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The self-incompatibility locus (S-locus) of flowering plants displays a striking allelic diversity. How such a diversity has emerged remains unclear. In this paper, we performed numerical simulations in a finite island population genetics model to investigate how population subdivision affects the diversification process at a S-locus, given that the two-genes architecture typical of S-loci involves the crossing of a fitness valley. We show that population structure slightly reduces the parameter range allowing for the diversification of self-incompatibility haplotypes (S-haplotypes), but at the same time also increases the number of these haplotypes maintained in the whole metapopulation. This increase is partly due to a higher rate of diversification and replacement of S-haplotypes within and among demes. We also show that the two-genes architecture leads to a higher diversity in structured populations compared with a simpler genetic architecture where new S-haplotypes appear in a single mutation step. Overall, our results suggest that population subdivision can act in two opposite directions: it renders S-haplotypes diversification easier, although it also increases the risk that the self-incompatibility system is lost.

Direct policy search (DPS) is emerging as one of the most effective and widely applied reinforcement learning (RL) methods to design optimal control policies for multiobjective Markov decision processes (MOMDPs). Traditionally, DPS defines the control policy within a preselected functional class and searches its optimal parameterization with respect to a given set of objectives. The functional class should be tailored to the problem at hand and its selection is crucial, as it determines the search space within which solutions can be found. In MOMDPs problems, a different objective tradeoff determines a different fitness landscape, requiring a tradeoff-dynamic functional class selection. Yet, in state-of-the-art applications, the policy class is generally selected a priori and kept constant across the multidimensional objective space. In this work, we present a novel policy search routine called neuro-evolutionary multiobjective DPS (NEMODPS), which extends the DPS problem formulation to conjunctively search the policy functional class and its parameterization in a hyperspace containing policy architectures and coefficients. NEMODPS begins with a population of minimally structured approximating networks and progressively builds more sophisticated architectures by topological and parametrical mutation and crossover, and selection of the fittest individuals concerning multiple objectives. We tested NEMODPS for the problem of designing the control policy of a multipurpose water system. Numerical results show that the tradeoff-dynamic structural and parametrical policy search of NEMODPS is consistent across multiple runs, and outperforms the solutions designed via traditional DPS with predefined policy topologies.

Fitness landscapes map genotypes to their corresponding fitness under given environments and allow explaining and predicting evolutionary trajectories. Of particular interest is the landscape ruggedness or the unevenness of the landscape, because it impacts many aspects of evolution such as the likelihood that a population is trapped in a local fitness peak. Although the ruggedness has been inferred from a number of empirically mapped fitness landscapes, it is unclear to what extent this inference is affected by fitness estimation error, which is inevitable in the experimental determination of fitness landscapes. Here we address this question by simulating fitness landscapes under various theoretical models, with or without fitness estimation error. We find that all eight examined measures of landscape ruggedness are overestimated due to imprecise fitness quantification, but different measures are affected to different degrees. We devise a method to use replicate fitness measures to correct this bias and show that our method performs well under realistic conditions. We conclude that previously reported fitness landscape ruggedness is likely upward biased owing to the negligence of fitness estimation error and advise that future fitness landscape mapping should include at least three biological replicates to permit an unbiased inference of the ruggedness. This article is protected by copyright. All rights reserved.

BackgroundAsexually reproducing populations of single cells evolve through mutation, natural selection, and genetic drift. Environmental conditions in which the evolution takes place define the emergent fitness landscapes. In this work, we used Avida—a digital evolution framework—to uncover a hitherto unexplored interaction between mutation rates, population size, and the relative abundance of metabolizable resources, and its effect on evolutionary outcomes in small populations of digital organisms.ResultsOver each simulation, the population evolved to one of several states, each associated with a single dominant phenotype with its associated fitness and genotype. For a low mutation rate, acquisition of fitness by organisms was accompanied with, and dependent on, an increase in rate of genomic replication. At an increased mutation rate, phenotypes with high fitness values were similarly achieved through enhanced genome replication rates. In addition, we also observed the frequent emergence of suboptimal fitness phenotype, wherein neighboring organisms signaled to each other information relevant to performing metabolic tasks. This metabolic signaling was vital to fitness acquisition and was correlated with greater genotypic and phenotypic heterogeneity in the population. The frequency of appearance of signaling populations increased with population size and with resource abundance.ConclusionsOur results reveal a minimal set of environment–genotype interactions that lead to the emergence of metabolic signaling within evolving populations.

For real parameter single objective optimization, Differential Evolution (DE) performs better than other types of population-based metaheuristic. Nevertheless, in the field of DE, it is impossible for a given combination of operators to perform well in all fitness landscapes. Practice has proved that assembling more than one combinations of operators may lead to improvement in solution. However, some DE algorithms with good performance, e.g., one of the best performers in competitions of real parameter single objective optimization among population-based metaheuristics held by the series of IEEE Congress on Evolutionary Computation - L-SHADE-EpSin, are still not involved in ensemble. Furthermore, ensemble based on similar DE algorithms is rarely reported. Based on such a background, we propose L-SHADE-E, ensemble of L-SHADE-EpSin and L-SHADE-RSP in this paper. The two constituent algorithms are both variants of L-SHADE and belong to similar DE algorithms. In our algorithm, L-SHADE-EpSin or L-SHADE-RSP is selected randomly to run at the beginning. If progress on fitness is low for generations, the other constituent algorithm takes over population immediately. Our experiments are based on the CEC 2014 and CEC 2017 benchmark test suites. Altogether, our algorithm is compared with nine DE algorithms and three population-based metaheuristics other than DE. Experimental results show that our algorithm is very competitive.

PSO is a simple and yet powerful metaheuristic search algorithm widely used to solve various optimization problems. Nevertheless, conventional PSO tends to lose its population diversity drastically and suffer with compromised performance when encountering the optimization problems with complex fitness landscapes. Extensive studies suggest the needs of preserving high population diversity for PSO to escape from the local optima in order to solve complex optimization problems effectively. Inspired by these ideas, a hovering swarm PSO (HSPSO) is proposed in this paper, where a computationally efficient diversity preservation scheme is first introduced to divide the population of HSPSO into a main swarm and a hovering swarm. An exemplar construction scheme is subsequently proposed in the main swarm of HSPSO to generate a universal exemplar by considering the promising directional information contributed by the other non-fittest particles. The proposed universal exemplar is envisioned to suppress the negative impacts of global best particle, while remain effective to guide all particles of main swarm converging towards the promising solution regions. While hovering around the main swarm, an intelligent scheme is introduced to dynamically adjust inertia weights of all hovering swarm members to achieve proper balancing of exploration and exploitation searches at swarm levels. Extensive performance analyses are conducted by using the proposed HSPSO to solve 30 benchmark functions of CEC 2014 and five real-world engineering applications. Simulation results reveal that the HSPSO is able outperform the state-of-art optimizers when solving most tested functions due to its excellent diversity preservation capability.

The genetic algorithm-backpropagation neural network algorithm (GA-BP) makes full use of the advantages of genetic algorithm (GA) and BP neural network (BPNN). It has been widely used in practical problems, but it also has shortcomings such as slow convergence. Inspired by the generative adversarial network, a population competition mechanism (PCM) is proposed to improve the search ability of the GA, two populations are generated to compete, and the winning population can obtain the optimal individual from the failed population to ensure that the winning population has a sustainable advantage. The failed population will randomly generate new individuals and add new genes so as to get better individuals, through such a mechanism to ensure the rapid optimization of the entire population, avoid the risk of premature convergence, speed up the iterative speed and improve the stability of the GA. According to the characteristics of the fitness landscape, the learning rate of the BPNN is optimized, and it can change adaptively, which can effectively improve the network convergence speed and greatly reduce the time cost. We define the GA-BP that improves the learning rate based on fitness landscape as FL-GA-BP algorithm. On the basis of the FL-GA-BP algorithm, adding GA improved with PCM, we define this new algorithm as I-GA-BP algorithm, namely the I-GA-BP algorithm that combines PCM-improved GA and fitness landscape-improved BPNN. In this paper, we use two types of test functions with different characteristics and complexity to conduct experiments to verify the effectiveness of the I-GA-BP algorithm. By comparing the experimental data of the three algorithms GA-BP, FL-GA-BP and I-GA-BP, it is obtained that the I-GA-BP algorithm can better escape from the local optimal solution, which is more conducive to finding the global optimal solution. It also greatly improves the convergence speed of the neural network. Finally, we briefly discussed the effect of adjusting the number of neurons on the stability of the I-GA-BP algorithm.

Evolutionary algorithms are popular optimization tools for real-world applications due to their numerous advantages such as capability of parallel search along multiple directions by maintaining a population of candidates, invariance to certain mathematical properties (convexity, continuity and hardness) of fitness landscape and ability to handle black-box problems. However, most of the current evolutionary algorithms are loosely based on heuristics inspired by nature and lack the crucial theoretical background. Motivated by the overwhelming advantages of such optimization algorithms and the necessity for theoretical foundation, this paper presents a new evolutionary algorithm - UDE (Uniform Differential Evolution) for solving single- objective optimization problems along with a theoretical analysis of the proposed UDE algorithm. Thus, this paper formally gives insights about the features and properties of the various optimization strategies used. This method is different from traditional Differential Evolution variants as it employs a uniform probability distribution for generating new candidate solutions. UDE is further developed to obtain an adaptive evolutionary algorithm - Adaptive UDE (AUDE), which has shown to obtain significant improvements in the performance and convergence speeds compared to other algorithms on a benchmark set of 19 test problems. The source codes are available at http://worksupplements.droppages.com/ude_aude .

Mitochondrial genetic material is widely used for phylogenetic reconstruction and as a barcode for species identification. Here we study how mito-nuclear interactions affect the accuracy of species identification by mtDNA, as well as the speciation process itself. We simulate the evolution of a population of individuals who carry a recombining nuclear genome and a mitochondrial genome inherited maternally. We compare a null model fitness landscape that lacks any mito-nuclear interaction against a scenario in which interactions influence fitness. Fitness is assigned to individuals according to their mito-nuclear compatibility, which drives the coevolution of the nuclear and mitochondrial genomes. When the population breaks into distinct species we analyze the accuracy of mtDNA barcode for species identification. Remarkably, we find that species identification by mtDNA is equally accurate in the presence or absence of mito-nuclear coupling and that the success of the DNA barcode derives mainly from population geographical isolation during speciation. Nevertheless, selection imposed by mito-nuclear compatibility influences the diversification process and leaves signatures in the genetic content and spatial distribution of the populations, in three ways: phylogenetic trees are more balanced; clades correlate strongly with the spatial distribution and; there is a substantial increase in the intraspecies mtDNA similarity. We compare the evolutionary patterns observed in our model to empirical data from copepods (\textit{T. californicus}). We find good qualitative agreement in the geographic patterns and the topology of the phylogenetic tree, provided the model includes selection based on mito-nuclear interactions. These results highlight the role of mito-nuclear compatibility in the speciation process and its reconstruction from genetic data., Comment: 27 pages, 6 figures

Evolutionary dynamics in hematopoiesis Cells accumulate mutations as we age, and these mutations can be a source of diseases such as cancer. How cells containing mutations evolve, are maintained, and proliferate within the body has not been well characterized. Using a quantitative framework, Watson et al. applied population genetic theory to estimate mutation accumulation in cells in blood from sequencing data derived from nearly 50,000 healthy individuals (see the Perspective by Curtis). By evaluating how mutations differ between blood cell populations, a phenomenon known as clonal hematopoiesis, the researchers could observe how recurrent mutations can drive certain clonal lineages to high frequencies within an individual. The risk of specific mutations, some of which are associated with leukemias, rising to high frequencies may therefore be a function of cellular selection and the age at which the mutation originated. Science , this issue p. 1449 ; see also p. 1426

Although intraindividual variability (IIV) in behavior is fundamental to ecological dynamics, the factors that contribute to the expression of IIV are poorly understood. Using an individual‐based model, this study examined the effects of stochasticity on the evolution of IIV represented by the residual variability of behavior. The model describes a population of prey with nonoverlapping generations, in which prey take refuge upon encountering a predator. The strategy of a prey is characterized by the mean and IIV (i.e., standard deviation) of hiding duration. Prey with no IIV will spend the same duration hiding in a refuge at each predator encounter, while prey with IIV will have variable hiding durations among encounters. For the sources of stochasticity, within‐generation stochasticity (represented by random predator encounters) and between‐generation stochasticity (represented by random resource availability) were considered. Analysis of the model indicates that individuals with high levels of IIV are maintained in a population in the presence of between‐generation stochasticity even though the optimal strategy in each generation is a strategy with no IIV, regardless of the presence or absence of within‐generation stochasticity. This contradictory pattern emerges because the mean behavioral trait and IIV do not independently influence fitness (e.g., the sign of the selection gradient with respect to IIV depends on the mean trait). Consequently, even when evolution eventually leads toward a strategy with no IIV (i.e., the optimal strategy), greater IIV may be transiently selected. Between‐generation stochasticity consistently imposes such transient selection and maintain high levels of IIV in a population., Fitness contours based on the mean (horizontal axis) and intraindividual variability (IIV) (vertical axis) in behavior are tilted and create positive selection gradients with respect to IIV even though the optimal strategy is a strategy with no IIV. When populations consist of individuals with nonoptimal traits (e.g., [population 1] mean = 15 & IIV = 0, [population 2] mean = 20 & IIV = 0, [population 3] mean = 25 & IIV = 0), evolution takes long detours and transiently increase IIV, whose trajectories are depicted by the black lines.

The study focuses on the mechanisms of crossing the valleys of fitness by a population of haploid microorganisms, whose fitness depends on allelic values at two different loci and is determined by a complex landscape, the shape of which corresponds to the pattern “a mountain in the field surrounded by a trench”; these mechanisms are analyzed using computer modeling. We have studied the influence of various biological factors on the evolutionary perspective of microbial colonies, the reproduction rate of which is controlled by a protein consisting of two subunits encoded at different loci. Molecular genetic (mutation rate, affinity of subunits), population (fitness function landscape and population density), and ecological (concentration of available substrate in the habitat, flow intensity) factors have been considered. Our results demonstrate that the difference in fitness for various allelic combinations, while determining the shape of the fitness landscape, sets the optimal mutation rates to overcome its valleys and opens a window of opportunity for the evolution of the population toward the state of the highest average fitness. Moreover, depending on the fitness landscape type, either gradual or saltational evolutionary regimes are optimal for reaching the peak.

Due to that the performance of differential evolution (DE) significantly depends on offspring generation strategies, various DE variants have been reported with the improved mutation operators. However, on the one hand, the mutation operators in most DE variants are guided by the elites in terms of the fitness value, without considering their distribution information in the fitness landscape. It may lead to the population be evolving towards the unpromising areas more frequently if these elites are clustered in a locally optimal region. On the other hand, in most DE variants, the evolutionary information of the potential trial vectors is not fully utilized to guide the search, which will hamper the local exploitation in the promising regions that they are located in. To overcome these weaknesses, this article proposes an enhanced DE framework (DELDG) with a leaders-detection-and-guidance mechanism that consists of an adaptive leaders detection (ALD) and a neighborhood-based tournament selection (NTS). With these two novel operators, DELDG can not only guide the mutation process of each individual with multiple promising leaders detected by ALD, but also accelerate the convergence speed with the competition among the potential trial vectors by NTS. Therefore, DELDG is characterized by the explicit detection of the promising leaders according to their fitness values and distribution information and the effective use of the potential trial vectors in the neighborhood of each leader. Compared with 36 excellent DE variants and evolutionary algorithms (EAs), the experimental results on 28 IEEE CEC2013 real-parameter functions and 17 IEEE CEC2011 real-world problems have demonstrated the competitive performance of DELDG.

The Unequal Area Facility Layout Problem (UA-FLP) is a relevant optimization problem related to industrial design, that deals with obtaining the most effective allocation of facilities, that make up the rectangular manufacturing plant layout. The UA-FLP is known to be a hard optimization problem, where meta-heuristic approaches are a good option to obtain competitive solutions. Many of these computational approaches, however, usually fall into local optima, and suffer from lack of diversity in their population, mainly due to the huge search spaces and hard fitness landscapes produced by the traditional representation of UA-FLP. To solve these issues, in this paper we propose a novel hybrid meta-heuristic approach, which combines a Coral Reefs Optimization algorithm (CRO) with a Variable Neighborhood Search (VNS) and a new representation for the problem, called Relaxed Flexible Bay Structure (RFBS), which simplifies the encoding and makes its fitness landscape more affordable. Thus, the use of VNS allows more intensive exploitation of the searching space with an affordable computational cost, as well as the RFBS allows better management of the free space into the plant layout. This combined strategy has been tested over a set of UA-FLP instances of different sizes, which have been previously tackled in the literature with alternative meta-heuristics. The tests results show very good performance in all cases.

Many real-world problems are modeled as multi-objective optimization problems whose optimal solutions change with time. These problems are commonly termed dynamic multi-objective optimization problems (DMOPs). One challenge associated with solving such problems is the fact that the Pareto front or Pareto set often changes too quickly. This means that the optimal solution set at period $t$ may likely vary from that at $(t+1)$ , and this makes the process of optimizing such problems computationally expensive to implement. This article proposes the use of adaptive mutation and crossover operators for the non-dominated sorting genetic algorithm III (NSGA-III). The aim is to find solutions that can adapt to fitness changes in the objective function space over time. The proposed approach improves the capability of NSGA-III to solve multi-objective optimization problems with solutions that change quickly in both space and time. Results obtained show that this method of population reinitialization can effectively optimize selected benchmark dynamic problems. In addition, we test the capability of the proposed algorithm to select robust solutions over time. We recognize that DMOPs are characterized by rapidly changing optimal solutions. Therefore, we also test the ability of our proposed algorithm to handle these changes. This is achieved by evaluating its performance on selected robust optimization over time (ROOT) and robust Pareto-optimality over time (RPOOT) benchmark problems.

The dynamics of evolution is intimately shaped by epistasis — interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of “ruggedness” are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness “seascapes” cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

Fitness landscape mapping and the prediction of evolutionary trajectories on these landscapes are major tasks in evolutionary biology research. Evolutionary dynamics is tightly linked to the landscape topography, but this relation is not straightforward. Models predict different evolutionary outcomes depending on mutation rates: high-fitness genotypes should dominate the population under low mutation rates and lower-fitness, mutationally robust (also called 9flat9) genotypes - at higher mutation rates. Yet, so far, flat genotypes have been demonstrated in very few cases, particularly in viruses. The quantitative conditions for their emergence were studied only in simplified single-locus, two-peak landscapes. In particular, it is unclear whether within the same genome some genes can be flat while the remaining ones are fit. Here, we analyze a previously measured fitness landscape of a yeast tRNA gene. We found that the wild type allele is sub-optimal, but is mutationally robust (9flat9). Using computer simulations, we estimated the critical mutation rate in which transition from fit to flat allele should occur for a gene with such characteristics. We then used a scaling argument to extrapolate this critical mutation rate for a full genome, assuming the same mutation rate for all genes. Finally, we propose that while the majority of genes are still selected to be fittest, there are a few mutation hot-spots like the tRNA, for which the mutationally robust flat allele is favored by selection.

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

There still are no effective long-term protective vaccines against viruses that continuously evolve under immune pressure such as seasonal influenza, which has caused, and can cause, devastating epidemics in the human population. For finding such a broadly protective immunization strategy it is useful to know how easily the virus can escape via mutation from specific antibody responses. This information is encoded in the fitness landscape of the viral proteins (i.e., knowledge of the viral fitness as a function of sequence). Here we present a computational method to infer the intrinsic mutational fitness landscape of influenza-like evolving antigens from yearly sequence data. We test inference performance with computer-generated sequence data that are based on stochastic simulations mimicking basic features of immune-driven viral evolution. Although the numerically simulated model does create a phylogeny based on the allowed mutations, the inference scheme does not use this information. This provides a contrast to other methods that rely on reconstruction of phylogenetic trees. Our method just needs a sufficient number of samples over multiple years. With our method we are able to infer single-as well as pairwise mutational fitness effects from the simulated sequence time series for short antigenic proteins. Our fitness inference approach may have potential future use for design of immunization protocols by identifying intrinsically vulnerable immune target combinations on antigens that evolve under immune-driven selection. This approach may in the future be applied to influenza and other novel viruses such as SARS-CoV-2, which evolves and, like influenza, might continue to escape the natural and vaccine-mediated immune pressures.

Mutation rate plays an important role in adaptive evolution due to its effect on the rate of appearance of both beneficial and deleterious mutations and is therefore subject to second-order selection. The mutation rate varies between and within species and populations, increases under some stresses, and can be modified by mutator and anti-mutator alleles. It may also vary among genetically identical individuals: empirical evidence from bacteria suggests that the mutation rate can be affected by translation errors and expression noise in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to mutator phenotype switching that is independent from mutator alleles. Here we investigate mathematically how the rate of adaptive evolution on rugged, complex fitness landscapes is affected by the rate of mutation rate phenotype switching. Motivated by recent experimental results of mutation rate variation, we model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. Thus, the mutation rate can be interpreted as a genetically inherited trait when the switching rate is low, as an epigenetically inherited trait when the switching rate is intermediate, or as a randomly determined trait when the switching rate is high. We find that intermediate switching rates maximize the rate of adaptation on rugged fitness landscapes. This is because an intermediate switching rate can maintain within the same individuals both a mutator phenotype and pre-existing mutations, a combination that facilitates the crossing of fitness valleys. Further, intermediate switching rates allow the population to quickly revert to a low mutation rate after adaptation is achieved, avoiding the accumulation of deleterious mutations linked to mutator alleles. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

A fitness landscape describes the interaction of a search domain, a cost function on designs drawn from the domain, and a neighbourhood function defining the adjacency of designs --- induced by the optimisation method used. Fitness landscapes can be represented in a compact form as Local Optima Networks (LONs). Although research has been conducted on LONs in continuous domains, the majority of work has focused on combinatorial landscapes. LONs are often used to understand the landscape encountered by population-based search heuristics, but are usually constructed via point-based search. This paper proposes the first construction of LONs by a population-based algorithm, applied to continuous optimisation problems. We construct LONs for three benchmark functions with well-known global structure using the widely used Nelder-Mead downhill simplex algorithm, and contrast these to the LONs from a point-based approach. We also investigate the sensitivity of the LON visualisation to the downhill simplex algorithm's hyperparameters, by varying the initial step size of the simplex and the step size for connectivity of optima. Our results suggest that large initial simplex sizes fragment the landscape structure, and exclude some local optima from the fitness landscape.

This paper presents a surrogate-based approach that uses a relatively simple population-based optimisation algorithm, a basic Differential Evolution algorithm (DE), and experiments with two complementary approaches to construct a surrogate. This surrogate-based optimisation uses a predictive model in-line and decides whether to calculate a candidate individual (using the simulation model) or discard it as part of the optimisation process. The complementary approaches for the design of the surrogate are (1) a traditional regression-based surrogate that approximates the surface of the fitness landscape using a supervised continuous machine learning algorithm (XGBoost), and (2) a pairwise approach that models the surrogate as a binary classification problem for a machine learning algorithm (in this experiment we proposed a Decision Tree binary classifier). Although there is no statistical difference in the performance of both surrogate approaches, the surface/regression one obtains a slightly better performance when the execution is limited to 200 fitness evaluations. In contrast, the pairwise/classification approach obtains the lowest value and a lower mean in executions with 750 fitness evaluations.

In the area of evolutionary computation the calculation of diverse sets of high-quality solutions to a given optimization problem has gained momentum in recent years under the term evolutionary diversity optimization. Theoretical insights into the working principles of baseline evolutionary algorithms for diversity optimization are still rare. In this paper we study the well-known Minimum Spanning Tree problem (MST) in the context of diversity optimization where population diversity is measured by the sum of pairwise edge overlaps. Theoretical results provide insights into the fitness landscape of the MST diversity optimization problem pointing out that even for a population of $\mu=2$ fitness plateaus (of constant length) can be reached, but nevertheless diverse sets can be calculated in polynomial time. We supplement our theoretical results with a series of experiments for the unconstrained and constraint case where all solutions need to fulfill a minimal quality threshold. Our results show that a simple $(\mu+1)$-EA can effectively compute a diversified population of spanning trees of high quality.

Linkage effects in a multi-locus population strongly influence its evolution. The models based on the traveling wave approach enable us to predict the average speed of evolution and the statistics of phylogeny. However, predicting statistically the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effects of epistasis, the interaction of gene regions contributing to phenotype, is difficult to predict theoretically and detect experimentally in sequence data. A large number of false-positive interactions arises from stochastic linkage effects and indirect interactions, which mask true epistatic interactions. Here we develop a proof-of-principle method to filter out false-positive interactions. We start by demonstrating that the averaging of haplotype frequencies over multiple independent populations is necessary but not sufficient for epistatic detection, because it still leaves high numbers of false-positive interactions. To compensate for the residual stochastic noise, we develop a three-way haplotype method isolating true interactions. The fidelity of the method is confirmed analytically and on simulated genetic sequences evolved with a known epistatic network. The method is then applied to a large sequence database of neurominidase protein of influenza A H1N1 obtained from various geographic locations to infer the epistatic network responsible for the difference between the pre-pandemic virus and the pandemic strain of 2009. These results present a simple and reliable technique to measure epistatic interactions of any sign from sequence data., Author summary Interactions between genomic sites create a fitness landscape. The knowledge of topology and strength of interactions is vital for predicting the escape of viruses from drugs and immune response and their passing through fitness valleys. Many efforts have been invested into measuring these interactions from DNA sequence sets. Unfortunately, reproducibility of the results remains low due partly to a very small fraction of interaction pairs and partly to stochastic linkage noise masking true interactions. Here we propose a method to separate stochastic linkage and indirect interactions from epistatic interactions and apply it to influenza virus sequence data.

In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the ‘replicator-mutator equation’ often neglect this generation-time effect. In this study, we investigate the emergence of a positive dependence between the birth rate and the mutation rate in models of asexual adaptation and the consequences of this dependence. We show that it emerges naturally at the population scale, based on a large population limit of a stochastic time-continuous individual-based model with elementary assumptions. We derive a reaction-diffusion framework that describes the evolutionary trajectories and steady states in the presence of this dependence. When this model is coupled with a phenotype to fitness landscape with two optima, one for birth, the other one for survival, a new trade-off arises in the population. Compared to the standard approach with a constant mutation rate, the symmetry between birth and survival is broken. Our analytical results and numerical simulations show that the trajectories of mean phenotype, mean fitness and the stationary phenotype distribution are in sharp contrast with those displayed for the standard model. The reason for this is that the usual weak selection limit does not hold in a complex landscape with several optima associated with different values of the birth rate. Here, we obtain trajectories of adaptation where the mean phenotype of the population is initially attracted by the birth optimum, but eventually converges to the survival optimum, following a hook-shaped curve which illustrates the antagonistic effects of mutation on adaptation.

International audience; The question of complexity in biological systems is recurrent in evolutionary biology and is central in complex systems science for obvious reasons. But this question is surprisingly overlooked by Evolutionary Systems Biology. This comes unexpected given the roots of systems biology in complex systems science but also given that a proper understanding of the origin and evolution of complexity would provide clues for a better understanding of extant biological systems. In this chapter we will explore the links between evolutionary systems biology and biological systems complexity, in terms of concepts, tools, and results. In particular, we will show how complex models can be used to explore this question and show that complexity can spontaneously accumulate even in simple conditions owing to a “complexity ratchet” fuelled by sign-epistasis.

Various metaheuristic optimization algorithms are being developed to obtain optimal solutions to real-world problems. Metaheuristic algorithms are inspired by various metaphors, resulting in different search mechanisms, operators, and parameters, and thus algorithm-specific strengths and weaknesses. Newly developed algorithms are generally tested using benchmark problems. However, for existing traditional benchmark problems, it is difficult for users to freely modify the characteristics of a problem. Thus, their shapes and sizes are limited, which is a disadvantage. In this study, a modified Gaussian fitness landscape generator is proposed based on a probability density function, to make up for the disadvantages of traditional benchmark problems. The fitness landscape developed in this study contains a total of six features and can be employed to easily create various problems depending on user needs, which is an important advantage. It is applied to quantitatively evaluate the performance and reliability of eight reported metaheuristic algorithms. In addition, a sensitivity analysis is performed on the population size for population-based algorithms. Furthermore, improved versions of the metaheuristic algorithm are considered, to investigate which performance aspects are enhanced by applying the same fitness landscape. The modified Gaussian fitness landscape generator can be employed to compare the performances of existing optimization algorithms and to evaluate the performances of newly developed algorithms. In addition, it can be employed to develop methods of improving algorithms by evaluating their strengths and weaknesses.

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation‐limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive‐walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.

Recently, the improvements of artificial bee colony (ABCs) have attracted increasing interest in the studies of single optimization problems. However, most existing work of ABC aims to design new solution search equations and is still challenged when solving optimization problems with variable linkages. To overcome this limit, an adaptive encoding learning for ABCs (AEL + ABCs) is proposed in this paper. In AEL + ABCs, the solution search equations are encoded in both natural coordinate system and eigen coordinate system guided by covariance matrix learning. The purpose of the former is to maintain the diversity of population, while the latter aims at directing the evolution of population toward the promising directions by identifying the properties of fitness landscape. In addition, an adaptive selection mechanism is used to achieve a good tradeoff between convergence and diversity. For the comparison purposes, the proposed AEL strategy is applied to eight ABCs and their performance is tested on 30 CEC2014 benchmark functions. Experiment results show that the proposed AEL + ABCs can significantly improve the performance of the state-of-the-art ABCs in the majority of the benchmark functions.

The recently developed regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) and inverse models-based multi-objective evolutionary algorithm (IM-MOEA) have been shown to be two effective methods for solving some complex multi-objective optimization problems (MOPs). However, RM-MEDA and IM-MOEA are still challenged when solving MOPs with many local Pareto fronts, and usually generate poor solutions when the population has no obvious regularity. In order to overcome these limits, an ensemble of RM-MEDA and IM-MOEA, denoted as RM-IM-EDA, is proposed in this paper. This ensemble is based on a dynamic mixture of the sampling in the decision space by the regularity-based learning model and the sampling in the objective space using the inverse learning models. In addition, a sequence-based deterministic initialization method is introduced to identify the properties of fitness landscape. The objective behind this scheme is to reduce the probability of sinking into the local Pareto optimum. For the comparison purposes, the proposed RM-IM-EDA is tested on 32 benchmark problems. Experiment results statistically affirm the efficiency of the proposed approach to obtain better results compared with each individual algorithm and other four state-of-the-art MEDAs.

Understanding the dynamics of species adaptation to their environments has long been a central focus of the study of evolution. Early adaptive theories proposed that populations evolve by “walking” in a fitness landscape. This “adaptive walk” is characterised by a pattern of diminishing returns, where populations further away from their fitness optimum take larger steps than those closer to their optimal conditions. This theory can also be used to understand molecular evolution in time, particularly across genes of different ages. We expect young genes to evolve faster and experience mutations with stronger fitness effects than older genes because they are further away from their fitness optimum. Testing this hypothesis, however, constitutes an arduous task. Young genes are small, encode proteins with a higher degree of intrinsic disorder, are expressed at lower levels, and are involved in species-specific adaptations. Since all these factors lead to increased protein evolutionary rates, they could be masking the effect of gene age. While controlling for these factors, we fitted models of the distribution of fitness effects to population genomic datasets of animals and plants. We found that a gene’s evolutionary age significantly impacts the molecular adaptive rate. Moreover, we observed that substitutions in young genes tend to have larger fitness effects. Our study, therefore, provides the first evidence of an “adaptive walk” model of molecular evolution in large evolutionary timescales. Significant statement How does molecular adaptation occur? John Maynard Smith was one of the first to address this question by introducing the notion of “adaptive walk”, which defines the “walk” of a gene towards higher fitness. At the start of this walk, genes tend to experience mutations with larger fitness effects than those closer to their fitness peak. Whilst being well-established, this theory has never been tested on large evolutionary timescales. Here, we achieve this by comparing molecular adaptive rates across genes of different ages in plants and animals. We showed that a gene’s age acts as a significant determinant of molecular adaptation, where young genes adapt faster than old ones. We, therefore, provide evidence for an “adaptive walk” through time.

Bacterial persistence is a potential cause of antibiotic therapy failure. Antibiotic-tolerant persisters originate from phenotypic differentiation within a susceptible population, occurring with a frequency that can be altered by mutations. Recent studies have proven that persistence is a highly evolvable trait and, consequently, an important evolutionary strategy of bacterial populations to adapt to high-dose antibiotic therapy. Yet, the factors that govern the evolutionary dynamics of persistence are currently poorly understood. Theoretical studies predict far-reaching effects of bottlenecking on the evolutionary adaption of bacterial populations, but these effects have never been investigated in the context of persistence. Bottlenecking events are frequently encountered by infecting pathogens during host-to-host transmission and antibiotic treatment. In this study, we used a combination of experimental evolution and barcoded knockout libraries to examine how population bottlenecking affects the evolutionary dynamics of persistence. In accordance with existing hypotheses, small bottlenecks were found to restrict the adaptive potential of populations and result in more heterogeneous evolutionary outcomes. Evolutionary trajectories followed in small-bottlenecking regimes additionally suggest that the fitness landscape associated with persistence has a rugged topography, with distinct trajectories toward increased persistence that are accessible to evolving populations. Furthermore, sequencing data of evolved populations and knockout libraries after selection reveal various genes that are potentially involved in persistence, including previously known as well as novel targets. Together, our results do not only provide experimental evidence for evolutionary theories, but also contribute to a better understanding of the environmental and genetic factors that guide bacterial adaptation to antibiotic treatment., Molecular Biology and Evolution, 38 (8), ISSN:0737-4038, ISSN:1537-1719

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus.

In migratory species, the timing of arrival at the breeding grounds is a life-history trait with major fitness consequences. The optimal arrival date varies from year-to-year, and animals use cues to adjust their arrival dates to match this annual variation. However, which cues they use to time their arrival and whether these cues actually predict the annual optimal arrival date is largely unknown. Here, we integrate causal and evolutionary analysis by identifying the environmental variables used by a migratory songbird to time its arrival dates and testing whether these environmental variables also predicted the optimal time to arrive. We used 11 years of male arrival data of a pied flycatcher population. Specifically, we tested whether temperature and normalized difference vegetation index (NDVI) values from their breeding grounds in the Netherlands and from their wintering grounds in Ivory Coast explained the variation in arrival date, and whether these variables correlated with the position of the annual fitness peak at the breeding grounds. We found that temperature and NDVI, both from the wintering and the breeding grounds, explained the annual variation in arrival date, but did not correlate with the optimal arrival date. We explore three alternative explanations for this lack of correlation. Firstly, the date of the fitness peak may have been incorrectly estimated because a potentially important component of fitness (i.e., migration date dependent mortality en route or directly upon arrival) could not be measured. Secondly, we focused on male timing but the fitness landscape is also likely to be shaped by female timing. Finally, the correlation has recently disappeared because climate change disrupted the predictive value of the cues that the birds use to time their migration. In the latter case, birds may adapt by altering their sensitivity to temperature and NDVI.

SimBit is a general purpose, high performance forward-in-time population genetics simulator. SimBit can simulate a wide variety of selection scenarios (any selection and dominance coefficients variation, any epistatic interaction, any spatial and temporal changes of selection scenario, etc.), demographic scenarios (any changes in patch sizes, migration rates, realistic demography dependent on fecundity, hard vs. soft selection, exponential vs. logistic growth, gametic or zygotic dispersion, etc.) and mating systems (cloning and selfing rates, hermaphrodites or males and females). SimBit can also track QTLs (with hyperdimensional phenotypes, explicit fitness landscape, plasticity, developmental noise, etc.). Finally, SimBit can simulate multiple species with their ecological relationships. SimBit comes with a R wrapper that simplifies the management of an entire research project from the creation of a grid of parameters and corresponding inputs, running simulations and gathering outputs for analysis. SimBit's performance was extensively benchmarked in comparison to SLiM, Nemo and SFS_CODE, varying population size, recombination rate, mutation rate, and the number of loci. I also reproduced simulations from previous studies, benchmarked QTLs and coalescent tree recording techniques. SimBit was most often the highest performing program with the only notable exception of SLiM outperforming SimBit in scenarios with few loci and low genetic diversity.

The prisoner's dilemma (PD) game offers a simple paradigm of competition between two players who can either cooperate or defect. Since defection is a strict Nash equilibrium, it is an asymptotically stable state of the replicator dynamical system that uses the PD payoff matrix to define the fitness landscape of two interacting evolving populations. The dilemma arises from the fact that the average payoff of this asymptotically stable state is suboptimal. Coaxing the players to cooperate would result in a higher payoff for both. Here we develop an optimal control theory for the prisoner's dilemma evolutionary game in order to maximize cooperation (minimize the defector population) over a given cycle time $T$, subject to constraints. Our two time-dependent controllers are applied to the off-diagonal elements of the payoff matrix in a bang-bang sequence that dynamically changes the game being played by dynamically adjusting the payoffs, with optimal timing that depends on the initial population distributions. Over multiple cycles $nT$ $(ng1)$, the method is adaptive as it uses the defector population at the end of the $n\mathrm{th}$ cycle to calculate the optimal schedule over the $n+1\mathrm{st}$ cycle. The control method, based on Pontryagin's maximum principle, can be viewed as determining the optimal way to dynamically alter incentives and penalties in order to maximize the probability of cooperation in settings that track dynamic changes in the frequency of strategists, with potential applications in evolutionary biology, economics, theoretical ecology, social sciences, reinforcement learning, and other fields where the replicator system is used.

We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the population is driven by births, deaths, competition, and mutations along the edges of $G$. We are interested in the large population limit under a mutation rate $\mu_K$ given by a negative power of the carrying capacity $K$ of the system: $\mu_K=K^{-1/\alpha},\alpha>0$. This results in several mutant traits being present at the same time and competing for invading the resident population. We describe the time evolution of the orders of magnitude of each sub-population on the $\log K$ time scale, as $K$ tends to infinity. Using techniques developed in [Champagnat, M\'el\'eard, Tran, 2019] we show that these are piecewise affine continuous functions, whose slopes are given by an algorithm describing the changes in the fitness landscape due to the succession of new resident or emergent types. This work generalises [Kraut, Bovier, 2019] to the stochastic setting, and Theorem 3.2 of [Bovier, Coquille, Smadi, 2018] to any finite mutation graph. We illustrate our theorem by a series of examples describing surprising phenomena arising from the geometry of the graph and/or the rate of mutations., Comment: 39 pages, 7 figures

In the context of the dynamical systems approach, species are of central importance as quantities of living matter with defined structural and kinetic characteristics. A brief review of the species concept is given, followed by quantitative treatment of mutation-selection equilibria that describe species as distributions in the genotype space. Different fitness landscapes are considered, including the master sequence landscape of the classical quasi-species theory, and existence of error thresholds in the maintenance of genetic distributions is analyzed. The static view of fitness landscapes is complemented by treatment of self-organization in genotype space that accompanies emergence of reproductive isolation in neutral sympatric speciation.

Significance The gradual character of evolution is a key feature of the Darwinian worldview. However, macroevolutionary events are often thought to occur in a nongradualist manner, in a regime known as punctuated equilibrium, whereby extended periods of evolutionary stasis are punctuated by rapid transitions between states. Here we analyze a simple mathematical model of population evolution on fitness landscapes and show that, for a large population in the weak-mutation limit, the process of adaptive evolution consists of extended periods of stasis, which the population spends around saddle points on the landscape, interrupted by rapid transitions to new saddle points when a beneficial mutation is fixed. Thus, phenomenologically, the default regime of biological evolution seems to closely resemble punctuated equilibrium., A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe/s time (Ne, effective population size; s, selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of “avalanches” in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.

37 pages, 10 figures, 3 tables, 2 appendices, supplement https://doi.org/10.5194/gmd-14-1949-2021-supplement, Diversity plays a key role in the adaptive capacity of marine ecosystems to environmental changes. However, modelling the adaptive dynamics of phytoplankton traits remains challenging due to the competitive exclusion of sub-optimal phenotypes and the complexity of evolutionary processes leading to optimal phenotypes. Trait diffusion (TD) is a recently developed approach to sustain diversity in plankton models by introducing mutations, therefore allowing the adaptive evolution of functional traits to occur at ecological timescales. In this study, we present a model called Simulating Plankton Evolution with Adaptive Dynamics (SPEAD) that resolves the eco-evolutionary processes of a multi-trait plankton community. The SPEAD model can be used to evaluate plankton adaptation to environmental changes at different timescales or address ecological issues affected by adaptive evolution. Phytoplankton phenotypes in SPEAD are characterized by two traits, the nitrogen half-saturation constant and optimal temperature, which can mutate at each generation using the TD mechanism. SPEAD does not resolve the different phenotypes as discrete entities, instead computing six aggregate properties: total phytoplankton biomass, the mean value of each trait, trait variances, and the inter-trait covariance of a single population in a continuous trait space. Therefore, SPEAD resolves the dynamics of the population's continuous trait distribution by solving its statistical moments, wherein the variances of trait values represent the diversity of ecotypes. The ecological model is coupled to a vertically resolved (1D) physical environment, and therefore the adaptive dynamics of the simulated phytoplankton population are driven by seasonal variations in vertical mixing, nutrient concentration, water temperature, and solar irradiance. The simulated bulk properties are validated by observations from Bermuda Atlantic Time-series Studies (BATS) in the Sargasso Sea. We find that moderate mutation rates sustain trait diversity at decadal timescales and soften the almost total inter-trait correlation induced by the environment alone, without reducing the annual primary production or promoting permanently maladapted phenotypes, as occur with high mutation rates. As a way to evaluate the performance of the continuous trait approximation, we also compare the solutions of SPEAD to the solutions of a classical discrete entities approach, with both approaches including TD as a mechanism to sustain trait variance. We only find minor discrepancies between the continuous model SPEAD and the discrete model, with the computational cost of SPEAD being lower by 2 orders of magnitude. Therefore, SPEAD should be an ideal eco-evolutionary plankton model to be coupled to a general circulation model (GCM) of the global ocean, This work was funded by national research grant CTM2017-87227-P (SPEAD) from the Spanish government. We acknowledge support for the publication fee by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI). The Institute of Marine Sciences (ICM – CSIC) is supported by a “Severo Ochoa” Centre of Excellence grant (CEX2019-000928-S) from the Spanish government

Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly understood. We study a particular model of antibiotic resistance evolution in bacteria where the antibiotic concentration is an environmental parameter and the fitness landscapes incorporate tradeoffs between adaptation to low and high antibiotic concentration. With evolutionary dynamics that follow fitness gradients, the evolution of the system under slowly changing antibiotic concentration resembles the athermal dynamics of disordered physical systems under external drives. Exploiting this resemblance, we show that our model can be described as a system with interacting hysteretic elements. As in the case of the driven disordered systems, adaptive evolution under antibiotic concentration cycling is found to exhibit hysteresis loops and memory formation. We derive a number of analytical results for quasistatic concentration changes. We also perform numerical simulations to study how these effects are modified under driving protocols in which the concentration is changed in discrete steps. Our approach provides a general framework for studying motifs of evolutionary dynamics in biological systems in a changing environment.

Evolutionary diversification can occur in allopatry or sympatry, can be driven by selection or unselected, and can be phenotypically manifested immediately or remain latent until manifested in a newly encountered environment. Diversification of host–parasite interactions is frequently studied in the context of intrinsically selective coevolution, but the potential for host–parasite interaction phenotypes to diversify latently during parasite-blind host evolution is rarely considered. Here, we use a social bacterium experimentally adapted to several environments in the absence of phage to analyse allopatric diversification of host quality—the degree to which a host population supports a viral epidemic. Phage-blind evolution reduced host quality overall, with some bacteria becoming completely resistant to growth suppression by phage. Selective-environment differences generated only mild divergence in host quality. However, selective environments nonetheless played a major role in shaping evolution by determining the degree of stochastic diversification among replicate populations within treatments. Ancestral motility genotype was also found to strongly shape patterns of latent host-quality evolution and diversification. These outcomes show that (i) adaptive landscapes can differ in how they constrain stochastic diversification of a latent phenotype and (ii) major effects of selection on biological diversification can be missed by focusing on trait means. Collectively, our findings suggest that latent-phenotype evolution should inform host–parasite evolution theory and that diversification should be conceived broadly to include latent phenotypes., Proceedings of the Royal Society B: Biological Sciences, 288 (1949), ISSN:0080-4649, ISSN:0950-1193, ISSN:1471-2954, ISSN:0962-8452

Growing efforts to measure fitness landscapes in molecular and microbial systems are motivated by a longstanding goal to predict future evolutionary trajectories. Sometimes under-appreciated, however, is that the fitness landscape and its topography do not by themselves determine the direction of evolution: under sufficiently high mutation rates, populations can climb the closest fitness peak (survival of the fittest), settle in lower regions with higher mutational robustness (survival of the flattest), or even fail to adapt altogether (error catastrophes). I show that another measure of reproductive success, Fisher’s reproductive value, resolves the trade-off between fitness and robustness in the quasi-species regime of evolution: to forecast the motion of a population in genotype space, one should look for peaks in the (mutation-rate dependent) landscape of genotypic reproductive values—whether or not these peaks correspond to local fitness maxima or flat fitness plateaus. This new landscape picture turns quasi-species dynamics into an instance of non-equilibrium dynamics, in the physical sense of Markovian processes, potential landscapes, entropy production, etc.

Distinguishing cell types and cell states is one of the fundamental questions in single-cell studies. Meanwhile, exploring the lineage relations among cells and finding the path and critical points in the cell fate transition are also of great importance.Existing unsupervised clustering methods and lineage trajectory reconstruction methods often face several challenges such as clustering data of arbitrary shapes, tracking precise trajectories and identifying critical points. Certain adaptive landscape approach1–3, which constructs a pseudo-energy landscape of the dynamical system, may be used to explore such problems. Thus, we propose Markov hierarchical clustering algorithm (MarkovHC), which reconstructs multi-scale pseudo-energy landscape by exploiting underlying metastability structure in an exponentially perturbed Markov chain4. A Markov process describes the random walk of a hypothetically traveling cell in the corresponding pseudo-energy landscape over possible gene expression states. Technically, MarkovHC integrates the tasks of cell classification, trajectory reconstruction, and critical point identification in a single theoretical framework consistent with topological data analysis (TDA)5.In addition to the algorithm development and simulation tests, we also applied MarkovHC to diverse types of real biological data: single-cell RNA-Seq data, cytometry data, and single-cell ATAC-Seq data. Remarkably, when applying to single-cell RNA-Seq data of human ESC derived progenitor cells6, MarkovHC not only could successfully identify known cell types, but also discover new cell types and stages. In addition, when using MarkovHC to analyze single-cell RNA-Seq data of human preimplantation embryos in early development7, the hierarchical structure of the lineage trajectories was faithfully reconstituted. Furthermore, the critical points representing important stage transitions had also been identified by MarkovHC from early gastric cancer data8.In summary, these results demonstrate that MarkovHC is a powerful tool based on rigorous metastability theory to explore hierarchical structures of biological data, to identify a cell sub-population (basin) and a critical point (stage transition), and to track a lineage trajectory (differentiation path).HighlightsMarkovHC explores the topology hierarchy in high-dimensional data.MarkovHC can find clusters (basins) and cores (attractors) of clusters in different scales.The trajectory of state transition (transition paths) and critical points in the process of state transition (critical points) among clusters can be tracked.MarkovHC can be applied on diverse types of single-cell omics data.

When divergent populations form hybrids, hybrid fitness can vary with genome composition, current environmental conditions, and the divergence history of the populations. We develop analytical predictions for hybrid fitness, which incorporate all three factors. The predictions are based on Fisher's geometric model, and apply to a wide range of population genetic parameter regimes and divergence conditions, including allopatry and parapatry, local adaptation, and drift. Results show that hybrid fitness can be decomposed into intrinsic effects of admixture and heterozygosity, and extrinsic effects of the (local) adaptedness of the parental lines. Effect sizes are determined by a handful of geometric distances, which have a simple biological interpretation. These distances also reflect the mode and amount of divergence, such that there is convergence toward a characteristic pattern of intrinsic isolation. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This means that the geometrical distances can be estimated from cross data, and provides a simple interpretation of the “composite effects.” Finally, we develop extensions to the model, involving selectively induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.

Effective prophylactic vaccines usually induce the immune system to generate potent antibodies that can bind to an antigen and thus prevent it from infecting host cells. B cells produce antibodies by a Darwinian evolutionary process called affinity maturation (AM). During AM, the B cell population evolves in response to the antigen to produce antibodies that bind specifically and strongly to the antigen. Highly mutable pathogens pose a major challenge to the development of effective vaccines because antibodies that are effective against one strain of the virus may not protect against a mutant strain. Antibodies that can protect against diverse strains of a mutable pathogen have high “breadth” and are called broadly neutralizing antibodies (bnAbs). In spite of extensive studies, an effective vaccination strategy that can generate bnAbs in humans does not exist for any highly mutable pathogen. Here we study a minimal model to explore the mechanisms underlying how the selection forces imposed by antigens can be optimally chosen to guide AM to maximize the evolution of bnAbs. For logistical reasons, only a finite number of antigens can be administered in a finite number of vaccinations; that is, guiding the non-equilibrium dynamics of AM to produce bnAbs must be accomplished non-adiabatically. The time-varying Kullback-Leibler divergence (KLD) between the existing B cell population distribution and the fitness landscape imposed by antigens is a quantitative metric of the thermodynamic force acting on B cells. If this force is too small, adaptation is minimal. If the force is too large, contrary to expectations, adaptation is not faster; rather, the B cell population is extinguished for reasons that we describe. We define the conditions necessary for the force to be set optimally such that the flux of B cells from low to high breadth states is maximized. Even in this case we show why the dynamics of AM prevent perfect adaptation. If two shots of vaccination are allowed, the optimal protocol is characterized by a relatively low optimal KLD during the first shot that appropriately increases the diversity of the B cell population so that the surviving B cells have a high chance of evolving into bnAbs upon subsequently increasing the KLD during the second shot. Phylogenetic tree analysis further reveals the evolutionary pathways that lead to bnAbs. The connections between the mechanisms revealed by our analyses and recent simulation studies of bnAb evolution, the problem of generalist versus specialist evolution, and learning theory are discussed.

Dengue virus (DENV) cycles between mosquito and mammalian hosts. To examine how DENV populations adapt to these different host environments, we used serial passage in human and mosquito cell lines and estimated fitness effects for all single-nucleotide variants in these populations using ultra-deep sequencing. This allowed us to determine the contributions of beneficial and deleterious mutations to the collective fitness of the population. Our analysis revealed that the continuous influx of a large burden of deleterious mutations counterbalances the effect of rare, host-specific beneficial mutations to shape the path of adaptation. Beneficial mutations preferentially map to intrinsically disordered domains in the viral proteome and cluster to defined regions in the genome. These phenotypically redundant adaptive alleles may facilitate host-specific DENV adaptation. Importantly, the evolutionary constraints described in our simple system mirror trends observed across DENV and Zika strains, indicating it recapitulates key biophysical and biological constraints shaping long-term viral evolution., eLife digest Viruses are constantly evolving as a result of mutations in their genetic material and environmental pressures. Viruses switching between insects and mammals face unique evolutionary pressures because they must retain their ability to infect both types of organisms. Yet, the mutations in a virus that may be beneficial in an insect may be different from the ones that may be beneficial in a mammal. Mutations in one host may be even harmful in the other. To learn more about how such viruses thrive as they switch between hosts, Dolan, Taguwa et al. studied the dengue virus, which causes over 390 million infections and over 10,000 deaths each year around the globe. They compared the mutations that occurred as the virus multiplied in human and mosquito cells grown in a laboratory. In the experiments, they used a method called ultra-deep RNA sequencing to identify every change that occurred in the genetic material of the virus each time it multiplied. They determined whether the mutations were beneficial or harmful based on whether they became more common – suggesting they helped the virus survive – or whether they did not persist because they were likely harmful or even fatal to the virus. The experiments showed that many harmful mutations constantly occur in the virus, in both human and mosquito cells. Beneficial changes happen rarely, and those that do are usually only helpful in one type of cell. Fatal mutations tended to occur in parts of the genetic material that encodes regions in the viral proteins that must remain the same. These structural elements appear to be essential to the virus’s survival and unable to undergo change, which makes them good targets for antiviral drugs or vaccines. The techniques used in the study may be useful for investigating other viruses and for understanding the evolutionary constraints on viruses more generally. This may help scientists develop antiviral drugs or vaccines that will remain effective even as viruses continue to evolve and mutate.

The metaphor of fitness landscapes is common in evolutionary biology, as a way to visualise the change in allele or phenotypic frequencies of a population under selection. Understanding how different factors in the evolutionary process affect the trajectory of the population across the landscape is of interest to both theoretical and empirical evolutionary biologists. However, fitness landscape studies often have to rely heavily on mathematical methods that are not easy to access by biologically trained researchers. Here, we used a method borrowed from engineering - genetic algorithms - to simulate the evolutionary process and study how different components affect the path taken through a phenotypic fitness landscape. In a simple study, we compare five selection models that reflect different degrees of dependency of fitness on trait quality: this includes strengths of selection, trait-quality dependent reproductive hierarchy and the amount of stochasticity in the reproductive process. We include an analysis of other evolutionary variables such as population size and mutation rate. We analyse a game theory problem, as a test landscape, that lends itself to analysis through a deterministic mathematical simulation, which we use for comparison. Our results show that there are differences in the speed with which different models of selection lead to the fitness optimum.Author summaryEvolution and adaptation in biology occurs in fitness landscapes, multidimensional spaces representing all possible genotypic or phenotypic combinations, where population adapt by following the cline of the fitness dimension. The study of adaptation on complex fitness landscapes has so far been limited by the need for mathematically heavy methods. Here, we present a simulation modelling framework, genetic algorithms, that can be used for evolutionary simulations of a population on a fitness landscape of chosen features and with custom evolutionary parameters.

We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation relates these two samplings, independently of the model used to generate divisions and growth in the cell population. These relations lead to estimators of the population growth rate, which can be very efficient as we demonstrate by an analysis of a set of mother machine data. These fluctuation relations lead to general and important inequalities between the mean number of divisions and the doubling time of the population. We also study the fitness landscape, a concept based on the two samplings mentioned above, which quantifies the correlations between a phenotypic trait of interest and the number of divisions. We obtain explicit results when the trait is the age or the size, for age and size-controlled models.