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.     

Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching

Stochastic phenotype switching--often considered a bet hedging or risk-reducing strategy--can enhance the probability of survival in fluctuating environments. A recent experiment provided direct evidence for an adaptive origin by showing the de novo evolution of switching in bacterial populations propagated under a selective regime that captured essential features of the host immune response. The regime involved strong frequency-dependent selection realized via dual imposition of an exclusion rule and population bottleneck. Applied at the point of transfer between environments, the phenotype common in the current environment was assigned a fitness of zero and was thus excluded from participating in the next round (the exclusion rule). In addition, also at the point of transfer, and so as to found the next bout of selection, a single phenotypically distinct type was selected at random from among the survivors (the bottleneck). Motivated by this experiment, we develop a mathematical model to explore the broader significance of key features of the selective regime. Through a combination of analytical and numerical results, we show that exclusion rules and population bottlenecks act in tandem as potent selective agents for stochastic phenotype switching, such that even when initially rare, and when switching engenders a cost in Malthusian fitness, organisms with the capacity to switch can invade non-switching populations and replace non-switching types. Simulations demonstrate the robustness of our findings to alterations in switching rate, fidelity of exclusion, bottleneck size, duration of environmental state and growth rate. We also demonstrate the relevance of our model to a range of biological scenarios such as bacterial persistence and the evolution of sex.     

The evolutionary emergence of stochastic phenotype switching in bacteria

Stochastic phenotype switching - or bet hedging - is a pervasive feature of living systems and common in bacteria that experience fluctuating (unpredictable) environmental conditions. Under such conditions, the capacity to generate variable offspring spreads the risk of being maladapted in the present environment, against offspring likely to have some chance of survival in the future. While a rich subject for theoretical studies, little is known about the selective causes responsible for the evolutionary emergence of stochastic phenotype switching. Here we review recent work - both theoretical and experimental - that sheds light on ecological factors that favour switching types over non-switching types. Of particular relevance is an experiment that provided evidence for an adaptive origin of stochastic phenotype switching by subjecting bacterial populations to a selective regime that mimicked essential features of the host immune response. Central to the emergence of switching types was frequent imposition of 'exclusion rules' and 'population bottlenecks' - two complementary faces of frequency dependent selection. While features of the immune response, exclusion rules and bottlenecks are likely to operate in many natural environments. Together these factors define a set of selective conditions relevant to the evolution of stochastic switching, including antigenic variation and bacterial persistence.     

Phenotype Switching and Mutations in Random Environments

Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates, and analyze how the optimal switching rates depend on the frequency of environmental changes. If environmental changes are as rare as mutations, then the optimal switching rates mimic the rates of environmental changes. If the environment changes more frequently, then the optimal genotype either maximally favors fitness in the more common environment or has the maximal switching rate to each phenotype. Our results also explain why the optimum is relatively insensitive to fitness in each environment.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Evolution of alternative insect life histories in stochastic seasonal environments

Deterministic seasonality can explain the evolution of alternative life history phenotypes (i.e., life history polyphenism) expressed in different generations emerging within the same year. However, the influence of stochastic variation on the expression of such life history polyphenisms in seasonal environments is insufficiently understood. Here, we use insects as a model and explore (1) the effects of stochastic variation in seasonality and (2) the life cycle on the degree of life history differentiation among the alternative developmental pathways of direct development and diapause (overwintering), and (3) the evolution of phenology. With numerical simulation, we determine the values of development (growth) time, growth rate, body size, reproductive effort, adult life span, and fecundity in both the overwintering and directly developing generations that maximize geometric mean fitness. The results suggest that natural selection favors the expression of alternative life histories in the alternative developmental pathways even when there is stochastic variation in seasonality, but that trait differentiation is affected by the developmental stage that overwinters. Increasing environmental unpredictability induced a switch to a bet‐hedging type of life history strategy, which is consistent with general life history theory. Bet‐hedging appeared in our study system as reduced expression of the direct development phenotype, with associated changes in life history phenotypes, because the fitness value of direct development is highly variable in uncertain environments. Our main result is that seasonality itself is a key factor promoting the evolution of seasonally polyphenic life histories but that environmental stochasticity may modulate the expression of life history phenotypes.     

The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype‐by‐environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long‐term evolutionary change. Such mismatches permit strong evolutionary constraints—despite an abundance of beneficial fitness variation within single environmental contexts—and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.     

The spatial scale of local adaptation in a stochastic environment

The distribution of phenotypes in space will be a compromise between adaptive plasticity and local adaptation increasing the fit of phenotypes to local conditions and gene flow reducing that fit. Theoretical models on the evolution of quantitative characters on spatially explicit landscapes have only considered scenarios where optimum trait values change as deterministic functions of space. Here, these models are extended to include stochastic spatially autocorrelated aspects to the environment, and consequently the optimal phenotype. Under these conditions, the regression of phenotype on the environmental variable becomes steeper as the spatial scale on which populations are sampled becomes larger. Under certain deterministic models – such as linear clines – the regression is constant. The way in which the regression changes with spatial scale is informative about the degree of phenotypic plasticity, the relative scale of effective gene flow and the environmental dependency of selection. Connections to temporal models are discussed.     

Memory shapes microbial populations

Correct decision making is fundamental for all living organisms to thrive under environmental changes. The patterns of environmental variation and the quality of available information define the most favourable strategy among multiple options, from randomly adopting a phenotypic state to sensing and reacting to environmental cues. Cellular memory—the ability to track and condition the time to switch to a different phenotypic state—can help withstand environmental fluctuations. How does memory manifest itself in unicellular organisms? We describe the population-wide consequences of phenotypic memory in microbes through a combination of deterministic modelling and stochastic simulations. Moving beyond binary switching models, our work highlights the need to consider a broader range of switching behaviours when describing microbial adaptive strategies. We show that memory in individual cells generates patterns at the population level coherent with overshoots and non-exponential lag times distributions experimentally observed in phenotypically heterogeneous populations. We emphasise the implications of our work in understanding antibiotic tolerance and, in general, bacterial survival under fluctuating environments.     

Evolution of regulated phenotypic expression during a transition to multicellularity

Multicellular organisms coordinate growth and differentiation from single cell starting points with developmental programs. While the evolutionary origins of these programs are unknown, it is likely that they are closely tied to the evolution of regulated—not stochastic—phenotypic expression. To determine how such regulation might arise, we consider experimental populations of Pseudomonas fluorescens which evolved stochastic switching in the lab. This switching is directly coupled with environmental oscillations generated by the bacteria themselves. This unique example of niche construction provides reliable information that organisms may incorporate into regulation of phenotypes. We use mathematical models to investigate the success of two forms of regulation that rely on sensing either external or internal information. We find that both strategies can outcompete stochastic strategies for certain combinations of parameters. In particular, external sensing mechanisms are very effective over a large range of parameter space—including parameters that correspond to poor sensing of the extracellular signal and gradual responses. We show with evolutionary simulations that this robustness makes them more likely to evolve from initially stochastically switching populations rather than internal sensing mechanisms which require more tuning of parameters. These results demonstrate that, within this oscillating system, if regulatory mechanisms can evolve to incorporate environmental information then their selective advantage is sufficient for them to fix in the population.     

Evolution and maintenance of the environmental component of the phenotypic variance: benefit of plastic traits under changing environments

How environmental variances in quantitative traits are influenced by variable environments is an important problem in evolutionary biology. In this study, the evolution and maintenance of phenotypic variance in a plastic trait under stabilizing selection are investigated. The mapping from genotypic value to phenotypic value of the quantitative trait is approximated by a linear reaction norm, with genotypic effects on its phenotypic mean and sensitivity to environment. The environmental deviation is assumed to be decomposed into environmental quality, which interacts with genotypic value, and residual developmental noise, which is independent of genotype. Environmental quality and the optimal phenotype of stabilizing selection are allowed to randomly fluctuate in both space and time, and individuals migrate equally before development and reproduction among different niches. Analyses show that phenotypic plasticity is adaptive within variable environments if correlations have become established between the optimal phenotype and environmental quality in space and/or time. The evolved plasticity increases with variances in optimal phenotypes and correlations between optimal phenotype and environmental quality; this further induces increases in mean fitness and the environmental variance in the trait. Under certain circumstances, however, the environmental variance may decrease with increase in variation in environmental quality.     

The impact of bottlenecks on microbial survival,adaptation, and phenotypic switching in host–pathogen interactions

Microbial pathogens and viruses can often maintain sufficient population diversity to evade a wide range of host immune responses. However, when populations experience bottlenecks, as occurs frequently during initiation of new infections, pathogens require specialized mechanisms to regenerate diversity. We address the evolution of such mechanisms, known as stochastic phenotype switches, which are prevalent in pathogenic bacteria. We analyze a model of pathogen diversification in a changing host environment that accounts for selective bottlenecks, wherein different phenotypes have distinct transmission probabilities between hosts. We show that under stringent bottlenecks, such that only one phenotype can initiate new infections, there exists a threshold stochastic switching rate below which all pathogen lineages go extinct, and above which survival is a near certainty. We determine how quickly stochastic switching rates can evolve by computing a fitness landscape for the evolutionary dynamics of switching rates, and analyzing its dependence on both the stringency of bottlenecks and the duration of within‐host growth periods. We show that increasing the stringency of bottlenecks or decreasing the period of growth results in faster adaptation of switching rates. Our model provides strong theoretical evidence that bottlenecks play a critical role in accelerating the evolutionary dynamics of pathogens.     

Plastic inducible morphologies are not always adaptive: The importance of time delays in a stochastic environment

Summary We present a mathematical model for predicting the expected fitness of phenotypically plastic organisms experiencing a variable environment. We assume that individuals experience two discrete environments probabilistically in time (as a Markov process) and that there are two different phenotypic states, each yielding the highest fitness in one of the two environments. We compare the expected fitness of a phenotypically fixed individual to that of an individual whose phenotype is induced to produce the better phenotype in each environment with a time lag between experiencing a new environment and realization of the new phenotype. Such time lags are common in organisms where phenotypically plastic, inducible traits have been documented. We find that although plasticity is generally adaptive when time lags are short (relative to the time scale of environmental variability), plasticity can be disadvantageous for longer lag times. Asymmetries in environmental change probabilities and/or the relative fitnesses of each phenotype strongly influence whether plasticity is favoured. In contrast to other models, our model does not require costs for plasticity to be disadvantageous; costs affect the results quantitatively, not qualitatively.     

Fifteen minutes of fim: control of type 1 pili expression in E. coli

Pili are used by Escherichia coli to attach to and invade mammalian tissues during host infection and colonization. Expression of type 1 pili, believed to act as virulence factors in urinary tract infections, is under control of the 'firm' genetic network. This network is able to sense the environment and actuate phase variation control. It is a prime exemplar of an integrative regulatory system because of its role in mediating a complex infection process, and because it instantiates a number of regulatory motifs, including DNA inversion and stochastic variation. With the help of a mathematical model, we explore the mechanisms and architecture of the fim network. We explain (1) basic network operation, including the roles of the recombinase and global regulatory protein concentrations, their DNA binding affinities, and their switching rates in observed phase variation behavior; (2) why there are two recombinases when one would seem to suffice; (3) the source of on-to-off switching specificity of FimE; (4) the role of fimE orientational control in switch dynamics; and (5) how temperature tuning of piliation is achieved. In the process, we identify a general regulatory motif that tunes phenotype to an environmental variable, and explain a number of apparent experimental inconsistencies.     

Human brain evolution: harnessing the genomics (r)evolution to link genes, cognition, and behavior

The evolution of the human brain has resulted in numerous specialized features including higher cognitive processes such as language. Knowledge of whole-genome sequence and structural variation via high-throughput sequencing technology provides an unprecedented opportunity to view human evolution at high resolution. However, phenotype discovery is a critical component of these endeavors and the use of nontraditional model organisms will also be critical for piecing together a complete picture. Ultimately, the union of developmental studies of the brain with studies of unique phenotypes in a myriad of species will result in a more thorough model of the groundwork the human brain was built upon. Furthermore, these integrative approaches should provide important insights into human diseases.     

Adaptation to an extraordinary environment by evolution of phenotypic plasticity and genetic assimilation

Adaptation to a sudden extreme change in environment, beyond the usual range of background environmental fluctuations, is analysed using a quantitative genetic model of phenotypic plasticity. Generations are discrete, with time lag τ between a critical period for environmental influence on individual development and natural selection on adult phenotypes. The optimum phenotype, and genotypic norms of reaction, are linear functions of the environment. Reaction norm elevation and slope (plasticity) vary among genotypes. Initially, in the average background environment, the character is canalized with minimum genetic and phenotypic variance, and no correlation between reaction norm elevation and slope. The optimal plasticity is proportional to the predictability of environmental fluctuations over time lag τ. During the first generation in the new environment the mean fitness suddenly drops and the mean phenotype jumps towards the new optimum phenotype by plasticity. Subsequent adaptation occurs in two phases. Rapid evolution of increased plasticity allows the mean phenotype to closely approach the new optimum. The new phenotype then undergoes slow genetic assimilation, with reduction in plasticity compensated by genetic evolution of reaction norm elevation in the original environment.     

Evolution of innate behavioral strategies through competitive population dynamics

Many organism behaviors are innate or instinctual and have been “hard-coded” through evolution. Current approaches to understanding these behaviors model evolution as an optimization problem in which the traits of organisms are assumed to optimize an objective function representing evolutionary fitness. Here, we use a mechanistic birth-death dynamics approach to study the evolution of innate behavioral strategies in a simulated population of organisms. In particular, we performed agent-based stochastic simulations and mean-field analyses of organisms exploring random environments and competing with each other to find locations with plentiful resources. We find that when organism density is low, the mean-field model allows us to derive an effective objective function, predicting how the most competitive phenotypes depend on the exploration-exploitation trade-off between the scarcity of high-resource sites and the increase in birth rate those sites offer organisms. However, increasing organism density alters the most competitive behavioral strategies and precludes the derivation of a well-defined objective function. Moreover, there exists a range of densities for which the coexistence of many phenotypes persists for evolutionarily long times.     

Evolution of phenotypic fluctuation under host-parasite interactions

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host–parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host–parasite interactions.