Mutation accumulation in growing asexual lineages

Mutational meltdown in asexual populations doomed to extinction

Asexual populations are expected to accumulate deleterious mutations through a process known as Muller's ratchet. Lynch and colleagues proposed that the ratchet eventually results in a vicious cycle of mutation accumulation and population decline that drives populations to extinction. They called this phenomenon mutational meltdown. Here, we analyze mutational meltdown using a multi-type branching process model where, in the presence of mutation, populations are doomed to extinction. We analyse the change in size and composition of the population and the time of extinction under this model.

Dynamics and Fate of Beneficial Mutations Under Lineage Contamination by Linked Deleterious Mutations

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 [Formula: see text] where U is deleterious mutation rate and [Formula: see text] is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by [Formula: see text] 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 [Formula: see text] where [Formula: see text] is mean selective advantage of beneficial mutations, and [Formula: see text] 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.

Genomic mutation rates that neutralize adaptive evolution and natural selection

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.

Interactions between evolutionary processes at high mutation rates

Evolution at high mutation rates is minimally affected by six processes: mutation-selection balance, error catastrophes, Muller's Ratchet, robustness and compensatory evolution, and clonal interference. Including all of these processes in a tractable, analytical model is difficult, but they can be captured in simulations that utilize realistic genotype-phenotype-fitness maps, as done here by modeling RNA folding. Subjecting finite, asexual populations to a range of mutation rates revealed simple criteria that predict when particular evolutionary processes are important. Populations were initiated with a genotype encoding the most fit phenotype. When purifying selection was strong relative to mutation, the initial genotype was replaced by one more mutationally robust, and the maximally fit phenotype was maintained in a mutation-selection balance where the deleterious mutation rate determined mean fitness. With weaker purifying selection, the most fit genotypes were lost. Although loss of the best genotype was ongoing and might have led to a progressive fitness decline, continual compensatory evolution led to an approximate fitness equilibration. Per total genomic mutation rate, mean fitness was similar for strong and weak purifying selection. These results represent a first step at separating interactions between evolutionary processes at high mutation rate, but additional theory is needed to interpret some outcomes.

Analytical results on Muller's ratchet effect in growing populations

Fontanari introduced [Phys. Rev. Lett. 91, 218101 (2003)] a model for studying Muller's ratchet phenomenon in growing asexual populations. They studied two situations, either including a death probability for each newborn or not, but were able to find analytical (recursive) expressions only in the no-decay case. In this Brief Report a branching process formalism is used to find recurrence equations that generalize the analytical results of the original paper besides confirming the interesting effects their simulations revealed.

Effects of spatial competition on the diversity of a quasispecies

The diversity harbored by populations of RNA viruses results from high mutation rates, as well as from the characteristics of the environment where they evolve. By means of a simple model for structured quasispecies, we quantify how competition for space among phenotypic types shapes their distribution at the mutation-selection equilibrium. We introduce a general framework to treat this problem and relate mutation rate and competition strength to the quasispecies composition. For diffusion limited competition, diversity typically increases and the asymptotic growth rate of the population diminishes as diffusion decreases. Limited mobility confers a relative advantage to worse competitors. The stationary state is characterized by an over-production of viral particles. Empirical data allow an estimation of mutation rates compatible with the diversity observed in viral populations infecting cellular monolayers.

Comparison of three replication strategies in complex multicellular organisms: asexual replication, sexual replication with identical gametes, and sexual replication with distinct sperm and egg gametes

This paper studies the mutation-selection balance in three simplified replication models. The first model considers a population of organisms replicating via the production of asexual spores. The second model considers a sexually replicating population that produces identical gametes. The third model considers a sexually replicating population that produces distinct sperm and egg gametes. All models assume diploid organisms whose genomes consist of two chromosomes, each of which is taken to be functional if equal to some master sequence, and defective otherwise. In the asexual population, the asexual diploid spores develop directly into adult organisms. In the sexual populations, the haploid gametes enter a haploid pool, where they may fuse with other haploids. The resulting immature diploid organisms then proceed to develop into mature organisms. Based on an analysis of all three models, we find that, as organism size increases, a sexually replicating population can only outcompete an asexually replicating population if the adult organisms produce distinct sperm and egg gametes. A sexual replication strategy that is based on the production of large numbers of sperm cells to fertilize a small number of eggs is found to be necessary in order to maintain a sufficiently low cost for sex for the strategy to be selected for over a purely asexual strategy. We discuss the usefulness of this model in understanding the evolution and maintenance of sexual replication as the preferred replication strategy in complex, multicellular organisms.

Asexual and sexual replication in sporulating organisms

Replication via sporulation is the replication strategy for all multicellular life, and may even be observed in unicellular life (such as with budding yeast). We consider diploid populations replicating via one of two possible sporulation mechanisms. (1) Asexual sporulation, whereby adult organisms produce single-celled diploid spores that grow into adults themselves. (2) Sexual sporulation, whereby adult organisms produce single-celled diploid spores that divide into haploid gametes. The haploid gametes enter a haploid "pool," where they may recombine with other haploids to form a diploid spore that then grows into an adult. We consider a haploid fusion rate given by second-order reaction kinetics. We work with a simplified model where the diploid genome consists of only two chromosomes, each of which may be rendered defective with a single point mutation of the wild-type. We find that the asexual strategy is favored when the rate of spore production is high compared to the characteristic growth rate from a spore to a reproducing adult. Conversely, the sexual strategy is favored when the rate of spore production is low compared to the characteristic growth rate from a spore to a reproducing adult. As the characteristic growth time increases, or as the population density increases, the critical ratio of spore production rate to organism growth rate at which the asexual strategy overtakes the sexual one is pushed to higher values. Therefore, the results of this model suggest that, for complex multicellular organisms, sexual replication is favored at high population densities and low growth and sporulation rates.

Preservation of information in a prebiotic package model

The coexistence between different informational molecules has been the preferred mode to circumvent the limitation posed by imperfect replication on the amount of information stored by each of these molecules. Here we reexamine a classic package model in which distinct information carriers or templates are forced to coexist within vesicles, which in turn can proliferate freely through binary division. The combined dynamics of vesicles and templates is described by a multitype branching process which allows us to write equations for the average number of the different types of vesicles as well as for their extinction probabilities. The threshold phenomenon associated with the extinction of the vesicle population is studied quantitatively using finite-size scaling techniques. We conclude that the resultant coexistence is too frail in the presence of parasites and so confinement of templates in vesicles without an explicit mechanism of cooperation does not resolve the information crisis of prebiotic evolution.

Muller's ratchet in random graphs and scale-free networks

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of mitochondria, the degeneration of the Y chromosome, the evolution of sex and recombination and the evolution of microbes. Here we study the speed of Muller's ratchet in a population subdivided into many small subpopulations connected by migration, and distributed on a network. We compare the speed of the ratchet in two distinct types of topologies: scale free networks and random graphs. The difference between the topologies is noticeable when the average connectivity of the network and the migration rate is large. In this situation we observe that the ratchet clicks faster in scale free networks than in random graphs. So contrary to intuition, scale free networks are more prone to loss of genetic information than random graphs. On the other hand, we show that scale free networks are more robust to the random extinction than random graphs. Since these complex networks have been shown to describe well real-life systems, our results open a framework for studying the evolution of microbes and disease epidemics.

The cell clone ecology hypothesis and the cell fusion model of cancer progression and metastasis: History and experimental support

The two-stage initiation-progression model of cancer is widely accepted. Although mutations explain initiation of neoplasia, the assumption that mutations are responsible for progression of neoplasia to cancer appears to have little experimental support. The "cell clone ecology hypothesis" explains why neoplasia evolve and the "cell fusion model of cancer progression and metastasis" describes how they evolve into clinically significant tumors. A brief history of important concepts and experiments is provided. Clinically significant cancers are effectively new parasite species that live, expand and evolve within the host. It is hypothesized that survival and fate of the parasite clones called "cancer" are governed by the principles of ecology. It is argued that while mutations or aneuploidy (asexual reproduction) can result in transient/self-limiting neoplasia, neither of these asexual modes of forming new karyotypes can maintain the ecologically fit parasites that develop into clinically significant cancer. Mutations and/or unstable genomes (aneuploidy) progressively degrade cell lines and if only these mechanisms were at work, neoplasia would spontaneously become extinct or benign (enfeebled) before reaching clinical significance (an example of "Muller's ratchet"). In the cell fusion model of (clinically significant) cancer progression and metastasis, cell-cell fusion is the essential element allowing normal cells or (transient) neoplasia to evolve into clinically significant cancers. Cell-cell fusion is required for producing and sustaining clinically significant cancer because it provides a sex-like mode of reproduction essential for an ecologically fit parasite organism. Cell-cell fusion provides the opportunity needed for tumors to rejuvenate cell lines containing abnormal genomes and rapidly evolve to acquire dramatically aggressive traits such as metastasis. Indeed, metastasis appears to require cell-cell fusion. Cell-cell fusion also partially overcomes erosion of teleomeres during clone expansion and allows the essential elements of a tumorigenic genome to hide from chemotherapy as recessive traits in cells with normal phenotypes and re-emerge (by cell-cell fusion) as a new cancer after the phenotypically cancerous cells have been eradicated by classical chemotherapy. Eradication of the cancer parasite cannot be routinely achieved by classical toxic chemotherapy alone or even by chemotherapy augmented with techniques needed to overcome anti-apoptotic traits of cancer cells. Direct chemical intervention against cell-cell fusion concurrent with classical toxic chemotherapy holds a promise of preventing re-lapse of the disease. Intervention against cell-cell fusion may also directly suppress metastasis based on the model presented here. The paper also summarizes work on the cell surface glycoprotein CD44 that implicates it as a key element in cell-cell fusion and hence cancer.

Nonequilibrium model for estimating parameters of deleterious mutations

Deleterious mutations are of extreme evolutionary importance because, even though they are eliminated by natural selection, their continuous pressure creates a pool of variability in natural populations. They are of potential relevance for the existence of several features in evolution, such as sexual reproduction, and pose a risk to small asexual populations. Despite their extreme importance, the deleterious mutation rate and the effects of each mutation on fitness are poorly known quantities. Here we analyze a simple model that can be applied to simple experiments, in microorganisms, aiming at the quantification of these values.