Journal of Heredity 2004:95(4):277-283
© 2004 The American Genetic Association
Premeiotic Clusters of Mutation and the Cost of Natural Selection
From the Department of Biological Sciences, Bowling Green State University, Bowling Green, OH 43403 (Woodruff and Gu); and Department of Zoology, University of Oklahoma, Norman, OK 73019 (Thompson).
Address correspondence to R. C. Woodruff at the address above, or e-mail: rwoodru{at}bgnet.bgsu.edu.
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Abstract |
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Haldane stated that there is a cost of natural selection for new beneficial alleles to be substituted over time. Most of this cost, which leads to "genetic deaths," is in the early generations of the substitution process when the new allele is low in frequency. It depends on the initial frequency and dominance value, but not the selection coefficient, of the advantageous allele. There have been numerous suggestions on how to reduce the cost for preexisting genetic variation that goes from disadvantageous, or neutral, to advantageous with a change in the environment. However, the cost of natural selection for new alleles that arise by mutation is assumed to be high, based on the assumption that new mutant alleles arise in natural populations as single events [1/(2N) of the total alleles]. However, not all mutant alleles arise as single events. Premeiotic mutations occur frequently in individuals (germinal mosaics), giving rise to multiple copies of identical mutant alleles called a "cluster" (C) with an initial allele frequency of C/(2N) instead of 1/(2N). These clusters of new mutant alleles reduce the cost of natural selection in direct proportion to the relative size of the cluster. Hence new advantageous alleles that arise by mutation have the greatest chance of going to fixation if they occur in large clusters in small populations.
"Haldane (1957) gave expressions for the ‘cost’ of natural selection, that is, for the total number of deaths, or their equivalents in reduced fertility, sometimes called ‘genetic deaths,’ which must occur in a population of constant size before a gene is replaced by one of its allelomorphs" (Haldane 1960). "In my opinion, the problem (Haldane's dilemma) was never solved by Wallace or anyone else. It merely faded away, because people got interested in other things. I think the time has come for renewed discussions and experimental attacks on Haldane's dilemma" (Williams 1992).
Haldane (1957) stated that there is a cost to organisms for new beneficial alleles to become fixed over time. This cost of natural selection, which has also been called the substitutional (or evolutional) load (Kimura 1960), is caused by the production of individuals that have the original less-fit allele during the time to fixation (or to a mutation selection equilibrium point) of the new beneficial allele. A simple representation of the cost of natural selection is shown in Figure 1.
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Haldane (1957, 1960) observed that the mean cost is about 30 for diploid organisms, meaning that for an allele substitution on average about 30 times the population size will suffer a "genetic death," and this cost sets an upper limit of about one substitution every 300 generations for mammals. Many have referred to this cost as Haldane's dilemma.
Kimura found the substitutional load to be too large to be tolerated by any mammalian species and used this result as the main argument for his neutral theory of molecular evolution (Kimura 1968, 1983; Kimura and Maruyama 1969). In support of this high cost in mammals, Fay et al. (2001) estimated that about 35% of amino acid substitutions between humans and Old World monkeys are due to positive selection and that there has been about one advantageous substitution every 200 years since these two groups separated 30 million years ago. After making several simplifying assumptions, Nachman (2001) suggests that there has been about one adaptive substitution every 300 years since the split of humans and chimpanzees about 5 million years ago, giving a total of about 16,700 adaptive substitutions, and probably more frequent substitutions during the human/Old World monkey evolution. Hence, based on the above estimations of substitution rates and a generation time of about 20 years for humans and chimpanzees (Nachman and Crowell 2000), there has been approximately one advantageous substitution every 15 generations during human/chimpanzee evolution. In addition, Smith and Eyre-Walker (2002) estimated that Drosophila simulans and Drosophila yakuba have undergone an adaptive substitution every 450 generations. These results can be compared with the estimation of Haldane (1957): "It is suggested that, in horotelic evolution, the mean time taken for each gene substitution is about 300 generations."
However, not everyone agrees that the cost is as large as proposed by Haldane and Kimura. For example, the cost for one allele or a group of alleles of different genes may be reduced by truncation or soft selection, by a subdivided population, by alleles of different loci not acting independently, by alleles changing slowly from deleterious to neutral to advantageous, and by no change in the environment. Some even state that there is no cost for allele substitutions, based in part because cost depends on a comparison with an ideal and very rare genotype (although not all agree; see discussions in Barton 1995; Bruce 1964, 1969; Crow 1970; Ewens 1970, 1993; Feller 1967; Felsenstein 1971; Flake and Grant 1974; Gillespie 1991; Grant and Flake 1974; Haldane 1960; Hoyle 1999; Kimura and Crow 1969; King 1967; Mather 1969; Maynard Smith 1968; Mayr 1963; Milkman 1967; O'Donald 1969; Sved 1968; Sved et al. 1967; Van Valen 1963; Wallace 1991; Wright 1977). But even if there is a cost to natural selection as proposed by Haldane, patterns of mutation can cause it to be significantly reduced, as we discuss in the next section.
Haldane (1957) showed that the cost of natural selection depends on the initial frequency of the favorable allele and not on its selection coefficient. Hence most of the cost is in the early generations of the substitution process. This has led to the speculation that one way to reduce the cost would be for the advantageous allele not to be initially rare and to begin as only slightly disadvantageous or neutral, as might occur, for example, when originating in a different environment (Crow and Kimura 1970). An example is heavy metal tolerance in plants, where some plants with the tolerance allele(s) seem to be less fit in an environment without heavy metals but more fit in a mining area (Macnair 1987). The substitutional cost could also be reduced if the beneficial allele has dominance or occurs in a small population. These mechanisms would give more importance to evolution under the direction of preexisting genetic variation than mutation. But what happens to the cost of natural selection when a beneficial allele arises as a new mutation?
It has traditionally been assumed that mutations arise in natural populations as single events with a frequency of 1/(2N) of the total alleles at that locus. If this is true, then the cost to fixation will be high and will depend on population size, since po = 1/(2N) is a key parameter in determining cost. However, not all mutant alleles arise as single events. It is increasingly clear that premeiotic mutations occur frequently in individuals that give rise to multiple copies of identical mutant alleles, called clusters or germinal mosaics (Figure 2) (see discussions of this topic in Drake et al. 1998; Drost and Lee 1998; Fu and Huai 2003; Huai and Woodruff 1997, 1998; Neel 1998; Russell and Russell 1996; Selby 1998; Thompson et al. 1998; Woodruff and Thompson 1992, 2002; Woodruff et al. 1996). These clusters are common in all higher organisms that have been tested, from worms to insects to vertebrates, and have been observed for all types of genetic damage, including base-pair changes, frame-shift events, tandem repeats, insertions, excisions, chromosome rearrangements (deficiencies, duplications, inversions, and translocations), and aneuploidy (Woodruff et al. 1996).
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Influence of Premeiotic Clusters of Mutation on the Cost of Natural Selection |
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TopAbstractInfluence of Premeiotic Clusters...DiscussionReferences |
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Haldane (1957) first formulated the cost of natural selection for haploid and diploid organisms, and Crow (1968) and Crow and Kimura (1970) discussed an improved derivation of this formula. With the following diploid fitness model, the cost of natural selection is given for h (the dominance coefficient).
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1 (i.e., 0 < h < 1). Using a stochastic model and diffusion equations, Kimura and Ohta (1971) got a similar cost. Note that s (the selection coefficient) is not part of this formula, and the cost is determined by h and the initial frequency of the beneficial mutant allele (po). From the formulas it is clear that most of the cost occurs at the beginning of the substitution process when the allele is rare, that is, when po is small. For example, with h = 0.5 and N = 10,000, the cost is 19.8 for po = 0.00005 [= 1/(2N)], whereas the cost is 15.2 for po = 0.0005 [= 10/(2N)]. Crow and Kimura (1970) proposed that one way to reduce the cost would be if the new beneficial allele starts at a high frequency. This is assumed to occur either by the allele being initially common, but not advantageous, or for there to be a high mutation rate giving rise to multiple, independent forms of the new allele. An additional mechanism would be for an advantageous allele to migrate into a population that does not contain this allele.
If new advantageous alleles are due to mutation, there is another more likely mechanism to reduce the cost of natural selection: the mutation arises as a premeiotic cluster, especially in a small population (Woodruff et al. 1996). In this event, the new advantageous allele would occur in an initial frequency (po) of C/(2N) instead of 1/(2N), with C being the cluster size. How does a cluster of mutation affect the cost of natural selection as given in equation (2)? As the size of the cluster (C) increases, the cost of natural selection decreases. This is shown in Figure 3, where the cost is determined for single mutations (C = 1) up to a cluster of C = 30, with h values ranging from 0.01 to 0.8 and po values ranging from 0.0001 to 0.003 (N = 5000). For example, the cost at h = 0.5 for a single mutation to go to fixation is 18.4, whereas the cost for a cluster of 30 is 11.6. In this example, assuming a constant population size, a total of 92,000 genetic deaths would occur during the substitution process if the mutant allele arises as a single event, whereas only 58,000 genetic deaths would occur if it arises in a cluster of 30, giving a 37% decrease in the number of expected genetic deaths.
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Alternatively, one can view the effect in terms of the population excess needed for a single substitution (Crow 1968). Beginning with a single new mutant allele, it would require about a 6.1% reproductive excess each generation for a species to undergo one gene substitution in 300 generations, but it would only require about a 3.9% reproductive excess if the new allele arose in a cluster of 30. Additional examples of the cost of natural selection and associated genetic deaths are given in Table 1.
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It should also be noted that the effect of clusters on the cost is greater with higher h values (Figure 4). Clearly the cost goes up as the dominance of the advantageous allele goes down, and the cost is reduced at all h values by clusters. Hence the more dominant the advantageous allele and the larger the cluster, the lower the cost of natural selection.
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Figure 5 also shows the influence of clusters and population size on the cost of natural selection with different h values. The lowest cost is in the presence of a large cluster in a small population.
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Discussion |
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TopAbstractInfluence of Premeiotic Clusters...DiscussionReferences |
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Haldane (1957) was concerned with the cost of natural selection for preexisting genetic variation using po = 0.00001 for partially or wholly dominant alleles and po = 0.01 for recessive ones. On the other hand, in this article we are concerned with the cost of new beneficial alleles that arise by mutation. There may be times that there is not the appropriate genetic variation for continuous adaptive evolution and evolution is stalled until a new advantageous allele(s) arises by mutation. Although beneficial mutations are usually assumed to be rare events in comparison with deleterious or neutral mutations, when advantageous alleles do occur, they have a much higher probability of becoming fixed than do neutral alleles, which may become advantageous later. For example, the probability of fixation of an additive advantageous allele with s = 0.1 in a population of N = 1000 is about 0.1, compared with a probability of 0.0005 for a neutral mutant if it arises as a single allele.
However, during the process of fixation of these beneficial alleles, the cost of natural selection will limit the number of advantageous alleles that can be in transition to fixation at any one time (Haldane 1957; Kimura 1995). Other than having the new mutant allele be dominant, there are few mechanisms that reduce this cost. For example, the cost can be reduced by an increase in population size during the substitution process (Ewens 1967; Otto and Whitlock 1997) and tight linkage to other advantageous or deleterious genes may alter the cost (Barton 1995; Charlesworth and Charlesworth 1998). Yet if population size is kept constant, as assumed by Haldane (1957), one has to look elsewhere for mechanisms to reduce this cost. A constant small population size will help, but the occurrence of new beneficial mutants in such a population would be extremely rare and would still carry a cost. Cell lineage selection may also increase the proportion of gametes in an individual with a new beneficial mutant allele (Hastings 1989, 1991; Otto and Hastings 1998; Otto and Orive 1995), but the cost of natural selection will occur in progeny and future generations of this individual.
As shown herein, another mechanism to reduce the cost of natural selection for a new advantageous allele is for the allele to arise as a cluster in an individual, especially in small populations. Since such premeiotic clusters of mutation are not rare and probably occur in all eukaryotes, this could be a common, even likely, mechanism to reduce the cost of natural selection and may therefore increase the importance of mutation in adaptive evolution.
Adaptive evolution can occur by two main mechanisms: either by selection on preexisting genetic variation that was previously neutral or deleterious in a former environment, but that becomes advantageous in a new environment [examples are industrial melanism in peppered moths (Lees 1981) and heavy metal tolerance in plants (Macnair 1981)], or by selection on new beneficial alleles that arise by mutation [examples are warfarin resistance in rats (Drummond 1966) and herbicide resistance in plants (Macnair 1981)]. One of the main reasons that selection of new mutant alleles is considered less likely than selection of preexisting genetic variation is that beneficial mutations are assumed to be very rare, and when they do occur, they arise in a low frequency of 1/(2N). However, the rate of beneficial mutations in eukaryotes is not actually known (Bataillon 2000; Gessler and Xu 1998), although recent reports suggest that they may not be so rare in bacteria (Giraud et al. 2001; Remold and Lenski 2001; Ritz et al. 2001) and bacteriophage (Burch and Chao 1999; Wichman et al. 1999), and slightly beneficial ones may not be uncommon (Kondrashov 1998). For example, about 45% of all amino acid substitutions in Drosophila simulans and at least 25% in Drosophila melanogaster are beneficial (Bustamante et al. 2002; Fay et al. 2002; Smith and Eyre-Walker 2002).
An additional example of the possible high cost of natural selection is the estimation that during the evolution of humans and Old World monkeys, advantageous substitutions are estimated to have occurred at the amazing rate of one change about every 10 generations (Fay et al. 2001). There have also been about four to six amino acid substitutions per human diploid genome per generation since human divergence from chimpanzees (Eyre-Walker and Keightley 1999; Keightley and Eyre-Walker 2000). For those substitutions that arose by mutation, there was a potentially large cost of natural selection. There must have been ways to reduce this cost, including small population sizes, soft selection, epistasis, genomic duplications (Johnson et al. 2001), and as we show here, premeiotic clusters of mutation.
Although premeiotic clusters of mutation do not eliminate the cost of natural selection, the occurrence of multiple copies of the same advantageous allele at one time in one place can substantially decrease this cost. Furthermore, this reduction will increase the number of favorable mutant alleles that can simultaneously go to fixation in a population. These mutation clusters may therefore increase the importance of mutation in adaptive evolution.
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Acknowledgments |
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We thank Juan Bouzat, Pierre Capy, James Crow, Damian Gessler, Philip Hedrick, Norman Johnson, Volker Loeschcke, Sarah Otto, and John Sved for their comments on this manuscript. This work was partially funded by NASA grant NAG2-1427.
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Footnotes |
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Corresponding Editor: Ross MacIntyre
Received July 29, 2003
Accepted March 29, 2004
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