Evolution of digital organisms at high mutation rates leads to survival of the flattest

Evolutionary coupling between the deleteriousness of gene mutations and the amount of non-coding sequences

The phenotypic effects of random mutations depend on both the architecture of the genome and the gene-trait relationships. Both levels thus play a key role in the mutational variability of the phenotype, and hence in the long-term evolutionary success of the lineage. Here, by simulating the evolution of organisms with flexible genomes, we show that the need for an appropriate phenotypic variability induces a relationship between the deleteriousness of gene mutations and the quantity of non-coding sequences maintained in the genome. The more deleterious the gene mutations, the shorter the intergenic sequences. Indeed, in a shorter genome, fewer genes are affected by rearrangements (duplications, deletions, inversions, translocations) at each replication, which compensates for the higher impact of each gene mutation. This spontaneous adjustment of genome structure allows the organisms to retain the same average fitness loss per replication, despite the higher impact of single gene mutations. These results show how evolution can generate unexpected couplings between distinct organization levels.

A system for studying evolution of life-like virtual organisms

Background

Fitness landscapes, the dependences of fitness on the genotype, are of critical importance for the evolution of living beings. Unfortunately, fitness landscapes that are relevant to the evolution of complex biological functions are very poorly known. As a result, the existing theory of evolution is mostly based on postulated fitness landscapes, which diminishes its usefulness. Attempts to deduce fitness landscapes from models of actual biological processes led, so far, to only limited success.

Results

We present a model system for studying the evolution of biological function, which makes it possible to attribute fitness to genotypes in a natural way. The system mimics a very simple cell and takes into account the basic properties of gene regulation and enzyme kinetics. A virtual cell contains only two small molecules, an organic nutrient A and an energy carrier X, and proteins of five types – two transcription factors, two enzymes, and a membrane transporter. The metabolism of the cell consists of importing A from the environment and utilizing it in order to produce X and an unspecified end product. The genome may carry an arbitrary number of genes, each one encoding a protein of one of the five types. Both major mutations that affect whole genes and minor mutations that affect individual characteristics of genes are possible. Fitness is determined by the ability of the cell to maintain homeostasis when its environment changes. The system has been implemented as a computer program, and several numerical experiments have been performed on it. Evolution of the virtual cells usually involves a rapid initial increase of fitness, which eventually slows down, until a fitness plateau is reached. The origin of a wide variety of genetic networks is routinely observed in independent experiments performed under the same conditions. These networks can have different, including very high, levels of complexity and often include large numbers of non-essential genes.

Conclusion

The described system displays a rich repertoire of biologically sensible behaviors and, thus, can be useful for investigating a number of unresolved issues in evolutionary biology, including evolution of complexity, modularity and redundancy, as well as for studying the general properties of genotype-to-fitness maps.

Reviewers

This article was reviewed by Drs. Eugene Koonin, Shamil Sunyaev and Arcady Mushegian.

In vivo molecular evolution reveals biophysical origins of organismal fitness

In nature, evolution occurs through the continuous adaptation of a population to its environment. At the molecular level, adaptive changes in protein sequence and expression impact organismal fitness and, consequently, dictate population dynamics. Here, we have used a "weak link" method to favor variations in one gene, allowing adaptation to thermostability to be studied in molecular detail as bacteria were grown continuously for approximately 1500 generations. Surprisingly, only six mutant alleles, representing less than 1% of the possible missense mutations, were observed, suggesting a highly constrained molecular landscape during protein evolution. The changes in organismal fitness were linked directly to incremental increases in enzyme stability and activity maxima and corresponded to the narrow temperature ranges where each mutant enjoyed success within the overall population. Thus, continuous evolution of a single gene permits a quantitative approach that extends from the phenotypes of the microbial populations to their underlying biophysical basis.

Sexual reproduction reshapes the genetic architecture of digital organisms

Modularity and epistasis, as well as other aspects of genetic architecture, have emerged as central themes in evolutionary biology. Theory suggests that modularity promotes evolvability, and that aggravating (synergistic) epistasis among deleterious mutations facilitates the evolution of sex. Here, by contrast, we investigate the evolution of different genetic architectures using digital organisms, which are computer programs that self-replicate, mutate, compete and evolve. Specifically, we investigate how genetic architecture is shaped by reproductive mode. We allowed 200 populations of digital organisms to evolve for over 10 000 generations while reproducing either asexually or sexually. For 10 randomly chosen organisms from each population, we constructed and analysed all possible single mutants as well as one million mutants at each mutational distance from 2 to 10. The genomes of sexual organisms were more modular than asexual ones; sites encoding different functional traits had less overlap and sites encoding a particular trait were more tightly clustered. Net directional epistasis was alleviating (antagonistic) in both groups, although the overall strength of this epistasis was weaker in sexual than in asexual organisms. Our results show that sexual reproduction profoundly influences the evolution of the genetic architecture.

Digital genetics: unravelling the genetic basis of evolution

Digital genetics, or the genetics of digital organisms, is a new field of research that has become possible as a result of the remarkable power of evolution experiments that use computers. Self-replicating strands of computer code that inhabit specially prepared computers can mutate, evolve and adapt to their environment. Digital organisms make it easy to conduct repeatable, controlled experiments, which have a perfect genetic 'fossil record'. This allows researchers to address fundamental questions about the genetic basis of the evolution of complexity, genome organization, robustness and evolvability, and to test the consequences of mutations, including their interaction and recombination, on the fate of populations and lineages.

Population bottlenecks in quasispecies dynamics

The characteristics of natural populations result from different stochastic and deterministic processes that include reproduction with error, selection, and genetic drift. In particular, population fluctuations constitute a stochastic process that may play a very relevant role in shaping the structure of populations. For example, it is expected that small asexual populations will accumulate mutations at a higher rate than larger ones. As a consequence, in any population the fixation of mutations is accelerated when environmental conditions cause population bottlenecks. Bottlenecks have been relatively frequent in the history of life and it is generally accepted that they are highly relevant for speciation. Although population bottlenecks can occur in any species, their effects are more noticeable in organisms that form large and heterogeneous populations, such as RNA viral quasispecies. Bottlenecks can also positively select and isolate particles that still keep the ability to infect cells from a disorganized population created by crossing the error threshold.

Quasispecies in time-dependent environments

In recent years, quasispecies theory in time-dependent (that is, dynamically changing) environments has made dramatic progress. Several groups have addressed questions such as how the time scale of the changes affect viral adaptation and quasispecies formation, how environmental changes affect the optimal mutation rate, or how virus and host co-evolve. Here, we review these recent developments, and give a nonmathematical introduction to the most important concepts and results of quasispecies theory in time-dependent environments. We also compare the theoretical results with results from evolution experiments that expose viruses to successive regimes of replication in two or more different hosts.

Mechanisms of genetic robustness in RNA viruses

Two key features of RNA viruses are their compacted genomes and their high mutation rate. Accordingly, deleterious mutations are common and have an enormous impact on viral fitness. In their multicellular hosts, robustness can be achieved by genomic redundancy, including gene duplication, diploidy, alternative metabolic pathways and biochemical buffering mechanisms. However, here we review evidence suggesting that during RNA virus evolution, alternative robustness mechanisms may have been selected. After briefly describing how genetic robustness can be quantified, we discuss mechanisms of intrinsic robustness arising as consequences of RNA-genome architecture, replication peculiarities and quasi-species population dynamics. These intrinsic robustness mechanisms operate efficiently at the population level, despite the mutational sensitivity shown by individual genomes. Finally, we discuss the possibility that viruses might exploit cellular buffering mechanisms for their own benefit, producing a sort of extrinsic robustness.

On The Necessity to Study Natural Bacterial Populations-The Model of Bacillus Simplex From "Evolution Canyons" I and II, Israel

How do bacteria evolve and speciate in natural environments? How does bacterial evolution relate to bacterial systematics? Exploring these answers is essential because bacteria profoundly impact life in general and, in particular, that of humans. Much insight into bacterial microevolution has come from theoretical and computational studies and from multigenerational laboratory systems ("Experimental Evolution"). These studies, however, do not take into account the diversity of modes of how bacteria can evolve under the complexity of the real world, i.e., nature. We argue, therefore, that for a comprehensive understanding of bacterial microevolution, it is essential to study natural populations. We underline our argument by introducing theBacillus simplexmodel from "Evolution Canyon", Israel. This metapopulation splits into different evolutionary lineages that have adapted to the microclimatically different slopes of "Evolution Canyon". It was shown that temperature stress is a major environmental factor driving theB. simplexadaptation and speciation progress. Therefore, this model population has proven highly suitable to study bacterial microevolution in natural habitats. Finally, we discuss theB. simplexintrapopulation divergence of lineages in light of current controversies on bacterial species concepts and taxon identification.

Direct evolution of genetic robustness in microRNA

Genetic robustness, the invariance of the phenotype in the face of genetic perturbations, can endow the organism with reduced susceptibility to mutations. A large body of work in recent years has focused on the origins, mechanisms, and consequences of robustness in a wide range of biological systems. Despite the apparent prevalence of mutational robustness in nature, however, its evolutionary origins are still unclear. Does robustness evolve directly by natural selection or is it merely a correlated byproduct of other phenotypic traits? By examining microRNA (miRNA) genes of several eukaryotic species, we show that the structure of miRNA precursor stem-loops exhibits a significantly high level of mutational robustness in comparison with random RNA sequences with similar stem-loop structures. Hence, this excess robustness of miRNA goes beyond the intrinsic robustness of the stem-loop hairpin structure. Furthermore, we show that it is not the byproduct of a base composition bias or of thermodynamic stability. These findings suggest that the excess robustness of miRNA stem-loops is the result of direct evolutionary pressure toward increased robustness. We further demonstrate that this adaptive robustness evolves to compensate for structures with low intrinsic robustness.

Sexual reproduction selects for robustness and negative epistasis in artificial gene networks

The mutational deterministic hypothesis for the origin and maintenance of sexual reproduction posits that sex enhances the ability of natural selection to purge deleterious mutations after recombination brings them together into single genomes. This explanation requires negative epistasis, a type of genetic interaction where mutations are more harmful in combination than expected from their separate effects. The conceptual appeal of the mutational deterministic hypothesis has been offset by our inability to identify the mechanistic and evolutionary bases of negative epistasis. Here we show that negative epistasis can evolve as a consequence of sexual reproduction itself. Using an artificial gene network model, we find that recombination between gene networks imposes selection for genetic robustness, and that negative epistasis evolves as a by-product of this selection. Our results suggest that sexual reproduction selects for conditions that favour its own maintenance, a case of evolution forging its own path.

Exact solution of the Eigen model with general fitness functions and degradation rates

We present an exact solution of Eigen's quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasispecies under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady-state solution shows a multicenter behavior.

Recombination and the evolution of mutational robustness

Mutational robustness is the degree to which a phenotype, such as fitness, is resistant to mutational perturbations. Since most of these perturbations will tend to reduce fitness, robustness provides an immediate benefit for the mutated individual. However, robust systems decay due to the accumulation of deleterious mutations that would otherwise have been cleared by selection. This decay has received very little theoretical attention. At equilibrium, a population or asexual lineage is expected to have a mutation load that is invariant with respect to the selection coefficient of deleterious alleles, so the benefit of robustness (at the level of the population or asexual lineage) is temporary. However, previous work has shown that robustness can be favoured when robustness loci segregate independently of the mutating loci they act upon. We examine a simple two-locus model that allows for intermediate rates of recombination and inbreeding to show that increasing the effective recombination rate allows for the evolution of greater mutational robustness.

Selective advantage for multicellular replicative strategies: a two-cell example

This paper develops a quasispecies model where cells can adopt a two-cell survival strategy. Within this strategy, pairs of cells join together, at which point one of the cells sacrifices its own replicative ability for the sake of the other cell. We develop a simplified model for the evolutionary dynamics of this process, allowing us to solve for the steady state using standard approaches from quasispecies theory. We find that our model exhibits two distinct regimes of behavior: At low concentrations of limiting resource, the two-cell strategy outcompetes the single-cell survival strategy, while at high concentrations of limiting resource, the single-cell survival strategy dominates. The single-cell survival strategy becomes disadvantageous at low concentrations of limiting resource because the energetic costs of maintaining reproductive and metabolic pathways approach, and may even exceed, the rate of energy production, leaving little excess energy for the purposes of replicating a new cell. However, if the rate of energy production exceeds the energetic costs of maintaining metabolic pathways, then the excess energy, if shared among several cells, can pay for the reproductive costs of a single cell, leaving energy to replicate a new cell. Associated with the two solution regimes of our model is a localization to delocalization transition over the portion of the genome coding for the multicell strategy, analogous to the error catastrophe in standard quasispecies models. The existence of such a transition indicates that multicellularity can emerge because natural selection does not act on specific cells, but rather on replicative strategies. Within this framework, individual cells become the means by which replicative strategies are propagated. Such a framework is therefore consistent with the concept that natural selection does not act on individuals, but rather on populations.

Through the interaction of neutral and adaptive mutations, evolutionary search finds a way

An evolutionary system that supports the interaction of neutral and adaptive mutations is investigated. Experimental results on a Boolean function and needle-in-haystack problems show that this system enables evolutionary search to find better solutions faster. Through a novel analysis based on the ratio of neutral to adaptive mutations, we identify this interaction as an engine that automatically adjusts the relative amounts of exploration and exploitation to achieve effective search (i.e., it is self-adaptive). Moreover, a hypothesis to describe the search process in this system is proposed and investigated. Our findings lead us to counter the arguments of those who dismiss the usefulness of neutrality. We argue that the benefits of neutrality are intimately related to its implementation, so that one must be cautious about making general claims about its merits or demerits.

Resilient individuals improve evolutionary search

Results from the artificial life community show that under some conditions evolving populations converge on broader, but less fit peaks in the fitness landscape and avoid more fit, but narrower peaks. Results from the evolutionary computation community show that over time genotypes evolve to become more resilient, where resiliency (or genetic robustness) is defined as the ability of an individual to resist the potentially negative effects of genetic operations. This article demonstrates a previously unobserved evolutionary dynamic: in populations initially favoring a low, broad fitness peak, increases in resiliency result in the population shifting to a higher, narrower fitness peak. In these cases increasing resiliency is a necessary precondition for finding narrower peaks. If increasing resiliency is restricted, for example by restricting growth, populations fail to shift to the narrower peak and remain stuck on the broader, less fit peaks. Thus, restricting growth or other resiliency-enhancing strategies may significantly inhibit evolutionary search by making it impossible for an evolutionary algorithm to find solutions represented by better, but narrower, peaks.

Evolution of mutational robustness in an RNA virus

Mutational (genetic) robustness is phenotypic constancy in the face of mutational changes to the genome. Robustness is critical to the understanding of evolution because phenotypically expressed genetic variation is the fuel of natural selection. Nonetheless, the evidence for adaptive evolution of mutational robustness in biological populations is controversial. Robustness should be selectively favored when mutation rates are high, a common feature of RNA viruses. However, selection for robustness may be relaxed under virus co-infection because complementation between virus genotypes can buffer mutational effects. We therefore hypothesized that selection for genetic robustness in viruses will be weakened with increasing frequency of co-infection. To test this idea, we used populations of RNA phage φ6 that were experimentally evolved at low and high levels of co-infection and subjected lineages of these viruses to mutation accumulation through population bottlenecking. The data demonstrate that viruses evolved under high co-infection show relatively greater mean magnitude and variance in the fitness changes generated by addition of random mutations, confirming our hypothesis that they experience weakened selection for robustness. Our study further suggests that co-infection of host cells may be advantageous to RNA viruses only in the short term. In addition, we observed higher mutation frequencies in the more robust viruses, indicating that evolution of robustness might foster less-accurate genome replication in RNA viruses.

RNA phage viruses evolved under high co-infection of host cells are less robust to mutations than those propagated under low co-infection, suggesting that co-infection may be advantageous to RNA viruses only in the short term.

A life-history perspective on short- and long-term consequences of compensatory growth

Compensatory or catch-up growth (CG) is widely observed following periods of resource deprivation. Because of this commonness, it is generally assumed that compensatory growth is adaptive, but most theory to date has explicitly ignored considerations of fitness. Following a period of deprivation, when resources become plentiful again, individuals may not respond at all and continue on a "normal" trajectory from a smaller size at age, may exhibit faster-than-normal growth immediately following the end of the period, or may adopt a growth strategy that involves faster-than-normal growth at some later time. Compensating individuals may also overtake control individuals who have been growing normally throughout. We hypothesize that the key to understanding CG is that growth leads to the accumulation of damage at the cellular level that is expressed (and thus must be modeled) at the level of the organism. We show that a life-history model incorporating the mortality consequences of both size and damage provides a framework for understanding compensatory growth. We use the theory to classify physiological and life-history characteristics for which CG is predicted to be the optimal response to deprivation.

Tradeoff between short-term and long-term adaptation in a changing environment

We investigate the competition dynamics of two microbial or viral strains that live in an environment that switches periodically between two states. One of the strains is adapted to the long-term environment, but pays a short-term cost, while the other is adapted to the short-term environment and pays a cost in the long term. We explore the tradeoff between these alternative strategies in extensive numerical simulations and present a simple analytic model that can predict the outcome of these competitions as a function of the mutation rate and the time scale of the environmental changes. Our model is relevant for arboviruses, which alternate between different host species on a regular basis.

The Evolutionary Genetics of Canalization

Evolutionary genetics has recently made enormous progress in understanding how genetic variation maps into phenotypic variation. However why some traits are phenotypically invariant despite apparent genetic and environmental changes has remained a major puzzle. In the 1940s, Conrad Hal Waddington coined the concept and term "canalization" to describe the robustness of phenotypes to perturbation; a similar concept was proposed by Waddington's contemporary Ivan Ivanovich Schmalhausen. This paper reviews what has been learned about canalization since Waddington. Canalization implies that a genotype's phenotype remains relatively invariant when individuals of a particular genotype are exposed to different environments (environmental canalization) or when individuals of the same single- or multilocus genotype differ in their genetic background (genetic canalization). Consequently, genetic canalization can be viewed as a particular kind of epistasis, and environmental canalization and phenotypic plasticity are two aspects of the same phenomenon. Canalization results in the accumulation of phenotypically cryptic genetic variation, which can be released after a "decanalizing" event. Thus, canalized genotypes maintain a cryptic potential for expressing particular phenotypes, which are only uncovered under particular decanalizing environmental or genetic conditions. Selection may then act on this newly released genetic variation. The accumulation of cryptic genetic variation by canalization may therefore increase evolvability at the population level by leading to phenotypic diversification under decanalizing conditions. On the other hand, under canalizing conditions, a major part of the segregating genetic variation may remain phenotypically cryptic; canalization may therefore, at least temporarily, constrain phenotypic evolution. Mechanistically, canalization can be understood in terms of transmission patterns, such as epistasis, pleiotropy, and genotype by environment interactions, and in terms of genetic redundancy, modularity, and emergent properties of gene networks and biochemical pathways. While different forms of selection can favor canalization, the requirements for its evolution are typically rather restrictive. Although there are several methods to detect canalization, there are still serious problems with unambiguously demonstrating canalization, particularly its adaptive value.

Quasispecies theory in the context of population genetics

BACKGROUND

A number of recent papers have cast doubt on the applicability of the quasispecies concept to virus evolution, and have argued that population genetics is a more appropriate framework to describe virus evolution than quasispecies theory.

RESULTS

I review the pertinent literature, and demonstrate for a number of cases that the quasispecies concept is equivalent to the concept of mutation-selection balance developed in population genetics, and that there is no disagreement between the population genetics of haploid, asexually-replicating organisms and quasispecies theory.

CONCLUSION

Since quasispecies theory and mutation-selection balance are two sides of the same medal, the discussion about which is more appropriate to describe virus evolution is moot. In future work on virus evolution, we would do good to focus on the important questions, such as whether we can develop accurate, quantitative models of virus evolution, and to leave aside discussions about the relative merits of perfectly equivalent concepts.

Evolutionary capacitance may be favored by natural selection

Evolutionary capacitors phenotypically reveal a stock of cryptic genetic variation in a reversible fashion. The sudden and reversible revelation of a range of variation is fundamentally different from the gradual introduction of variation by mutation. Here I study the invasion dynamics of modifiers of revelation. A modifier with the optimal rate of revelation mopt has a higher probability of invading any other population than of being counterinvaded. mopt varies with the population size N and the rate theta at which environmental change makes revelation adaptive. For small populations less than a minimum cutoff Nmin, all revelation is selected against. Nmin is typically quite small and increases only weakly, with theta-1/2. For large populations with N>1/theta, mopt is approximately 1/N. Selection for the optimum is highly effective and increases in effectiveness with larger N>>1/theta. For intermediate values of N, mopt is typically a little less than theta and is only weakly favored over less frequent revelation. The model is analogous to a two-locus model for the evolution of a mutator allele. It is a fully stochastic model and so is able to show that selection for revelation can be strong enough to overcome random drift.

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.

The speed of adaptation in large asexual populations

In large asexual populations, beneficial mutations have to compete with each other for fixation. Here, I derive explicit analytic expressions for the rate of substitution and the mean beneficial effect of fixed mutations, under the assumptions that the population size N is large, that the mean effect of new beneficial mutations is smaller than the mean effect of new deleterious mutations, and that new beneficial mutations are exponentially distributed. As N increases, the rate of substitution approaches a constant, which is equal to the mean effect of new beneficial mutations. The mean effect of fixed mutations continues to grow logarithmically with N. The speed of adaptation, measured as the change of log fitness over time, also grows logarithmically with N for moderately large N, and it grows double-logarithmically for extremely large N. Moreover, I derive a simple formula that determines whether at given N beneficial mutations are expected to compete with each other or go to fixation independently. Finally, I verify all results with numerical simulations.

Recombination in primeval genomes: a step forward but still a long leap from maintaining a sizable genome

A stubborn question in early molecular evolution is how to sustain the "minimum" informational length required for the basic features of life with a putative low-copying fidelity RNA polymerase ribozyme. Proposals to circumvent the information crisis have primarily focused on networks of cooperative molecules or compartmentalization of non-cooperative unlinked templates, but success has been very limited so far. Lehman (2003) has recently suggested that recombination--a frequently ignored player in early evolution--could have been crucial to building up primeval genomes of sizable length. Here we investigate this claim by assuming (without loss of generality) that genes were already enclosed in a compartment (vesicle, protocell). The numerical results show a quite intricate interplay among mutation, recombination, and gene redundancy. Provided that the minimum number of gene copies per protocell was enough for recombination to recreate wildtype templates--but not too high to impose an unbearable burden of mutants--informational content could have increased by at least 25% by keeping the same mutational load as that for a population without recombination. However, the upper bound of informational length would still be far from the "minimal life" provisions.

Following the very initial growth of biological RNA viral clones

Due to their extremely high genetic diversity, which is a direct consequence of high mutation rates, RNA viruses are often described as molecular quasispecies. According to this theory, RNA virus populations cannot be understood in terms of individual viral clones, as they are clouds of interconnected mutants, but this prediction has not yet been demonstrated experimentally. The goal of this study was to determine the fitness of individual clones sampled from a given RNA virus population, a necessary previous step to test the above prediction. To do so, limiting dilutions of a vesicular stomatitis virus population were employed to isolate single viral clones and their initial growth dynamics were followed, corresponding to the release of the first few hundred viral particles. This technique is useful for estimating basic fitness parameters, such as intracellular growth rate, viral yield per cell, rate at which cells are infected and time spent in cell-to-cell transmission. A combination of these parameters allows estimation of the fitness of individual clones, which seems to be determined mainly by their ability to complete infection cycles more quickly. Interestingly, fitness was systematically higher for initial clones than for their derived populations. In addition to environmental changes, such as cellular defence mechanisms, these differences are attributable to high RNA virus mutation rates.

Validating viral quasispecies with digital organisms: a re-examination of the critical mutation rate

Background

In this report we re-examine some recent experiments with digital organisms to test some predictions of quasispecies theory. These experiments revealed that under high mutation rates populations of less fit organisms previously adapted to such high mutation rates were able to outcompete organisms with higher average fitness but adapted to low mutation rates.

Results

We have verified that these results do hold in the original conditions and, by extending the set of initial parameters, we have also detected that the critical mutation rate was independent of population size, a result that we have found to be dependent on a different, contingent factor, the initial fitness vector. Furthermore, in all but one case, the critical mutation rate is higher than the error threshold, a key parameter in quasispecies theory, which prevents its extrapolation to natural viral populations.

Conclusion

From these results we conclude that digital organisms are useful tools for investigating evolutionary patterns and processes including some predictions from the quasispecies theory.

The opportunity for canalization and the evolution of genetic networks

There has been a recent revival of interest in how genetic interactions evolve, spurred on by an increase in our knowledge of genetic interactions at the molecular level. Empirical work on genetic networks has revealed a surprising amount of robustness to perturbations, suggesting that robustness is an evolved feature of genetic networks. Here, we derive a general model for the evolution of canalization that can incorporate any form of perturbation. We establish an upper bound to the strength of selection on canalization that is approximately equal to the fitness load in the system. This method makes it possible to compare different forms of perturbation, including genetic, developmental, and environmental effects. In general, load that arises from mutational processes is low because the mutation rate is itself low. Mutation load can create selection for canalization in a small network that can be achieved through dominance evolution or gene duplication, and in each case selection for canalization is weak at best. In larger genetic networks, selection on genetic canalization can be reasonably strong because larger networks have higher mutational load. Because load induced through migration, segregation, developmental noise, and environmental variance is not mutation limited, each can cause strong selection for canalization.

Imperfect DNA lesion repair in the semiconservative quasispecies model: derivation of the Hamming class equations and solution of the single-fitness peak landscape

This paper develops a Hamming class formalism for the semiconservative quasispecies equations with imperfect lesion repair, first presented and analytically solved in Y. Brumer and E.I. Shakhnovich (q-bio.GN/0403018, 2004). Starting from the quasispecies dynamics over the space of genomes, we derive an equivalent dynamics over the space of ordered sequence pairs. From this set of equations, we are able to derive the infinite sequence length form of the dynamics for a class of fitness landscapes defined by a master genome. We use these equations to solve for a generalized single-fitness-peak landscape, where the master genome can sustain a maximum number of lesions and remain viable. We determine the mean equilibrium fitness and error threshold for this class of landscapes, and show that when lesion repair is imperfect, semiconservative replication displays characteristics from both conservative replication and semiconservative replication with perfect lesion repair. The work presented here provides a formulation of the model which greatly facilitates the analysis of a relatively broad class of fitness landscapes, and thus serves as a convenient springboard into biological applications of imperfect lesion repair.

Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme

In a recent paper [Phys. Rev. E 69, 046121 (2004)]], we used the Suzuki-Trottere formalism to study a quasispecies biological evolution model in a parallel mutation-selection scheme with a single-peak fitness function and a point mutation. In the present paper, we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation-selection scheme. We give some analytical equations to define the error thresholds for some general cases of mean-field-like or symmetric mutation schemes and fitness functions. We derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions. We derive exact dynamics for two-point mutations, asymmetric mutations, and the four-value spin model with a single-peak fitness function. The same method is applied for the model with a royal road fitness function. We derive the steady-state distribution for the single-peak fitness function.

Solution of the quasispecies model for an arbitrary gene network

In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of N genes, so that the full genome sequence sigma may be written as sigma= sigma1sigma2...sigmaN, where sigma(i) are sequences of individual genes. We assume a single fitness peak model for each gene, so that gene i has some "master" sequence sigma(i,0) for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an "error cascade." As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard "deletion set" method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed "survival of the flattest."

Replication at periodically changing multiplicity of infection promotes stable coexistence of competing viral populations

RNA viruses are widely used to study evolution experimentally. Many standard protocols of virus propagation and competition are done at nominally low multiplicity of infection (m.o.i.), but lead during one passage to two or more rounds of infection, of which the later ones are at high m.o.i. Here, we develop a model of the competition between wild type (wt) and a mutant under a regime of alternating m.o.i. We assume that the mutant is deleterious when it infects cells on its own, but derives a selective advantage when rare and coinfecting with wt, because it can profit from superior protein products created by the wt. We find that, under these assumptions, replication at alternating low and high m.o.i. may lead to the stable coexistence of wt and mutant for a wide range of parameter settings. The predictions of our model are consistent with earlier observations of frequency-dependent selection in vesicular stomatitis virus and human immunodeficiency virus type 1. Our results suggest that frequency-dependent selection may be common in typical evolution experiments with viruses.

The population genetics and evolutionary epidemiology of RNA viruses

The authors discuss the main mechanisms of RNA virus evolution — mutation, recombination, natural selection, genetic drift and migration, and how these interact to shape the genetic structure of populations. The quasispecies model of RNA virus evolution is explained and the question of whether this model provides an accurate description of RNA virus evolution is discussed. Experiments that can be carried out to test the basic principles of evolutionary theory are briefly described. The authors review what such experiments have told us about virus evolution and, more widely, what these experiments have revealed in terms of general evolutionary principles. RNA viruses evolve quickly, so a detailed reconstruction of their epidemiological history can be undertaken. The authors show how epidemiological patterns of viruses result from their evolution at two different levels: within individual hosts (and vectors) and among hosts at the population level. Using several examples, including HIV and SARS, the authors describe how studying RNA virus evolution could be used to understand virus emergence. Finally, the important topics of the evolution of virulence and resistance to drugs are discussed.

RNA viruses are ubiquitous intracellular parasites that are responsible for many emerging diseases, including AIDS and SARS. Here, we discuss the principal mechanisms of RNA virus evolution and highlight areas where future research is required. The rapidity of sequence change in RNA viruses means that they are useful experimental models for the study of evolution in general and it enables us to watch them change in 'real time', and retrace the spread through populations with molecular phylogenies. An understanding of the mechanisms of RNA virus sequence change is also crucial to predicting important aspects of their emergence and long-term evolution.

Solvable biological evolution model with a parallel mutation-selection scheme

Based on the connection between a quantum spin model and an asexual biological evolution model with a single-peak fitness function in parallel mutation-selection scheme, we solve exactly both static and dynamics of the evolution model. We find that relaxation in such a parallel scheme is faster than that in a connected scheme of Eigen model. Our method can also be extended to other fitness functions.

A quasispecies approach to viral evolution in the context of an adaptive immune system

A deeper understanding of the mechanisms that determine viral evolution in the context of an adaptive immune system is vital for the development of efficient strategies to defeat viral infections. The problem of describing these mechanisms is discussed using the concept of quasispecies. Conditions for both an optimal immune response and for highest viral viability are derived from theoretical models and are supported by empirical data.

Thermodynamical interpretation of an adaptive walk on a Mt. Fuji-type fitness landscape: Einstein relation-like formula holds in a stochastic evolution

We have theoretically studied the statistical properties of adaptive walks (or hill-climbing) on a Mt. Fuji-type fitness landscape in the multi-dimensional sequence space through mathematical analysis and computer simulation. The adaptive walk is characterized by the "mutation distance" d as the step-width of the walker and the "population size" N as the number of randomly generated d-fold point mutants to be screened. In addition to the fitness W, we introduced the following quantities analogous to thermodynamical concepts: "free fitness" G(W) is identical with W+T x S(W), where T is the "evolutionary temperature" T infinity square root of d/lnN and S(W) is the entropy as a function of W, and the "evolutionary force" X is identical with d(G(W)/T)/dW, that is caused by the mutation and selection pressure. It is known that a single adaptive walker rapidly climbs on the fitness landscape up to the stationary state where a "mutation-selection-random drift balance" is kept. In our interpretation, the walker tends to the maximal free fitness state, driven by the evolutionary force X. Our major findings are as follows: First, near the stationary point W*, the "climbing rate" J as the expected fitness change per generation is described by J approximately L x X with L approximately V/2, where V is the variance of fitness distribution on a local landscape. This simple relationship is analogous to the well-known Einstein relation in Brownian motion. Second, the "biological information gain" (DeltaG/T) through adaptive walk can be described by combining the Shannon's information gain (DeltaS) and the "fitness information gain" (DeltaW/T).

Negative effect of genetic bottlenecks on the adaptability of vesicular stomatitis virus

Muller's ratchet is a principle of evolutionary genetics describing mutant accumulation in populations that are repeatedly subjected to genetic bottleneck. The immediate effect of Muller's ratchet, overall loss of fitness, has been confirmed in several viral systems belonging to different groups. This report shows that in addition to fitness loss, genetic bottlenecks also have longer-term effects, namely changes in the capacity of viral populations to adapt. Thus, vesicular stomatitis virus strains with a history of genetic bottleneck have lower adaptability than strains maintained at relatively large population sizes. This lower adaptability is illustrated by their reduced ability to regain fitness and by their inability to outcompete wild-type populations in situations where the initial fitness of the bottlenecked mutant is the same or even higher than the initial fitness of the wild-type.

Perspective: Evolution and detection of genetic robustness

Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g., mutations) or nonheritable perturbations (e.g., the weather). Here we primarily focus on the first kind of robustness--genetic robustness--and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory; (2) understanding the evolution of genetic robustness: and (3) exploring the implications of genetic robustness for future evolution.

Digital evolution in time-dependent fitness landscapes

We study the response of populations of digital organisms that adapt to a time-varying (periodic) fitness landscape of two oscillating peaks. We corroborate in general predictions from quasi-species theory in dynamic landscapes, such as adaptation to the average fitness landscape at small periods (high frequency) and quasistatic adaptation at large periods (low frequency). We also observe adaptive phase shifts (time lags between a change in the fitness landscape and an adaptive change in the population) that indicate a low-pass filter effect, in agreement with existing theory. Finally, we witness long-term adaptation to fluctuating environments not anticipated in previous theoretical work.

Avida: a software platform for research in computational evolutionary biology

Avida is a software platform for experiments with self-replicating and evolving computer programs. It provides detailed control over experimental settings and protocols, a large array of measurement tools, and sophisticated methods to analyze and post-process experimental data. We explain the general principles on which Avida is built, as well as its main components and their interactions. We also explain how experiments are set up, carried out, and analyzed.

Error and repair catastrophes: A two-dimensional phase diagram in the quasispecies model

This paper develops a two-gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by sigma(via), yields a viable organism with first-order growth rate constant k>1 if it is equal to some target "master" sequence sigma(via,0). The second gene, denoted by sigma(rep), yields an organism capable of genetic repair if it is equal to some target "master" sequence sigma(rep,0). This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on micro identical with Lepsilon, the product of sequence length and per base pair replication error probability, and epsilon(r), the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of the three possible "phases." In the first phase, the population is localized about the viability and repairing master sequences. As epsilon(r) exceeds the fraction of deleterious mutations, the population undergoes a "repair" catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when micro exceeds ln k/epsilon(r), while above the repair catastrophe, the distribution undergoes the error catastrophe when micro exceeds ln k/f(del), where f(del) denotes the fraction of deleterious mutations.

Synchronous loss of quasispecies memory in parallel viral lineages: a deterministic feature of viral quasispecies

Viral quasispecies are endowed with a memory of their past evolutionary history in the form of minority genomes of their mutant spectra. To determine the fate of memory genomes in evolving viral quasispecies, we have measured memory levels of antigenic variant of foot-and-mouth disease virus (FMDV) RED, which includes an Arg-Glu-Asp (RED) at a surface antigenic loop of the viral capsid. The RED reverted to the standard Arg-Gly-Asp (RGD), and the RED remained as memory in the evolving quasispecies. In four parallel evolutionary lineages, memory reduction followed a strikingly similar pattern, and at passage 60 memory levels were indistinguishable from those of control populations (devoid of memory). Nucleotide sequence analyses indicated that memory loss occurred synchronously despite its ultimate molecular basis being the stochastic occurrence of mutations in the evolving quasispecies. These results on the kinetics of memory levels have unveiled a deterministic feature of viral quasispecies. Molecular mechanisms that may underlie synchronous memory loss are the averaging of noise signals derived from mutational input, and constraints to genome diversification imposed by a nucleotide sequence context in the viral genome. Possible implications of the behaviour of complex, adaptive viral systems as experimental models to address primary mechanisms of neurological memory are discussed.

Origin of sex revisited

Why did sex ever arise in the first place? Why it does not disappear in view of the greater efficiency of asexuals? These are clearly two different questions, and we suggest here that the solution for the origin of sex does not necessarily come from theoretical considerations based on currently existing genetic systems. Thus, while we agree with a number of authors in that the emergence of sex (understood as the exchange of genetic material between genomes) is deeply rooted in the origin of life and happened during the very early stages in the transition from individual genes ('replicators') to bacteria-like cells ('reproducers'), we challenge the idea that recombinational repair was the major selective force for the emergence of sex. Taking the stochastic corrector model as a starting point, we provide arguments that question the putative costs of redundancy in primitive protocells. In addition, if genes that cause intragenomic conflict (i.e., parasites) are taken into account, it is certainly wrong to suggest that cellular fusion would be beneficial at the population level (although this strong claim needs some qualifications). However, when a continuous input of deleterious mutations that impair the fitness of the protocell as a whole is considered in the model (in the realistic range in which stable mutant distributions of quasi-species within compartments are established), there are circumstances when sex could be beneficial as a side effect of the dynamic equilibrium between cellular fusion-mutation-selection. The scenario we have explored numerically is fully consistent with the idea that the universal ancestor was not a discrete entity but an ensemble of proto-organisms that exchanged much genetic information.

Increase in error threshold for quasispecies by heterogeneous replication accuracy

In this paper we investigate the error threshold for quasispecies with heterogeneous replication accuracy. We show that the coexistence of error-free and error-prone polymerases can greatly increase the error threshold without a catastrophic loss of genetic information. We also show that the error threshold is influenced by the number of replicores. Our research suggests that quasispecies with heterogeneous replication accuracy can reduce the genetic cost of selective evolution while still producing a variety of mutants.