GENETIC LOAD: THREE VIEWVS'

1. The Concept of Genetic Load: A CritiqueL. D. SANGHVI2

Department of Human Genetics, University of MichiganMedical School, Ann Arbor, Michigan

CURRENT METHODS of assessment of genetic hazards of radiation in mandepend on answering satisfactorily three broad questions. The first questionrequires information on the incidence of diseases, defects, and deaths primarilyof genetic origin, an estimate of our hereditary burden. The second questionrelates to an ascertainment of the fraction of this burden that is dependent forits maintenance on recurrent mutation. The third question is concerned withdetermination of relationships between a given dose of radiation and a corre-sponding increase in mutation rates under a variable set of physical andbiological conditions. The available evidence from observations in man andexperimental organisms is largely restricted to answering the first and the thirdquestions. The second question has given rise to theoretical thinking, somespeculation and some controversy. (United Nations, 1962).

If our hereditary burden is maintained by recurrent mutation, any permanentincrease in current radiation levels would proportionately increase such ill-effects eventually. Muller (1950) presented a most illuminating thesis alongthis line. An alternative mechanism has long been known to students ofpopulation genetics which could maintain, in theory, a major fraction of thisburden without necessarily relying on recurrent mutation (Fisher, 1930;Wright, 1931; Haldane, 1932; Ford, 1940). Linder the simplest geneticmodel of a population, with segregation of two allelic genes A and a at a locus,this mechanism depends upon a selective advantage of the intermediate genotype

Received February 13, 1963.'Editor's note: This article and the two immediately following present three contrasting

views of a topic of considerable importance to human genetics. In the first articleDr. Sanghvi criticizes a method of evaluating the genetic load that was first presented byMorton, Crow and Muller (1956) and later elaborated by Crow (1958), and a con-trasting method is presented. In the second article Professor Crow clarifies and defendshis previous position. The discussion is continued in the third article by Professor C. C. Li,who elaborates certain conclusions published (Li, 1963a, b) after Dr. Sanghvi's paper wassubmitted that are similar to those of Dr. Sanghvi.

It should be noted that the differences expressed are primarily philosophical ratherthan statistical, and are concerned with the proper choice of definitions for setting upmathematical models for examining biological systems. The usefulness of such statisticalmodels lies in their ability to detect and discriminate specific components contributing to acomplex biological mechanism. It is hoped that these discussions will serve to emphasizeboth areas of agreement and disagreement in theory, and will contribute to the develop-ment of a more unified theory.

2Present address: World Health Organization, Palais des Nations, Geneva, Switzerland.Dr. Sanghvi is on leave from the Human Variations Unit, Indian Cancer Research Center,Bombay, India.

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(heterozygous individuals Aa) over the other two types (homozygotes AA andaa). Genetic loci which maintain deleterious t;raits by this mechanism havebeen termed "segregational loci" to distinguish them from the former oneswhich are termed "mutational." Interpretation of the maintenance of anyfraction of the hereditary burden along this line would reduce the significanceof radiation hazards to a corresponding extent. It has thus become an importantquestion in population genetics as to whether we can distinguish the burdenmaintained by recurrent mutation from the portion that does not primarilydepend on this process.

Any answer to this question based on observations in man is likely to comevery slowly if current activity is any guide to future course. Morton, Crow andMuller (1956) attempted to assess the relative importance of these twvomechanisms and concluded, by applying an original scheme, that most ofthe hereditary burden revealed by inbreeding is supported by recurrent muta-tion. The scheme, described in detail by Crow ( 1958), makes use of a propertyof differential response of mutational and segregational loci to inbreedingeffects. Morton (1960) strengthened this conclusion by applying the sameargument to the results of inbreeding in the parents of individuals afflictedwith muscular dystrophy, deaf-mutism, and low--grade mental defect. On theother hand, Neel and Schull (1962) have presented recent data from Japanindicating that inbreeding effects are consistent with a larger component ofsegregational loci in that population.

These evaluations are based on acceptance of the theoretical scheme suggestedby Crow. There are, however, conceptual and other difficulties involved inaccepting this scheme. The purpose of this communication is to outline thesedifficulties and present an alternative approach for reconsideration of theproblem.

THE CONCEPT OF GENETIC LOAD

There are several ways in which the term genetic load has been used inrecent years. Muller (1950) used the term to express the proportion of popula-tion suffering genetic elimination or the amount of disability suffered by theaverage individual. Morton, Crow and Muller (1956) used the term "geneticdamage," which implied the same general idea. Crow (1958) gave this idea aformal definition and some rules of operation. He defined the genetic load of apopulation as the proportion by which the population fitness (or whatever othertrait is being considered) is decreased in comparison with an optimum genotype.He further stated that the genetic load has many possible components like themutation load (genetic load due to mutational loci), the segregation load(genetic load due to segregational loci) and others. Crow (1960) has modifiedthis definition as follows: the genetic load is defined as the proportion by whichthe average fitness in the population is decreased in comparison with what itwould be if the factor under consideration (mutation) were absent (see alsoFraser, 1962). Dobzhansky (1957) and Wallace and Dobzhansky (1959)suggested that deleterious mutant genes of all kinds constitute the genetic loadof a population. As the idea has not vet reached the stage of any different

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quantitative formulation from the one suggested above, it xvill not be discussedfurther in this communication.

MEANING OF GENETIC FITNESS

The genetic load as defined by Crow measures a decline in the average fitnessof the population as compared to some "standard" population. The standardaccording to the first definition is a population of one optimum genotype andaccording to the modified version is a population under some specified condition,e.g., a population in which no mutation occurs. For our present purpose, it isimmaterial which definition we take. Both relate to a decline in average fitnessof the population and it will, therefore, be appropriate for us to understand theterm fitness, first.

The fitness of a population, considered over a large number of generations,determines its numerical strength. If the value of fitness is greater than unity,it means an expanding population. If it is less than unity, it is a declining popu-lation. If the estimates prepared by the United Nations (1958) about the sizeof the human population since the beginning of the Christian Era are accepted,they would tell us that we were increasing at the rate of about 1 per cent pergeneration at the beginning of the Era. This rate increased to about 10 per centin the seventeenth century and we are currently increasing at a rate of about50 per cent per generation. In terms of fitness, the value which was 1.01 at thebeginning of the Era is currently running at 1.50 per generation. We assumehere that the population at a particular time produces the next generation at aninterval of 25 years. It is not necessary to enter into some of the complexities ofthe real situation resulting from overlapping generations and the age structure.

This rate of increase, described by Malthus as the law of geometric increaseof population, bears a close analogy with the growth of capital invested at com-pound interest, (1 + m)t, where m could be taken as the rate of increaseand t is the number of generations. When in is small and t becomes large,

(1 +1n)t -) Ctit,an expression used by Fisher (1930) to develop a related concept of reproduc-tive value. He termed m the Mialthusian parameter of population increase. Anegative value of m would mean a decline in population number.The fitness of a population can alternatively be considered as an average

fitness of individuals of this population. The fitness of an individual (or agenotype) is measured (Haldane, 1949; Penrose, 1949) by the number of itsprogeny, different generations being counted at the same stage of the life cycle(say, at birth). Fitness is thus concerned with the survival and reproduction ofthe individual. A tacit assumption in this extension of the idea of fitness fromthe population to individuals at a particular point of time is a stationary value ofm over the span of generations covered by the birth of the oldest individual inthe population to the time when all of them including the youngest had pro-duced their last offspring.

If we are interested in changes of the composition of a population, we needonly consider the relative fitness of different groups of individuals or genotypes.In the following argument we are not only concerned with relative fitness of

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different genotypes of a population but also with relative fitness of populationsunder different systems of mating. This distinction should be carefully noted.

Fitness, as thus used, is strictly in the Darwinian sense of "success in leavingprogeny" and is not intended to measure any other attribute of the individualor the population.

THE SCHEME SUGGESTED BY CROW

Crow's scheme is presented in table 1. Select.on coefficients s, tj, and t2, aswvell as h, are all positive quantities and take values between zero and one. Toillustrate the components of the genetic load, a numerical illustration is given inthe lower portion of the table. It is chosen to have a frequency of q = .005 forthe rare gene which corresponds to an incidence of 1 in 40,000 for a deleterioustrait like phenylketonuria in a random-mating population. The fitness of theafflicted recessive homozvgote is taken to be zero, and this mav mean inability tosurvive or inability to reproduce.

The models under the scheme are based or: assumption of a stable geneequilibrium from one generation to the next. Equilibrium in the mutationmodel is maintained by the appropriate amount of recurrent mutation from Ato a to compensate for loss of a alleles. The condition of equilibrium in thesegregation model under random mating requires that

t_ qt2 p

giving t1 -995 -.005025 when t., 1l. The value of s under the mutationmodel is unity and the value of h is taken to be .005 to correspond closely withthe value of t1. The chief result of Crow depends upon the ratio

Genetic load under inbreeding (Inbred load)Genetic load under random mating (Random load)

which is sq 1 under the mutation model2hspq + sq- 2hp + q

and is t1p + t2q 2 under the segregation model.tlp:' + t2q2

For the numerical illustration in the table, this ratio comes out to be 67 forthe mutation model and 2 (as expected) for the segregation model. The argu-ment has been generalized to cover other human loci including those withmultiple alleles. A large value of this ratio (sav, 15), which is often referred toas the B:A ratio criterion, has been used as an evidence that segregational locido not make any substantial contribution to our hereditary burden (Morton,Crow, and Muller, 1956) and a smaller value is taken to be consistent with alarger component of segregational loci (Neel and Schull, 1962).

Random MatingLet us now examine the component parts of this genetic load. We will start

with the population under random mating.In the mutation model, the standard of comparison for calculation of genetic

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load is a hypothetical population consisting of individuals of AA genotype, anoptimum under this model. The genetic load is contributed by the heterozygotesAa and the deleterious homozygotes aa. The contribution of Aa to this load istwice that of aa for the value of h = .005. It will be 8 times and 20 times forvalues of h = .02 and .05, respectively.

In the segregation model, our standard of conparison changes. It is now anonexistent population consisting of individuals of genotype Aa, which is opti-mum under this model and the genetic load is contributed by the genotypes AAand aa. The genetic load contributed by ala remains the same under both models.The genotype AA, which has become relatively slightly reduced in fitness underthis model, contributes an enormous amount of genetic load- 199 times theload contributed by aa. Thus, at the end, the genetic load under the segregationmodel comes out to be 67 times the load under the mutation model. It may bepointed out that such a difference in the genetic loads under the two modelsexists not because of any real demonstration of an inferiority of the segregationalloci in natural populations, but arises as a result of the wvax in which the geneticload is defined. In other words, it is an algebraic artifact.

InbreedingWhen we examine the component parts of the genetic loads under inbreeding,

the artifact becomes even more obvious. We observe that the load contributed bythe genotype aa increases 200 times from a value of .000025 to .005 underboth models. The load contributed by Aa under the mutation model disappears;and finally, the large amount of load contributed bv AA in the segregation modelchanges quite insignificantly from a value of .004975 to .005. The net result isthat the real inbreeding effect under the segregation model, which is not sub-stantially different from that under the mutation model, is obscured by thisenormous weight attached to the homozygote AA.

Another difficultv in the scheme arises from the fact that for the segregationmodel the selection coefficients t1 and t9 cannot remain stationary under inbreed-ing, but change according to the following formulae for gene equilibrium (Li,1955):

- q + Fpt2 p + Fq

When F 0, t1 q as we have taken; butt2 p

when F 1, t- 1t2

In other words, if the gene frequency is to remain stationary, the deleteriousgenotype aa and the genotype AA have to have the same fitness when F = 1.The ratio (inbred load: random load) thus will not be 2, but will be large underall conditions except when aa becomes almost as harmless as AA underinbreeding.

A CRITIQUE OF THE CONCEPT OF GENETIC LOAD

The authors of the concept of genetic load h1ave not stated explicitly theirmain purpose in developing it. If the paper of Muller (1950) is any guide to its

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origin, one of the purposes was probably to bring to focus the role of mutation inhuman morbidity and mortality. The concept will retain its validity if appliedto loci with mutants having deleterious effects under all combinations of geno-type and variations of environment. The concept will, however, remain oftheoretical interest, so long as such mutants cannot be separated out in practice.

From a social point of view, a useful concept would have been the one whichtakes into account the contribution of various genotypes to the maintenance andprogress in relation to their cost to the human society, along the lines ingeniouslyleveloped by Wright (1960). From a humanistic point of view, a useful con-cept should separate the components of fitness like survival and reproductionand assign appropriate weights (depending on cultural values) to these com-ponents and their subcomponents according to the hardship and human suffer-ing they entail. The concept of genetic load as currently formulated does nottake such views in account although it may have originated with such intentions.On the other hand, if the purpose in developing this concept was a more

general one, as it appears from the paper of Crow (1958), such as to under-stand the respective roles of mutational and segregational loci in natural popula-tions, the concept has failed.

The standard of comparison chosen to measure a decline in fitness as original-ly defined by Crow (1958) cannot be accepted. A genotype with optimumfitness in the Darwinian sense is the one whose contribution to future genera-tions is optimum strictly in terms of the number of descendants it leaves. In ahumanistic or a social sense, such a genotype may not necessarily be optimumfor any other objective consideration of human progress. Crowv's revised defini-tion (1960), where an attempt was perhaps made to rectify this defect, runsinto trouble when applied to the segregation model. Under this model, it isdifficult to find out which "factor is under consideration." Is it the segregationof alleles? Not reallyt since they are also segregating under the mutation model.Is it the advantage of the heterozvgote? In that case, the standard populationwill consist of normal homozygotes not acceptable under the first definition.

Furthermore, the concept is developed in such a fashion that it puts thesegregational loci at a disadvantage to start with. This is accomplished by notaccepting any advantage of the heterozygote under the same working model.The artificial nature of this dichotomy of the mutation and segregation modelsmay perhaps become more evident by a consideration of a general scheme out-lined below. This scheme not only, covers the mutation and segregation modelsas its particular cases but reveals a class of loci not covered by either of thesemodels.

GENERAL SCHEME

The fitness of genotypes Aa and aa is considered as relative to the fitness ofAA, which is taken to be unity. The coefficient of inbreeding F is incorporatedin the genotypic frequencies. The scheme stands is follows:

Genotype zAA Aa aa

Frequency p2 + Fpq 2pl(I - F) q2 + Fpqfo < t < 1

Relative fitness 1 1 +- Kt 1 -t tKt > 1

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The scheme gives the mutation model of Crow by substituting the relationsK = -h and t s. Genetic load and mutation rate at equilibrium are given bythe following formulae:

Genetic load tq(q + Fp) - 2Ktpq(I - F)

Mutation rate tq(q - K+ 2Kq ) (1 - F) + Ftq.

The scheme covers the segregation model of Crow by noting the followingset of relations obtained by equating 1 t: 1: I - t2 1 : 1 + Kt : 1 - t.

K t=J;t 2 t- or tlj Kt; t.,= t(1 + K)t I1- ti I1 t- I+ Kt

In the absence of mutation, the condition of equilibrium requires thatt q + Fp Kt2 p + Fq 14- K

The main difference between the result of Crow and the one given here arisesin the measure of genetic load for the segregation model. Under the presentscheme for random mating (F 0), the change in fitness is

~~~~tq:. q_tq! 2Ktpq I4 2q when K q fr equilibrium.

This result, which amounts to a "negative genetic load," shows that theaverage fitness of the population in this case is slightly greater than unity and isbased on the premise that a small advantage in fitness of Aa over AA can com-pensate for the loss of a alleles. For inbreeding, the average fitness is lowered bytq, a value also obtained for mutational loci under this scheme.The apparent contradiction in the results of the two schemes can be resolved

if we consider the variation in fitness of the population under inbreeding inrelation to its initial fitness under random mating. The point is illustrated intable 2 by the numerical example considered before.

It will be seen from the table that the changes in average fitness of the popula-tion as a result of inbreeding are identical under the two schemes as would beexpected. In other words, the appropriate test criterion should be 1-B/i-A andnot B/A. One of the unexpected results that comes out rather clearly is that al-though the inbreeding effect is generally comparable for the two types of loci,it is slightly worse for the segregational ones. It may be indicated here that it isnot essential to take the relative fitness of AA as unity under this general scheme.This value could have been assigned to any one of the other two genotypes.An interesting outcome of this general scheme is to disclose more clearly the

loci in which heterozygotes have a nominal advantage, but still require a sub-stantial amount of mutation to maintain gene equilibrium at a given level. Anumerical example is given in table 3 to illustrate this point. The table indicatesthat the classification of loci on the basis of relative fitness of the heterozygoteis artificial to some extent, as it does not reveal any abrupt differences in be-havior with respect to mutation rates.

There are three points which require some comment in relation to this generalscheme. The first is the condition of equilibrium. Although this condition hasshown itself to be a very convenient tool for theoretical reasoning, it is a question

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of some practical importance as to how long such conditions prevail in naturalpopulations. The number of generations required to approach equilibrium incertain cases is so large that major changes in environment may vitiate any long-term interpretation.

The second limitation to a theoretical formulation arises out of our very staticconcept of environment. We recognize, in principle, that development of anindividual is an interaction between his genotype and his environment. Detailed('enetic observations have led us to a fair amount of understanding of the pos-sible array of genotypes in a population. On the other hand, our knowledgeabout the main components of our environment, their variation in time andplace and their relationship with organisms is very limited. We still continue tothink that any change in environment worth considering by geneticists couldonly occur over a span of hundreds of generations.

The third point relates to the heterozygote vhich is slightly different fromthe normal homozy'gote. We are somewhat in a position to measure the fitness ofa frankly deleterious homozygote or heterozygote. In the case of a heterozygoteslightly different from the normal homozygote there is no easy way; and it ishere that environment and genetic background are both likely to have a pro-portionately larger effect in its expression. It is even possible that the spread ofthe values of relative fitness of the heterozygote is of greater consequence to theultimate fate of the mutant allele than its average value. In this connection, itmay be pointed out that the variate K used in the present scheme permits a bet-ter understanding for small values of q and F which are critical for a transitionof some of the mutational alleles to become segregational ones and a gradualacceptance of rare useful ones amongst them as respectable members of our genepool. For values of q beyond 1/, however, the ratio t1 :t. is more convenient touse.

INTERPRETATION OF INBREEDING EFFECTS

One of the difficulties in the scheme suggested by Crow has arisen out of thefact that some of the primary changes occurring under inbreeding have not beenkept under view. Inbreeding reduces the frequency of heterozvgotes and dis-tributes equally to the two homozy'gotes. The homozvgote which is rare has aproportionately bigger gain. No amount of formulation can alter this basic fact.If the frequency of two alleles at a locus are equal, inbreeding has equal effectson both homozVgotes. This balance progressively changes as the frequency ofone of the alleles gets smaller and smaller. The inbreeding effect is most pro-found on homozygotes determined by' very rare genes.

If we are interested in the utilization of inbreeding effects for any rationalgenetic formulation, we should deal with genes which are very rare and exerttheir deleterious effects primarily through horniozygotes. \W'hether the relativefitness of the heterozygote is slightly better than normal homozygotes or slightlyworse cannot, in principle, be measured by inbreeding effects unless these effectsare different in nature and distinguishable in practice.

The Hardv-W\einberg Law requires random mating and absence of mutationand selection in a closed population to maintain equilibrium. If we introduce

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inbreeding in this population, in which we also add mutation and selection, wecome out with unforseen results. The numerical illustration in table 3 demon-strates these variable effects. For the mutational loci, a fixed value of K leads toan increase in mutation rates for maintenance of the equilibrium. For the segre-gational loci, inbreeding requires greater values of heterozygote advantage formaintenance of the equilibrium.

SUMMARY

Crow suggested a provocative scheme to evaluate the relative importance ofmutational and segregational loci in maintaining our hereditary burden. Thegenotype used as standard of comparison in his mutation model is not the sameas the one used in his segregation model. A logical approach will require a fixedstandard of comparison for the two models. A scheme is outlined here in whichthe same genotype is used for evaluating the inbreeding effects on the two typesof loci. It turns out that the appropriate test criterion for this purpose should be1-B/1 -A and not B/A as suggested by Crow. This and some other pointsrelated to the concept of "genetic load" are discussed.

ACKNOWLEDGMENTS

The author is grateful to Professors J. V. Neel and W. J. Schull for stimulating dis-cussions and a number of useful suggestions made during the preparation of this paperand to all those who read and commented on the manuscript.

REFERENCES

CROW, J. F. 1958. Some possibilities for measuring selection intensities in man. HumanBiol. 30: 1-13.

CROW, J. F. 1960. Mutation and selective balance as factors influencing population fitness.In: Mlolecular Genetics and Human Discase, Gardner, L. I., ed. Springfield: CharlesC. Thomas.

DOBZHANSKY, T. 1957. Genetic loads in natural populations. Science 126: 191-194.FRASER, G. R. 1962. Our genetical "load." A review of some aspects of genetical variation.

Ann. Human Genet. 25: 387-4 15.FISHER, R. A. 1930. The Genetical Theory of Natural Selection. Oxford: Clarendon Press.FORD, E. B. 1940. The New Systematics. Oxford: Oxford University Press.HALDANE, J. B. S. 1932. The Causes of Evolution. London: Harper.HALDANE, J. B. S. 1949. Parental and fraternal correlations for fitness Ann Eug. 14:

288-292.Li, C. C. 1955. The stability of an equilibrium and the average fitness of a population.

Amer. Naturalist 89: 281-295.MORTON, N. E. 1960. The mutational load due to detrimental genes in man. Amer. J.

Hum. Genet. 12: 348-364.MIORTON, N. E., CROW, J. F., AND MULLER, H. J. 1956. An estimate of the mutational

damage in man from data on consanguineous marriages. Proc. Nat. Acad. Sci. 42:855-863.

\ULLER, H. J. 1950. Our load of mutations. Amer. J. Hum. Genet. 2: 111-176.NEEL, J. V., AND SCHULL, W. J. 1962. The effect of inbreeding on mortality and morbidity-

in two Japanese cities. Proc. Nat. Acad. Sci. 48: 573-582.PENROSE, L. S. 1949. The meaning of "fitness" in human populations. Ann. Eug. 14:

301-304.Report of the U. N. Scientific Committee on the Effects of Atomic Radiation. 1962. New

York: United Nations.

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WALLACE, B., AND DOBZHANSKY, T. 1959. Radiation, Genes and Man. New York: HenryHolt.

WRIGHT, S. 1931. Evolution in Mendelial populations. Genetics 16: 97-159.WRIGHT, S. 1960. On the appraisal of genetic effects of radiation. In: The Biological

Effects of Atomic Radiation, Summary Reports. Washington: National Academy ofSciences-National Research Council.

United Nations Publication No. STISOAISer. A/28. 1'358.