arXiv subjects

Claus O. Wilke

Publications and source records attributed to Claus O. Wilke.

At least 37 records · Page 2Linked to original sources

arXiv2004

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.

q-bio.PE↗

arXiv2004

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

RNA viruses are a widely used tool 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 VSV and HIV-1. Our results suggest that frequency-dependent selection may be common in typical evolution experiments with viruses.

q-bio.PE↗

arXiv2003

Phenotypic mixing and hiding may contribute to memory in viral quasispecies

Background. In a number of recent experiments with food-and-mouth disease virus, a deleterious mutant, was found to avoid extinction and remain in the population for long periods of time. This observation was called quasispecies memory. The origin of quasispecies memory is not fully understood. Results. We propose and analyze a simple model of complementation between the wild type virus and a mutant that has an impaired ability of cell entry. The mutant will go extinct unless it is recreated from the wild type through mutations. However, under phenotypic mixing-and-hiding as a mechanism of complementation, the time to extinction in the absence of mutations increases with increasing multiplicity of infection (m.o.i.). The mutant's frequency at equilibrium under selection-mutation balance also increases with increasing m.o.i. At high m.o.i., a large fraction of mutant genomes are encapsidated with wild-type protein, which enables them to infect cells as efficiently as the wild type virions, and thus increases their fitness to the wild-type level. Moreover, even at low m.o.i. the equilibrium frequency of the mutant is higher than predicted by the standard quasispecies model, because a fraction of mutant virions generated from wild-type parents will also be encapsidated by wild-type protein. Conclusions. Our model predicts that phenotypic hiding will strongly influence the population dynamics of viruses, particularly at high m.o.i., and will also have important effects on the mutation--selection balance at low m.o.i. The delay in mutant extinction and increase in mutant frequencies at equilibrium may, at least in part, explain memory in quasispecies populations.

physics.bio-ph↗

arXiv2003

Modeling stochastic clonal interference

We study the competition between several advantageous mutants in an asexual population (clonal interference) as a function of the time between the appearance of the mutants, their selective advantages, and the rate of deleterious mutations. We find that the overall probability of fixation (the probability that at least one of the mutants becomes the ancestor of the entire population) does not depend on the time interval between the appearance of these mutants, and equals the probability that a genotype bearing all of these mutations reaches fixation. This result holds also in the presence of deleterious mutations, and for an arbitrary number of competing mutants. We also show that if mutations interfere, an increase in the mean number of fixation events is associated with a decrease in the expected fitness gain of the population.

physics.bio-ph↗

arXiv2003

Does the Red Queen reign in the kingdom of digital organisms?

In competition experiments between two RNA viruses of equal or almost equal fitness, often both strains gain in fitness before one eventually excludes the other. This observation has been linked to the Red Queen effect, which describes a situation in which organisms have to constantly adapt just to keep their status quo. I carried out experiments with digital organisms (self-replicating computer programs) in order to clarify how the competing strains' location in fitness space influences the Red-Queen effect. I found that gains in fitness during competition were prevalent for organisms that were taken from the base of a fitness peak, but absent or rare for organisms that were taken from the top of a peak or from a considerable distance away from the nearest peak. In the latter two cases, either neutral drift and loss of the fittest mutants or the waiting time to the first beneficial mutation were more important factors. Moreover, I found that the Red-Queen dynamic in general led to faster exclusion than the other two mechanisms.

physics.bio-ph↗

arXiv2002

Probability of fixation of an advantageous mutant in a viral quasispecies

The probability that an advantageous mutant rises to fixation in a viral quasispecies is investigated in the framework of multi-type branching processes. Whether fixation is possible depends on the overall growth rate of the quasispecies that will form if invasion is successful, rather than on the individual fitness of the invading mutant. The exact fixation probability can only be calculated if the fitnesses of all potential members of the invading quasispecies are known. Quasispecies fixation has two important characteristics: First, a sequence with negative selection coefficient has a positive fixation probability as long as it has the potential to grow into a quasispecies with an overall growth rate that exceeds the one of the established quasispecies. Second, the fixation probabilities of sequences with identical fitnesses can nevertheless vary over many orders of magnitudes. Two approximations for the probability of fixation are introduced. Both approximations require only partial knowledge about the potential members of the invading quasispecies. The performance of these two approximations is compared to the exact fixation probability on a network of RNA sequences with identical secondary structure.

physics.bio-ph↗

arXiv2002

Viral evolution under the pressure of an adaptive immune system - optimal mutation rates for viral escape

Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is limited from above due to genomic information deterioration, and from below by insufficient sequence diversity, which leads to a quick eradication of the virus by the immune system. The mutation rate that optimally balances these two requirements depends to first order on the ratio of the inverse of the virus' growth rate and the time the immune system needs to develop a specific answer to an antigen. We find that a virus is most viable if it generates exactly one mutation within the time it takes for the immune system to adapt to a new viral epitope. Experimental viral mutation rates, in particular for HIV (human immunodeficiency virus), seem to suggest that many viruses have achieved their optimal mutation rate. [1] C.Kamp and S. Bornholdt, Phys. Rev. Lett., 88, 068104 (2002)

cond-mat.stat-mech↗

arXiv2001

Finite genome size can halt Muller's ratchet

We study the accumulation of deleterious mutations in a haploid, asexually reproducing population, using analytical models and computer simulations. We find that Muller's ratchet can come to a halt in small populations as a consequence of a finite genome size only, in the complete absence of backward or compensatory mutations, epistasis, or recombination. The origin of this effect lies in the fact that the number of loci at which mutations can create considerable damage decreases with every turn of the ratchet, while the total number of mutations per genome and generation remains constant. Whether the ratchet will come to a halt eventually depends on the ratio of the per-locus deleterious mutation rate $u$ and the selection strength $s$. For sufficiently small $u/s$, the ratchet halts after only a few clicks. We discuss the implications of our results for bacterial and virus evolution.

physics.bio-ph↗

arXiv2001

Optimal adaptive performance and delocalization in NK fitness landscapes

We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small but finite, rather than vanishing, mutation rate. The highest local maxima in the landscape are visited for even larger mutation rates, close to a transition point at which the population delocalizes (i.e., leaves the fitness peak at which it was localized) and starts traversing the sequence space. If the mutation rate is increased even further, the population undergoes a second transition and loses all sensitivity to fitness peaks. This second transition corresponds to the standard error threshold transition first described by Eigen. We discuss the implications of our results for biological evolution and for evolutionary optimization techniques.

physics.bio-ph↗

arXiv2001

Interaction between directional epistasis and average mutational effects

We investigate the relationship between the average fitness decay due to single mutations and the strength of epistatic interactions in genetic sequences. We observe that epistatic interactions between mutations are correlated to the average fitness decay, both in RNA secondary structure prediction as well as in digital organisms replicating in silico. This correlation implies that during adaptation, epistasis and average mutational effect cannot be optimized independently. In experiments with RNA sequences evolving on a neutral network, the selective pressure to decrease the mutational load then leads to a reduction of the amount of sequences with strong antagonistic interactions between deleterious mutations in the population.

physics.bio-ph↗

arXiv2001

Maternal effects in molecular evolution

We introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent's genotype. The model can be solved by means of a nonlinear mapping onto the standard quasispecies model. The dependency on the parental genotypes cancels from the mean fitness, but not from the individual sequence concentrations. For finite populations, the position of the error threshold is very sensitive to the influence from parent genotypes. In addition to biological applications, our model is important for understanding the dynamics of self-replicating computer programs.

physics.bio-ph↗

arXiv2001

Selection for Fitness vs. Selection for Robustness in RNA Secondary Structure Folding

We investigate the competition between two quasispecies residing on two disparate neutral networks. Under the assumption that the two neutral networks have different topologies and fitness levels, it is the mutation rate that determines which quasispecies will eventually be driven to extinction. For small mutation rates, we find that the quasispecies residing on the neutral network with the lower replication rate will disappear. For higher mutation rates, however, the faster replicating sequences may be outcompeted by the slower replicating ones in case the connection density on the second neutral network is sufficiently high. Our analytical results are in excellent agreement with flow-reactor simulations of replicating RNA sequences.

physics.bio-ph↗

arXiv2001

Adaptive evolution on neutral networks

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the population dynamics can be subdivided into separate epochs, with rapid transitions between them. Within one epoch, the average fitness in the population is approximately constant. The transitions between epochs, however, are generally accompanied by a significant increase in the average fitness. We verify our theoretical considerations with two analytically tractable bitstring models.

physics.bio-ph↗

arXiv2000

Dynamic Fitness Landscapes in Molecular Evolution

We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates of the molecules. In general, therefore, molecular evolution takes place in a dynamic rather than a static fitness landscape. We incorporate dynamic replication and decay rates into the standard quasispecies theory of molecular evolution, and show that for periodic time-dependencies, a system of evolving molecules enters a limit cycle for $t\to\infty$. For fast periodic changes, we show that molecules adapt to the time-averaged fitness landscape, whereas for slow changes they track the variations in the landscape arbitrarily closely. We derive a general approximation method that allows us to calculate the attractor of time-periodic landscapes, and demonstrate using several examples that the results of the approximation and the limiting cases of very slow and very fast changes are in perfect agreement. We also discuss landscapes with arbitrary time dependencies, and show that very fast changes again lead to a system that adapts to the time-averaged landscape. Finally, we analyze the dynamics of a finite population of molecules in a dynamic landscape, and discuss its relation to the infinite population limit.

physics.bio-ph↗

arXiv1999

Molecular Evolution in Time Dependent Environments

The quasispecies theory is studied for dynamic replication landscapes. A meaningful asymptotic quasispecies is defined for periodic time dependencies. The quasispecies' composition is constantly changing over the oscillation period. The error threshold moves towards the position of the time averaged landscape for high oscillation frequencies and follows the landscape closely for low oscillation frequencies.

physics.bio-ph↗

arXiv1999

Genetic Algorithms in Time-Dependent Environments

The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize the asymptotic states in dependence on the mutation rate and the time scale of changes. Furthermore, the notion of regular changes is raised for which the population can be shown to converge towards a generalized quasispecies. Based on this, error thresholds and an optimal mutation rate are approximately calculated for a generational genetic algorithm with a moving needle-in-the-haystack landscape. The so found phase diagram is fully consistent with our general considerations.

physics.bio-ph↗

arXiv1999

Adaptive walks on time-dependent fitness landscapes

The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of static fitness contributions are investigated for model landscapes derived from Kauffman's $NK$ landscapes. Depending on the amount of static fitness contributions in the landscape, the evolutionary dynamics can be divided into a percolating and a non-percolating phase. In the percolating phase, the walker performs a random walk over the regions of the landscape with high fitness.

physics.bio-ph↗

arXiv1998

Lifetimes of agents under external stress

An exact formula for the distribution of lifetimes in coherent-noise models and related models is derived. For certain stress distributions, this formula can be analytically evaluated and yields simple closed expressions. For those types of stress for which a closed expression is not available, a numerical evaluation can be done in a straightforward way. All results obtained are in perfect agreement with numerical experiments. The implications for the coherent-noise models' application to macroevolution are discussed.

physics.data-an↗