J. theor. Biol. (1976) 63, 479-484
LETTER
TO THE EDITOR
The “Cost of Meiosis”:
is there any?
Williams (1971) states: “there is near unanimity on the point that sexuality functions to facilitate long-range evolutionary adaptation, and that it is irrelevant and even detrimental to the reproductive interests of an individual”. This presents evolutionary theory with the problem of accounting for the development of sexual reproduction despite its disadvantage as compared with asexuality. However, two different analyses of what this disadvantage may be have been offered. Williams (1971) writes: “Suppose there were two kinds of females in a population; one produced monoploid, fertilizable eggs, and the other . . . diploid eggs . . . each with exactly the mother’s genetic makeup. These parthenogenetic eggs would each contain twice as much of the mother’s genotype as is present in a reduced and fertilized egg. Other things being equal, the parthenogenetic female would be twice as well represented in the next generation as the normal one. In a few generations, meiosis and sexual recombination should disappear . . . Meiosis is therefore a way in which an individual actively reduces its genetic representation in its own offspring. Any success that these offspring achieve is shared equally by the mother and the father. The parthenogenetic female shares her reproductive success with no one. Sexual reproduction is analogous to a roulette game in which the player throws away half his chips at each spin.” Williams & Mitton (1973) and Williams (1975) have attempted to model situations in which selection for sexual reproduction might proceed despite the “cost of meiosis”. They consider that “the 50:; loss of genetic material in meiotic oogenesis” (WilIiams & Mitton, 1973) necessarily implies a twoto-one disadvantage of sexuality. Maynard Smith (1974) has argued that this disadvantage would not be present in isogamous organisms. A gene will be as well represented in the resulting population if it is transmitted in an isogamete which fuses with another, forming a zygote which then divides, as if the parents had simply divided asexually. But in organisms with anisogamy an allele involved in meiosis will have only half the chance of being transmitted to the next generation that is enjoyed by an allele transferred by parthenogenesis. It follows that there is no special problem in explaining the development 479
480
M.
TREISMAN
AND
R.
DAWKINS
of isogamous sexuality, but the pressures which subsequently favoured anisogamy would have favoured reversion to obligate asexuality even more strongly, since the former would incur and the latter avoid the cost of meiosis. The problem is thus to explain the evolution of heterogametes, but the difficulty envisaged is essentially the same as that assumed by Williams. The discussion below will be concerned only with the evolution of heterogamous sexuality. A different analysis of the disadvantage attaching to sexuality is included in a model put forward earlier by Maynard Smith (1971). He considered a sexual species among whom parthenogenetic females appeared. The number of eggs laid by a female, k, would depend not on her sexual status but on the resources available for this purpose. Since the sexual females each produce k/2 females and k/2 males, while the parthenogenetic females each produce k daughters, the proportion of parthenogenetic females in the population will increase. The greater fertility, measured in daughters, of the parthenogenetic strain is the advantage which the forces maintaining sexuality need to outweigh. These are different arguments. The apparent two-to-one disadvantage implied by the “cost of meiosis” derives from the meiotic reduction division and is invariant; Maynard Smith’s fertility difference depends on the sex ratio, which is flexible. Which argument is valid? Before addressing this question, we may put a general objection to Williams’ notion of the “efficiency” of genotype transmission, as expressed in the quotation given above and in the remark that biologists “have intuitively recognized the sexual process as genetically inefficient (it transmits only part of the genotype of the reproducing individual) and therefore as unfavorable” (Williams & Mitton, 1973). In his valuable book of 1966, Williams has done as much as anyone to discredit Panglossism of the groupselectionist variety, but he now seems to be substituting a new Panglossism of individual selection. In sexually reproducing organisms, individual selection is only incidentally relevant to evolution. Fundamentally it is gene selection which matters. An individual is not a machine for maximizing the proportion of its own genes which appear in the next generation. It is a machine built by a temporary federation of genes, each gene intent on maximizing its representation in the next generation. The reason for this, as Williams (1966) makes clear, is that genes, not individuals, are potentially immortal in a gene pool. The permanence of the particular combination of genes contained in any one individual is of no evolutionary importance. A gene does not “care” what other genes it shares a body with, except in so far as they may assist it to achieve its long term end of persistence in the gene pool. “Individual selection” would tend to favour eternal life. but it is not
LETTER
TO
THE
EDITOR
481
obvious that gene selection would! Therefore, we must suspect the metaphor of the sexual mother who throws away half her chips with each spin. Further, we must note that there are two sorts of “chip”: there is the portion of the genome determining the mode of reproduction, and there is the remainder, and these require to be considered separately. To investigate the effect of manner of reproduction on the fraction of the genome determining procreation, consider a diploid population in which reproductive mode depends on a pair of alleles at one locus. Suppose that SS individuals reproduce sexually, ss are asexual, and for simplicity let heterozygotes not occur. Then asexual mothers wili, of course, have only ss daughters. Sexual mothers will produce haploid S gametes, but since these combine only with S gametes produced by sexual fathers syngamy must always produce homozygous SS offspring. Thus as far as the maternal genotype at the locus determining manner of reproduction is concerned there is no meiotic cost to the mother: that part of her genotype is as well represented in her offspring as is that of the parthenogenetic female in hers. Meiosis does not result in the maternal reproduction-determining genome being diluted in her descendants as a result of her “sharing” her reproductive success with the father. Thus selection between the two alleles, and the modes of reproduction they determine, must depend only on the fertility of the two types and the fitness of their offspring. But what of the non-reproduction-determining residue of the mother’s genome? In parthenogenesis this is wholly preserved in the daughters. If it is the case that it is diluted in the descendants of sexual females, this will be not a cost but a consequence of sexual reproduction. As emphasized above, the preservation of similarity between successive generations is not a force directing selection. Loss of nonsexual genotypical similarity will not in itself levy a price that must be paid in order for selection for S to proceed. Changes in genotype may affect this selection: recombinational load may oppose it: the production of favourable recombinants may favour it; but these are quite different considerations from Williams’ meiotic cost. But, in any case, is there really a relative loss of representation of the nonsexual genome in the sexual female’s offspring? It is a critical feature of the notion of meiotic cost that it is normally inescapable. Thus it would deprive it of importance if it could be shown that one or more simple systems for determining the manner of reproduction did not incur such a cost. Consider again a population in which SS individuals reproduce sexually and ss asexually (heterozygotes do not occur or else they reproduce asexually), and which consists of nP parthenogenetic females, n, sexual females and r~r, sexual males, where r is the ratio of males to females. To avoid the objection that an asexual clone cannot be considered to be part of a Mendelian
482
M.
TREISMAN
AND
R.
DAWKINS
population we may assume that the genes for parthenogenesis have imperfect penetrance, so that lineages may alternate irregularly between the two modes of reproduction. However, for the several generations covered by the model it will be simplest to let descendants retain their parents’ status. We assume that each female, parthenogenetic or sexual, produces k otfspring. It is readily seen that a given asexual female, ,4fi, will produce l//7, of the members of the first filial asexua! generation, and the same proportion of any later generation, assuming that her genotype is of average fitness and there are no disturbing factors. The genotype of a given sexual female, S~j, will constitute l/(1 +r)n, of the initial sexual gene pool. (We are, of course, concerned with the genotype at a locus. Thus the effects of recombination are irrelevant.) In the females of the sexual F, generation the gene pool will contain a proportion l/24 of genes identical by descent with those of Sf;. and the same will be true of the male gene pool. Assuming random mating and no selection, the conditions for a Hardy-Weinberg equilibrium now obtain and the Sf, genotype will continue in this proportion in subsequent generations. If the sex ratio is unity this will be the proportion initially considered, for r > 1 it will be greater than the initial proportion, and for I’ < 1 it will be less, but in each case it will be stable. Since there is no cause to suppose that gene frequencies are initially other than equal in the two sexes, it might seem reasonable to start with a genotype present among both males and females in the same initial proportion, say l/n, in each case. Then the Hardy-Weinberg law would apply immediately and genes identical by descent with the starting genotypes would continue indefinitely to constitute this same proportion of the gene pool, whatever I hc sex ratio. The argument can be put more simply by noting that if .4j; is one of an original population of n parthenogenetic animals, and Sfj is one 01 IZ(=2n,) original sexual animals, then in each case, other things equal, their genotype must continue to constitute l//z of the respective population’s gene pool in subsequent generations. Thus neither for the reproduction-determining part of the genome (which is here under selection), nor for the residue (which is not), does a sexual female “actively reduce its genetic representation in its own offspring” (Williams, 1971). Meiotic cost in this sense appears to be a mistaken concept. The relative contribution of Sfj to the total population’s gene pool at any later date will be less than that of /1.~i if and only if the fitness or the fertility (measured in females) of the sexual females is less than that of their parthenogenetic conspecifics. If both types of female each produced k equally fit female offspring then both would continue in the same proportion in the common population. When fertility is equal in this sense, any slight advantage
LETTER
TO
THE
EDITOR
483
of sexual reproduction would result in its selection. Thus the forces selecting sexual reproduction must overcome the disadvantage not of “meiotic cost” but of differential fertility, as suggested by Maynard Smith (1971). The argument above was developed for homozygous sexual (SS) and asexual (ss) organisms, with heterozygotes asexual or ignored. To examine the case in which SS and Ss are sexual, ss asexual, we may consider an initial population of n, sexual and nP parthenogenetic females, each producing k daughters, the initial frequency of S among the sexual animals being p,,, and of s, q,. Then the frequency of the S allele in the combined population will be P,,~~/(H~+IQ. In each sexual generation the ss animals produced are recruited to the asexual population. Then it can be shown that, asymptotically, the proportion of sexual animals (now homozygous SS) in the population as a whole will be pons/(np + n,) and this will also be the frequency of the S allele in the combined population. Thus, again, meiosis results in no fall in the representation of the allele which causes reproduction to be sexual, but its distribution changes to produce wholly homozygous sexual and asexual populations, with no heterozygotes, as assumed in the case considered earlier. Another
way of putting the argument
would
be to note that we shouId
reach much the same conclusions if we were dealing with an allele, s, which produced raised fertility and complete positive assortative mating in the homozygote. But in this case there could be no doubt of the inapplicability of the concept of meiotic cost. Indeed, it is sufficient to observe that, from first principles, a neutral gene will not be reduced in frequency as a result of sexual reproduction, for it to be evident that the concept, as usually presented. is invalid. The difficulty raised by sexual reproduction is not that there is a fixed two-to-one cost to it, deriving from the haploid-diploid ratio and invariant, but that there may be a difference in fertility fin daughters) deriving from the sex ratio, which is flexible. Since sex ratios commonly tend to unity (Maynard Smith, 1971) this cost will also tend to two-to-one. It is possible that the sex ratio may not have been. unity in at least some cases in which sporadic sexuality started to become more general and to displace asexual reproduction. Thus sexuality might have developed by a gradual increase in the presence (and utilization) of males in an initially mainly parthenogenetic female population, in which case the sex ratio, Y, could well have been considerably less than one to start with. Sexual females would then each produce [l/(1 +r)]k femaIe offspring, a number not much less than the X young produced by a parthenogenetic female, for Y small. The shortfall would be compensated for if the average fitness of sexual females exceeded that of the asexual by more than the ratio (1 +u)/l, which could have been considerably less than two-to-one. As selection in the direction of a sex ratio of unity proceeded, asexual reproduct ion would have become relatively more
484
M.
TREISMAN
AND
R.
DAWKINS
attractive. Thus the stability of sexual reproduction in so many species indicates that it must have been maintained by advantages easily able to outweigh even the two-to-one disadvantage in fertility implied by a sex ratio of one. A model which may account for this is presented elsewhere (Treisman, 1976). University of Oxford, Department of Experimental Oxford OX1 3UD. University of Oxjbrd, Department of Zoology, Oxford OX1 3PS. (Received 30 October
MICHEL
TREISMAN
RICHARD
DAWKINS
Psychoiogjz,
1975, and in revised form 15 December
1975)
This paper was written while M. Treismanwas in receipt of support from the ScienceResearchCouncil. REFERENCES SMITH,J. (1971).The Origin and Maintenanceof Sex. In Group Selecrion (ed. G. C. Williams).Chicago:Aldine-Atherton. MAYNARD SMITH, J. (1974).Genetics, 78,299. MAYNARD
TREISMAN, WILLIAMS,
Press. WILLIAMS, WILLIAMS, WILLIAMS,
M. (1976). J. theor. Biol. 60,421. G. C. (1966).Adaptation and Natural Selection. Princeton:PrincetonUniversity
G. C. (Ed.), (1971).Group Selection. Chicago:Aldine-Atherton. Princeton:PrincetonUniversityPress.
G. C. (1975).Sexand Evolution. G. C. & MITTON, J. B. (1973). J.
theor. Biol. 39, 545.
LETTER
TO THE EDITOR
The “Cost of Meiosis”:
is there any?
Williams (1971) states: “there is near unanimity on the point that sexuality functions to facilitate long-range evolutionary adaptation, and that it is irrelevant and even detrimental to the reproductive interests of an individual”. This presents evolutionary theory with the problem of accounting for the development of sexual reproduction despite its disadvantage as compared with asexuality. However, two different analyses of what this disadvantage may be have been offered. Williams (1971) writes: “Suppose there were two kinds of females in a population; one produced monoploid, fertilizable eggs, and the other . . . diploid eggs . . . each with exactly the mother’s genetic makeup. These parthenogenetic eggs would each contain twice as much of the mother’s genotype as is present in a reduced and fertilized egg. Other things being equal, the parthenogenetic female would be twice as well represented in the next generation as the normal one. In a few generations, meiosis and sexual recombination should disappear . . . Meiosis is therefore a way in which an individual actively reduces its genetic representation in its own offspring. Any success that these offspring achieve is shared equally by the mother and the father. The parthenogenetic female shares her reproductive success with no one. Sexual reproduction is analogous to a roulette game in which the player throws away half his chips at each spin.” Williams & Mitton (1973) and Williams (1975) have attempted to model situations in which selection for sexual reproduction might proceed despite the “cost of meiosis”. They consider that “the 50:; loss of genetic material in meiotic oogenesis” (WilIiams & Mitton, 1973) necessarily implies a twoto-one disadvantage of sexuality. Maynard Smith (1974) has argued that this disadvantage would not be present in isogamous organisms. A gene will be as well represented in the resulting population if it is transmitted in an isogamete which fuses with another, forming a zygote which then divides, as if the parents had simply divided asexually. But in organisms with anisogamy an allele involved in meiosis will have only half the chance of being transmitted to the next generation that is enjoyed by an allele transferred by parthenogenesis. It follows that there is no special problem in explaining the development 479
480
M.
TREISMAN
AND
R.
DAWKINS
of isogamous sexuality, but the pressures which subsequently favoured anisogamy would have favoured reversion to obligate asexuality even more strongly, since the former would incur and the latter avoid the cost of meiosis. The problem is thus to explain the evolution of heterogametes, but the difficulty envisaged is essentially the same as that assumed by Williams. The discussion below will be concerned only with the evolution of heterogamous sexuality. A different analysis of the disadvantage attaching to sexuality is included in a model put forward earlier by Maynard Smith (1971). He considered a sexual species among whom parthenogenetic females appeared. The number of eggs laid by a female, k, would depend not on her sexual status but on the resources available for this purpose. Since the sexual females each produce k/2 females and k/2 males, while the parthenogenetic females each produce k daughters, the proportion of parthenogenetic females in the population will increase. The greater fertility, measured in daughters, of the parthenogenetic strain is the advantage which the forces maintaining sexuality need to outweigh. These are different arguments. The apparent two-to-one disadvantage implied by the “cost of meiosis” derives from the meiotic reduction division and is invariant; Maynard Smith’s fertility difference depends on the sex ratio, which is flexible. Which argument is valid? Before addressing this question, we may put a general objection to Williams’ notion of the “efficiency” of genotype transmission, as expressed in the quotation given above and in the remark that biologists “have intuitively recognized the sexual process as genetically inefficient (it transmits only part of the genotype of the reproducing individual) and therefore as unfavorable” (Williams & Mitton, 1973). In his valuable book of 1966, Williams has done as much as anyone to discredit Panglossism of the groupselectionist variety, but he now seems to be substituting a new Panglossism of individual selection. In sexually reproducing organisms, individual selection is only incidentally relevant to evolution. Fundamentally it is gene selection which matters. An individual is not a machine for maximizing the proportion of its own genes which appear in the next generation. It is a machine built by a temporary federation of genes, each gene intent on maximizing its representation in the next generation. The reason for this, as Williams (1966) makes clear, is that genes, not individuals, are potentially immortal in a gene pool. The permanence of the particular combination of genes contained in any one individual is of no evolutionary importance. A gene does not “care” what other genes it shares a body with, except in so far as they may assist it to achieve its long term end of persistence in the gene pool. “Individual selection” would tend to favour eternal life. but it is not
LETTER
TO
THE
EDITOR
481
obvious that gene selection would! Therefore, we must suspect the metaphor of the sexual mother who throws away half her chips with each spin. Further, we must note that there are two sorts of “chip”: there is the portion of the genome determining the mode of reproduction, and there is the remainder, and these require to be considered separately. To investigate the effect of manner of reproduction on the fraction of the genome determining procreation, consider a diploid population in which reproductive mode depends on a pair of alleles at one locus. Suppose that SS individuals reproduce sexually, ss are asexual, and for simplicity let heterozygotes not occur. Then asexual mothers wili, of course, have only ss daughters. Sexual mothers will produce haploid S gametes, but since these combine only with S gametes produced by sexual fathers syngamy must always produce homozygous SS offspring. Thus as far as the maternal genotype at the locus determining manner of reproduction is concerned there is no meiotic cost to the mother: that part of her genotype is as well represented in her offspring as is that of the parthenogenetic female in hers. Meiosis does not result in the maternal reproduction-determining genome being diluted in her descendants as a result of her “sharing” her reproductive success with the father. Thus selection between the two alleles, and the modes of reproduction they determine, must depend only on the fertility of the two types and the fitness of their offspring. But what of the non-reproduction-determining residue of the mother’s genome? In parthenogenesis this is wholly preserved in the daughters. If it is the case that it is diluted in the descendants of sexual females, this will be not a cost but a consequence of sexual reproduction. As emphasized above, the preservation of similarity between successive generations is not a force directing selection. Loss of nonsexual genotypical similarity will not in itself levy a price that must be paid in order for selection for S to proceed. Changes in genotype may affect this selection: recombinational load may oppose it: the production of favourable recombinants may favour it; but these are quite different considerations from Williams’ meiotic cost. But, in any case, is there really a relative loss of representation of the nonsexual genome in the sexual female’s offspring? It is a critical feature of the notion of meiotic cost that it is normally inescapable. Thus it would deprive it of importance if it could be shown that one or more simple systems for determining the manner of reproduction did not incur such a cost. Consider again a population in which SS individuals reproduce sexually and ss asexually (heterozygotes do not occur or else they reproduce asexually), and which consists of nP parthenogenetic females, n, sexual females and r~r, sexual males, where r is the ratio of males to females. To avoid the objection that an asexual clone cannot be considered to be part of a Mendelian
482
M.
TREISMAN
AND
R.
DAWKINS
population we may assume that the genes for parthenogenesis have imperfect penetrance, so that lineages may alternate irregularly between the two modes of reproduction. However, for the several generations covered by the model it will be simplest to let descendants retain their parents’ status. We assume that each female, parthenogenetic or sexual, produces k otfspring. It is readily seen that a given asexual female, ,4fi, will produce l//7, of the members of the first filial asexua! generation, and the same proportion of any later generation, assuming that her genotype is of average fitness and there are no disturbing factors. The genotype of a given sexual female, S~j, will constitute l/(1 +r)n, of the initial sexual gene pool. (We are, of course, concerned with the genotype at a locus. Thus the effects of recombination are irrelevant.) In the females of the sexual F, generation the gene pool will contain a proportion l/24 of genes identical by descent with those of Sf;. and the same will be true of the male gene pool. Assuming random mating and no selection, the conditions for a Hardy-Weinberg equilibrium now obtain and the Sf, genotype will continue in this proportion in subsequent generations. If the sex ratio is unity this will be the proportion initially considered, for r > 1 it will be greater than the initial proportion, and for I’ < 1 it will be less, but in each case it will be stable. Since there is no cause to suppose that gene frequencies are initially other than equal in the two sexes, it might seem reasonable to start with a genotype present among both males and females in the same initial proportion, say l/n, in each case. Then the Hardy-Weinberg law would apply immediately and genes identical by descent with the starting genotypes would continue indefinitely to constitute this same proportion of the gene pool, whatever I hc sex ratio. The argument can be put more simply by noting that if .4j; is one of an original population of n parthenogenetic animals, and Sfj is one 01 IZ(=2n,) original sexual animals, then in each case, other things equal, their genotype must continue to constitute l//z of the respective population’s gene pool in subsequent generations. Thus neither for the reproduction-determining part of the genome (which is here under selection), nor for the residue (which is not), does a sexual female “actively reduce its genetic representation in its own offspring” (Williams, 1971). Meiotic cost in this sense appears to be a mistaken concept. The relative contribution of Sfj to the total population’s gene pool at any later date will be less than that of /1.~i if and only if the fitness or the fertility (measured in females) of the sexual females is less than that of their parthenogenetic conspecifics. If both types of female each produced k equally fit female offspring then both would continue in the same proportion in the common population. When fertility is equal in this sense, any slight advantage
LETTER
TO
THE
EDITOR
483
of sexual reproduction would result in its selection. Thus the forces selecting sexual reproduction must overcome the disadvantage not of “meiotic cost” but of differential fertility, as suggested by Maynard Smith (1971). The argument above was developed for homozygous sexual (SS) and asexual (ss) organisms, with heterozygotes asexual or ignored. To examine the case in which SS and Ss are sexual, ss asexual, we may consider an initial population of n, sexual and nP parthenogenetic females, each producing k daughters, the initial frequency of S among the sexual animals being p,,, and of s, q,. Then the frequency of the S allele in the combined population will be P,,~~/(H~+IQ. In each sexual generation the ss animals produced are recruited to the asexual population. Then it can be shown that, asymptotically, the proportion of sexual animals (now homozygous SS) in the population as a whole will be pons/(np + n,) and this will also be the frequency of the S allele in the combined population. Thus, again, meiosis results in no fall in the representation of the allele which causes reproduction to be sexual, but its distribution changes to produce wholly homozygous sexual and asexual populations, with no heterozygotes, as assumed in the case considered earlier. Another
way of putting the argument
would
be to note that we shouId
reach much the same conclusions if we were dealing with an allele, s, which produced raised fertility and complete positive assortative mating in the homozygote. But in this case there could be no doubt of the inapplicability of the concept of meiotic cost. Indeed, it is sufficient to observe that, from first principles, a neutral gene will not be reduced in frequency as a result of sexual reproduction, for it to be evident that the concept, as usually presented. is invalid. The difficulty raised by sexual reproduction is not that there is a fixed two-to-one cost to it, deriving from the haploid-diploid ratio and invariant, but that there may be a difference in fertility fin daughters) deriving from the sex ratio, which is flexible. Since sex ratios commonly tend to unity (Maynard Smith, 1971) this cost will also tend to two-to-one. It is possible that the sex ratio may not have been. unity in at least some cases in which sporadic sexuality started to become more general and to displace asexual reproduction. Thus sexuality might have developed by a gradual increase in the presence (and utilization) of males in an initially mainly parthenogenetic female population, in which case the sex ratio, Y, could well have been considerably less than one to start with. Sexual females would then each produce [l/(1 +r)]k femaIe offspring, a number not much less than the X young produced by a parthenogenetic female, for Y small. The shortfall would be compensated for if the average fitness of sexual females exceeded that of the asexual by more than the ratio (1 +u)/l, which could have been considerably less than two-to-one. As selection in the direction of a sex ratio of unity proceeded, asexual reproduct ion would have become relatively more
484
M.
TREISMAN
AND
R.
DAWKINS
attractive. Thus the stability of sexual reproduction in so many species indicates that it must have been maintained by advantages easily able to outweigh even the two-to-one disadvantage in fertility implied by a sex ratio of one. A model which may account for this is presented elsewhere (Treisman, 1976). University of Oxford, Department of Experimental Oxford OX1 3UD. University of Oxjbrd, Department of Zoology, Oxford OX1 3PS. (Received 30 October
MICHEL
TREISMAN
RICHARD
DAWKINS
Psychoiogjz,
1975, and in revised form 15 December
1975)
This paper was written while M. Treismanwas in receipt of support from the ScienceResearchCouncil. REFERENCES SMITH,J. (1971).The Origin and Maintenanceof Sex. In Group Selecrion (ed. G. C. Williams).Chicago:Aldine-Atherton. MAYNARD SMITH, J. (1974).Genetics, 78,299. MAYNARD
TREISMAN, WILLIAMS,
Press. WILLIAMS, WILLIAMS, WILLIAMS,
M. (1976). J. theor. Biol. 60,421. G. C. (1966).Adaptation and Natural Selection. Princeton:PrincetonUniversity
G. C. (Ed.), (1971).Group Selection. Chicago:Aldine-Atherton. Princeton:PrincetonUniversityPress.
G. C. (1975).Sexand Evolution. G. C. & MITTON, J. B. (1973). J.
theor. Biol. 39, 545.
