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Chaplter XV PERMISSIBLE INFERENCES 15.1 Basic data necessary to reaching per- missible inferences.-There would at this junc- ture be ample justification, judging from the genetic literature of recent years, to utilize the findings of this study, taken in conjunction with other available information, as the basis for a semi-quantitative treatment of the problem of the genetic risks of increased radiation of the human species. Such calculations proceed in general along the following lines: On the basis of existing data, one estimates the average spontaneous mutation rate of human genes and the number of genes in man. From this one obtains an estimate of the average number of mutations per human gamete per generation (a "total" mutation rate). Then, again on the basis of existing data, one estimates the probability of mutation/locus/r in man, and from this the amount of radiation required to double, triple, or otherwise increase the mutation rate over the spontaneous baseline. Next, then, by one ap- proach or the other, one estimates the ratio of "recessive" mutations which have been accumu- lated in the population to "recessive" mutations arising anew each generation, the so-called "accumulation factor." Given this, one can esti- mate by how much, on the basis of the preceding calculations, this frequency will be altered by any arbitrary increase in radiation. Finally, on the basis of certain assumptions concerning gene physiology and the operation of natural selection in man, one attempts to evaluate the phenotypic impact of this increase in radiation. There are, then, five estimates which are basic to these semi-quantitative treatments: 1. The spontaneous mutation rate in man. 2. The induced mutation rate/locus/r in man. 3. The total number of genes in man.1 1 The product of (1)X(3), or (2)X(3), is the rate of mutation per gamete, spontaneous or induced, as the case may be. It is possible in suitably designed experiments to estimate this directly (cf. Muller, 205 4. The "accumulation factor." 5. The manner in which selection operates on the total gene complex. It is our contention, which we will now pro- ceed to document, that the available data on which these five estimates are based are so in- adequate that semi-quantitative treatments are ill-advised, since except to the relatively few who have made a detailed study of the problem, they impart an air of mathematical exactitude and scientific accuracy to an area where the errors are sometimes large and often inde- terminate. 15.2 The spontaneous mutation rate in man. Current thinking concerning the rate of mu- tation of mammalian genes is for obvious reasons strongly influenced by what is known concerning Drosophila rates. We will accord- ingly first consider briefly what seem to us to be some of the more pertinent data concerning this species. For methodological reasons it is customary to distinguish on the basis of their physiological effects between three categories of mutations, namely, those associated with visible effects, those associated with lethal ef- fects, and those which express themselves through a reduction of viability in the absence of detectable somatic effects, the so-called semi- lethal mutations (1-10 per cent viability) and deleterious mutations (over 10 but less than 100 per cent viability). Terminology in this field leaves something to be desired. Thus, the "deleterious" mutations must have an organic basis, so that many of them would be found on careful study to be also "visibles." By the same token, most "visibles" are also "deleterious." Finally, the dividing line between "lethals" and "semi-lethals" may be altered by culture conditions. Be that as it may, the division into i955), and so decrease the number of variables in- volved in the calculation.

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206 Genetic Effects of Atomic Bombs Chapter XV these three categories has an operational useful- ness, as we shall now see. Beginning with the pioneer attempts of Muller (1934; see also Kerkis, 1935, and Timofeef-Ressovsky, 1935 ), a number of efforts have been made to establish the relative fre- quencies with which these types of mutations are represented among all mutations. These at- tempts have involved radiation-induced rather than spontaneous mutations because of the much more laborious nature of the problem if at- tacked through the study of spontaneously oc- curring mutations. In view of the possibility that the relative frequency of lethals is higher among the radiation-induced mutations because of the increased proportion of minute deletions, the estimate of the ratio, (semi-lethels + delete- rious) /lethals, may be a minimum estimate. Muller (1954; see also Falk, 1955) places this ratio at 3-5 to 1. This same author goes on to state that ". . . the ratio may indeed be con- siderably higher than this, since the technique was hardly refined enough for the detection of detrimentals with a viability greater than some 85 per cent of normal. Other studies have shown that 'invisible' mutants causing sterility or lowered fertility of some degree also form a very large group. This group, however, overlaps, to an extent not yet well investigated, that of the detrimental mutations" (p. 396~. The significance of information concerning the relative frequency of mutants with viability in the 85-99 per cent range in attempts to quantitate the genetic risks of radiation is of course enormous. A related problem concerns the frequency of mutations for which the or- ganism at the time is able to compensate com- pletely, the undetectable mutations. Lately con- siderable attention has been directed towards the genetic basis and evolutionary implications of physiological homeostasis (refs. in Lerner, 1955~. The possibility cannot be ruled out that the principle of homeostasis enables some or- ganisms to compensate entirely, under particular sets of circumstances, for the effects of certain mutations. It may be argued that there is no reason to be concerned about the relative frequency of mutants with undetectable effects in a considera- tion of the deleterious effects of radiation. How- ever these mutations are undetectable only under the conditions set by the observer. Under other conditions, set by nature and not by man, they might have decided effects. It is not at all difficult to argue that the mutants-with-over- 85~o viability which cannot now be studied in Drosophila may in evolutionary importance far outweigh the visibles. Muller (1950) in a discussion of the question of the numerical relationship between lethals, on the one hand, and semi-lethals and deleterious mutations, on the other hand, has made the following statement: "However, studies carried on in Drosophila during the past year by Meyer, Edmondson, and the writer indicate that in this organism the assumption of an equal distribu- tion of detrimental mutations throughout all iho values 2 (when represented on an arithmetic scale) does not hold. Instead, it appears that, following the high but descending peak formed by complete lethals (is =100~) and nearly complete lethals ~ ~ u , ~ , ~ , (ihO=between 98~o and 1005to), there is a marked drop in the frequency of mutations. The mutations studied were in- duced in an autosome (the second chromosome) by ultraviolet light acting on an interphase stage (in the polar cap). Along with 208 complete lethals there were 20 mutants found in the range of iho between 9870 and 100~o' and again only 20 in the range of Ho between 90~o and 98~o, although this range is four times as wide as the preceding one. If the rest of the distribution, as far as iho=lO~o, had only the same fre- quency of mutations as in the range between 90~O and 98~o there would have been only 240 detrimentals in the entire interval between loom and 10~o, to set against the 208 complete lethals found. But since we know from other work, previously cited, that the detrimentals in this internal are in reality several (about 5) times as numerous as the complete lethals, it is evident that their frequency must, at lower de- grees of detriment (lower iho), rise very much above that existing in the 90:fO to 98~o range. The distribution of frequencies of iho therefore forms a bimodal curve with one peak at the left origin, lethality (the = LOOM ), and another peak somewhere to the right. "Little more than this is yet known definitely about the shape of the curve in question, im- portant though this genetic question is. How- ever, there are grounds, both theoretical and observational, for regarding it as very unlikely that the second peak is near the first or that the rise towards it is sharp. Hence it is probable that silo the amount of impairment produced by a gene when homozygous.

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Permissible l~ferences detrimental mutations, instead of having an even distribution with respect to values of Ho, form a curve which, except for its peak of near-Iethals at the left end, is massively skewed towards the right, with its mean at a value of Ho significantly beyond the middle (0.5~" (pp. 140-141~. If we consider these remarks of Muller in conjunction with the possibility of "invisible" mutants discussed earlier, then the problem of estimating the relative frequency of lethal mu- tants vs. those viable to some degree assumes new complexity. Figure 15.1 attempts to present -- > RANGE Of PRESENT OBSERVATIONS < NU MBE Q OF MUTATIONS 207 cased two of the principal alternatives. Cube A assumes a mode at 60-70 per cent viability, from which it would seem likely that the pro- portion of mutations in the 85-100 per cent and normal viability range is small. Curve B assumes that the mode is farther to the right with the corollary that there is a considerable group of mutations not now being detected. How large that group is depends of course on the shape of the curve. The question of the relative frequency of lethal mutations as contrasted to visibles, is on somewhat more secure footing than the question l l l lO 20 30 40 50 i0 70 80 90 LETHALS SEMI- LTHALS AND DELETERIOUS NORMALS AND BETTER FIGURE 15.1 A schematic representation of two different "mutation spectra" with reference to degree of viability, both compatible with the present data. Further explanation in text. some of this complexity graphically. The ab- scissa of this figure represents viability of the homozygous genotype in some arbitrary environ- ment. In this connection, it is apparent that the term "lethal" is relative, some lethal mutations having effects under no known circumstances compatible with life, other lethal mutations having far lesser effects. Likewise, the term "normal" as applied to viability is relative, some normals being more normal than others, with the differences brought out only under unusual circumstances. Thus far, observations have been limited to the range of lethality and 1-85 per cent viability. As Muller has pointed out in the statement quoted above, there is great doubt concerning the shape of the curve of numerical relationships within this range. We have indi of the ratio of lethal mutations to mutations reducing viability to a lesser degree. In tabulat- ing the results of radiation experiments by five different workers, Schultz (1936) found this ratio to be 7.4:1. In view of the well recognized differences in the ability of individuals to recog- nize mutant phenotypes, the true ratio is prob- ably somewhat lower. We prefer, for instance, the ratio of 5.2:1 which obtained in the exten- sive and meticulous experiments of Spencer and Stern (1948~. For all three groups, the ratio of visibles: lethals: semi-lethals and deleterious has been set at approximately 1:5:20, although, as noted above, the third figure is certainly an underestimate. The important question of the mutation spec- trum at individual loci remains in its early stages

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208 Genetic EJects of Atomic Bounds Chapter XV because of the amount of labor involved in se- curing reliable data. There is evidence that in Drosophila some few genetic loci which are associated with visible mutants are not abso- lutely essential to life, although in the absence of these loci viability is usually markedly re- duced. On the other hand, there are numerous illustrations of lethal and visible mutations arising at what seems to be the same locus. It should also be pointed out that the question of the total relative frequency of mutation at differ- ent loci is in a very unsettled state. Although there seems no doubt that the rate of recovery of mutations differs from locus to locus, care must be exercised in reasoning to the magnitude of the true differences (cf. Neel and Schull, 1954~. In the following discussion of mutation rates at specific loci, the fact that these are selected loci must constantly be borne in mind. mutations per generation, a rate some fourfold that ordinarily observed. Since the numbers in- volved are not given, the reliability of this apparent fourfold increase cannot be evaluated. Muller et al. argue, from this fourfold increase in recovered lethals, that "the frequency of ,ene-mutations at the nine loci would ordinarily average between 10-5 and 7 x 10-6 per locus in females" (p. 125~.3 For our present pur- poses, it will be sufficient to average all three of these series together, with no attempt to introduce the correction suggested by Muller et al. (which would in any event then appear to create a possible discrepancy between their find- ings and those of Glass and Ritterhoff~. In a total of 1,665,345 locus tests, at least 32 muta- tions were recovered, a rate of 1.9 x 10-5. However, this applies only lo "visible mz~ta- tior;~." If lethals, semi-lethals, and deleterious TABLE 15.1 FREQUENCY OF OCCURRENCE OF SPONTANEOUS V~s~stE MuTA-rioNs IN VARIOUS SPECIES No. of No. of Total locus Author Chromosome organisms loci tests Mutations ,u Drosophila Muller, Valencia, and Valencia, 1950 X Alexander, 1954 III Glass and Ritterhoff, un- (Multiple (males) published ~ Multiple (females House mouse Russell, 1954 Several Three recent studies on the rate of occurrence of spontaneous "visible mutations" in Dro- sophila appear outstanding. The results, in terms of frequency of appearance of visible mutations, are summarized in Table 15.1. There appear to be significant differences between the studies with respect to the observed frequencies, al- though it must be kept in mind that different loci are involved in the three studies. Further- more, the work (unpublished) of Glass and Ritterhoff suggests that the mutation rates of males and females differ, although different loci were being tested in the two sexes. This ob- senation may provide a clue to the apparent difference between the Endings of Muller, Valencia, and Valencia (1950) and Alexander (1954), since the former were studying muta- tion rates in females and the latter in males. It is also noteworthy that in other experiments with the same strain used for the "visible muta- tion" studies, Muller, Valencia, and Valencia (1950) recovered 0.7 per cent sex-linked lethal -60,000 9 45,504 8 102,759 4 100,414 4 37,868 540,000 152.8 X 10-5 364,032 00 359,657 16-214.5-5.8 X 10-5 401,656 13.1 X 10-0 7 265,076 2 .8 X 10-5 mutations are arising at these same loci, the mutation rate must be higher. If, for instance, the ratio of visibles: (undetected lethal+semi- lethal+deleterious mutations) at these loci was a conservative 1:4, the mutation rate per locus becomes 1 x 10-4! Two other studies involving individual loci should be quoted: Lefevre (1955), in a paper which contains an excellent discussion of the problem of estimating spontaneous mutation rates, reports that the rate of appearance of mutants with visible or lethal effects at the y locus is "about 1 per 75,000" (P. 3791. On the other hand, Bonnier and Luning (1949), in a paper criticized by Muller (1954) because the rate of recovery of spontaneous mutations ap 3 The questior1 of the frequency of these "high mutation rate' lines has been discussed by Ives (19SO; see also Neel, 1942), who suggests that the mutator genes which are responsible for these high rates "are the major cause of both gene mutations and inversions in natural populations" (p. 251~.

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Permissible l~ferences peered to be too low in comparison with certain other findings, observed only one mutation at the white and forked loci among 153,579 flies tested for visible mutations, a rate of .4 x 10-5. Both of these estimates do not take into account the semi-lethal and deleterious mutations. The same conservative 1:5 ratio applied in the pre- ceding paragraph would bring these estimates well within the range of the others quoted earlier. Utilizing a somewhat different approach, Dob~hansky, Spassky, and Spassky ~ 1952 ~ have estimated the average rate of mutation to lethals, semi-lethals (1-20 per cent viability), and visi- bles per lethal producing locals in different spe- cies. These estimates, which they feel are more likely to be overestimates than underestimates, are reproduced in Table 15.2. Again, the esti- mate does not include the deleterious mutants. TABLE 15.2 ESTIMATED AvE8AGE MUTATION RATES PER LETHA~-PRoDuc~NG Locus IN SEVERAL DROSOPHILA SPECIES (After Dobzhansky, Spassky, and Spassky [19523. These estimates are felt by the investigators to be more likely overestimates than underestimates.) Species D. melanogaster .. D. pseudo-obsura . D. willistoni .... D. prosaltans ........ . . . . Second chromosome . . 1.1 X 10 2.2 X 10-5 1.1 X 10-6 Third chromosome 1.1 X 10-6 3.0 X 10-5 2.1 X 10-5 In summary, then, it would appear that de- pending on one's view of the representativeness of the loci studied, and the problem of the rela- tive frequency of mutations not detected by current techniques, there is room for a wide divergence of opinion concerning the average rate of mutation of Drosophila genes, with the range of possibilities perhaps extending from 0~5 X 10-5 to 5 x 10-5. It is in our opinion not permissible to apply even this wide range of estimates directly to human problems, since even within species of the same genus mutation rates appear to differ significantly (cf. Table 15.2) . Turning now to mammals, we find that s~g- nificant studies are available for only two spe- cies, the house mouse and man himself. The figures for the house mouse were derived in much the same fashion as the figures quoted for Drosophila, namely, through a search for mu- tant individuals among animals simultaneously 209 heterozygous at multiple loci. Russell (1954), in connection with the important observations on radiation-induced mutations in the house mouse which we will refer to shortly, has now amassed the control data shown in Table 15.1. The rate of appearance of visible mutations in 265,076 locus tests was 0.8 X 1O-5. The ob- servational error is of course large. Again it must be recognized that these tests detect only a fraction of the mutations occurring at these loci. The available estimates for the frequency of occurrence in man of mutations with certain visible effects are shown in Table 15.3, prepared by Dr. T. E. Reed in collaboration with one of us (~.V.N.~. Many of the problems involved in estimating human mutation rates have been discussed elsewhere (Haldane, 1948, 1949; Neel, 1952; Neel and Schull, 1954; Nacht- sheim, 1954~. Because of the particular prob- lems associated with the study of incompletely recessive genes, no estimates based on such genes are included. The average of the estimates in Table 15.3 is approximately 3 x 10-5. This estimate, now, is entirely limited to dominant mutations with visible effects. Even what would seem a very conservative allowance for recessive visibles and for the lethal, semi-lethal, and deleterious mutations would bring the average estimate up to 1 X 1O-4 for these loci. The representativeness of these estimates has been repeatedly challenged. There can be no doubt that there is definite selection in the loci studied. How this influences our estimates is not at all clear. As we have pointed out else- where (Neel and Schull, 1954), mutation at any particular locus may be thought of in terms of these aspects: (1) the frequency of mutation at that locus; (2) the number of alternative forms of the gene which may occur at any locus, i.e., the number of multiple alleles; and (3) the ease with which the effect associated with each of these multiple alleles can be detected. We assume that some loci are more mutable than others because we detect the results of mutation more frequently at these loci. How- ever, making allowance for "unstable loci," the hypothesis has not been disproven that the inherent instability of all the genes is, by virtue of their biochemical complexity, very similar, but that the results of mutation are more readily detected at some loci than at others because of the role of that particular locus in the animal's physiology. It is entirely conceivable that the

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210 loci 4 thus far selected for study in man are those at which a high proportion of all possible alleles at that locus results in readily detectable effects, but at which the per locus mutation rate is fairly representative of the human species. This problem is discussed further in Neel and Schull (1954~. For purposes of calculation, estimates of the rate of mutation of human genes have included 10-5 (Evans, 1949), 10-7 (Wright, 1950), and 2 X 1O-5 (Muller, 1950; Slatis, 1955~. In the current state of our knowledge students of the problem can select and justify estimates differ- ing from one another by a factor of 100. 15.3 The radiation-induced m~tatiorz rate ire 4 In point of accuracy, we do not know but what any particular mutation rate study in man is detecting mutation at several loci. Genetic Effects of Atomic Bombs Chapter XV man. If we turn now to the estimation of the sensitivity of human genes to irradiation, we must first of all take cognizance of the same technical problems that exist in the estimation of spontaneous rates, as well as additional prob- lems discussed by Muller (1954~. For reasons brought out earlier, we are interested in effects on spermatogonia rather than mature sperm. For obvious reasons, no precise estimates are available for man. Until relatively recently, there was no mammalian material whatsoever. Now, however, Russell's (1954) figures, based on specific locus tests, indicate a visible mutation rate in spermatogonial cells of ~ 25.0 + 3.7 ~ X 10-S/gene/r. Russell has emphasized the danger of generalizing from these limited results, a point with which we heartily agree. But as long as these are the only figures available, they can TABLE 15.3 FREQUENCY OF OCCURRENCE OF NINE DIFFERENT DOMINANT OR SEX-LINKED MUTATIONS TN MAN Epilaia ... Character Chondrodystrophy b Direct Direct Pelger's nuclear anomaly. . Direct Aniridia Direct Retinoblastoma Direct Direct Direct Waardenburg's syndrome. Direct Neurofibromatosis Direct Method of Mutations per gene estimation aper generation . . . Direct0.4-0.8 X 10-6 4.2 X 10-5C E. 4.3 X 10-5 J 49X 10-5C J 7X 10-5 2-7X 10-5 0~5 X 10-6 C. 1.4 X 10-5 U. 2.3 X 10= J 4.3 X 10-0'l F. 3~7X 10- 1.3-2.5 X 10-4 0.8-1.0 X 10-4 [. Dominant genes A Source M. Gunther and L. S. Penrose (1935, I. Genet. 31: 413), L. S. Penrose (1936, Ann Eagen. 7: 1~. T. March ~ 1941, Opera ex Domo Biologiae Hereditariae H~marzue Universitatis Hafnien- sis, Vol. 3~. B. S. Haldane (1949, Proc. 8th Int. Cong. Genet., Hereditas, suppl.: 267) from data of March (1941, vice supra). B. S. Haldane (1949, vice supra from data of March, 1941, vice supra). J. A. Book (1952, .7. Genet. Hemline 1: 24~. H. Nachtsheim (1954, Natarwiss. 17:385 ~ . J. M011enbach ~ 1947, Opera ex Domo Bio- logiae Hereditariae H~mazzue Unirersitatis Haf nie~zsis, Vol. 15 ~ . Philip and A. Sorsby (unpublished, quoted by Haldane, 1949, vice supra). V. Neel and H. F. Falls (1951, Science 114: 419~. Vogel ~ 1954, Ztschr. menschl. Vererbungs-~. Konstitutionslehre 32 :308 ) . P. J. Waardenburg (1951, Amer. i. Hem. Genet 3: 195~. F. W. Crowe, W. J. Schull, and J. V. Neel (1956, Multiple Neurofibromatosis, American Lectures in Dermatology series, C. C. Thomas ~ . W. Crowe, V7. J. Schull, and J. V. Neel, loc. cit.

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Pes~missilole Inferences TABLE 15.3 Copied Sex-linked recessive ger~es Method of Mutations per gene Character estimation a per generation Hemophilia Indirect 3.2 X lO - e Childhood progressive muscular dystrophy .... Direct 211 Source J. B. S. Haldane (1947, Ann. Eagen. 13: 262) from data of M. Andreassen ( 1943, Opera ex Domo Biologiae Hereditariae Hamanae U'zive~itatis Haf niensis, Vol. 6 ~ . 1 X 10-` F. E. Stephens and F. H. Tyler (1951, Amer. f. Ham. Genet. 3: 111~. Indirect1 X 10 - F. E. Stephens and F. H. Tyler (1951, loc. city. Indirect4.5-6.5 X 10-6 A. C. Stevenson (1953, Ann. Eager. 18: 50~. n Estimation is considered to be direct when based on observed mutations, indirect when not so based. All indirect estimation makes use of estimates of the relative fitness and frequency at birth of the trait, and assumes that the population is in equilibrium. b Slatis (1955, Amer. f. Hum. Genet. 7: 76) has suggested that these estimates may be spuriously high In this case because of some evidence for the occurrence of phenocopies. c Independent estimates from different data contained in the paper of Morch (1951~. ~ This estimate is based on the proposition that approximately 75 per cent of all sporadic cases of reti- noblastoma are phenocopies. There are reasons to believe that this is an overestimate of the proportion of phenocopies. OR the other hand, the estimates of Philip and Sorsby, and Neel and Falls, which treated all spo- radic cases as due to mutation, are undoubtedly too high. e This study may have included three distinct types of hemophilia: (a) classical sex-linked hemophilia resulting from deficiency of anti-hemophilic globulin (AHG), (b) a sex-linked clotting defect from lack of "plasma thromboplastin component" (PTC), and (c) an autosomally-inherited clotting defect from lack of "plasma thromboplastin antecedent" (PTA). Frick (1954, J. Lab. & C1in. Med. 43:860) found that of 55 patients with coagulation defects, 45 had AHG deficiency, 6 had PTC deficiency, and 4 had PTA deficiency. Probably, therefore, Andreassen's study was mainly concerned with AHG deficiency; the mutation rate es- timate for this deficiency may be about 15 per cent too hitch. ~ Strictly, not a true direct estimate but an approximation which overestimates the mutation rate. not help but strongly influence current thought. For what it is worth this average rate is about 15-20 times the figure of 1.5 X 10-~/gene/r obtained for Drosophila melanogaster sperma- togonia under comparable conditions (Alexan- der, 1954~. Again, we emphasize that these estimates are undoubtedly based on the recovery of only a portion of the mutations occurring at these loci, with no assurance that the relative recovery rates are the same in the two species. Even so, taken at face value, the data would seem to indicate that mouse genes are decidedly more sensitive to irradiation than Drosophila genes. However, Ives (1954) has recently drawn attention to a number of factors which make it difficult to say precisely how much (if any) more sensitive mouse genes are than Dro- sophila genes, concluding that "for the present the radiation-induced mutation rate per r per locus appears to be similar in flies and mice" (p. 364~. Although Ives' paper was written prior to the appearance of the paper by Alex- ander, quoted above, some of his objections would doubtless still stand, particularly the point concerning the disproportionate contribu- tion of mutation at one particular locus to Russell's conclusions. Many of Ives' objections seem to have been met by a recent paper by Russell (1956~. Early discussions of the genetic effects of radiation on human populations used an estimate of the frequency of induced muta- tion (3 X 10-~/gene/r) based on work on ma- ture Drosophila sperm (Evans, 1949; Wright, 1950~; more recent treatments (Muller, 1955; Slatis, 1955) have used a figure (2 X 10-7/- gene/~) based on Russell's work on mouse spermatogonia, although Sturtevant (1955) pre- fers to retain the figures based on Drosophila. In a discussion of radiation hazards, it is sometimes convenient to think in terms of the amount of radiation necessary to double the spontaneous mutation rate. This is obviously a function of the average spontaneous mutation rate per locus and the probability of mutation per locus per r. For purposes of discussion, Muller (1954; 1955), on the basis of Russell's (1954) work, has utilized figures ranging be- tween 37 and 80r as the doubling dose. Haldane (1955), on the other hand, appears to feel that the doubling dose is closer to 3r, which would seem to imply a belief that the average spon- taneous mutation rate per locus is in the neigh

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212 Genetic Elfects of Atomic Bomios Chapter XN7 borhood of 1 X 10-6. Westergaard (1955 ~ also stresses the possibility that the doubling dose may be low, in the neighborhood of 3-6r. 15.4 Estimates of the number of genes in man. The haploid gene number in Dro- sophila is commonly placed at 5,000 to 10,000 (cf. Muller, 1935~. The existence of the rela- tively enormous salivary gland cell chromosomes in Drosophila, and the usual correspondence be- tween a genetic locus and a visible "band" in these chromosomes, provides an unusual oppor- tunity for gene number estimates in this species. No corresponding situation has been established in man or any other mammal. It is commonly argued that man, because of his greater physio- logical complexity, must have more genes than Drosophila. There exists only one piece of ob- jective evidence in support of this argument. Spuhler (1948) has pointed out that the mean total length of the chromosomes in late prophase nuclei in man is some 8.5 times that of Dro- sophila. If one assumes that the spacing of the genes in the chromosomes is similar in the two species, this permits an estimate of the haploid gene number in man of between 42,000 and 85,000. Current treatments of the problem use estimates of the haploid gene number of from 100,000 (Evans, 1949) to 5,000 (Muller, 1950; Slatis, 1955~. The data, then, permit competent students of the problem to make as- sumptions varying by a factor of 20. 15.5 The "accumulation factor."-The term "accumulation factor" is applied to the ratio of "recessive" genes already present in the popu- lation to those arising spontaneously each gen- eration through mutation. Evans (1949), the first to make use of this factor in calculations, assumed, "somewhat arbitrarily," a value of 50. No discussion of the basis for this estimate is given. With his assumptions concerning average mutation rate (1 X 1O-5) and haploid gene number (1 x 105), the total mutation rate per zygote would be 2.0, and the average number of accumulated "recessive" genes per individual would be 100. Muller (1950), on the other hand, after an extensive discussion of the evidence regarding the average degree of dominance of Drosophila genes, arrives at an "accumulation factor" his p value of 40, writing at the same time that there is "such a lamentable paucity of numerical values for human beings, or for any vertebrates, of a type which would throw light , ~, on the actual values of these factors, that we cannot feel too secure in regarding even 40 as a lower limit for p" (p. 141) . The total mutation rate per gamete (in), i.e., the product of gene number X average mutation rate, is set for pur- poses of calculation at 0.1. Introducing a factor of 2 to make allowance for the fact that selection probably operates predominantly on heterozy- gotes, the average number of "recessive" dele- terious genes carried by a human being is placed at 2 X 0.1 x 40 = 8. In a later calculation, Muller (1954) adopts a figure of 0.3 as the total mutation rate, and suggests a figure of 100 for p. This leads to an estimate of 60 for the average number of recessive deleterious genes for which each individual is heterozygous. Slatis (1954) has attempted a direct calcula- tion of the frequency of abnormal autosomal recessive genes in man, from a consideration of the outcome of first cousin marriages. Data are presented on 17 sibships, in nine of which defects occur that are attributed to recessive inheritance. This leads to the estimate that "the average person is heterozygous for eight ab- normal genes" (p. 418~. Although the method is a valuable contribution, the data are un- fortunately so biased as to be practically worth- less for a calculation of this type. As Slatis points out, five of these nine families were ascer- tained because of the abnormality. Furthermore, two of the four remaining traits (polydactyly, distal webbing of the digits) are frequently due to dominant genes of irregular penetrance. If one discards those sibships, the data remaining are insufficient for a calculation of this type. The extensive data on the children born to consanguineous parents which were collected in the course of the present study, although still incompletely analyzed, are at marked variance with those of Slatis as regards frequency of appearance of genetic defect in the offspring. In his later discussion of the results of the induction of mutations by irradiation, Slatis (1955) uses this figure of 8 for the average number of recessive deleterious genes present in man. Muller's above-quoted estimate of 60 is dismissed as "obviously too high," on the basis of a calculation which assumes that each of these recessive genes has a clear-cut and readily demonstrable effect. While we hold no particu- lar brief for either Evans' estimate of 50 nor Muller's of 60, Slatis' rejection of estimates of this magnitude appears to be based on the mis

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Permissible inferences conception that all deleterious genes of any im- portance to the problem should result in clear- cut, readily diagnosable defect. 15.6 The rare of 'mural selection. We come now to the last of the factors which enter into attempts to quantitate the genetic effects of the irradiation of human populations. All treat- ments of this subject, implicitly or explicitly, make certain assumptions concerning the mode of operation of natural selection. This problem has been treated most extensively by Muller (1950, 1954~. In his earlier treatment, Muller (1950) writes: "Moreover since, firstly, the extinction rate due to an individual locus is exceedingly small and since, secondly, in the great majority of cases the extinctions caused by any locus are probably only in small proportion (relatively to the whole) determinately con- nected with those caused by particular genes at other loci, we may tentatively and as a first ap- proximation consider the genetic deaths asso- ciated with different loci as occurring inde- pendently" (p. 121~. Later (p. 151) we read: "We have seen (p. 138) that if A, the total mutation rate per gamete, is 0.1, and if the dominance is 'effective,' then no, the frequency of newly manifested cases per individual, is the same as the frequency of individuals eliminated at equilibrium under natural selection, and has a value only slightly less than 0.2, namely, 0.18, provided we assume (1) the independence of distribution and (2) the independence of detri- mental action of the mutant genes. Although the second assumption is certainly inaccurate, as pointed out previously, nevertheless provi- sional consideration of the matter indicates that it is unlikely for the frequency and strength of synergistic action of mutant genes to be so great as to reduce the frequency of elimination from a value of 0.18 to below, say, 0.15." We inter- pret this passage to mean that, given Muller's assumptions, at genetic equilibrium, at a mini- mum, the reproductive performance of the population will be, as a result of natural selec- tior~, some 15 per cent below what it would have been in the absence of these mutations. Somewhat later, however, it is pointed out that, given the assumption of an average of 8 dele- terious genes per individual, artificial selection which prohibited that 3 per cent of the popula- tion with the highest concentration of deleteri- ous genes from breeding could balance the total mutation rate of 0.1 per individual which is 213 assumed. Thus, the operation of natural selec- tion is postulated to involve the elimination at equilibrium of approximately five times as many individuals as a "completely efficient" system of artificial selection. As Neel and Falls (1951) have emphasized in considering this problem, the survival of an individual under competition is as a rule not determined by single genes but by constellations of genes. These constellations of genes may be considered as having either additive or non- additive effects- a variety of observations sug- gest that non-additive effects are rather common where combinations of mutant genes are con- cerned (e.g., in Drosophila, Neel, 1941, 1943; House, 1953a, b; in the guinea pig, Wright, 1949~. Non-additive effects suggest that an in- dividual with 12 deleterious "recessives" does not necessarily carry double the handicap of one with 6. The concept of synergistic gene action was given the term "dependent over- lapping" by Muller (1954~. It is to be dis- tinguished from "independent overlapping," the latter illustrated by the case of an individual who meets genetic extinction through the effect of a given gene who would have met extinction anyway through the effect of one or more other independently acting genes which he also hap- pened to carry. Muller (1954) in his most recent treatment of dependent overlapping modifies the earlier position stated in the pre- ceding paragraph, and now considers it very unlikely that dependent overlapping "would reduce the elimination rate of individuals by a factor of more than 2 or 3," but after a con- sideration of the probable distribution of mu- tant genes in the individuals of a population, does not introduce this factor into his most recent calculation of the average number of deleterious genes per individual (60), although introduction of the factor would of course re- duce the estimate to a half or third. It is to us not clear how our present knowledge permits assigning a definite numerical value to the role of dependent overlapping. This question must certainly be considered one of the most impor- tant in the field of natural selection. The problem of defining the balance between selection and mutation is extremely complex. Thus, Muller (1950) on pages 149-50 argues as follows: "Whatever the values finally found, it is evident that the natural rate of mutation of man is so high, and his natural rate of repro

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214 auction so low, that not a great deal of margin is left for selection. Thus if at has the minimal value of 0.1 (~ = 0.18) an average reproduc- tive rate of 2.4 children per individual would be necessary to compensate for individuals genetically eliminated, without taking any ac- count whatever of all the deaths and failures to reproduce due to non-genetic causes. But when these are taken into account as well (even though we allow only that reduced number of them that occur under modern conditions) it becomes perfectly evident that the present num- ber of children per couple cannot be great enough to allow selection to keep pace with a mutation rate of 0.1. If, to make matters worse, at should be anything like as high as 0.5, a possibility that cannot yet be ignored, our pres- ent reproductive practices would be utterly out of line with human requirements." Now, if at equilibrium, and invariably, over a long period of time, each member of one generation contributes genetically to, on the average, two members of the next, then there is no question whatever of a decrease in the size of the population. This condition is both neces- sary and sufficient to define the restriction on a population of unaltering size, and the mortality experience of the population-intrinsic or ex- trinsic in source will effect no change in number provided the condition is met. Suppose, for example, there are N individuals in one generation. These N individuals will, under the condition, contribute 2N gametes to the next generation. Since the number of individuals equals -I- the number of gametes, there will be N individuals in the next generation.5 Therefore, Muller's statement that there must be on the average 2.4 children per individual to compensate for those lost through selection is somewhat ambiguous, and his assertion that still further compensation is necessary for additional sources of mortality is even more difficult to interpret. Without meaning to belabor the point, suppose, to take a simple and extreme case, there are N individuals born into one genera- tion, and It's of them are completely sterile. If the condition for unaltering size, given in the above paragraph, is met, there will still be 21V gametes contributed to the next generation, and therefore N individuals. 5 We are indebted to Dr. Robert Krooth for calling our attention to the line of reasoning developed in this and the following several paragraphs. Genetic Ejects of Atomic Bombs Chapter XV Let us accept the assumption that selection acts primarily through the heterozygote. If there are pi heterozygotes at locus i (and let us con- sider but one mutant allele), and if W. is the mean number of children to whom persons heterozygous at locus i contribute genetically ("fitness"), W is the mean fitness of the whole population, hi is the mutation rate per chromo- some per generation from the normal allele to the mutant gene, and if, Anally, there are but N individuals in the population, then there will be Npt heterozygotes in one generation who will contribute Np~Wt gametes so that there will be -2-Np,W*"affected" genes from "affected" par ents. There will be NW loci (of the type in question) in the whole of the next generation, and of these (near enough) Newt will be represented by "affected" genes newly mutated from the wild type. Since the population is in equilibrium, there will be no change in gene frequency from the first generation to the second, hence NW~+-~-Ni~Wt Npt_o , or NW 2N NW2~i = NWpt-NW~pt. Therefore, 2,ui is the ratio of gametes lost through selection acting on the parents of the second generation to the number of gametes actually present in the form of zygotes in the second generation. Now in the passage quoted, Muller assumes that ,u~ a quantity which he considers to be roughly, though not exactly, equivalent to 2X,u (the sum being over all loci) is equal to 0.18. Thus, ignoring overlapping effects, as Muller does,6 the ratio of gametes lost through selection to gametes actually realized in zygotes is 0.18. If WO is the mean fitness which would prevail in the absence of this gametic loss, and if W is the fitness which in fact does prevail, then WO-W at= ~ Substituting 0.18 for at and letting W equal 2, the minimum fitness which will enable the popu- lation to maintain its numbers, we find WO= 2.36. This then is presumably the origin of 6 And we shall not in this section consider whether this is permissible.

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Permissible Ir~ferer~ces Muller's 2.4-it is a virtual fertility, not an actual one. It is the fertility which would pre- vail if there were no gametic loss due to muta- tion and if the population were just maintaining itself; it is not the fertility which must prevail to maintain the size of the population. If the actual fertility of the population were 2.4, the population of the United States would increase by 20 per cent within a single generation. If now we substitute 2.4 for W. the actual fertility, and 0.18 for A, we find the virtual fertility of the population to be 2.832. Substi- tuting Wo=2.832 and W=2 into the formula, we can determine the maximum total mutation rate which would permit the population to maintain its numbers. This quantity equals 0.416, which is slightly more than twice as large as the figure given above for Mu (=0.18~. In other words, if the "average reproductive rate of 2.4 children per individual" actually did prevail, a human population could experience a permanent doubling of Muller's estimate of the total natural mutation rate without loss in number. Finally, and in summary, if one really did take all the genetic arid non-genetic factors into account in the computations, a minimum viral fertility far higher than those considered above would result, but the population of the country would still maintain itself (and it Is in fact increasing exponentially) provided W averages 2, even if ww averaged, say, but 10 per cent! In addition to the question of the extent to which selection may be considered to involve single genes as contrasted to constellations of genes, and the relationship at equilibrium be- tween fertility and mutation rate, there is per- haps an even more basic assumption as regards selection which enters into treatments of this problem. It is customary to assume that the mutations produced by irradiation have with very rare exceptions harmful effects; one accord- ingly calculates the increase in "undesirable recessive traits," "congenital malformations," etc. In point of fact, however, irradiation, inso- far as it increases the appearance of mutations which would occur anyway, accelerates a process which modern biology accepts as the cornerstone of evolution. Although the results of mutation are from the standpoint of the organism usually unfortunate, they may sometimes be beneficial. Natural selection, it is assumed, sorts out the 215 beneficial from the harmful. Treatments of the problem of the genetic effects of irradiation tend to assume that modern civilization has so blunted the effectiveness of selection that the ill-effects of radiation-induced mutation far outweigh the potential good. In view of our abysmal ignorance of the actual selective forces which have shaped mankind, there is no way to reach a valid opinion concerning the extent to which Western culture does in fact negate the selective mechanisms which are responsible for Homo sapiens as we know him today. There is also no real information on the extent to which certain characteristics which are of great importance to the species and which have a strong genetic component, such as intelligence, are maintained by "balanced polymorphic" sys- tems (cf. Penrose, 1950), which systems would be relatively resistant to increased mutation pressure. Of all the gaps in the background in- formation necessary to an accurate quantitative approach to the genetic effects of increased radiation, the deficiency of data on this point is perhaps the most striking. Muller (1954, pp. 43~37) has spelled out the conditions under which radiation might speed the evolutionary advance of man (or any inch ~~ ~ n im ~ l ~ ~ c fail l r``xrc " V~1~_~ ~ ^~ ~- ^~,^~ . ... the first is that the spontaneous mutation rate should not be already so high that when irradiation is applied mutations occur too frequently to allow an equilibrium elimination rate and/or a genetic load low enough to be tolerated by the popula- tion. A second condition is that the advan- tageous mutants should multiply fast enough to replace the original type at a rate commen- surate with their increased rate of origination. A third requirement is that the organism should not be at the limit of an evolutionary blind end, i.e., that pathways of advantageous change still remain open to it. Such opportunities will be present in greater abundance, allowing more of the mutations that occur to be helpful in the given situation, if the population has been placed in an environment, and subjected to conditions of living, somewhat different from those previously natural to it; for it must already have become so highly adapted to its natural conditions as to make further progress difficult. Advance is also achieved more readily if the population is one which has to some extent lost, through genetic changes or recombinations, its original nicety of adaptation. This may have

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216 Genetic Ejects of Atomic Bombs Chapter XV come about through the prior establishment of some more or less harmful mutations, the effects of which can now be overcome by reverse or counteracting mutations. Such prior retrogres- sion is likely to have occurred if the given population has recently been derived from one or from a mixture of a few more or less inbred lines, or from relatively few progenitors; in that case, moreover, the population will also start out with unusually restricted genetic variability, which the application of radiation will tend to remedy." With respect to the first two of these condi- tions, Muller argues that very probably "human beings are already near if not at or beyond the mutation rate which, in relation to their condi- tions of living and breeding, is the 'critical' one." With respect to the second condition, Muller contends that the reproductive differen- tials between members of the human species are insufficient to allow for the necessary rate of incorporation of advantageous mutations into the genotype. For both of these arguments, it is important to recognize that although they may be in essence correct, we are in no position to supply the precise figures on which quantitative treatments of the problem of the genetic risks of irradiation must be based. Finally, with re- spect to the third condition, one can argue that in view of the striking changes in the circum- stances under which man lives which have occurred during the past century, man is enter- ing a period of biological readjustment, during which he will need an increased store of genetic variability on which to draw. Wallace (1951, et seq.) has recently irradiated Drosophila populations under circumstances which, as Mul- ler (1954) points out, fulfill these very condi- tions. At the end of 100 generations of exposure to 2,000r each generation, viability and fertility appeared unimpaired. While extrapolation to human populations can under no circumstances be justified, this does remain an illustration of the amount of irradiation which trader special circumstances a species can tolerate. In a recent paper, Keosian (1955) has taken the extreme point of view that on the basis of the existing evidence, it can actually be argued that increased radiation will lead to genetic betterment. The gist of the argument is that with respect to human populations much room exists for biological progress, so that "increased genetic variability can lead to an accelerated evolution along beneficial lines." This approach challenges the validity of the concept that man is near a "critical mutation load," and also assumes the normal operation of natural selec- tion, or at least sufficient natural selection, plus improved medical care, that the potential bene- ficial effects of radiation-induced mutations will outweigh the ill effects. In order to avoid possible misunderstanding, in closing this section we would emphasize that we do not mean, directly or by inference, to suggest that radiation will lead to the genetic betterment of human populations. Thus, quot- ing Keosian's speculations does not constitute endorsement of his position. Our purpose is solely to emphasize the present inadequacies in our knowledge of the operation of natural se- lection on human populations, inadequacies which permit widely different viewpoints. 15.7 Concluding remarks. It seems wise at this point to phrase as succinctly as possible the present position of the authors regarding the genetic risks of radiation. On the basis of exten- sive plant and animal work, it seems reasonable to conclude that all levels of irradiation of hu- man populations will result in mutation produc- tion. There is a high probability (but not cer- tainty) that under the conditions of Western culture, such mutations will act to the detriment of the populations concerned. However, the present data do not permit, in the authors' opinion, a satisfactory quantitative approach to this problem. Radiation is but one of a number of dysgenic influences at work in human populations. Two others commonly mentioned are war and differ- ential birth rates. The quantification of these influences is just as unsatisfactory as that of radiation. As coal and oil resources dwindle, increasing recourse will be had to atomic fuel as a source of energy. Our concern as to the undesirable consequences of increased radiation due to in- dustrial installations, as well as other sources, must find a frame of reference. If it were possi- ble to assess the sum total of the influences which would be considered dysgenic, does in- creased radiation of all types at the present and at foreseeable levels constitute 1%, 10:fo, or 50~O of that total and what is the size of the total? It will seem to many that to attempt to phrase the problem in those terms is hopelessly im

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Permissible Inferences practical. At the moment, yes. But it is the belief of the authors that the stage is now set for very substantial advances in our knowledge of the genetics of man. Given the facilities and the investigators, great progress can be made to- wards a better understanding of the problem of the genetic effects of the irradiation of human populations, and, on the time scale of human evolution, within a relatively short period of time. We have seen that great uncertainty exists concerning the value of each of the five factors which must be known to quantitate the genetic effects of the irradiation of human populations. The data presented in this monograph have potential value in the clarification of these fac- tors. Given independent approaches which lead to the elucidation of, for example, gene number or gene sensitivity to irradiation, these data then enable the next step to be taken. At the moment, however, we are reluctant to infer more than that the data remove the remote possibility of a conspicuous sensitivity of human genes to irradiation (i.e., marked mutability). Even this conclusion is open to challenge, de- pending on the definition given "conspicuous." As the term is here employed, we mean only that under circumstances where a group of geneticists felt that a clear-cut demonstration of genetic radiation effects was unlikely (Ge- netics Conference, 1947), no effects have been conclusively demonstrated. Conversely, had clearly significant effects on sex-ratio and mal- formation and stillbirth frequencies emerged, these would, on the basis of current knowledge, have qualified as "conspicuous" effects. More specifically, we feel that the present data render it improbable that, as has been suggested by some (Haldane, 1955), human genes are so sensitive that as little as 3r, or even for, will double the present mutation rate, although it must be admitted that a rigorous demonstration of this belief would be difficult. But, it may be argued, the urgency of the problem of setting "permissible" individual 217 radiation dosages is such that we must be guided by the data at hand. There is rho doubt concern- ing the urgency of the problem. There is doubt concerning the advisability of calculations which have the appearance of mathematical exactitude to persons not thoroughly indoc- trinated in genetics and unfamiliar with the shaky basis of the primary assumptions. Expo- sure to irradiation of all types should undoubt- edly be minimized until we have a clearer idea of just how harmful these effects are. Until the day of this better understanding, it is as un- fortunate, on the one hand, to deny the possi- bility that low doses are dysgenic at all as it is, on the other hand, to assert that a serious threat to the genetic integrity of mankind is involved. The practical difficulty in this position is the apparent necessity of setting tolerance limits for, e.g., workers in situations involving the produc- tion of atomic energy, or military personnel in- volved in the use of atomic weapons. However, it is well worth bearing in mind that even if the present "limits" are ultimately found to be too high, there are few who would argue that in the period it takes to establish that fact with certainty, man will have suffered serious genetic harm. There is, on the other hand, the possi- bility that by refusing to be drawn into prema- ture speculative calculations which in the nature of things will be "used" as soon as they have been set to paper, and by insisting on all possi- ble occasions that the work that should be done actually be carried forward, the geneticist in the long run will arrive more quickly at the goal of a lasting, valid appraisal of this problem. But although we entertain reservations con- cerning the inferences which can be drawn from the data presented in this report, this should not be construed to indicate doubts concerning the wisdom of collecting the material. A problem as complex as the evaluation of the genetic risks of human irradiation will only finally be solved through the combined efforts of many investigators. This study will have justified itself if in that final synthesis it proves of value. K..