If the cost-of-repair hypothesis is correct, then we would infer a higher cost of replication in multicellular species (where mutation rates are high) than in prokaryotes. However, the time necessary for the replication of large eukaryotic genomes is compensated by the population of chromosomes with multiple origins of replication (in contrast to the single origin in most bacterial chromosomes). Moreover, as will be discussed below, the burden of somatic mutations imposes a downward selective pressure on mutation rates in multicellular species which is not shared by unicellular species. Thus, an alternative explanation must be sought for the elevated rates of mutation in eukaryotes.
One possibility is that the lower bound on the mutation rate is not set by physiological or biochemical limitations, but by the intrinsic inability of selection to push the rate any lower. The power of random genetic drift (1/2Ne for diploid organisms, where Ne is the genetic effective population size) ultimately constrains what natural selection can accomplish with any trait, and once the mutation rate is pushed to such a low level that any further incremental improvement conveys a fitness advantage smaller than the power of drift, selection will be incapable of reducing the rate any further. Therefore, a key to understanding mutation rate evolution is determining the degree to which evolved mutation rates approach the barriers imposed by drift.
By producing a correlated genetic load through the recurrent influx of deleterious mutations at linked and unlinked sites, even the weakest of mutator alleles suffer an indirect selective disadvantage associated with the excess mutational burden contained within the genomes of carrier individuals (Kimura 1967
; Kondrashov 1995
; Dawson 1999
; Lynch 2008
). This disadvantage can be quite small, however, having a maximum value equal to twice the product of the average deleterious effect of a heterozygous mutation (sd
) and the diploid genome-wide reduction in the deleterious mutation rate (ΔU
, where U
is in the range of 0.01 to 1.0 per generation for multicellular eukaryotes, Lynch and Walsh 1998
; Baer et al. 2007
; and perhaps an order of magnitude lower in yeast, Wloch et al. 2001
; Joseph and Hall 2004
). The factor of two arises because most induced mutations arise on chromosomes unlinked to the mutator, retaining an association with the latter for an average of just two generations.
Two factors will reduce the selective advantage of an antimutator allele below 2sd
, where ΔU
is now the genome-wide reduction in the deleterious mutation rate. First, the full long-term advantage of an antimutator is not realized until it has reached selection-mutation balance with respect to its reduced mutation load (Johnson 1999
), thus making it more difficult for selection to initially promote such an allele towards fixation. Second, if there is any “cost of replication” associated with the antimutator (sr
), the maximum selective advantage becomes 2sd
. Thus, because allelic variants with selection coefficients much smaller than the power of random genetic drift evolve in an effectively neutral manner (Kimura 1983
), an antimutator allele will be insensitive to selection unless the change in the genome-wide deleterious mutation rate is considerably greater than [1/(2Ne
) + sr
). Assuming that sd
are independent of Ne
, this suggests that the mutation rate should scale negatively with Ne
up to the point where U
is so low that further incremental reductions cannot overcome the drift barrier.
Are eukaryotic mutation rates driven to such low levels? Although a definitive answer cannot yet be given, it is known that Ne
is typically in the range of 105
for the nuclear genomes of multicellular species (Lynch 2007
), and that the average value of sd
generally ranges from 10−3
(Lynch and Walsh 1998
). This implies that a selectable antimutator must reduce the deleterious genome-wide mutation rate in a multicellular lineage by an amount much greater than 10−4
. Because these values are ~1% of the genome-wide deleterious mutation rates known for multicellular species, it follows that an antimutator allele would have to reduce U
by much more than 1%, perhaps an order of magnitude more, to be promoted by selection. Although not impossible, given that DNA replication and repair are functions of dozens of loci, single amino acid altering mutations at such loci might only rarely have such large effects. Thus, the drift hypothesis appears to be quantitatively plausible.
The drift hypothesis derives further support from the distribution of average Ne
among phylogenetic lineages (Lynch 2006
). Under the assumption that nucleotide diversity at silent sites in natural populations is effectively neutral (due to the lack of impact at the amino acid level), the equilibrium level of heterozygosity (πs
) at such sites is ~4Neu
in diploid species (and 2Neu
in haploids), where u
is the mutation rate per site. Using previously summarized data on πs
from major phylogenetic groupings (Lynch 2006
), and factoring out the average mutation rates provided in , the average Ne
in these groups can be approximated. One then finds a significant negative correlation between u
in accordance with the drift hypothesis ().
Figure 2 The scaling of the base substitution mutation rate per generation (u) and the effective number of genes per locus (2Ne for diploids, and Ne for haploids). (a) The slope of the log-log regression for the nuclear genome of major phylogenetic groupings is (more ...)
A similar pattern is found for mammalian mitochondrial genomes using data from Piganeau and Eyre-Walker (2009)
. Here, Ne
is the effective number of females, as the mammalian mitochondrion is maternally inherited. The mutation rate was inferred indirectly from phylogenetic estimates of divergence at silent sites (assumed to be neutral), estimated times of divergence from the fossil record, and estimated mean generation times. Despite the greater degree of uncertainty in these data, the log-log regression of lineage-specific estimates of u
has a slope identical to that for the nuclear data described above ().
Because the indirect estimates of Ne
in both of these analyses are associated with a considerable (but unknown) degree of sampling error, the true scaling of u
might be more extreme than the observed −0.6 power. Nevertheless, that two analyses based on different phylogenetic groups, types of data analysis, and genomic compartments yield essentially the same result provides strong support for the hypothesis that declines in Ne
compromise the ability of selection to maintain high-fidelity replication and/or repair mechanisms. Still further support derives from a body of studies suggesting that several aspects of replication fidelity in eukaryotes are compromised relative to the situation in prokaryotes (Lynch 2008
), although some aspects of DNA repair seem to be enhanced in mammals relative to microbes (Saparbaev et al. 2000
These observations help explain a long-standing conundrum in evolutionary genetics – the near independence of nuclear molecular heterozygosity levels across phylogenetic groups with presumably large disparities in Ne
. Lewontin (1974)
dubbed this pattern “the paradox of variation,” although Nei (1983)
later pointed out a weak positive correlation between levels of variation and Ne
. We now see that the relative phylogenetic stability of πs
across broad domains of life is not a reflection of relatively constant Ne
, but of an inverse relationship between u
. This inverse relationship appears also to be responsible for the relative invariance of πs
in the mitochondrial genomes of diverse animals (Bazin et al. 2006
; Nabholz et al. 2008
The preceding arguments also provide a plausible explanation for the opposite scaling pattern of the mutation rate with genome size in viruses and prokaryotes. The case has been made that an upper-bound to Ne
, in the neighborhood of 109
, might exist in cellular species, dictated by the physical (linked) nature of the genome (Lynch 2007
). Assuming this upper bound is approximated in non-eukaryotic microbes, and the genome-wide deleterious mutation rate is driven to the lower limit compatible with the associated magnitude of drift, then because selection operates on the genome-wide deleterious mutation rate, any reduction in genome size would increase the lower limit of the achievable per site mutation rate by reducing the number of mutational targets, yielding the inverse scaling suggested by Drake. Such a response is quite notable in the endosymbiotic bacterium Buchnera aphidicola
(Moran et al. 2009
), which has a highly reduced genome size and the highest known mutation rate for a prokaryote (left-most eubacterial data point in ).
It also follows that if the average effect of a deleterious mutation (sd
) were to increase, the lower limit to the achievable mutation rate would decrease. Drawing from observations that mutations that are benign at low temperatures often have elevated deleterious effects at high temperatures, Drake (2009)
has argued that an elevation in sd
has promoted the evolution of reduced base-substitution mutation rates in thermophilic bacteria.
Finally, it should be noted that despite the similar scaling of the per site mutation rate with Ne
in both nuclear and mitochondrial genomes, the absolute values of u
are much greater for mitochondria (). Such a pattern is also in agreement with the expectations of the drift hypothesis, as the number of mutational targets in the animal mitochondrion (e.g., just 13 protein-coding genes) is far below the number in nuclear genomes. Thus, although it is often argued that elevated mitochondrial mutation rates in metazoans are an inevitable consequence of a highly oxidative mitochondrial environment, the drift hypothesis provides an explanation based purely on the efficiency of selection. Nonetheless, a remaining puzzle with respect to organelle mutation rates concerns the apparent ~ten-fold reduction in land plants relative to nuclear rates (Lynch 2007
). Plant organelle genomes can be up to ten-fold larger than animal mitochondrial genomes, but they are still vastly smaller than nuclear genomes, and the effective population sizes of such organelles do not appear to be unusually large (Lynch 2007
). Thus, to be consistent with the drift hypothesis, the average deleterious effects of organelle mutations in land plants must be unusually large, some aspects of the repair machinery must be driven by nuclear functions and/or there must be mechanisms for reducing plant organelle mutation rates in much smaller increments than in nuclear environments.