@article{723, abstract = {Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The (1+1) EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the Metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the (1+1) EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and Metropolis can also efficiently optimise a rugged function consisting of consecutive valleys.}, author = {Oliveto, Pietro and Paixao, Tiago and Pérez Heredia, Jorge and Sudholt, Dirk and Trubenova, Barbora}, journal = {Algorithmica}, number = {5}, pages = {1604 -- 1633}, publisher = {Springer}, title = {{How to escape local optima in black box optimisation when non elitism outperforms elitism}}, doi = {10.1007/s00453-017-0369-2}, volume = {80}, year = {2018}, } @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}, } @misc{9849, abstract = {This text provides additional information about the model, a derivation of the analytic results in Eq (4), and details about simulations of an additional parameter set.}, author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago}, publisher = {Public Library of Science}, title = {{Modelling and simulation details}}, doi = {10.1371/journal.pcbi.1005609.s001}, year = {2017}, } @misc{9850, abstract = {In this text, we discuss how a cost of resistance and the possibility of lethal mutations impact our model.}, author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago}, publisher = {Public Library of Science}, title = {{Extensions of the model}}, doi = {10.1371/journal.pcbi.1005609.s002}, year = {2017}, } @misc{9851, abstract = {Based on the intuitive derivation of the dynamics of SIM allele frequency pM in the main text, we present a heuristic prediction for the long-term SIM allele frequencies with χ > 1 stresses and compare it to numerical simulations.}, author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago}, publisher = {Public Library of Science}, title = {{Heuristic prediction for multiple stresses}}, doi = {10.1371/journal.pcbi.1005609.s003}, year = {2017}, } @misc{9852, abstract = {We show how different combination strategies affect the fraction of individuals that are multi-resistant.}, author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago}, publisher = {Public Library of Science}, title = {{Resistance frequencies for different combination strategies}}, doi = {10.1371/journal.pcbi.1005609.s004}, 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{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}, } @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{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{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}, } @inproceedings{1349, abstract = {Crossing fitness valleys is one of the major obstacles to function optimization. In this paper we investigate how the structure of the fitness valley, namely its depth d and length ℓ, influence the runtime of different strategies for crossing these valleys. We present a runtime comparison between the (1+1) EA and two non-elitist nature-inspired algorithms, Strong Selection Weak Mutation (SSWM) and the Metropolis algorithm. While the (1+1) EA has to jump across the valley to a point of higher fitness because it does not accept decreasing moves, the non-elitist algorithms may cross the valley by accepting worsening moves. We show that while the runtime of the (1+1) EA algorithm depends critically on the length of the valley, the runtimes of the non-elitist algorithms depend crucially only on the depth of the valley. In particular, the expected runtime of both SSWM and Metropolis is polynomial in ℓ and exponential in d while the (1+1) EA is efficient only for valleys of small length. Moreover, we show that both SSWM and Metropolis can also efficiently optimize a rugged function consisting of consecutive valleys.}, author = {Oliveto, Pietro and Paixao, Tiago and Heredia, Jorge and Sudholt, Dirk and Trubenova, Barbora}, booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference 2016 }, location = {Denver, CO, USA}, pages = {1163 -- 1170}, publisher = {ACM}, title = {{When non-elitism outperforms elitism for crossing fitness valleys}}, doi = {10.1145/2908812.2908909}, year = {2016}, } @article{1359, abstract = {The role of gene interactions in the evolutionary process has long been controversial. Although some argue that they are not of importance, because most variation is additive, others claim that their effect in the long term can be substantial. Here, we focus on the long-term effects of genetic interactions under directional selection assuming no mutation or dominance, and that epistasis is symmetrical overall. We ask by how much the mean of a complex trait can be increased by selection and analyze two extreme regimes, in which either drift or selection dominate the dynamics of allele frequencies. In both scenarios, epistatic interactions affect the long-term response to selection by modulating the additive genetic variance. When drift dominates, we extend Robertson ’ s [Robertson A (1960) Proc R Soc Lond B Biol Sci 153(951):234 − 249] argument to show that, for any form of epistasis, the total response of a haploid population is proportional to the initial total genotypic variance. In contrast, the total response of a diploid population is increased by epistasis, for a given initial genotypic variance. When selection dominates, we show that the total selection response can only be increased by epistasis when s ome initially deleterious alleles become favored as the genetic background changes. We find a sim- ple approximation for this effect and show that, in this regime, it is the structure of the genotype - phenotype map that matters and not the variance components of the population.}, author = {Paixao, Tiago and Barton, Nicholas H}, journal = {PNAS}, number = {16}, pages = {4422 -- 4427}, publisher = {National Academy of Sciences}, title = {{The effect of gene interactions on the long-term response to selection}}, doi = {10.1073/pnas.1518830113}, volume = {113}, year = {2016}, } @inproceedings{1430, 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 their runtime 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 occurrence of new mutations is much longer than the time it takes for a new beneficial mutation to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a (1+1)-type process where the probability of accepting a new genotype (improvements or worsenings) depends on the change in fitness. We present an initial runtime analysis of SSWM, quantifying its performance for various parameters and investigating differences to the (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 Sudholt, Dirk and Heredia, Jorge and Trubenova, Barbora}, booktitle = {Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation}, location = {Madrid, Spain}, pages = {1455 -- 1462}, publisher = {ACM}, title = {{First steps towards a runtime comparison of natural and artificial evolution}}, doi = {10.1145/2739480.2754758}, year = {2015}, } @article{1542, abstract = {The theory of population genetics and evolutionary computation have been evolving separately for nearly 30 years. Many results have been independently obtained in both fields and many others are unique to its respective field. We aim to bridge this gap by developing a unifying framework for evolutionary processes that allows both evolutionary algorithms and population genetics models to be cast in the same formal framework. The framework we present here decomposes the evolutionary process into its several components in order to facilitate the identification of similarities between different models. In particular, we propose a classification of evolutionary operators based on the defining properties of the different components. We cast several commonly used operators from both fields into this common framework. Using this, we map different evolutionary and genetic algorithms to different evolutionary regimes and identify candidates with the most potential for the translation of results between the fields. This provides a unified description of evolutionary processes and represents a stepping stone towards new tools and results to both fields. }, author = {Paixao, Tiago and Badkobeh, Golnaz and Barton, Nicholas H and Çörüş, Doğan and Dang, Duccuong and Friedrich, Tobias and Lehre, Per and Sudholt, Dirk and Sutton, Andrew and Trubenova, Barbora}, journal = { Journal of Theoretical Biology}, pages = {28 -- 43}, publisher = {Elsevier}, title = {{Toward a unifying framework for evolutionary processes}}, doi = {10.1016/j.jtbi.2015.07.011}, volume = {383}, year = {2015}, } @misc{9712, author = {Tugrul, Murat and Paixao, Tiago and Barton, Nicholas H and Tkačik, Gašper}, publisher = {Public Library of Science}, title = {{Other fitness models for comparison & for interacting TFBSs}}, doi = {10.1371/journal.pgen.1005639.s001}, year = {2015}, } @article{1666, abstract = {Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ∼ 10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of “pre-sites” or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genomics.}, author = {Tugrul, Murat and Paixao, Tiago and Barton, Nicholas H and Tkacik, Gasper}, journal = {PLoS Genetics}, number = {11}, publisher = {Public Library of Science}, title = {{Dynamics of transcription factor binding site evolution}}, doi = {10.1371/journal.pgen.1005639}, volume = {11}, year = {2015}, } @inproceedings{1835, 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 logics. 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}, location = {London, United Kingdom}, pages = {469 -- 483}, publisher = {Springer}, title = {{Model checking gene regulatory networks}}, doi = {10.1007/978-3-662-46681-0_47}, volume = {9035}, year = {2015}, } @article{2169, author = {Barton, Nicholas H and Novak, Sebastian and Paixao, Tiago}, journal = {PNAS}, number = {29}, pages = {10398 -- 10399}, publisher = {National Academy of Sciences}, title = {{Diverse forms of selection in evolution and computer science}}, doi = {10.1073/pnas.1410107111}, volume = {111}, year = {2014}, } @article{2252, abstract = {The pattern of inheritance and mechanism of sex determination can have important evolutionary consequences. We studied probabilistic sex determination in the ciliate Tetrahymena thermophila, which was previously shown to cause evolution of skewed sex ratios. We find that the genetic background alters the sex determination patterns of mat alleles in heterozygotes and that allelic interaction can differentially influence the expression probability of the 7 sexes. We quantify the dominance relationships between several mat alleles and find that A-type alleles, which specify sex I, are indeed recessive to B-type alleles, which are unable to specify that sex. Our results provide additional support for the presence of modifier loci and raise implications for the dynamics of sex ratios in populations of T. thermophila.}, author = {Phadke, Sujal and Paixao, Tiago and Pham, Tuan and Pham, Stephanie and Zufall, Rebecca}, issn = {00221503}, journal = {Journal of Heredity}, number = {1}, pages = {130 -- 135}, publisher = {Oxford University Press}, title = {{Genetic background alters dominance relationships between mat alleles in the ciliate Tetrahymena Thermophila}}, doi = {10.1093/jhered/est063}, volume = {105}, year = {2014}, }