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Department of Biology, University of Rochester, Rochester, New York 14627
1 Address for correspondence: Department of Biology, Hutchison Hall, River Campus, University of Rochester, Rochester, New York 14627-0211.
E-mail: jfry{at}mail.rochester.edu
RECENTLY, PETERS et al. (2003) reported that hybrids between EMS-mutagenized lines of Caenorhabditis elegans and the ancestral line in some cases had higher productivity and relative fitness than either parental line. They interpreted this as evidence for overdominance (heterozygote superiority) of EMS-induced mutations. A number of other authors have made claims for overdominance of induced or spontaneous mutations (see PETERS et al. 2003 for references). For example, using EMS-treated lines in Drosophila melanogaster, MUKAI (1970) observed a negative correlation between heterozygous and homozygous viability among the lines with relatively high homozygous viability, which he interpreted as evidence for overdominance.
If overdominant mutations are as common as these studies seem to suggest, then polymorphisms maintained by heterozygote superiority should be widespread. In spite of considerable effort, however, such polymorphisms have been documented in only a handful of cases. In addition, evidence from Drosophila is inconsistent with the view that a large fraction of genetic variation in life-history traits is maintained by heterozygote superiority (CHARLESWORTH and HUGHES 1999). This suggests that other explanations for the apparent overdominance of new mutations should be sought.
In this note I show that results like those of PETERS et al. (2003) and MUKAI (1970) can be explained if deleterious alleles are uniformly partially recessive, with a small fraction of mutations being beneficial under both heterozygous and homozygous conditions. Under these assumptions, apparent overdominance can readily result from the combined effects of the deleterious and beneficial mutations.
To illustrate this point, I consider a simple model in which all deleterious alleles reduce fitness by hs and s under heterozygous and homozygous conditions, respectively. Most mutations are from the beneficial allele to the deleterious one, but a few are from deleterious to beneficial. The beneficial mutations can be reversals of deleterious mutations that happened to be present in the original line or can be totally new mutations (e.g., mutations that compensate for the fixed deleterious mutations). I further assume that h < 0.5. A consequence of these assumptions is that beneficial mutations have higher dominance (1 – h) than do deleterious ones (h). This stems from the simple and arguably reasonable assumption that deleterious alleles are all partially recessive to the same degree.
With these assumptions, it is easy to derive the conditions under which a hybrid between a mutant line and the control will have higher fitness than either parent. If control fitness is wc, the fitness of a mutant line with b beneficial and d deleterious mutations will be wc + bs – ds, and the fitness of the hybrids will be wc + b (1 – h)s – dhs. The condition for hybrid fitness to exceed wc is simply p = b/(b + d) > h, where p is the proportion of mutations that are beneficial. The condition for hybrid fitness to be greater than that of the homozygous mutant line is simply 1 – p > h. If deleterious alleles are nearly or completely recessive, both conditions can be satisfied even when a line has many more deleterious than beneficial mutations. Contrary to the suggestion of PETERS et al. (2003)(p. 596), "spurious" overdominance does not require that a large proportion of mutations are beneficial.
The above assumptions can even lead to a negative correlation between heterozygous and homozygous viabilities, as observed by MUKAI (1970). The key requirement is that the variance in the number of mutations per line is considerably greater than expected if mutations are distributed among lines independently. Such a greater-than-Poisson variance can generate a positive correlation between the numbers of beneficial and deleterious mutations per line. Lines with relatively few mutations will have heterozygous and homozygous viability near that of the control. As the number of mutations increases, average homozygous viability will decrease, because most mutations are deleterious, but average heterozygous viability may increase, due to the increasing number of partially dominant beneficial mutations.
To examine the conditions under which the correlation between heterozygous and homozygous viability is negative, let the number of mutations per line, n, have mean µn and variance 
n2. I assume each mutation has independent probability p of being beneficial, regardless of the number of mutations per line. The covariance between heterozygous and homozygous viability is
 | (1) |
d2 and b2 are the variances in the number of deleterious and beneficial mutations, respectively, and bd is their covariance. These variances and covariance can be evaluated by conditioning on the number of mutations per line, n. For example, 
where
 |
Therefore 
. Applying the same reasoning to d2 and bd and substituting the results into (1) gives, after simplification,
 | (2) |
It is convenient to define 
(with a Poisson distribution, 
= 1). Using this definition, (2) will be negative when
 | (3) |
Assuming p < 0.5, p must be >h for (3) to be satisfied, and must be >2. Figure 1
shows minimum for (3) to be satisfied as a function of p for various values of h.
|
for EMS-induced mutations are not available, but there is reason to think it may be considerably greater than one. Individuals are likely to vary in both the amount of mutagen they ingest and how they respond to a given amount of ingested mutagen. When insertion mutations are induced by hybrid dysgenesis, the chromosomes recovered show a much-greater-than-Poisson variance in the number of inserts (EANES et al. 1988, = 2.6; MACKAY et al. 1992, = 3.2), even though all were exposed to the identical mutagenesis treatment. In summary, it is not necessary to invoke overdominance of individual mutations to explain either heterosis in crosses involving individual mutagenized lines (PETERS et al. 2003) or a negative correlation between heterozygous and homozygous viabilities (MUKAI 1970). Barring experimental artifacts such as stock contamination, which might explain MUKAI and YAMAZAKI's (1968) evidence for spontaneous overdominant mutations (FRY 2004), it is nonetheless necessary to postulate that a small but nontrivial fraction of mutations have beneficial effects. Determining whether such mutations are truly overdominant or simply partially dominant will require isolating the effects of individual mutations. One way this could be done is by inbreeding from the F2 of crosses between mutagenized and control lines. Under the dominance hypothesis advanced here, but not under the overdominance hypothesis, it should be possible to recover homozygous lines with higher fitness than that of the controls.
ACKNOWLEDGEMENTS
I thank R. Shaw, M. Simmons, and an anonymous reviewer for helpful comments on an earlier draft of this article. This work was supported by National Science Foundation grant DEB-0108730.
LITERATURE CITED
CHARLESWORTH, B., and K. A. HUGHES, 1999 The maintenance of genetic variation in life history traits, pp. 369–392 in Evolutionary Genetics from Molecules to Morphology, edited by R. S. SINGH and C. B. KRIMBAS. Cambridge University Press, Cambridge, UK.
EANES, W. F., C. WESLEY, J. HEY, D. HOULE and J. W. AJIOKA, 1988 The fitness consequences of P element insertion in Drosophila melanogaster. Genet. Res. 52: 17–26.
FRY, J. D., 2004 On the rate and linearity of viability declines in Drosophila mutation-accumulation experiments: genomic mutation rates and synergistic epistasis revisited. Genetics 166: 797–806.
MACKAY, T. F. C., R. F. LYMAN and M. S. JACKSON, 1992 Effects of P element insertions on quantitative traits in Drosophila melanogaster. Genetics 130: 315–332.[Abstract]
MUKAI, T., 1970 Viability mutations induced by ethyl methanesulfonate in Drosophila melanogaster. Genetics 65: 335–348.
MUKAI, T., and T. YAMAZAKI, 1968 The genetic structure of natural populations of Drosophila melanogaster. V. Coupling-repulsion effect of spontaneous mutant polygenes controlling viability. Genetics 59: 513–535.
PETERS, A. D., D. L. HALLIGAN, M. C. WHITLOCK and P. D. KEIGHTLEY, 2003 Dominance and overdominance of mildly deleterious induced mutations for fitness traits in Caenorhabditis elegans. Genetics 165: 589–599.
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