Diffusion approximations in population genetics and the rate of Muller's ratchet

Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size---a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, including in regimes where selection and/or mutation are strong compared to genetic drift. As an illustration, we use a diffusion approximation of the Wright-Fisher model to improve estimates for the expected time to fixation of a strongly deleterious allele, i.e. the rate of Muller's ratchet.

Muller’s ratchet of the Y chromosome with gene conversion

Muller’s ratchet is a process in which deleterious mutations are fixed irreversibly in the absence of recombination. The degeneration of the Y chromosome, and the gradual loss of its genes, can be explained by Muller’s ratchet. However, most theories consider single-copy genes, and may not be applicable to Y chromosomes, which have a number of duplicated genes in many species, which are probably undergoing concerted evolution by gene conversion. We developed a model of Muller’s ratchet to explore the evolution of the Y chromosome. The model assumes a non-recombining chromosome with both single-copy and duplicated genes. We used analytical and simulation approaches to obtain the rate of gene loss in this model, with special attention to the role of gene conversion. Homogenization by gene conversion makes both duplicated copies either mutated or intact. The former promotes the ratchet, and the latter retards, and we ask which of these counteracting forces dominates under which conditions. We found that the effect of gene conversion is complex, and depends upon the fitness effect of gene duplication. When duplication has no effect on fitness, gene conversion accelerates the ratchet of both single-copy and duplicated genes. If duplication has an additive fitness effect, the ratchet of single-copy genes is accelerated by gene duplication, regardless of the gene conversion rate, whereas gene conversion slows the degeneration of duplicated genes. Our results suggest that the evolution of the Y chromosome involves several parameters, including the fitness effect of gene duplication by increasing dosage and gene conversion rate.

Genotypic Males Play an Important Role in the Creation of Genetic Diversity in Gynogenetic Gibel Carp

Unisexual lineages are commonly considered to be short-lived in the evolutionary process as accumulation of deleterious mutations stated by Muller’s ratchet. However, the gynogenetic hexaploid gibel carp (Carassius gibelio) with existence over 0.5 million years has wider ecological distribution and higher genetic diversity than its sexual progenitors, which provides an ideal model to investigate the underlying mechanisms on countering Muller’s ratchet in unisexual taxa. Unlike other unisexual lineages, the wild populations of gibel carp contain rare and variable proportions of males (1–26%), which are determined via two strategies including genotypic sex determination and temperature-dependent sex determination. Here, we used a maternal gibel carp from strain F to be mated with a genotypic male from strain A+, a temperature-dependent male from strain A+, and a male from another species common carp (Cyprinus carpio), respectively. When the maternal individual was mated with the genotypic male, a variant of gynogenesis was initiated, along with male occurrence, accumulation of microchromosomes, and creation of genetic diversity in the offspring. When the maternal individual was mated with the temperature-dependent male and common carp, typical gynogenesis was initiated that all the offspring showed the same genetic information as the maternal individual. Subsequently, we found out that the genotypic male nucleus swelled and contacted with the female nucleus after fertilization although it was extruded from the female nucleus eventually, which might be associated with the genetic variation in the offspring. These results reveal that genotypic males play an important role in the creation of genetic diversity in gynogenetic gibel carp, which provides insights into the evolution of unisexual reproduction.

Avoiding organelle mutational meltdown across eukaryotes with or without a germline bottleneck

Mitochondrial DNA (mtDNA) and plastid DNA (ptDNA) encode vital bioenergetic apparatus, and mutations in these organelle DNA (oDNA) molecules can be devastating. In the germline of several animals, a genetic “bottleneck” increases cell-to-cell variance in mtDNA heteroplasmy, allowing purifying selection to act to maintain low proportions of mutant mtDNA. However, most eukaryotes do not sequester a germline early in development, and even the animal bottleneck remains poorly understood. How then do eukaryotic organelles avoid Muller’s ratchet—the gradual buildup of deleterious oDNA mutations? Here, we construct a comprehensive and predictive genetic model, quantitatively describing how different mechanisms segregate and decrease oDNA damage across eukaryotes. We apply this comprehensive theory to characterise the animal bottleneck with recent single-cell observations in diverse mouse models. Further, we show that gene conversion is a particularly powerful mechanism to increase beneficial cell-to-cell variance without depleting oDNA copy number, explaining the benefit of observed oDNA recombination in diverse organisms which do not sequester animal-like germlines (for example, sponges, corals, fungi, and plants). Genomic, transcriptomic, and structural datasets across eukaryotes support this mechanism for generating beneficial variance without a germline bottleneck. This framework explains puzzling oDNA differences across taxa, suggesting how Muller’s ratchet is avoided in different eukaryotes.

Selective Interference and the Evolution of Sex

Selection acts upon genes linked together on chromosomes. This physical connection reduces the efficiency by which selection can act because, in the absence of sex, alleles must rise and fall together in frequency with the genome in which they are found. This selective interference underlies such phenomena as clonal interference and Muller’s Ratchet and is broadly termed Hill-Robertson interference. In this review, I examine the potential for selective interference to account for the evolution and maintenance of sex, discussing the positive and negative evidence from both theoretical and empirical studies, and highlight the gaps that remain.

Spike protein mutational landscape in India: Could Muller’s ratchet be a future game-changer for COVID-19?

The dire need of effective preventive measures and treatment approaches against SARS-CoV-2 virus, causing COVID-19 pandemic, calls for an in-depth understanding of its evolutionary dynamics with attention to specific geographic locations, since lockdown and social distancing to prevent the virus spread could lead to distinct localized dynamics of virus evolution within and between countries owing to different environmental and host-specific selection pressures. To decipher any correlation between SARS-CoV-2 evolution and its epidemiology in India, we studied the mutational diversity of spike glycoprotein, the key player for the attachment, fusion and entry of virus to the host cell. For this, we analyzed the sequences of 630 Indian isolates as available in GISAID database till June 07, 2020, and detected the spike protein variants to emerge from two major ancestors – Wuhan-Hu-1/2019 and its D614G variant. Average stability of the docked spike protein – host receptor (S-R) complexes for these variants correlated strongly (R2=0.96) with the fatality rates across Indian states. However, while more than half of the variants were found unique to India, 67% of all variants showed lower stability of S-R complex than the respective ancestral variants, indicating a possible fitness loss in recently emerged variants, despite a continuous increase in mutation rate. These results conform to the sharply declining fatality rate countrywide (>7-fold during April 11 – June 28, 2020). Altogether, while we propose the potential of S-R complex stability to track disease severity, we urge an immediate need to explore if SARS-CoV-2 is approaching mutational meltdown in India.Author summaryEpidemiological features are intricately linked to evolutionary diversity of rapidly evolving pathogens, and SARS-CoV-2 is no exception. Our work suggests the potential of average stability of complexes formed by the circulating spike mutational variants and the human host receptor to track the severity of SARS-CoV-2 infection in a given region. In India, the stability of these complexes for recent variants tend to decrease relative to their ancestral ones, following countrywide declining fatality rate, in contrast to an increasing mutation rate. We hypothesize such a scenario as nascent footprints of Muller’s ratchet, proposing large-scale population genomics study for its validation, since this understanding could lead to therapeutic approaches for facilitating mutational meltdown of SARS-CoV-2, as experienced earlier for influenza A virus.

Sex, fitness decline and recombination – Muller’s ratchet vs. Ohta’s ratchet

It is generally accepted that the absence of recombination reduces the efficacy of natural selection for, or against, mutations. A special case is Muller’s Ratchet (MR) whereby non-recombining genomes experience irreversible fitness decline due to the accumulation of deleterious mutations. MR has been a main hypothesis for sexual reproduction as well as many other biological phenomena. We now ask whether the fitness decline can indeed be stopped if an asexual population turns sexual to become recombining. The possible fitness decline under recombination is referred to as Ohta’s Ratchet (OR). In comparison, MR is more effective in driving fitness reduction than OR, but only in a restricted parameter space of mutation rate, population size and selection. Outside of this space, the two ratchets are equally effective or, alternatively, neither is sufficiently powerful. Furthermore, beneficial mutations can affect the population fitness, which may diverge between the two ratchets, but only in a small parameter space. Since recombination plays a limited role in driving fitness decline, the operation of MR could be far less common in nature than believed. A companion report (see Supplement) surveying the biological phenomena attributed to MR indeed suggests the alternative explanations to be generally more compelling.