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.     

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.     

Enhancing evolvability with mutation buffering mediated through multiple weak interactions

The evolutionary adaptability of a system is dependent on three organizational properties, self-organizing dynamics that are hierarchically organized, component redundancy, and multiple weak interactions [Towards high evolvability dynamics, in: G. van de Vijver, S. Salthe, M. Delpos (Eds.), Evolutionary Systems, Kluwer Academic Publishers, Dordrecht, 1998, pp. 147-169]. This study reports on the use of the dual dynamics network model as an aid in understanding the role multiple weak interactions play in enhancing evolutionary adaptability. Dual dynamics networks are self-organizing systems that consist of simple components that change local state due to the coupled influences from connected components exerting strong discrete decision-making influences and from groups of components exerting multiple weak influences [J. Theor. Biol. 193 (1998) 287]. The dual dynamics model has been enhanced to support investigations of properties relevant to a system's capacity for evolvability, such as structure-function relationships, neutrality, adaptive tolerance, and evolutionary search performance.Three network types are investigated, each utilizing a different method of coupling strong and weak influences. The results demonstrate that the manner of coupling multiple weak interactions into the systems dynamics significantly affects the structure-function maps and the consequent evolvability characteristics. Specifically it is found that a form of coupling, denoted as linear modulation, enhances evolutionary adaptability. Linear modulation coupling requires that the weak interactions be integrated with strong interactions in a manner that implies a linear ordered relation between the possible state values of the components of the systems. When coupling functions that do not imply such an ordering of local state values are used, evolutionary adaptability is decreased.     

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 emotion system promotes diversity and evolvability

Studies on the relationship between the optimal phenotype and its environment have had limited focus on genotype-to-phenotype pathways and their evolutionary consequences. Here, we study how multi-layered trait architecture and its associated constraints prescribe diversity. Using an idealized model of the emotion system in fish, we find that trait architecture yields genetic and phenotypic diversity even in absence of frequency-dependent selection or environmental variation. That is, for a given environment, phenotype frequency distributions are predictable while gene pools are not. The conservation of phenotypic traits among these genetically different populations is due to the multi-layered trait architecture, in which one adaptation at a higher architectural level can be achieved by several different adaptations at a lower level. Our results emphasize the role of convergent evolution and the organismal level of selection. While trait architecture makes individuals more constrained than what has been assumed in optimization theory, the resulting populations are genetically more diverse and adaptable. The emotion system in animals may thus have evolved by natural selection because it simultaneously enhances three important functions, the behavioural robustness of individuals, the evolvability of gene pools and the rate of evolutionary innovation at several architectural levels.     

THE EVOLVABILITY OF GROWTH FORM IN A CLONAL SEAWEED

Although modular construction is considered the key to adaptive growth or growth‐form plasticity in sessile taxa (e.g., plants, seaweeds and colonial invertebrates), the serial expression of genes in morphogenesis may compromise its evolutionary potential if growth forms emerge as integrated wholes from module iteration. To explore the evolvability of growth form in the red seaweed, Asparagopsis armata, we estimated genetic variances, covariances, and cross‐environment correlations for principal components of growth‐form variation in contrasting light environments. We compared variance–covariance matrices across environments to test environmental effects on heritable variation and examined the potential for evolutionary change in the direction of plastic responses to light. Our results suggest that growth form in Asparagopsis may constitute only a single genetic entity whose plasticity affords only limited evolutionary potential. We argue that morphological integration arising from modular construction may constrain the evolvability of growth form in Asparagopsis, emphasizing the critical distinction between genetic and morphological modularity in this and other modular taxa.     

The origin of higher taxa: macroevolutionary processes, and the case of the mammals

The origin of a new higher taxon is characterized by a long‐term phylogenetic trend, involving evolutionary changes in a large number of characters. At this phylogenetic level, the conflict between internal integration of the phenotype and its evolvability can be resolved by the correlated progression model, in which many disparate traits evolve by a sequence of small increments in loose correlation with one another, rather than by the modularity model. The trend leading to the new higher taxon implies the existence of a long ridge in an adaptive landscape. An evolutionary lineage tracking it requires adaptive changes in broad biological characteristics, involving many traits. Species selection is a possible additional driver of the trend. These conclusions are tested against the synapsid fossil record of the origin of mammals. The reconstructed sequence of acquisition of mammalian traits supports the correlated progression model. The adaptive ridge involved is postulated to have been a sequence of overlapping niches requiring increasing ability to remain active in daily and seasonally fluctuating environments by means of increasing internal regulation. An inferred speciation bias in favour of relatively small, relatively more progressive carnivores indicates that species selection was also involved in driving the trend. Palaeoenvironmental evidence indicates that ecological opportunity probably played a role at certain points along the lineage.     

Phenotypic variability can promote the evolution of adaptive plasticity by reducing the stringency of natural selection

Adaptive phenotypic plasticity is a potent but not ubiquitous solution to environmental heterogeneity, driving interest in what factors promote and limit its evolution. Here, a novel computational model representing stochastic information flow in development is used to explore evolution from a constitutive phenotype to an adaptively plastic response. Results show that populations tend to evolve robustness to developmental stochasticity, but that this evolved robustness limits evolvability; specifically, robust genotypes have less ability to evolve adaptive plasticity when presented with a mix of both the ancestral environment and a new environment. Analytic calculations and computational experiments confirm that this constraint occurs when the initial mutational steps towards plasticity are pleiotropic, such that mutant fitnesses decline in the environment to which their parents are well‐adapted. Greater phenotypic variability improves evolvability in the model by lessening this decline as well as by improving the fitness of partial adaptations to the new environment. By making initial plastic mutations more palatable to natural selection, phenotypic variability can increase the evolvability of an innovative, plastic response without improving evolvability to simpler challenges such as a shifted optimum in a single environment. Populations that evolved robustness by negative feedback between the trait and its rate of change show a particularly strong constraining effect on the evolvability of plasticity, revealing another mechanism by which evolutionary history can limit later innovation. These results document a novel mechanism by which weakening selection could actually stimulate the evolution of a major innovation.     

The evolution of the evolvability properties of the yeast prion [PSI+

Abstract.— Saccharomyces cerevisiae's ability to form the prion [PSI⁺] may increase the rate of evolvability, defined as the rate of appearance of heritable and potentially adaptive phenotypic variants. The increase in evolvability occurs when the appearance of the prion causes read-through translation and reveals hidden variation in untranslated regions. Eventually the portion of the phenotypic variation that is adaptive loses its dependence on the revealing mechanism. The mechanism is reversible, so the restoration of normal translation termination conceals the revealed deleterious variation, leaving the yeast without a permanent handicap. Given that the ability to form [PSI⁺] is known to be fixed and conserved in yeast, we construct a mathematical model to calculate whether this ability is more likely to have become fixed due to chance alone or due to its evolvability characteristics. We find that evolvability is a more likely explanation, as long as environmental change makes partial read-through of stop codons adaptive at a frequency of at least once every million years.     

Evolvability and genetic constraint in Dalechampia blossoms: components of variance and measures of evolvability

Many evolutionary arguments are based on the assumption that quantitative characters are highly evolvable entities that can be rapidly moulded by changing selection pressures. The empirical evaluation of this assumption depends on having an operational measure of evolvability that reflects the ability of a trait to respond to a given external selection pressure. We suggest short-term evolvability be measured as expected proportional response in a trait to a unit strength of directional selection, where strength of selection is defined independently of character variation and in units of the strength of selection on fitness itself. We show that the additive genetic variance scaled by the square of the trait mean, IA, is such a measure. The heritability, h2, does not measure evolvability in this sense. Based on a diallel analysis, we use IA to assess the evolvability of floral characters in a population of the neotropical vine Dalechampia scandens (Euphorbiaceae). Although we are able to demonstrate that there is additive genetic variation in a number of floral traits, we also find that most of the traits are not expected to change by more than a fraction of a percent per generation. We provide evidence that the degree of among-population divergence of traits is related to their predicted evolvabilities, but not to their heritabilities.     

Evolution toward a new adaptive optimum: phenotypic evolution in a fossil stickleback lineage

Natural selection has almost certainly shaped many evolutionary trajectories documented in fossil lineages, but it has proven difficult to demonstrate this claim by analyzing sequences of evolutionary changes. In a recently published and particularly promising test case, an evolutionary time series of populations displaying armor reduction in a fossil stickleback lineage could not be consistently distinguished from a null model of neutral drift, despite excellent temporal resolution and an abundance of indirect evidence implicating natural selection. Here, we revisit this case study, applying analyses that differ from standard approaches in that: (1) we do not treat genetic drift as a null model, and instead assess neutral and adaptive explanations on equal footing using the Akaike Information Criterion; and (2) rather than constant directional selection, the adaptive scenario we consider is that of a population ascending a peak on the adaptive landscape, modeled as an Orstein-Uhlenbeck process. For all three skeletal features measured in the stickleback lineage, the adaptive model decisively outperforms neutral evolution, supporting a role for natural selection in the evolution of these traits. These results demonstrate that, at least under favorable circumstances, it is possible to infer in fossil lineages the relationship between evolutionary change and features of the adaptive landscape.     

Degeneracy: A design principle for achieving robustness and evolvability

Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems.     

The evolvability of herkogamy: Quantifying the evolutionary potential of a composite trait

Accurate estimates of trait evolvabilities are central to predicting the short‐term evolutionary potential of populations, and hence their ability to adapt to changing environments. We quantify and evaluate the evolvability of herkogamy, the spatial separation of male and female structures in flowers, a key floral trait associated with variation in mating systems. We compiled genetic‐variance estimates for herkogamy and related floral traits, computed evolvabilities, and compared these among trait groups and among species differing in their mating systems. When measured in percentage of its own size, the median evolvability of herkogamy was an order of magnitude greater than the evolvability of other floral size measurements, and was generally not strongly constrained by genetic covariance between its components (pistil and stamen lengths). Median evolvabilities were similar across mating systems, with only a tendency toward reduction in highly selfing taxa. We conclude that herkogamy has the potential to evolve rapidly in response to changing environments. This suggests that the extensive variation in herkogamy commonly observed among closely related populations and species may result from rapid adaptive tracking of fitness optima determined by variation in pollinator communities or other selective factors.     

Survivability is more fundamental than evolvability

For a lineage to survive over long time periods, it must sometimes change. This has given rise to the term evolvability, meaning the tendency to produce adaptive variation. One lineage may be superior to another in terms of its current standing variation, or it may tend to produce more adaptive variation. However, evolutionary outcomes depend on more than standing variation and produced adaptive variation: deleterious variation also matters. Evolvability, as most commonly interpreted, is not predictive of evolutionary outcomes. Here, we define a predictive measure of the evolutionary success of a lineage that we call the k-survivability, defined as the probability that the lineage avoids extinction for k generations. We estimate the k-survivability using multiple experimental replicates. Because we measure evolutionary outcomes, the initial standing variation, the full spectrum of generated variation, and the heritability of that variation are all incorporated. Survivability also accounts for the decreased joint likelihood of extinction of sub-lineages when they 1) disperse in space, or 2) diversify in lifestyle. We illustrate measurement of survivability with in silico models, and suggest that it may also be measured in vivo using multiple longitudinal replicates. The k-survivability is a metric that enables the quantitative study of, for example, the evolution of 1) mutation rates, 2) dispersal mechanisms, 3) the genotype-phenotype map, and 4) sexual reproduction, in temporally and spatially fluctuating environments. Although these disparate phenomena evolve by well-understood microevolutionary rules, they are also subject to the macroevolutionary constraint of long-term survivability.     

Evolution,plasticity and evolving plasticity of phenology in the tree species Alnus glutinosa

Both traits and the plasticity of these traits are subject to evolutionary change and therefore affect the long‐term persistence of populations and their role in local communities. We subjected clones from 12 different populations of Alnus glutinosa, located along a latitudinal gradient, to two different temperature treatments, to disentangle the distribution of genetic variation in timing of bud burst and bud burst plasticity within and among genotypes, populations, and regions. We calculated heritability and evolvability estimates for bud burst and bud burst plasticity and assessed the influence of divergent selection relative to neutral drift. We observed higher levels of heritability and evolvability for bud burst than for its plasticity, whereas the total phenological heritability and evolvability (i.e. combining timing of bud burst and bud burst plasticity) suggest substantial evolutionary potential with respect to phenology. Earlier bud burst was observed for the low‐latitudinal populations than for the populations from higher latitudes, whereas the high‐latitudinal populations did not show the expected delayed bud burst. This countergradient variation can be due to evolution towards increased phenological plasticity at higher latitudes. However, because we found little evidence for adaptive differences in phenological plasticity across the latitudinal gradient, we suggest differential frost tolerance as the most likely explanation for the observed phenological patterns in A. glutinosa.     

Evolutionary Connectionism: Algorithmic Principles Underlying the Evolution of Biological Organisation in Evo-Devo,Evo-Eco and Evolutionary Transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions.     

Limits to natural selection

We review the various factors that limit adaptation by natural selection. Recent discussion of constraints on selection and, conversely, of the factors that enhance "evolvability", have concentrated on the kinds of variation that can be produced. Here, we emphasise that adaptation depends on how the various evolutionary processes shape variation in populations. We survey the limits that population genetics places on adaptive evolution, and discuss the relationship between disparate literatures.     

Cooperation and conflict in the evolution of individuality. IV. Conflict mediation and evolvability in Volvox carteri

The continued well being of evolutionary individuals (units of selection and evolution) depends upon their evolvability, that is their capacity to generate and evolve adaptations at their level of organization, as well as their longer term capacity for diversifying into more complex evolutionary forms. During a transition from a lower- to higher-level individual, such as the transition between unicellular and multicellular organisms, the evolvability of the lower-level (cells) must be restricted, while the evolvability of the new higher-level unit (multicellular organism) must be enhanced. For these reasons, understanding the factors leading to an evolutionary transition should help us to understand the factors underlying the emergence of evolvability of a new evolutionary unit. Cooperation among lower-level units is fundamental to the origin of new functions in the higher-level unit. Cooperation can produce a new more complex evolutionary unit, with the requisite properties of heritable fitness variations, because cooperation trades fitness from a lower-level (the costs of cooperation) to the higher-level (the benefits for the group). For this reason, the evolution of cooperative interactions helps us to understand the origin of new and higher-levels of fitness and organization. As cooperation creates a new level of fitness, it also creates the opportunity for conflict between levels of selection, as deleterious mutants with differing effects at the two levels arise and spread. This conflict can interfere with the evolvability of the higher-level unit, since the lower and higher-levels of selection will often "disagree" on what adaptations are most beneficial to their respective interests. Mediation of this conflict is essential to the emergence of the new evolutionary unit and to its continued evolvability. As an example, we consider the transition from unicellular to multicellular organisms and study the evolution of an early-sequestered germ-line in terms of its role in mediating conflict between the two levels of selection, the cell and the cell group. We apply our theoretical framework to the evolution of germ/soma differentiation in the green algal group Volvocales. In the most complex member of the group, Volvox carteri, the potential conflicts among lower-level cells as to the "right" to reproduce the higher-level individual (i.e. the colony) have been mediated by restricting immortality and totipotency to the germ-line. However, this mediation, and the evolution of an early segregated germ-line, was achieved by suppressing mitotic and differentiation capabilities in all post-embryonic cells. By handicapping the soma in this way, individuality is ensured, but the solution has affected the long-term evolvability of this lineage. We think that although conflict mediation is pivotal to the emergence of individuality at the higher-level, the way in which the mediation is achieved can greatly affect the longer-term evolvability of the lineage.     

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.