Philip John Gerrish

A mutator is a variant in a population of organisms whose mutation rate is higher than the average mutation rate in the population. For genetic and population dynamics reasons, mutators are produced and survive with much greater frequency than anti-mutators (variants with a lower-than-average mutation rate). This strong asymmetry is a consequence of both fundamental genetics and natural selection; it can lead to a ratchet-like increase in the mutation rate. The rate at which mutators appear is, therefore, a parameter that should be of great interest to evolutionary biologists generally; for example, it can influence: (1) the survival duration of a species, especially asexual species (which are known to be short-lived), (2) the evolution of recombination, a process that can ameliorate the deleterious effects of mutator abundance, (3) the rate at which cancer appears, (4) the ability of pathogens to escape immune surveillance in their hosts, (5) the long-term fate of mitochondria, etc. In spite of its great relevance to basic and applied science, the rate of mutation to a mutator phenotype continues to be essentially unknown. The reasons for this gap in our knowledge are largely methodological; in general, a mutator phenotype cannot be observed directly, but must instead be inferred from the numbers of some neutral "marker" mutation that can be observed directly: different mutation-rate variants will produce this marker mutation at different rates. Here, we derive the expected distribution of the numbers of the marker mutants observed, accounting for the fact that some of the mutants will have been produced by a mutator phenotype that itself arose by mutation during the growth of the culture. These developments, together with previous enhancements of the Luria-Delbruck assay (by one of us, dubbed the "Jones protocol"), make possible a novel experimental protocol for estimating the rate of mutation to a mutator phenotype. Simulated experiments using biologically reasonable parameters that employ this protocol show that such experiments in the lab can give us fairly accurate estimates of the rate of mutation to a mutator phenotype. Although our ability to estimate mutation-to-mutator rates from simulated experiments is promising, we view this study as a proof-of-concept study and an important first step towards practical empirical estimation.

The evolutionary trend toward increasing complexity and social function is ultimately the result of natural selection's paradoxical tendency to foster cooperation through competition. Cooperating populations ranging from complex societies to somatic tissue are constantly under attack, however, by non-cooperating mutants or transformants, called 'cheaters'. Structure in these populations promotes the formation of cooperating clusters whose competitive superiority can alone be sufficient to thwart outgrowths of cheaters and thereby maintain cooperation. But we find that when cheaters appear too frequently - exceeding a threshold mutation or transformation rate - their scattered outgrowths infiltrate and break up cooperating clusters, resulting in a cascading loss of social cohesiveness, a switch to net positive selection for cheaters and ultimately in the loss of cooperation. Our findings imply that a critically low mutation rate had to be achieved (perhaps through the advent of proofreading and repair mechanisms) before complex cooperative functions, such as those required for multicellularity and social behaviour, could have evolved and persisted. When mutation rate in our model is also allowed to evolve, the threshold is crossed spontaneously after thousands of generations, at which point cheaters rapidly invade. Probing extrapolations of these findings suggest: (1) in somatic tissue, it is neither social retro-evolution alone nor mutation rate evolution alone but the interplay between these two that ultimately leads to oncogenic transitions; the rate of this coevolution might thereby provide an indicator of lifespan of species, terrestrial or not; (2) the likelihood that extraterrestrial life can be expected to be multicellular and social should be affected by ultraviolet and other mutagenic factors.

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane's application of single- type branching process theory showed that genetic drift alone could cause the extinction of newly arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as a multitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination. We first study the lineage- contamination phenomenon in isolation, deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when U greater than or similar to sb; where U is deleterious mutation rate and s(b) is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by similar to 1 - U/sb. We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is never zero but is depressed below classical predictions by a factor bounded from below by e(-epsilon U/sb), where s(b) is mean selective advantage of beneficial mutations, and epsilon = 1 - e(-1) approximate to 0.63. This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or (2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely.

When mutation rates are low, natural selection remains effective, and increasing the mutation rate can give rise to an increase in adaptation rate. When mutation rates are high to begin with, however, increasing the mutation rate may have a detrimental effect because of the overwhelming presence of deleterious mutations. Indeed, if mutation rates are high enough: (i) adaptive evolution may be neutralized, resulting in a zero (or negative) adaptation rate despite the continued availability of adaptive and/or compensatory mutations, or (ii) natural selection may be neutralized, because the fitness of lineages bearing adaptive and/or compensatory mutations—whether established or newly arising—is eroded by excessive mutation, causing such lineages to decline in frequency. We apply these two criteria to a standard model of asexual adaptive evolution and derive mathematical expressions—some new, some old in new guise—delineating the mutation rates under which either adaptive evolution or natural selection is neutralized. The expressions are simple and require no a priori knowledge of organism- and/or environment-specific parameters. Our discussion connects these results to each other and to previous theory, showing convergence or equivalence of the different results in most cases.