The effect of recombination on the neutral evolution of genetic robustness

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.     

Evolution of the genomic rate of recombination in mammals

Rates of recombination vary considerably between species. Despite the significance of this observation for evolutionary biology and genetics, the evolutionary mechanisms that contribute to these interspecific differences are unclear. On fine physical scales, recombination rates appear to evolve rapidly between closely related species, but the mode and tempo of recombination rate evolution on the broader scale is poorly understood. Here, we use phylogenetic comparative methods to begin to characterize the evolutionary processes underlying average genomic recombination rates in mammals. We document a strong phylogenetic effect in recombination rates, indicating that more closely related species tend to have more similar average rates of recombination. We demonstrate that this phylogenetic signal is not an artifact of errors in recombination rate estimation and show that it is robust to uncertainty in the mammalian phylogeny. Neutral evolutionary models present good fits to the data and we find no evidence for heterogeneity in the rate of evolution in recombination across the mammalian tree. These results suggest that observed interspecific variation in average genomic rates of recombination is largely attributable to the steady accumulation of neutral mutations over evolutionary time. Although single recombination hotspots may live and die on short evolutionary time scales, the strong phylogenetic signal in genomic recombination rates indicates that the pace of evolution on this scale may be considerably slower.     

DISSECTION OF EVOLUTIONARY NETWORKS TO ASSESS THEIR ROLE IN THE EVOLUTION OF ROBUSTNESS,FUNCTION, AND DIVERSIFICATION

Biological systems are remarkably robust in the face of environmental, mutational, and developmental perturbations. Analyses of molecular networks reveal recurrent features, such as modularity, that have been implicated in robustness and evolvability. Multiple theoretical models account for these features, yet few empirical tests of these models exist. Here I develop a set of broadly applicable methodologies to enable expanded empirical evaluation of model predictions. The methodologies focus on the inference and analysis of networks that depict evolutionary correlations among characters. I apply these methodologies to analyze an evolutionary network at a larger scale of organization among 42 stem anatomical and morphological characters of 52 species in the genus Adenia (Passifloraceae). I evaluate a model predicting that modular evolutionary networks will evolve in response to environmental change. The evolutionary network of Adenia is modular and “small‐world,” and the three diagnosed modules correspond roughly to functions of transport, storage, and mechanical support. The phylogenetically informed analyses suggest that the storage module is more impacted by environmental change than expected by chance. These results corroborate the hypothesis that modularity reduces the impact of environmental change, but this result requires further empirical evaluation that can be aided by the proposed methods in additional study systems.     

De Novo Evolution of Complex, Global and Hierarchical Gene Regulatory Mechanisms

Gene regulatory networks exhibit complex, hierarchical features such as global regulation and network motifs. There is much debate about whether the evolutionary origins of such features are the results of adaptation, or the by-products of non-adaptive processes of DNA replication. The lack of availability of gene regulatory networks of ancestor species on evolutionary timescales makes this a particularly difficult problem to resolve. Digital organisms, however, can be used to provide a complete evolutionary record of lineages. We use a biologically realistic evolutionary model that includes gene expression, regulation, metabolism and biosynthesis, to investigate the evolution of complex function in gene regulatory networks. We discover that: (i) network architecture and complexity evolve in response to environmental complexity, (ii) global gene regulation is selected for in complex environments, (iii) complex, inter-connected, hierarchical structures evolve in stages, with energy regulation preceding stress responses, and stress responses preceding growth rate adaptations and (iv) robustness of evolved models to mutations depends on hierarchical level: energy regulation and stress responses tend not to be robust to mutations, whereas growth rate adaptations are more robust and non-lethal when mutated. These results highlight the adaptive and incremental evolution of complex biological networks, and the value and potential of studying realistic in silico evolutionary systems as a way of understanding living systems.     

EXTINCTIONS IN HETEROGENEOUS ENVIRONMENTS AND THE EVOLUTION OF MODULARITY

Extinctions of local subpopulations are common events in nature. Here, we ask whether such extinctions can affect the design of biological networks within organisms over evolutionary timescales. We study the impact of extinction events on modularity of biological systems, a common architectural principle found on multiple scales in biology. As a model system, we use networks that evolve toward goals specified as desired input–output relationships. We use an extinction–recolonization model, in which metapopulations occupy and migrate between different localities. Each locality displays a different environmental condition (goal), but shares the same set of subgoals with other localities. We find that in the absence of extinction events, the evolved computational networks are typically highly optimal for their localities with a nonmodular structure. In contrast, when local populations go extinct from time to time, we find that the evolved networks are modular in structure. Modular circuitry is selected because of its ability to adapt rapidly to the conditions of the free niche following an extinction event. This rapid adaptation is mainly achieved through genetic recombination of modules between immigrants from neighboring local populations. This study suggests, therefore, that extinctions in heterogeneous environments promote the evolution of modular biological network structure, allowing local populations to effectively recombine their modules to recolonize niches.     

Modelling the evolution of genetic regulatory networks

An evolutionary model of genetic regulatory networks is developed, based on a model of network encoding and dynamics called the Artificial Genome (AG). This model derives a number of specific genes and their interactions from a string of (initially random) bases in an idealized manner analogous to that employed by natural DNA. The gene expression dynamics are determined by updating the gene network as if it were a simple Boolean network. The generic behaviour of the AG model is investigated in detail. In particular, we explore the characteristic network topologies generated by the model, their dynamical behaviours, and the typical variance of network connectivities and network structures. These properties are demonstrated to agree with a probabilistic analysis of the model, and the typical network structures generated by the model are shown to lie between those of random networks and scale-free networks in terms of their degree distribution. Evolutionary processes are simulated using a genetic algorithm, with selection acting on a range of properties from gene number and degree of connectivity through periodic behaviour to specific patterns of gene expression. The evolvability of increasingly complex patterns of gene expression is examined in detail. When a degree of redundancy is introduced, the average number of generations required to evolve given targets is reduced, but limits on evolution of complex gene expression patterns remain. In addition, cyclic gene expression patterns with periods that are multiples of shorter expression patterns are shown to be inherently easier to evolve than others. Constraints imposed by the template-matching nature of the AG model generate similar biases towards such expression patterns in networks in initial populations, in addition to the somewhat scale-free nature of these networks. The significance of these results on current understanding of biological evolution is discussed.     

New species in evolving networks--stochastic theory of sensitive networks and applications on the metaphorical level

In this paper we develop a theory to describe stochastic influences on the fate of new species with non-linear growth rates in evolutionary processes. We develop a theoretical framework based on notions of species, network, innovation, competition, survival and fitness. We introduce a stochastic picture describing the role of fluctuations in the survival of new species in non-linear systems. In particular we consider the fate of new species with non-linear growth. As an application of the general model framework we consider the fate of 'rare species' in early biological evolution. We show that hypercycle systems do not represent the end of the evolutionary process as they may evolve further in small niches. This has implications for different types of applications ranging from biological systems on one level to socio-technological systems on a more metaphoric level.     

Characterization of reticulate networks based on the coalescent with recombination

Phylogenetic networks aim to represent the evolutionary history of taxa. Within these, reticulate networks are explicitly able to accommodate evolutionary events like recombination, hybridization, or lateral gene transfer. Although several metrics exist to compare phylogenetic networks, they make several assumptions regarding the nature of the networks that are not likely to be fulfilled by the evolutionary process. In order to characterize the potential disagreement between the algorithms and the biology, we have used the coalescent with recombination to build the type of networks produced by reticulate evolution and classified them as regular, tree sibling, tree child, or galled trees. We show that, as expected, the complexity of these reticulate networks is a function of the population recombination rate. At small recombination rates, most of the networks produced are already more complex than regular or tree sibling networks, whereas with moderate and large recombination rates, no network fit into any of the standard classes. We conclude that new metrics still need to be devised in order to properly compare two phylogenetic networks that have arisen from reticulating evolutionary process.     

Survival of the sparsest: robust gene networks are parsimonious

Biological gene networks appear to be dynamically robust to mutation, stochasticity, and changes in the environment and also appear to be sparsely connected. Studies with computational models, however, have suggested that denser gene networks evolve to be more dynamically robust than sparser networks. We resolve this discrepancy by showing that misassumptions about how to measure robustness in artificial networks have inadvertently discounted the costs of network complexity. We show that when the costs of complexity are taken into account, that robustness implies a parsimonious network structure that is sparsely connected and not unnecessarily complex; and that selection will favor sparse networks when network topology is free to evolve. Because a robust system of heredity is necessary for the adaptive evolution of complex phenotypes, the maintenance of frugal network complexity is likely a crucial design constraint that underlies biological organization.     

Application of phylogenetic networks in evolutionary studies

The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.     

Epistasis can lead to fragmented neutral spaces and contingency in evolution

In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space--namely, that networks of genomes encoding the same phenotype may not be connected by single mutational moves. We use the folding of RNA sequences into secondary structures as a model genotype-phenotype map and explore the neutral spaces corresponding to networks of genotypes with the same phenotype. In most of these networks, we find that it is not possible to connect all genotypes to one another by single point mutations. Instead, a network for a phenotypic structure with n bonds typically fragments into at least 2(n) neutral components, often of similar size. While components of the same network generate the same phenotype, they show important variations in their properties, most strikingly in their evolvability and mutational robustness. This heterogeneity implies contingency in the evolutionary process.     

Inferring phylogenetic networks by the maximum parsimony criterion: a case study

Horizontal gene transfer (HGT) may result in genes whose evolutionary histories disagree with each other, as well as with the species tree. In this case, reconciling the species and gene trees results in a network of relationships, known as the "phylogenetic network" of the set of species. A phylogenetic network that incorporates HGT consists of an underlying species tree that captures vertical inheritance and a set of edges which model the "horizontal" transfer of genetic material. In a series of papers, Nakhleh and colleagues have recently formulated a maximum parsimony (MP) criterion for phylogenetic networks, provided an array of computationally efficient algorithms and heuristics for computing it, and demonstrated its plausibility on simulated data. In this article, we study the performance and robustness of this criterion on biological data. Our findings indicate that MP is very promising when its application is extended to the domain of phylogenetic network reconstruction and HGT detection. In all cases we investigated, the MP criterion detected the correct number of HGT events required to map the evolutionary history of a gene data set onto the species phylogeny. Furthermore, our results indicate that the criterion is robust with respect to both incomplete taxon sampling and the use of different site substitution matrices. Finally, our results show that the MP criterion is very promising in detecting HGT in chimeric genes, whose evolutionary histories are a mix of vertical and horizontal evolution. Besides the performance analysis of MP, our findings offer new insights into the evolution of 4 biological data sets and new possible explanations of HGT scenarios in their evolutionary history.     

Connectivity of Neutral Networks,Overdispersion, and Structural Conservation in Protein Evolution

Abstract Protein structures are much more conserved than sequences during evolution. Based on this observation, we investigate the consequences of structural conservation on protein evolution. We study seven of the most studied protein folds, determining that an extended neutral network in sequence space is associated with each of them. Within our model, neutral evolution leads to a non-Poissonian substitution process, due to the broad distribution of connectivities in neutral networks. The observation that the substitution process has non-Poissonian statistics has been used to argue against the original Kimura neutral theory, while our model shows that this is a generic property of neutral evolution with structural conservation. Our model also predicts that the substitution rate can strongly fluctuate from one branch to another of the evolutionary tree. The average sequence similarity within a neutral network is close to the threshold of randomness, as observed for families of sequences sharing the same fold. Nevertheless, some positions are more difficult to mutate than others. We compare such structurally conserved positions to positions conserved in protein evolution, suggesting that our model can be a valuable tool to distinguish structural from functional conservation in databases of protein families. These results indicate that a synergy between database analysis and structurally based computational studies can increase our understanding of protein evolution.     

Evolution of networks for body plan patterning; interplay of modularity, robustness and evolvability

A major goal of evolutionary developmental biology (evo-devo) is to understand how multicellular body plans of increasing complexity have evolved, and how the corresponding developmental programs are genetically encoded. It has been repeatedly argued that key to the evolution of increased body plan complexity is the modularity of the underlying developmental gene regulatory networks (GRNs). This modularity is considered essential for network robustness and evolvability. In our opinion, these ideas, appealing as they may sound, have not been sufficiently tested. Here we use computer simulations to study the evolution of GRNs' underlying body plan patterning. We select for body plan segmentation and differentiation, as these are considered to be major innovations in metazoan evolution. To allow modular networks to evolve, we independently select for segmentation and differentiation. We study both the occurrence and relation of robustness, evolvability and modularity of evolved networks. Interestingly, we observed two distinct evolutionary strategies to evolve a segmented, differentiated body plan. In the first strategy, first segments and then differentiation domains evolve (SF strategy). In the second scenario segments and domains evolve simultaneously (SS strategy). We demonstrate that under indirect selection for robustness the SF strategy becomes dominant. In addition, as a byproduct of this larger robustness, the SF strategy is also more evolvable. Finally, using a combined functional and architectural approach, we determine network modularity. We find that while SS networks generate segments and domains in an integrated manner, SF networks use largely independent modules to produce segments and domains. Surprisingly, we find that widely used, purely architectural methods for determining network modularity completely fail to establish this higher modularity of SF networks. Finally, we observe that, as a free side effect of evolving segmentation and differentiation in combination, we obtained in-silico developmental mechanisms resembling mechanisms used in vertebrate development.     

Comparative genomics of centrality and essentiality in three eukaryotic protein-interaction networks

Most proteins do not evolve in isolation, but as components of complex genetic networks. Therefore, a protein's position in a network may indicate how central it is to cellular function and, hence, how constrained it is evolutionarily. To look for an effect of position on evolutionary rate, we examined the protein-protein interaction networks in three eukaryotes: yeast, worm, and fly. We find that the three networks have remarkably similar structure, such that the number of interactors per protein and the centrality of proteins in the networks have similar distributions. Proteins that have a more central position in all three networks, regardless of the number of direct interactors, evolve more slowly and are more likely to be essential for survival. Our results are thus consistent with a classic proposal of Fisher's that pleiotropy constrains evolution.     

Robustness and state-space structure of Boolean gene regulatory models

Robustness to perturbation is an important characteristic of genetic regulatory systems, but the relationship between robustness and model dynamics has not been clearly quantified. We propose a method for quantifying both robustness and dynamics in terms of state-space structures, for Boolean models of genetic regulatory systems. By investigating existing models of the Drosophila melanogaster segment polarity network and the Saccharomyces cerevisiae cell-cycle network, we show that the structure of attractor basins can yield insight into the underlying decision making required of the system, and also the way in which the system maximises its robustness. In particular, gene networks implementing decisions based on a few genes have simple state-space structures, and their attractors are robust by virtue of their simplicity. Gene networks with decisions that involve many interacting genes have correspondingly more complicated state-space structures, and robustness cannot be achieved through the structure of the attractor basins, but is achieved by larger attractor basins that dominate the state space. These different types of robustness are demonstrated by the two models: the D. melanogaster segment polarity network is robust due to simple attractor basins that implement decisions based on spatial signals; the S. cerevisiae cell-cycle network has a complicated state-space structure, and is robust only due to a giant attractor basin that dominates the state space.     

Perspectives on protein evolution from simple exact models

Understanding the evolution of biopolymers is important to rationalise the directed and undirected design of functional molecules. Large scale experiments or detailed computational studies are often impractical. Therefore, simple model systems, such as RNA secondary structure and lattice proteins have been adapted to study general statistical and topological features of genotype (sequence) to phenotype (structure) maps. We review findings from such models that address aspects of thermodynamic and mutational robustness, neutral evolution and recombination of proteins. We compare various modelling approaches, and discuss their generality, parameter dependency and experimental verifications of their predictions. The most striking observation is the universal emergence of neutral nets--sets of phenotypically identical genotypes that are interconnected by series of point mutations. However, fast adaptation by point mutations appears to be problematic for proteins. This may explain why proteins appear to be more specific while RNA is rather versatile. This could even be the reason why RNA had to evolve before proteins. Similar principles of biological organisation are reflected in sequence and structure databases of real proteins. Insights gained from modelling are useful for designing more efficient database organisation and search strategies.