The genetic equidistance result of molecular evolution is independent of mutation rates

The well-established genetic equidistance result shows that sister species are approximately equidistant to a simpler outgroup as measured by DNA or protein dissimilarity. The equidistance result is the most direct evidence, and remains the only evidence, for the constant mutation rate interpretation of this result, known as the molecular clock. However, data independent of the equidistance result have steadily accumulated in recent years that often violate a constant mutation rate. Many have automatically inferred non-equidistance whenever a non-constant mutation rate was observed, based on the unproven assumption that the equidistance result is an outcome of constant mutation rate. Here it is shown that the equidistance result remains valid even when different species can be independently shown to have different mutation rates. A random sampling of 50 proteins shows that nearly all proteins display the equidistance result despite the fact that many proteins have non-constant mutation rates. Therefore, the genetic equidistance result does not necessarily mean a constant mutation rate. Observations of different mutation rates do not invalidate the genetic equidistance result. New ideas are needed to explain the genetic equidistance result that must grant different mutation rates to different species and must be independently testable

Whole genome sequencing of Mycobacterium tuberculosis reveals slow growth and low mutation rates during latent infections in humans

Very little is known about the growth and mutation rates of Mycobacterium tuberculosis during latent infection in humans. However, studies in rhesus macaques have suggested that latent infections have mutation rates that are higher than that observed during active tuberculosis disease. Elevated mutation rates are presumed risk factors for the development of drug resistance. Therefore, the investigation of mutation rates during human latency is of high importance. We performed whole genome mutation analysis of M. tuberculosis isolates from a multi-decade tuberculosis outbreak of the New Zealand Rangipo strain. We used epidemiological and phylogenetic analysis to identify four cases of tuberculosis acquired from the same index case. Two of the tuberculosis cases occurred within two years of exposure and were classified as recently transmitted tuberculosis. Two other cases occurred more than 20 years after exposure and were classified as reactivation of latent M. tuberculosis infections. Mutation rates were compared between the two recently transmitted pairs versus the two latent pairs. Mean mutation rates assuming 20 hour generation times were 5.5X10⁻¹⁰ mutations/bp/generation for recently transmitted tuberculosis and 7.3X10⁻¹¹ mutations/bp/generation for latent tuberculosis. Generation time versus mutation rate curves were also significantly higher for recently transmitted tuberculosis across all replication rates (p = 0.006). Assuming identical replication and mutation rates among all isolates in the final two years before disease reactivation, the u20hr mutation rate attributable to the remaining latent period was 1.6×10⁻¹¹ mutations/bp/generation, or approximately 30 fold less than that calculated during the two years immediately before disease. Mutations attributable to oxidative stress as might be caused by bacterial exposure to the host immune system were not increased in latent infections. In conclusion, we did not find any evidence to suggest elevated mutation rates during tuberculosis latency in humans, unlike the situation in rhesus macaques

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference

The Importance of DNA Repair in Tumor Suppression

The transition from a normal to cancerous cell requires a number of highly specific mutations that affect cell cycle regulation, apoptosis, differentiation, and many other cell functions. One hallmark of cancerous genomes is genomic instability, with mutation rates far greater than those of normal cells. In microsatellite instability (MIN tumors), these are often caused by damage to mismatch repair genes, allowing further mutation of the genome and tumor progression. These mutation rates may lie near the error catastrophe found in the quasispecies model of adaptive RNA genomes, suggesting that further increasing mutation rates will destroy cancerous genomes. However, recent results have demonstrated that DNA genomes exhibit an error threshold at mutation rates far lower than their conservative counterparts. Furthermore, while the maximum viable mutation rate in conservative systems increases indefinitely with increasing master sequence fitness, the semiconservative threshold plateaus at a relatively low value. This implies a paradox, wherein inaccessible mutation rates are found in viable tumor cells. In this paper, we address this paradox, demonstrating an isomorphism between the conservatively replicating (RNA) quasispecies model and the semiconservative (DNA) model with post-methylation DNA repair mechanisms impaired. Thus, as DNA repair becomes inactivated, the maximum viable mutation rate increases smoothly to that of a conservatively replicating system on a transformed landscape, with an upper bound that is dependent on replication rates. We postulate that inactivation of post-methylation repair mechanisms are fundamental to the progression of a tumor cell and hence these mechanisms act as a method for prevention and destruction of cancerous genomes.Comment: 7 pages, 5 figures; Approximation replaced with exact calculation; Minor error corrected; Minor changes to model syste

Wright-Fisher diffusion with negative mutation rates

We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the classical Wright-Fisher diffusions, except that the "mutation rates" are now nonpositive. This model, suggested by Aldous, appears in the study of a conjectured diffusion limit for a Markov chain on Cladograms. The striking feature of these models is that the boundary is not reflecting, and we kill the process once it hits the boundary. We derive the explicit exit distribution from the simplex and probabilistic bounds on the exit time. We also prove that these processes can be viewed as a "stochastic time-reversal" of a Wright-Fisher process of increasing dimensions and conditioned at a random time. A key idea in our proofs is a skew-product construction using certain one-dimensional diffusions called Bessel-square processes of negative dimensions, which have been recently introduced by Going-Jaeschke and Yor.Comment: Published in at http://dx.doi.org/10.1214/11-AOP704 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Repeatability of evolution on epistatic landscapes

Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an evolutionary process under varying mutation rates as well as varying fitness is still an open question. Experimental procedures, however, do include these complexities along with fluctuating population sizes and stochastic events such as extinctions. We investigate the mutational path probabilities of systems having epistatic effects on both fitness and mutation rates using a theoretical and computational framework. In contrast to previous models, we do not limit ourselves to the typical strong selection, weak mutation (SSWM)-regime or to fixed population sizes. Rather we allow epistatic interactions to also affect mutation rates. This can lead to qualitatively non-trivial dynamics. Pathways, that are negligible in the SSWM-regime, can overcome fitness valleys and become accessible. This finding has the potential to extend the traditional predictions based on the SSWM foundation and bring us closer to what is observed in experimental systems