This post is mostly a technical summary of the paper by Tenaillon, Le Nagard, Godelle and Taddei (2000). I wrote the summary because I use it as a baseline for my own research, which involves the evolution of stress-induced mutators (Ram & Hadany, 2012).
The hypothesis the paper deals with is:
The existence of genetic exchanges could modify the dynamics of adaptation and limits the success of mutator alleles1.
It is stated that previous models (Leigh, 1973; Johnson, 1999) have considered mutators in a sexual population, but didn't consider the case of adaptation with multiple beneficial mutations - which can involve different Hill-Robertson effects (Hill & Robertson, 1966).
This hypothesis was tested using simulations. The main conclusion, in comparison to a previous work in which the authors studies the evolution of mutators (Tenaillon et al. 1999):
Rare genetic exchanges have a dramatic (i.e. negative) effect on the fixation of mutators.
In addition, the paper presents some evidence on why genetic exchanges (recombination) have such an effect of the evolution of mutators.
The model is an extension of the density-based model2 used in (Tenaillon et al. 1999). The extension is the addition of genetic exchanges ("bacterial recombination"). Both conjugation and transformation were used, but only the results of transformation are shown.
The model is built using:
The basic model of the genome (in parentheses are the values used in my own work for comparison):
Rates are modified from the original to units of events per genome per generation. (in parentheses are the rates used in my own work for comparison):
When the rate of genetic exchanges increases, the fixation probability of mutators decreases. Figure 1A shows this very clearly for a 100-fold mutator:
Figure 1 from (Tenaillon et al. 2000).
A) Fixation probability of a 100-fold fold mutator, population size 109.
B) Adaptation times of populations with: circle - low mutation rate, square - high mutation rate, triangle - mixed populations.
However, the B panel shows that the adaptation time of a mutator population is still shorter than that of a non-mutator population, even when mutators are loosing. This is due to the contribution of mutators to adaptation - in a recombining population mutators are "altruistic" alleles because they give away the beneficial mutations they generate. This causes them to lose their adaptive advantage and therefore their fixation probability drops, but it still increases the ability of the whole population to adapt.
Note that the rates of recombination in the figure are per gene. Converted to per genome they would be: 0, 10-5, 10-4, 10-3, 10-2, 10-1, or in decimal representation: 0, 0.00001, 0.0001, 0.001, 0.01, 0.1. Another useful presentation is the ratio of recombination to mutation, using the highest genomic mutation rate (10-4): 0, 0.1, 1, 10, 100, 1000, or compared to the 100-fold mutator: 0, 0.001, 0.01, 0.1, 1, 10.
So we see that as soon as the recombination to mutation ratio is 0.1 or lower (4^th^ column from the left in Fig. 1A, if we consider the 100-fold increae), the fixation probability of mutators is ~50% or more. The conclusion here could be that mutators can evolve in a recombining population as long as recombination in not more than 10-fold stronger than mutation
Of course this 10-fold estimate is highly dependent on the other paramters: the population size, the selection coefficients, the beneficial mutation rate, not to mention parameters that are not dealt with here such as epistasis.
A recombination barrier, in the context of these simulations, prevents recombination between mutator and non-mutator individuals, limiting recombination events to within the sub-populations.
This is useful here because it allows to test if the source of the effect of recombination on the fixation of mutators is: 1) breaking the linkage of the mutator with the beneficial mutations it generates, or 2) competing adaptive strategy.
The 1^st^ effect is usually called the hitch-hiking effect, or selective sweeps (Charlesworth, 2007): mutators can "hitch-hike" with the beneficial mutations they generate to high frequencies as long as the LD (linkage disequilibrium) between them is intact. recombination tends to break this LD, robbing the mutators from their precious beneficial mutations. Even worse, recombination doesn't only take away the beneifical mutations, it even gives them to the mutators' "rivals" - the competing non-mutator alleles.
The 2^nd^ effect is general - competing adadptive strategy. How is recombination an adaptive strategy?
Asexual populations are limited by clonal interference (Gerrish & Lenski, 1998; Martens & Hallatschek, 2011). The following figure illustrates the idea:
Clonal interference diagram from Wikipedia. This diagram illustrates how sex might create novel genotypes more rapidly. Two beneficial mutations A and B occur at random. The two mutations are recombined rapidly in a sexual population (top), but in an asexual population (bottom) the two mutations must independently arise because of clonal interference. The effect of recombination and sex on the adaptation rate via the reduction of clonal interference is also called the Fisher-Muller effect.
If the reduction in fixation probability is due to the 1st effect - separation of the mutators from the beneficial mutations they generate - then recombination barriers are expected to revert the outcome, at least partially, to that of asexual populations.
However, the results showed that recombination barriers didn't recover the fixation probability of mutators to their levels without recombination. No figure presents the data, but the text provides some information: 7% fixation instead of 60% with beneficial mutation rate 10-8 and 0.3% instead of 16% with a rate of 10-9. The conclusion is therefore that the 1st effect is not enough to explain the reduction in the mutators adaptive advantage in the presence of recombination.
To check that the 2nd effect is the determining effect, a 100-fold mutator invaded another mutator (instead of a non-mutator). The results are in Figure 2 - in general the fixation probability of a 100-fold mutator drops rapidly when competing with a 10-fold mutator and even a 5-fold mutator.
This illustrates that competing adaptive strategies can reduce the fixation of mutators, and therefore that is is plausible that this is why recombination reduces the fixation of mutators.
Setting the recombination rate at 10^-4^ gene conversions per individual per generations, the effect of other parameters was investigated:
In asexuals, increasing the population size increases the fixation rate of mutators (Tenaillon et al. 1999).
In recombining populations, this is not the case. Figure 3A shows that for a population size <106, recombination has a very small effect on the fixation of a 100-fold mutator. However, the trends of the fixation probability are completely different for population size >106. In asexual populations it increases (rapidly after 10^7^), but in recombining populations it decreases and then increases a bit again at 10^9^, but not much, never surprassing 0.2.
The lower the beneficial mutation rate, the lower the fixation probability of mutators. Figure 4 shows that the fixation probability of mutators starts to increase at a beneficial mutation rate of 10-9 for asexual populations, but only at 10-8 for sexual populations.
Figure 5 shows that the negative effect of recombination of the fixation of mutators decreases when the selection coefficient of beneficial mutations increases.
For a selection coefficient of 0.01 (Kibota & Lynch, 1996) recombination reduced the fixation probability of mutators 17-fold.
A selection coefficient of 0.1, used in my own work (Ram & Hadany, 2012), falls between the two right most points of Figure 5 - 2.5 and 3 - and the fixation probability of a 100-fold mutator allele drops ~10-fold due to recombination at a rate of 10^-4^ per gene per generation in a population with size 10^9^.
This paper is packed with interesting results. The effect of recombination on mutator evolution has not recieved alot of treatment using simulation (but see (Levin & Cornejo, 2009) and (Sloan & Panjeti, 2010) on which I hope to write some other time). So this is really interesting to someone interesed in the evolution of the mutation rate, even 12 years later.
This work shows that indeed recombination has an effect on mutator evolution, and that this effect is highly sensitive - it is (I'm concentrating on when the effect is weak because that's when mutators are still going to evolve):
It seems that in general the effect of recombination on mutator evolution (that is, on the evolution of high mutation rates) is weak when the adaptation rate of the population is low. In turn, the adaptation rate is a function of the supply of beneficial mutations which is a function of population size and beneficial mutation rate, and of fixation time of beneficial mutations which is a function of population size and selection strength.
Selection of mutators is second-order selection, in the sense that it indirectly affecting mutators. Because their results imply that second-order selection of mutators is very sensitive to the system parameters, Tenaillon et al. propose that it may be unable to optimize the rates of mutation - in the sense that mutators will not be selected even when increasing the mutation rate will be beneficial to the population, in terms of fitness and adaptation rate. This can be resolved by transient hypermutation:
Sex would therefore help bacteria approach an optimized mutation rate strategy composed of shifts towards high mutation rates in phases of adaptation under strong selective pressure and rapid recovery of low mutation rate once adaptation is achieved.
This view was also proposed by Ninio (1991) and expanded in a review from the same lab with the attractive title The Rise and Fall of Mutator Bacteria (Giraud et al. 2001).
I'm not sure if and how these results would change if a weaker mutator (10-fold mutation rate increase?) was used instead of the strong mutator (100-fold). For example, a paper from the same lab (Taddei et al. 1997) showed that a 10-fold mutator is more successful in invading finite populations (see Figure 3A).
I learned alot from this paper (and it predecessors (Taddei et al. 1997; Tenaillon et al. 1999) about how to think of evolutionary simulations. And of course the science itself - the diverse network of interactions and effects between selection, drift, mutation and recombination.
This is in contrast to frequency-dependent models in which the frequency of individuals in each class is monitored.
a mutant allele of the mutS gene can reduce the efficiency of DNA repair, allowing more mutations to slip though the repair mechanisms.