@article{1077,
abstract = {Viral capsids are structurally constrained by interactions among the amino acids (AAs) of their constituent proteins. Therefore, epistasis is expected to evolve among physically interacting sites and to influence the rates of substitution. To study the evolution of epistasis, we focused on the major structural protein of the fX174 phage family by first reconstructing the ancestral protein sequences of 18 species using a Bayesian statistical framework. The inferred ancestral reconstruction differed at eight AAs, for a total of 256 possible ancestral haplotypes. For each ancestral haplotype and the extant species, we estimated, in silico, the distribution of free energies and epistasis of the capsid structure. We found that free energy has not significantly increased but epistasis has. We decomposed epistasis up to fifth order and found that higher-order epistasis sometimes compensates pairwise interactions making the free energy seem additive. The dN/dS ratio is low, suggesting strong purifying selection, and that structure is under stabilizing selection. We synthesized phages carrying ancestral haplotypes of the coat protein gene and measured their fitness experimentally. Our findings indicate that stabilizing mutations can have higher fitness, and that fitness optima do not necessarily coincide with energy minima.},
author = {Fernandes Redondo, Rodrigo A and Vladar, Harold and Włodarski, Tomasz and Bollback, Jonathan P},
issn = {17425689},
journal = {Journal of the Royal Society Interface},
number = {126},
publisher = {Royal Society of London},
title = {{Evolutionary interplay between structure, energy and epistasis in the coat protein of the fX174 phage family}},
doi = {10.1098/rsif.2016.0139},
volume = {14},
year = {2017},
}
@article{1111,
abstract = {Adaptation depends critically on the effects of new mutations and their dependency on the genetic background in which they occur. These two factors can be summarized by the fitness landscape. However, it would require testing all mutations in all backgrounds, making the definition and analysis of fitness landscapes mostly inaccessible. Instead of postulating a particular fitness landscape, we address this problem by considering general classes of landscapes and calculating an upper limit for the time it takes for a population to reach a fitness peak, circumventing the need to have full knowledge about the fitness landscape. We analyze populations in the weak-mutation regime and characterize the conditions that enable them to quickly reach the fitness peak as a function of the number of sites under selection. We show that for additive landscapes there is a critical selection strength enabling populations to reach high-fitness genotypes, regardless of the distribution of effects. This threshold scales with the number of sites under selection, effectively setting a limit to adaptation, and results from the inevitable increase in deleterious mutational pressure as the population adapts in a space of discrete genotypes. Furthermore, we show that for the class of all unimodal landscapes this condition is sufficient but not necessary for rapid adaptation, as in some highly epistatic landscapes the critical strength does not depend on the number of sites under selection; effectively removing this barrier to adaptation.},
author = {Heredia, Jorge and Trubenova, Barbora and Sudholt, Dirk and Paixao, Tiago},
issn = {00166731},
journal = {Genetics},
number = {2},
pages = {803 -- 825},
publisher = {Genetics Society of America},
title = {{Selection limits to adaptive walks on correlated landscapes}},
doi = {10.1534/genetics.116.189340},
volume = {205},
year = {2017},
}
@article{1351,
abstract = {The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives higher assurance and scalability. We focus on Wagner’s weighted GRN model with varying weights, which is used in evolutionary biology. In the model, weight parameters represent the gene interaction strength that may change due to genetic mutations. For a property of interest, we synthesise the constraints over the parameter space that represent the set of GRNs satisfying the property. We experimentally show that our parameter synthesis procedure computes the mutational robustness of GRNs—an important problem of interest in evolutionary biology—more efficiently than the classical simulation method. We specify the property in linear temporal logic. We employ symbolic bounded model checking and SMT solving to compute the space of GRNs that satisfy the property, which amounts to synthesizing a set of linear constraints on the weights.},
author = {Giacobbe, Mirco and Guet, Calin C and Gupta, Ashutosh and Henzinger, Thomas A and Paixao, Tiago and Petrov, Tatjana},
issn = {00015903},
journal = {Acta Informatica},
number = {8},
pages = {765 -- 787},
publisher = {Springer},
title = {{Model checking the evolution of gene regulatory networks}},
doi = {10.1007/s00236-016-0278-x},
volume = {54},
year = {2017},
}
@article{910,
abstract = {Frequency-independent selection is generally considered as a force that acts to reduce the genetic variation in evolving populations, yet rigorous arguments for this idea are scarce. When selection fluctuates in time, it is unclear whether frequency-independent selection may maintain genetic polymorphism without invoking additional mechanisms. We show that constant frequency-independent selection with arbitrary epistasis on a well-mixed haploid population eliminates genetic variation if we assume linkage equilibrium between alleles. To this end, we introduce the notion of frequency-independent selection at the level of alleles, which is sufficient to prove our claim and contains the notion of frequency-independent selection on haploids. When selection and recombination are weak but of the same order, there may be strong linkage disequilibrium; numerical calculations show that stable equilibria are highly unlikely. Using the example of a diallelic two-locus model, we then demonstrate that frequency-independent selection that fluctuates in time can maintain stable polymorphism if linkage disequilibrium changes its sign periodically. We put our findings in the context of results from the existing literature and point out those scenarios in which the possible role of frequency-independent selection in maintaining genetic variation remains unclear.
},
author = {Novak, Sebastian and Barton, Nicholas H},
journal = {Genetics},
number = {2},
pages = {653 -- 668},
publisher = {Genetics Society of America},
title = {{When does frequency-independent selection maintain genetic variation?}},
doi = {10.1534/genetics.117.300129},
volume = {207},
year = {2017},
}
@article{953,
abstract = {The role of natural selection in the evolution of adaptive phenotypes has undergone constant probing by evolutionary biologists, employing both theoretical and empirical approaches. As Darwin noted, natural selection can act together with other processes, including random changes in the frequencies of phenotypic differences that are not under strong selection, and changes in the environment, which may reflect evolutionary changes in the organisms themselves. As understanding of genetics developed after 1900, the new genetic discoveries were incorporated into evolutionary biology. The resulting general principles were summarized by Julian Huxley in his 1942 book Evolution: the modern synthesis. Here, we examine how recent advances in genetics, developmental biology and molecular biology, including epigenetics, relate to today's understanding of the evolution of adaptations. We illustrate how careful genetic studies have repeatedly shown that apparently puzzling results in a wide diversity of organisms involve processes that are consistent with neo-Darwinism. They do not support important roles in adaptation for processes such as directed mutation or the inheritance of acquired characters, and therefore no radical revision of our understanding of the mechanism of adaptive evolution is needed.},
author = {Charlesworth, Deborah and Barton, Nicholas H and Charlesworth, Brian},
journal = {Proceedings of the Royal Society of London Series B Biological Sciences},
number = {1855},
publisher = {Royal Society, The},
title = {{The sources of adaptive evolution}},
doi = {10.1098/rspb.2016.2864},
volume = {284},
year = {2017},
}
@inproceedings{1112,
abstract = {There has been renewed interest in modelling the behaviour of evolutionary algorithms by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogs of the additive and multiplicative drift theorems for SDEs. We exemplify the use of these methods for two model algorithms ((1+1) EA and RLS) on two canonical problems(OneMax and LeadingOnes).},
author = {Paixao, Tiago and Pérez Heredia, Jorge},
booktitle = {Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms},
isbn = {978-145034651-1},
location = {Copenhagen, Denmark},
pages = {3 -- 11},
publisher = {ACM},
title = {{An application of stochastic differential equations to evolutionary algorithms}},
doi = {10.1145/3040718.3040729},
year = {2017},
}
@article{954,
abstract = {Understanding the relation between genotype and phenotype remains a major challenge. The difficulty of predicting individual mutation effects, and particularly the interactions between them, has prevented the development of a comprehensive theory that links genotypic changes to their phenotypic effects. We show that a general thermodynamic framework for gene regulation, based on a biophysical understanding of protein-DNA binding, accurately predicts the sign of epistasis in a canonical cis-regulatory element consisting of overlapping RNA polymerase and repressor binding sites. Sign and magnitude of individual mutation effects are sufficient to predict the sign of epistasis and its environmental dependence. Thus, the thermodynamic model offers the correct null prediction for epistasis between mutations across DNA-binding sites. Our results indicate that a predictive theory for the effects of cis-regulatory mutations is possible from first principles, as long as the essential molecular mechanisms and the constraints these impose on a biological system are accounted for.},
author = {Lagator, Mato and Paixao, Tiago and Barton, Nicholas H and Bollback, Jonathan P and Guet, Calin C},
issn = {2050084X},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{On the mechanistic nature of epistasis in a canonical cis-regulatory element}},
doi = {10.7554/eLife.25192},
volume = {6},
year = {2017},
}
@article{1199,
abstract = {Much of quantitative genetics is based on the ‘infinitesimal model’, under which selection has a negligible effect on the genetic variance. This is typically justified by assuming a very large number of loci with additive effects. However, it applies even when genes interact, provided that the number of loci is large enough that selection on each of them is weak relative to random drift. In the long term, directional selection will change allele frequencies, but even then, the effects of epistasis on the ultimate change in trait mean due to selection may be modest. Stabilising selection can maintain many traits close to their optima, even when the underlying alleles are weakly selected. However, the number of traits that can be optimised is apparently limited to ~4Ne by the ‘drift load’, and this is hard to reconcile with the apparent complexity of many organisms. Just as for the mutation load, this limit can be evaded by a particular form of negative epistasis. A more robust limit is set by the variance in reproductive success. This suggests that selection accumulates information most efficiently in the infinitesimal regime, when selection on individual alleles is weak, and comparable with random drift. A review of evidence on selection strength suggests that although most variance in fitness may be because of alleles with large Nes, substantial amounts of adaptation may be because of alleles in the infinitesimal regime, in which epistasis has modest effects.},
author = {Barton, Nicholas H},
journal = {Heredity},
pages = {96 -- 109},
publisher = {Nature Publishing Group},
title = {{How does epistasis influence the response to selection?}},
doi = {10.1038/hdy.2016.109},
volume = {118},
year = {2017},
}
@article{1074,
abstract = {Recently it has become feasible to detect long blocks of nearly identical sequence shared between pairs of genomes. These IBD blocks are direct traces of recent coalescence events and, as such, contain ample signal to infer recent demography. Here, we examine sharing of such blocks in two-dimensional populations with local migration. Using a diffusion approximation to trace genetic ancestry, we derive analytical formulae for patterns of isolation by distance of IBD blocks, which can also incorporate recent population density changes. We introduce an inference scheme that uses a composite likelihood approach to fit these formulae. We then extensively evaluate our theory and inference method on a range of scenarios using simulated data. We first validate the diffusion approximation by showing that the theoretical results closely match the simulated block sharing patterns. We then demonstrate that our inference scheme can accurately and robustly infer dispersal rate and effective density, as well as bounds on recent dynamics of population density. To demonstrate an application, we use our estimation scheme to explore the fit of a diffusion model to Eastern European samples in the POPRES data set. We show that ancestry diffusing with a rate of σ ≈ 50–100 km/√gen during the last centuries, combined with accelerating population growth, can explain the observed exponential decay of block sharing with increasing pairwise sample distance.},
author = {Ringbauer, Harald and Coop, Graham and Barton, Nicholas H},
issn = {00166731},
journal = {Genetics},
number = {3},
pages = {1335 -- 1351},
publisher = {Genetics Society of America},
title = {{Inferring recent demography from isolation by distance of long shared sequence blocks}},
doi = {10.1534/genetics.116.196220},
volume = {205},
year = {2017},
}
@article{570,
abstract = {Most phenotypes are determined by molecular systems composed of specifically interacting molecules. However, unlike for individual components, little is known about the distributions of mutational effects of molecular systems as a whole. We ask how the distribution of mutational effects of a transcriptional regulatory system differs from the distributions of its components, by first independently, and then simultaneously, mutating a transcription factor and the associated promoter it represses. We find that the system distribution exhibits increased phenotypic variation compared to individual component distributions - an effect arising from intermolecular epistasis between the transcription factor and its DNA-binding site. In large part, this epistasis can be qualitatively attributed to the structure of the transcriptional regulatory system and could therefore be a common feature in prokaryotes. Counter-intuitively, intermolecular epistasis can alleviate the constraints of individual components, thereby increasing phenotypic variation that selection could act on and facilitating adaptive evolution. },
author = {Lagator, Mato and Sarikas, Srdjan and Acar, Hande and Bollback, Jonathan P and Guet, Calin C},
issn = {2050084X},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{Regulatory network structure determines patterns of intermolecular epistasis}},
doi = {10.7554/eLife.28921},
volume = {6},
year = {2017},
}
@article{626,
abstract = {Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, …. We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Simulations suggest that in some cases the convergence may be as fast as 1∕M.},
author = {Barton, Nicholas H and Etheridge, Alison and Véber, Amandine},
issn = {00405809},
journal = {Theoretical Population Biology},
pages = {50 -- 73},
publisher = {Academic Press},
title = {{The infinitesimal model: Definition derivation and implications}},
doi = {10.1016/j.tpb.2017.06.001},
volume = {118},
year = {2017},
}
@article{614,
abstract = {Moths and butterflies (Lepidoptera) usually have a pair of differentiated WZ sex chromosomes. However, in most lineages outside of the division Ditrysia, as well as in the sister order Trichoptera, females lack a W chromosome. The W is therefore thought to have been acquired secondarily. Here we compare the genomes of three Lepidoptera species (one Dytrisia and two non-Dytrisia) to test three models accounting for the origin of the W: (1) a Z-autosome fusion; (2) a sex chromosome turnover; and (3) a non-canonical mechanism (e.g., through the recruitment of a B chromosome). We show that the gene content of the Z is highly conserved across Lepidoptera (rejecting a sex chromosome turnover) and that very few genes moved onto the Z in the common ancestor of the Ditrysia (arguing against a Z-autosome fusion). Our comparative genomics analysis therefore supports the secondary acquisition of the Lepidoptera W by a non-canonical mechanism, and it confirms the extreme stability of well-differentiated sex chromosomes.},
author = {Fraisse, Christelle and Picard, Marion A and Vicoso, Beatriz},
issn = {20411723},
journal = {Nature Communications},
number = {1},
publisher = {Nature Publishing Group},
title = {{The deep conservation of the Lepidoptera Z chromosome suggests a non canonical origin of the W}},
doi = {10.1038/s41467-017-01663-5},
volume = {8},
year = {2017},
}
@article{955,
abstract = {Gene expression is controlled by networks of regulatory proteins that interact specifically with external signals and DNA regulatory sequences. These interactions force the network components to co-evolve so as to continually maintain function. Yet, existing models of evolution mostly focus on isolated genetic elements. In contrast, we study the essential process by which regulatory networks grow: the duplication and subsequent specialization of network components. We synthesize a biophysical model of molecular interactions with the evolutionary framework to find the conditions and pathways by which new regulatory functions emerge. We show that specialization of new network components is usually slow, but can be drastically accelerated in the presence of regulatory crosstalk and mutations that promote promiscuous interactions between network components.},
author = {Friedlander, Tamar and Prizak, Roshan and Barton, Nicholas H and Tkacik, Gasper},
issn = {20411723},
journal = {Nature Communications},
number = {1},
publisher = {Nature Publishing Group},
title = {{Evolution of new regulatory functions on biophysically realistic fitness landscapes}},
doi = {10.1038/s41467-017-00238-8},
volume = {8},
year = {2017},
}
@article{1063,
abstract = {Severe environmental change can drive a population extinct unless the population adapts in time to the new conditions (“evolutionary rescue”). How does biparental sexual reproduction influence the chances of population persistence compared to clonal reproduction or selfing? In this article, we set up a one‐locus two‐allele model for adaptation in diploid species, where rescue is contingent on the establishment of the mutant homozygote. Reproduction can occur by random mating, selfing, or clonally. Random mating generates and destroys the rescue mutant; selfing is efficient at generating it but at the same time depletes the heterozygote, which can lead to a low mutant frequency in the standing genetic variation. Due to these (and other) antagonistic effects, we find a nontrivial dependence of population survival on the rate of sex/selfing, which is strongly influenced by the dominance coefficient of the mutation before and after the environmental change. Importantly, since mating with the wild‐type breaks the mutant homozygote up, a slow decay of the wild‐type population size can impede rescue in randomly mating populations.},
author = {Uecker, Hildegard},
issn = {00143820},
journal = {Evolution},
number = {4},
pages = {845 -- 858},
publisher = {Wiley-Blackwell},
title = {{Evolutionary rescue in randomly mating, selfing, and clonal populations}},
doi = {10.1111/evo.13191},
volume = {71},
year = {2017},
}
@article{1169,
abstract = {Dispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e., genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behavior of Fisher waves, which change from being “pulled” to being “pushed” wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies.},
author = {Novak, Sebastian and Kollár, Richard},
issn = {00166731},
journal = {Genetics},
number = {1},
pages = {367 -- 374},
publisher = {Genetics Society of America},
title = {{Spatial gene frequency waves under genotype dependent dispersal}},
doi = {10.1534/genetics.116.193946},
volume = {205},
year = {2017},
}
@phdthesis{6291,
abstract = {Bacteria and their pathogens – phages – are the most abundant living entities on Earth. Throughout their coevolution, bacteria have evolved multiple immune systems to overcome the ubiquitous threat from the phages. Although the molecu- lar details of these immune systems’ functions are relatively well understood, their epidemiological consequences for the phage-bacterial communities have been largely neglected. In this thesis we employed both experimental and theoretical methods to explore whether herd and social immunity may arise in bacterial popu- lations. Using our experimental system consisting of Escherichia coli strains with a CRISPR based immunity to the T7 phage we show that herd immunity arises in phage-bacterial communities and that it is accentuated when the populations are spatially structured. By fitting a mathematical model, we inferred expressions for the herd immunity threshold and the velocity of spread of a phage epidemic in partially resistant bacterial populations, which both depend on the bacterial growth rate, phage burst size and phage latent period. We also investigated the poten- tial for social immunity in Streptococcus thermophilus and its phage 2972 using a bioinformatic analysis of potentially coding short open reading frames with a signalling signature, encoded within the CRISPR associated genes. Subsequently, we tested one identified potentially signalling peptide and found that its addition to a phage-challenged culture increases probability of survival of bacteria two fold, although the results were only marginally significant. Together, these results demonstrate that the ubiquitous arms races between bacteria and phages have further consequences at the level of the population.},
author = {Payne, Pavel},
pages = {83},
publisher = {IST Austria},
title = {{Bacterial herd and social immunity to phages}},
year = {2017},
}
@article{696,
abstract = {Mutator strains are expected to evolve when the availability and effect of beneficial mutations are high enough to counteract the disadvantage from deleterious mutations that will inevitably accumulate. As the population becomes more adapted to its environment, both availability and effect of beneficial mutations necessarily decrease and mutation rates are predicted to decrease. It has been shown that certain molecular mechanisms can lead to increased mutation rates when the organism finds itself in a stressful environment. While this may be a correlated response to other functions, it could also be an adaptive mechanism, raising mutation rates only when it is most advantageous. Here, we use a mathematical model to investigate the plausibility of the adaptive hypothesis. We show that such a mechanism can be mantained if the population is subjected to diverse stresses. By simulating various antibiotic treatment schemes, we find that combination treatments can reduce the effectiveness of second-order selection on stress-induced mutagenesis. We discuss the implications of our results to strategies of antibiotic therapy.},
author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago},
issn = {1553734X},
journal = {PLoS Computational Biology},
number = {7},
publisher = {Public Library of Science},
title = {{Stress induced mutagenesis: Stress diversity facilitates the persistence of mutator genes}},
doi = {10.1371/journal.pcbi.1005609},
volume = {13},
year = {2017},
}
@article{951,
abstract = {Dengue-suppressing Wolbachia strains are promising tools for arbovirus control, particularly as they have the potential to self-spread following local introductions. To test this, we followed the frequency of the transinfected Wolbachia strain wMel through Ae. aegypti in Cairns, Australia, following releases at 3 nonisolated locations within the city in early 2013. Spatial spread was analysed graphically using interpolation and by fitting a statistical model describing the position and width of the wave. For the larger 2 of the 3 releases (covering 0.97 km2 and 0.52 km2), we observed slow but steady spatial spread, at about 100–200 m per year, roughly consistent with theoretical predictions. In contrast, the smallest release (0.11 km2) produced erratic temporal and spatial dynamics, with little evidence of spread after 2 years. This is consistent with the prediction concerning fitness-decreasing Wolbachia transinfections that a minimum release area is needed to achieve stable local establishment and spread in continuous habitats. Our graphical and likelihood analyses produced broadly consistent estimates of wave speed and wave width. Spread at all sites was spatially heterogeneous, suggesting that environmental heterogeneity will affect large-scale Wolbachia transformations of urban mosquito populations. The persistence and spread of Wolbachia in release areas meeting minimum area requirements indicates the promise of successful large-scale population transfo},
author = {Schmidt, Tom and Barton, Nicholas H and Rasic, Gordana and Turley, Andrew and Montgomery, Brian and Iturbe Ormaetxe, Inaki and Cook, Peter and Ryan, Peter and Ritchie, Scott and Hoffmann, Ary and O’Neill, Scott and Turelli, Michael},
issn = {15449173},
journal = {PLoS Biology},
number = {5},
publisher = {Public Library of Science},
title = {{Local introduction and heterogeneous spatial spread of dengue-suppressing Wolbachia through an urban population of Aedes Aegypti}},
doi = {10.1371/journal.pbio.2001894},
volume = {15},
year = {2017},
}
@article{1191,
abstract = {Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher–Kolmogorov–Petrovskii–Piskunov (F–KPP) equation. This generalized F–KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F–KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth–decay rate in the generalized F–KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.},
author = {Kollár, Richard and Novak, Sebastian},
journal = {Bulletin of Mathematical Biology},
number = {3},
pages = {525--559},
publisher = {Springer},
title = {{Existence of traveling waves for the generalized F–KPP equation}},
doi = {10.1007/s11538-016-0244-3},
volume = {79},
year = {2017},
}
@article{1336,
abstract = {Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse the runtimes of EAs on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrences of new mutations is much longer than the time it takes for a mutated genotype to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a stochastic process evolving one genotype by means of mutation and selection between the resident and the mutated genotype. The probability of accepting the mutated genotype then depends on the change in fitness. We study this process, SSWM, from an algorithmic perspective, quantifying its expected optimisation time for various parameters and investigating differences to a similar evolutionary algorithm, the well-known (1+1) EA. We show that SSWM can have a moderate advantage over the (1+1) EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1) EA by taking advantage of information on the fitness gradient.},
author = {Paixao, Tiago and Pérez Heredia, Jorge and Sudholt, Dirk and Trubenova, Barbora},
issn = {01784617},
journal = {Algorithmica},
number = {2},
pages = {681 -- 713},
publisher = {Springer},
title = {{Towards a runtime comparison of natural and artificial evolution}},
doi = {10.1007/s00453-016-0212-1},
volume = {78},
year = {2017},
}