Novelty Search Promotes Antigenic Diversity in Microbial Pathogens.

Driven by host-pathogen coevolution, cell surface antigens are often the fastest evolving parts of a microbial pathogen. The persistent evolutionary impetus for novel antigen variants suggests the utility of novelty-seeking algorithms in predicting antigen diversification in microbial pathogens. In contrast to traditional genetic algorithms maximizing variant fitness, novelty-seeking algorithms optimize variant novelty. Here, we designed and implemented three evolutionary algorithms (fitness-seeking, novelty-seeking, and hybrid) and evaluated their performances in 10 simulated and 2 empirically derived antigen fitness landscapes. The hybrid walks combining fitness- and novelty-seeking strategies overcame the limitations of each algorithm alone, and consistently reached global fitness peaks. Thus, hybrid walks provide a model for microbial pathogens escaping host immunity without compromising variant fitness. Biological processes facilitating novelty-seeking evolution in natural pathogen populations include hypermutability, recombination, wide dispersal, and immune-compromised hosts. The high efficiency of the hybrid algorithm improves the evolutionary predictability of novel antigen variants. We propose the design of escape-proof vaccines based on high-fitness variants covering a majority of the basins of attraction on the fitness landscape representing all potential variants of a microbial antigen.

Research on Niche Improvement Path of Photovoltaic Agriculture in China.

To explore the niche improvement path of photovoltaic agriculture in China, a niche influencing factor system was constructed first. Then, this study innovatively combined the DEMATEL and analytic network process (DANP) method and the NK model, which can correct the defects of the traditional NK model. Based on the above method, the influence coefficients and index weight of each niche factor were calculated, and the niche fitness landscape of photovoltaic agriculture was constructed. Finally, according to the fitness landscape map of each combination state, the optimal configuration state of niche influencing factors of photovoltaic agriculture and the optimal niche improvement path of photovoltaic agriculture were explored. We found that the interaction between the six niche influencing factors determines the niche fitness of photovoltaic agriculture, and the changes in the niche fitness and the niche improvement of photovoltaic agriculture are coordinated. It was proposed that the optimal niche improvement path of photovoltaic agriculture in China is "technological innovation → policy formulation → resource allocation → economic improvement → social recognition → environmental protection", and the research conclusions were further explained and discussed.

Computational Modeling of the Value Co-Creation Process in Customer Service: An Application of the NK Model.

There has been an increasing interest to explore and gain knowledge about customer engagement behavior among academia and practitioners. Particularly, the value co-creation process in customer services is essential to explore the interaction structure. In this study, we applied the computational simulation of the NK model to identify the value co-creation process between service employees and customers in the service context. To specifically explore the dynamic interaction among them, we identified what kind of service is provided for what type of customers and when service performance improves according to the degree of interaction between service employees and customers. The simulations show that the greatest service value can be achieved when employees and customers jointly perform local search (90%) and long jump (10%). However, if both employees and customers jointly perform local search only, the service value can be stuck in a local optimum. In cases where employees and customers make their independent improvement, either through local search or long jump, the overall service value varies depending on the complexity of interactions between employees and customers. For example, the improvement in service value is the worst when employees and customers make long jumps at independent timings in high complex interactions. Our computational simulations offer visible experimental-based insights into understanding the value co-creation process with customers and promising results for customer service studies.

Unbiased inference of the fitness landscape ruggedness from imprecise fitness estimates.

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.

Quasi-species evolution maximizes genotypic reproductive value (not fitness or flatness).

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.

Average Fitness Differences on NK Landscapes.

The average fitness difference between adjacent sites in a fitness landscape is an important descriptor that impacts in particular the dynamics of selection/mutation processes on the landscape. Of particular interest is its connection to the error threshold phenomenon. We show here that this parameter is intimately tied to the ruggedness through the landscape's amplitude spectrum. For the NK model, a surprisingly simple analytical estimate explains simulation data with high precision.

Causation Analysis of Risk Coupling of Gas Explosion Accident in Chinese Underground Coal Mines.

The coal mine production industry is a complex sociotechnical system with interactive relationships among several risk factors. Currently, causation analysis of gas explosion accidents is mainly focused on the aspects of human error and equipment fault, while neglecting the interactive relationships among risk factors. A new method is proposed through risk coupling. First, the meaning of risk coupling of a gas explosion is defined, and types of risk coupling are classified. Next, the coupled relationship and coupled effects among risk factors are explored through combining the interpretative structural modeling (ISM) and the NK model. Twenty-eight representative risk factors and 16 coupled types of risk factors are obtained through analysis of 332 gas explosion accidents in coal mines in China. Through the application of the combined ISM-NK model, an eight-level hierarchical model of risk coupling of a gas explosion accident is established, and the coupled degrees of different types of risk coupling are assessed. The hierarchical model reveals that two of the 28 risk factors, such as state policies, laws, and regulations, are the root risk factors for gas explosions; nine of the 28 risk factors, such as flame from blasting, electric spark, and local gas accumulation, are direct causes of gas explosions; whereas 17 of the risk factors, such as three-violation actions, ventilation system, and safety management, are indirect ones. A quantitative analysis of the NK model shows that the probability of gas explosion increases with the increasing number of risk factors. Compared with subjective risk factors, objective risk factors have a higher probability of causing gas explosion because of risk coupling.

The Evolution of Sex through the Baldwin Effect.

This article suggests that the fundamental haploid-diploid cycle of eukaryotic sex exploits a rudimentary form of the Baldwin effect. With this explanation for the basic cycle, the other associated phenomena can be explained as evolution tuning the amount and frequency of learning experienced by an organism. Using the well-known NK model of fitness landscapes, it is shown that varying landscape ruggedness varies the benefit of the haploid-diploid cycle, whether based upon endomitosis or syngamy. The utility of pre-meiotic doubling and recombination during the cycle are also shown to vary with landscape ruggedness. This view is suggested as underpinning, rather than contradicting, many existing explanations for sex.

Evolving user needs and late-mover advantage.

We propose a generalized NK-model of late-mover advantage where late-mover firms leapfrog first-mover firms as user needs evolve over time. First movers face severe trade-offs between the provision of functionalities in which their products already excel and the additional functionalities requested by users later on. Late movers, by contrast, start searching when more functionalities are already known and typically come up with superior product designs. We also show that late-mover advantage is more probable for more complex technologies. Managerial implications follow.

Evolutionary dynamics of a polymorphic self-replicator population with a finite population size and hyper mutation rate.

Self-replicating biomolecules, subject to experimental evolution, exhibit hyper mutation rates where the genotypes of most offspring have at least a one point mutation. Thus, we formulated the evolutionary dynamics of an asexual self-replicator population with a finite population size and hyper mutation rate, based on the probability density of fitnesses (fitness distribution) for the evolving population. As a case study, we used a Kauffman's "NK fitness landscape". We deduced recurrence relations for the first three cumulants of the fitness distribution and compared them with the results of computer simulations. We found that the evolutionary dynamics is classified in terms of two modes of selection: the "radical mode" and the "gentle mode". In the radical mode, only a small number of genotypes with the highest or near highest fitness values can leave offspring. In the gentle mode, genotypes with moderate fitness values can leave offspring. We clarified how the evolutionary equilibrium and climbing rate depend on given parameters such as gradient and ruggedness of the landscape, mutation rate and population size, in terms of the two modes of selection. Roughly, the radical mode conducts the fast climbing but attains to the stationary states with low fitness, while the gentle mode conducts the slow climbing but attains to the stationary states with high fitness.

Trade-offs in antibody repertoires to complex antigens.

Pathogens vary in their antigenic complexity. While some pathogens such as measles present a few relatively invariant targets to the immune system, others such as malaria display considerable antigenic diversity. How the immune response copes in the presence of multiple antigens, and whether a trade-off exists between the breadth and efficacy of antibody (Ab)-mediated immune responses, are unsolved problems. We present a theoretical model of affinity maturation of B-cell receptors (BCRs) during a primary infection and examine how variation in the number of accessible antigenic sites alters the Ab repertoire. Naive B cells with randomly generated receptor sequences initiate the germinal centre (GC) reaction. The binding affinity of a BCR to an antigen is quantified via a genotype-phenotype map, based on a random energy landscape, that combines local and distant interactions between residues. In the presence of numerous antigens or epitopes, B-cell clones with different specificities compete for stimulation during rounds of mutation within GCs. We find that the availability of many epitopes reduces the affinity and relative breadth of the Ab repertoire. Despite the stochasticity of somatic hypermutation, patterns of immunodominance are strongly shaped by chance selection of naive B cells with specificities for particular epitopes. Our model provides a mechanistic basis for the diversity of Ab repertoires and the evolutionary advantage of antigenically complex pathogens.

A tortoise-hare pattern seen in adapting structured and unstructured populations suggests a rugged fitness landscape in bacteria.

In the context of Wright's adaptive landscape, genetic epistasis can yield a multipeaked or "rugged" topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to fix rapidly on one, which may not be the highest peak. In a spatially structured population, on the other hand, beneficial mutations take longer to spread. This slowdown allows distant parts of the population to explore the landscape semiindependently. Such a population can simultaneously discover multiple peaks, and the genotype at the highest discovered peak is expected to dominate eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the fable of the tortoise and the hare, the structured population (tortoise) starts relatively slow but eventually surpasses the unstructured population (hare) in average fitness. In contrast, on single-peak landscapes that lack epistasis, all uphill paths converge. Given such "smooth" topography, breadth of search is devalued and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the tortoise-hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a tortoise-hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright's shifting balance process.

Properties of selected mutations and genotypic landscapes under Fisher's geometric model.

The fitness landscape-the mapping between genotypes and fitness-determines properties of the process of adaptation. Several small genotypic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here, we generate several testable predictions for the properties of these small genotypic landscapes under Fisher's geometric model of adaptation. When the ancestral strain is far from the fitness optimum, we analytically compute the fitness effect of selected mutations and their epistatic interactions. Epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected, or coselected in an adaptive walk. Simulations show that genotypic landscapes built from Fisher's model are very close to an additive landscape when the ancestral strain is far from the optimum. However, when it is close to the optimum, a large diversity of landscape with substantial roughness and sign epistasis emerged. Strikingly, small genotypic landscapes built from several replicate adaptive walks on the same underlying landscape were highly variable, suggesting that several realizations of small genotypic landscapes are needed to gain information about the underlying architecture of the fitness landscape.