The geometry of evolution

Some structures are more suitable for self-organization through the Darwin-Wallace mechanism of variation and selection than others. Such evolutionary adaptability (or evolvability) can itself evolve through variation and selection, either by virtue of being associated with reliability and stability or by hitchhiking along with the advantageous traits whose appearance it facilitates. In order for a structure to evolve there must be a reasonable probability that genetic variation carries it from one adaptive peak to another; at the same time the structure should not be overly unstable to phenotypic perturbations, as this is incompatible with occupying a peak. Organizations that are complex in terms of numbers of components and interactions are more likely to meet the peak-climbing condition, but less likely to meet the stability condition. Biological structures that are characterized by a high degree of component redundancy and multiple weak interactions satisfy these conflicting pressures.     

The brain-machine disanalogy

The comparative study of information processing in brains and machines leads to a picture in which disanalogies are more fundamental than analogies. The major dichotomy is between evolvability and programmability. Brain models, to be tenable, must pass an extended Turing test in which the capacity to self organize through the Darwinian mechanism of variation and selection is a key element. Programmable machines that simulate the type of structure-function relations that allow evolution to occur are, however, too inefficient in their use of resources for problem solving to support cognitive abilities comparable to those of biological organisms. Furthermore, real evolutionary systems are open in that it is always possible for them to tap previously unexploited physical interactions for computing. Nevertheless, computer simulation provides a powerful tool for studying brain function; and non-programmable designs that exploit the high efficiency, high adaptability domain of computing are in principle possible.     

Guiding the self-organization of random Boolean networks

Random Boolean networks (RBNs) are models of genetic regulatory networks. It is useful to describe RBNs as self-organizing systems to study how changes in the nodes and connections affect the global network dynamics. This article reviews eight different methods for guiding the self-organization of RBNs. In particular, the article is focused on guiding RBNs toward the critical dynamical regime, which is near the phase transition between the ordered and dynamical phases. The properties and advantages of the critical regime for life, computation, adaptability, evolvability, and robustness are reviewed. The guidance methods of RBNs can be used for engineering systems with the features of the critical regime, as well as for studying how natural selection evolved living systems, which are also critical.     

Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.     

Computational strategies for protein conformational ensemble detection

Protein function is constrained by the three-dimensional structure but is delineated by its dynamics. This framework must satisfy specificity of function along with adaptability to changing environments and evolvability under external constraints. The accessibility of the available regions of the energy landscape for a set of conditions and shifts in the populations upon their modulation have effects propagating across scales, from biomolecular interactions, to organisms, to populations. Developing the ability to detect and juggle protein conformations supplemented by a physics-based understanding has implications for not only in vivo problems but also for resistance impeding drug discovery and bionano-sensor design.     

The role of epistatic gene interactions in the response to selection and the evolution of evolvability

It has been argued that the architecture of the genotype-phenotype map determines evolvability, but few studies have attempted to quantify these effects. In this article we use the multilinear epistatic model to study the effects of different forms of epistasis on the response to directional selection. We derive an analytical prediction for the change in the additive genetic variance, and use individual-based simulations to understand the dynamics of evolvability and the evolution of genetic architecture. This shows that the major determinant for the evolution of the additive variance, and thus the evolvability, is directional epistasis. Positive directional epistasis leads to an acceleration of evolvability, while negative directional epistasis leads to canalization. In contrast, pure non-directional epistasis has little effect on the response to selection. One consequence of this is that the classical epistatic variance components, which do not distinguish directional and non-directional effects, are useless as predictors of evolutionary dynamics. The build-up of linkage disequilibrium also has negligible effects. We argue that directional epistasis is likely to have major effects on evolutionary dynamics and should be the focus of empirical studies of epistasis.     

A hybrid stochastic-deterministic approach to explore multiple infection and evolution in HIV

To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, as well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.     

Maximization principles and daisyworld

We investigate whether the equilibrium time-averaged state of a self-organizing system with many internal degrees of freedom, 2D-daisyworld, can be described by optimizing a single quantity. Unlike physical systems where a principle of maximum energy production has been observed, daisyworld follows evolutionary dynamics rather than Hamiltonian dynamics. We find that this is sufficient to invalidate the maximum entropy production principle, finding instead a different principle, that the system self-organizes to a state which maximizes the amount of life.     

The evolutionary dynamics of evolvability in a gene network model

Evolvability, the ability of populations to adapt, has recently emerged as a major unifying concept in biology. Although the study of evolvability offers new insights into many important biological questions, the conceptual bases of evolvability, and the mechanisms of its evolution, remain controversial. We used simulated evolution of a model of gene network dynamics to test the contentious hypothesis that natural selection can favour high evolvability, in particular in sexual populations. Our results conclusively demonstrate that fluctuating natural selection can increase the capacity of model gene networks to adapt to new environments. Detailed studies of the evolutionary dynamics of these networks establish a broad range of validity for this result and quantify the evolutionary forces responsible for changes in evolvability. Analysis of the genotype–phenotype map of these networks also reveals mechanisms connecting evolvability, genetic architecture and robustness. Our results suggest that the evolution of evolvability can have a pervasive influence on many aspects of organisms.     

Nash Equilibria in Multi-Agent Motor Interactions

Social interactions in classic cognitive games like the ultimatum game or the prisoner''s dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner''s dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.     

Marine Ecosystems as Complex Adaptive Systems: Emergent Patterns,Critical Transitions,and Public Goods

Complex adaptive systems provide a unified framework for explaining ecosystem phenomena. In the past 20 years, complex adaptive systems have been sharpened from an abstract concept into a series of tools that can be used to solve concrete problems. These advances have been led by the development of new techniques for coupling ecological and evolutionary dynamics, for integrating dynamics across multiple scales of organization, and for using data to infer the complex interactions among different components of ecological systems. Focusing on the development and usage of these new methods, we discuss how they have led to an improved understanding of three universal features of complex adaptive systems, emergent patterns; tipping points and critical phenomena; and cooperative behavior. We restrict our attention primarily to marine ecosystems, which provide numerous successful examples of the application of complex adaptive systems. Many of these are currently undergoing dramatic changes due to anthropogenic perturbations, and we take the opportunity to discuss how complex adaptive systems can be used to improve the management of public goods and to better preserve critical ecosystem services.     

Adaptability and the integration of computer-based information processing into the dynamics of organizations

The structure of a system influences its adaptability. An important result of adaptability theory is that subsystem independence increases adaptability [Conrad, M., 1983. Adaptability. Plenum Press, New York]. Adaptability is essential in systems that face an uncertain environment such as biological systems and organizations. Modern organizations are the product of human design. And so it is their structure and the effect that it has on their adaptability. In this paper we explore the potential effects of computer-based information processing on the adaptability of organizations. The integration of computer-based processes into the dynamics of the functions they support and the effect it has on subsystem independence are especially relevant to our analysis.     

A genetic background with low mutational robustness is associated with increased adaptability to a novel host in an RNA virus

Although mutational robustness is central to many evolutionary processes, its relationship to evolvability remains poorly understood and has been very rarely tested experimentally. Here, we measure the evolvability of Vesicular stomatitis virus in two genetic backgrounds with different levels of mutational robustness. We passaged the viruses into a novel cell type to model a host‐jump episode, quantified changes in infectivity and fitness in the new host, evaluated the cost of adaptation in the original host and analyzed the genetic basis of this adaptation. Lineages evolved from the less robust genetic background demonstrated increased adaptability, paid similar costs of adaptation to the new host and fixed approximately the same number of mutations as their more robust counterparts. Theory predicts that robustness can promote evolvability only in systems where large sets of genotypes are connected by effectively neutral mutations. We argue that this condition might not be fulfilled generally in RNA viruses.     

Predator-prey coevolution driven by size selective predation can cause anti-synchronized and cryptic population dynamics

Population dynamics and evolutionary dynamics can occur on similar time scales, and a coupling of these two processes can lead to novel population dynamics. Recent theoretical studies of coevolving predator-prey systems have concentrated more on the stability of such systems than on the characteristics of cycles when they are unstable. Here I explore the characteristics of the cycles that arise due to coevolution in a system in which prey can increase their ability to escape from predators by becoming either significantly larger or significantly smaller in trait value (i.e., a bidirectional trait axis). This is a reasonable model of body size evolution in some systems. The results show that antiphase population cycles and cryptic cycles (large population fluctuation in one species but almost no change in another species) can occur in the coevolutionary system but not systems where only a single species evolves. Previously, those dynamical patterns have only been theoretically shown to occur in single species evolutionary models and the coevolutionary model which do not involve a bi-directional axis of adaptation. These unusual dynamics may be observed in predator-prey interactions when the density dependence in the prey species is strong.     

Predation risk tradeoffs in prey: effects on energy and behaviour

The complexity of behavioural interactions in predator-prey systems has recently begun to capture trait-effects, or non-lethal effects, of predators on prey via induced behavioural changes. Non-lethal predation effects play crucial roles in shaping population and community dynamics, particularly by inducing changes to foraging, movement and reproductive behaviours of prey. Prey exhibit trade-offs in behaviours while minimizing predation risk. We use a novel evolutionary ecosystem simulation EcoSim to study such behavioural interactions and their effects on prey populations, thereby addressing the need for integrating multiple layers of complexity in behavioural ecology. EcoSim allows complex intra- and inter-specific interactions between behaviourally and genetically unique individuals called predators and prey, as well as complex predator-prey dynamics and coevolution in a tri-trophic and spatially heterogeneous world. We investigated the effects of predation risk on prey energy budgets and fitness. Results revealed that energy budgets, life history traits, allocation of energy to movements and fitness-related actions differed greatly between prey subjected to low-predation risk and high-predation risk. High-predation risk suppressed prey foraging activity, increased total movement and decreased reproduction relative to low-risk. We show that predation risk alone induces behavioural changes in prey which drastically affect population and community dynamics, and when interpreted within the evolutionary context of our simulation indicate that genetic changes accompanying coevolution have long-term effects on prey adaptability to the absence of predators.     

The mutation matrix and the evolution of evolvability

Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, r(mu), the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at -1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.     

Emergence of robust regulatory motifs from in silico evolution of sustained oscillation

The relationship between robustness and evolvability (easiness to evolve), and the evolutionary emergence of robust genetic circuits in biology have attracted much attention in systems biology. This paper investigates in silico the influence of the cis-regulation logic and the coupling of feedback loops on the evolvability and robustness of gene regulatory motifs that can generate sustained oscillation. Our simulation results indicate that both evolvability and robustness of the considered regulatory motifs depend on the cis-regulation logic and the way in which positive and negative feedback loops are coupled. Most interestingly, our findings suggest that robust regulatory motifs can emerge from evolution without an explicit selection pressure on robustness and adding noise in the parameters during the evolution is likely to promote the evolution of sustained oscillation.     

Heterostyly accelerates diversification via reduced extinction in primroses

The exceptional species diversity of flowering plants, exceeding that of their sister group more than 250-fold, is especially evident in floral innovations, interactions with pollinators and sexual systems. Multiple theories, emphasizing flower–pollinator interactions, genetic effects of mating systems or high evolvability, predict that floral evolution profoundly affects angiosperm diversification. However, consequences for speciation and extinction dynamics remain poorly understood. Here, we investigate trajectories of species diversification focusing on heterostyly, a remarkable floral syndrome where outcrossing is enforced via cross-compatible floral morphs differing in placement of their respective sexual organs. Heterostyly evolved at least 20 times independently in angiosperms. Using Darwin''s model for heterostyly, the primrose family, we show that heterostyly accelerates species diversification via decreasing extinction rates rather than increasing speciation rates, probably owing to avoidance of the negative genetic effects of selfing. However, impact of heterostyly appears to differ over short and long evolutionary time-scales: the accelerating effect of heterostyly on lineage diversification is manifest only over long evolutionary time-scales, whereas recent losses of heterostyly may prompt ephemeral bursts of speciation. Our results suggest that temporal or clade-specific conditions may ultimately determine the net effects of specific traits on patterns of species diversification.     

On the origin of modular variation

We study the dynamics of modularization in a minimal substrate. A module is a functional unit relatively separable from its surrounding structure. Although it is known that modularity is useful both for robustness and for evolvability (Wagner 1996), there is no quantitative model describing how such modularity might originally emerge. Here we suggest, using simple computer simulations, that modularity arises spontaneously in evolutionary systems in response to variation, and that the amount of modular separation is logarithmically proportional to the rate of variation. Consequently, we predict that modular architectures would appear in correlation with high environmental change rates. Because this quantitative model does not require any special substrate to occur, it may also shed light on the origin of modular variation in nature. This observed relationship also indicates that modular design is a generic phenomenon that might be applicable to other fields, such as engineering: Engineering design methods based on evolutionary simulation would benefit from evolving to variable, rather than stationary, fitness criteria, as a weak and problem-independent method for inducing modularity.     

Quantifying epistatic interactions among the components constituting the protein translation system

In principle, the accumulation of knowledge regarding the molecular basis of biological systems should allow the development of large‐scale kinetic models of their functions. However, the development of such models requires vast numbers of parameters, which are difficult to obtain in practice. Here, we used an in vitro translation system, consisting of 69 defined components, to quantify the epistatic interactions among changes in component concentrations through Bahadur expansion, thereby obtaining a coarse‐grained model of protein synthesis activity. Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2‐body inter‐component epistatic interactions are negligible, despite the presence of larger than 2‐body physical interactions. These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems. Moreover, the average ratio of 2‐ to 1‐body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system.