular Genetics and Human Disease. Edited by L. I. GARDNER. Chas. C. Thomas, Springfield, Illinois Temporal changes in the roles of lethal semi-lethal chromosomes within populations of Drosophila melanogaster. Am. Naturalist, 96 : WALLACE, B., and TH. DOBZHANSKY, 1959 Radiation, Genes, and Man. Henry Holt and Co., New York, N.Y Experimental proof of balanced genetic loads in Drosophila. Genetics 47: