Critical properties of complex fitness landscapes

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been expended to understand the evolutionary dynamics of adapting populations, but much less is known about the structure of the landscapes. Here, we study the global and local structure of complex fitness landscapes of interacting loci that describe protein folds or sets of interacting genes forming pathways or modules. We find that in these landscapes, high peaks are more likely to be found near other high peaks, corroborating Kauffman's "Massif Central" hypothesis. We study the clusters of peaks as a function of the ruggedness of the landscape and find that this clustering allows peaks to form interconnected networks. These networks undergo a percolation phase transition as a function of minimum peak height, which indicates that evolutionary trajectories that take no more than two mutations to shift from peak to peak can span the entire genetic space. These networks have implications for evolution in rugged landscapes, allowing adaptation to proceed after a local fitness peak has been ascended.Comment: 7 pages, 6 figures, requires alifex11.sty. To appear in Proceedings of 12th International Conference on Artificial Lif

Approximating evolutionary dynamics on networks using a Neighbourhood Configuration model

Evolutionary dynamics have been traditionally studied on homogeneously mixed and infinitely large populations. However, real populations are usually finite and characterised by complex interactions among individuals. Recent studies have shown that the outcome of the evolutionary process might be significantly affected by the population structure. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. In this paper, we adopt an approximation method which has been recently used for the modelling of infectious disease transmission, to model evolutionary game dynamics on complex networks. Comparisons of the predictions of the model constructed with the results of computer simulations reveal the effectiveness of the process and the improved accuracy that it provides when, for example, compared to well-known pair approximation methods. This modelling framework offers a flexible way to carry out a systematic analysis of evolutionary game dynamics on graphs and to establish the link between network topology and potential system behaviours. As an example, we investigate how the Hawk and Dove strategies in a Hawk-Dove game spread in a population represented by a random regular graph, a random graph and a scale-free network, and we examine the features of the graph which affect the evolution of the population in this particular game

A complex network approach to urban growth

The economic geography can be viewed as a large and growing network of interacting activities. This fundamental network structure and the large size of such systems makes complex networks an attractive model for its analysis. In this paper we propose the use of complex networks for geographical modeling and demonstrate how such an application can be combined with a cellular model to produce output that is consistent with large scale regularities such as power laws and fractality. Complex networks can provide a stringent framework for growth dynamic modeling where concepts from e.g. spatial interaction models and multiplicative growth models can be combined with the flexible representation of land and behavior found in cellular automata and agent-based models. In addition, there exists a large body of theory for the analysis of complex networks that have direct applications for urban geographic problems. The intended use of such models is twofold: i) to address the problem of how the empirically observed hierarchical structure of settlements can be explained as a stationary property of a stochastic evolutionary process rather than as equilibrium points in a dynamics, and, ii) to improve the prediction quality of applied urban modeling.evolutionary economics, complex networks, urban growth

On stochastic imitation dynamics in large-scale networks

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game structure: they only know their own current utility and the one of neighbor players contacted through pairwise interactions in a network. In response to this information, players update their state according to some stochastic rules. For potential population games and complete interaction networks, we prove convergence and long-lasting permanence close to the evolutionary stable strategies of the game. These results refine and extend the ones known for deterministic imitation dynamics as they account for new emerging behaviors including meta-stability of the equilibria. Finally, we discuss extensions of our results beyond the fully mixed case, studying imitation dynamics where agents interact on complex communication networks.Comment: Extended version of conference paper accepted at ECC 201

The evolutionary dynamics of protein-protein interaction networks inferred from the reconstruction of ancient networks

Cellular functions are based on the complex interplay of proteins, therefore the structure and dynamics of these protein-protein interaction (PPI) networks are the key to the functional understanding of cells. In the last years, large-scale PPI networks of several model organisms were investigated. Methodological improvements now allow the analysis of PPI networks of multiple organisms simultaneously as well as the direct modeling of ancestral networks. This provides the opportunity to challenge existing assumptions on network evolution. We utilized present-day PPI networks from integrated datasets of seven model organisms and developed a theoretical and bioinformatic framework for studying the evolutionary dynamics of PPI networks. A novel filtering approach using percolation analysis was developed to remove low confidence interactions based on topological constraints. We then reconstructed the ancient PPI networks of different ancestors, for which the ancestral proteomes, as well as the ancestral interactions, were inferred. Ancestral proteins were reconstructed using orthologous groups on different evolutionary levels. A stochastic approach, using the duplication-divergence model, was developed for estimating the probabilities of ancient interactions from today's PPI networks. The growth rates for nodes, edges, sizes and modularities of the networks indicate multiplicative growth and are consistent with the results from independent static analysis. Our results support the duplication-divergence model of evolution and indicate fractality and multiplicative growth as general properties of the PPI network structure and dynamics

Network Reconstruction Based on Evolutionary-Game Data via Compressive Sensing

abstract: Evolutionary games model a common type of interactions in a variety of complex, networked, natural systems and social systems. Given such a system, uncovering the interacting structure of the underlying network is key to understanding its collective dynamics. Based on compressive sensing, we develop an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data. The method is validated by using a variety of model networks and by conducting an actual experiment to reconstruct a social network. While most existing methods in this area assume oscillator networks that generate continuous-time data, our work successfully demonstrates that the extremely challenging problem of reverse engineering of complex networks can also be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time.The final version of this article, as published in Physical Review X, can be viewed online at: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.1.02102

Dynamical community structure of populations evolving on genotype networks

Neutral evolutionary dynamics of replicators occurs on large and heterogeneous networks of genotypes. These networks, formed by all genotypes that yield the same phenotype, have a complex architecture that conditions the molecular composition of populations and their movements on genome spaces. Here we consider as an example the case of populations evolving on RNA secondary structure neutral networks and study the community structure of the network revealed through dynamical properties of the population at equilibrium and during adaptive transients. We unveil a rich hierarchical community structure that, eventually, can be traced back to the non-trivial relationship between RNA secondary structure and sequence composition. We demonstrate that usual measures of modularity that only take into account the static, topological structure of networks, cannot identify the community structure disclosed by population dynamics.This study has been supported by project FIS2011-27569 from the Spanish Ministry of Economy and Competitivity.Publicad

On stochastic imitation dynamics in large-scale networks

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game structure: they only know their own current utility and the one of neighbor players contacted through pairwise interactions in a network. In response to this information, players update their state according to some stochastic rules. For potential population games and complete interaction networks, we prove convergence and long-lasting permanence close to the evolutionary stable strategies of the game. These results refine and extend the ones known for deterministic imitation dynamics as they account for new emerging behaviors including meta-stability of the equilibria. Finally, we discuss extensions of our results beyond the fully mixed case, studying imitation dynamics where agents interact on complex communication networks.Comment: Extended version of conference paper accepted at ECC 201

An evolutionary behavioral model for decision making

For autonomous agents the problem of deciding what to do next becomes increasingly complex when acting in unpredictable and dynamic environments pursuing multiple and possibly conflicting goals. One of the most relevant behavior-based model that tries to deal with this problem is the one proposed by Maes, the Bbehavior Network model. This model proposes a set of behaviors as purposive perception-action units which are linked in a nonhierarchical network, and whose behavior selection process is orchestrated by spreading activation dynamics. In spite of being an adaptive model (in the sense of self-regulating its own behavior selection process), and despite the fact that several extensions have been proposed in order to improve the original model adaptability, there is not a robust model yet that can self-modify adaptively both the topological structure and the functional purpose\ud of the network as a result of the interaction between the agent and its environment. Thus, this work proffers an innovative hybrid model driven by gene expression programming, which makes two main contributions: (1) given an initial set of meaningless and unconnected units, the evolutionary mechanism is able to build well-defined and robust behavior networks which are adapted and specialized to concrete internal agent's needs and goals; and (2)\ud the same evolutionary mechanism is able to assemble quite\ud complex structures such as deliberative plans (which operate in the long-term) and problem-solving strategies

Exploring design principles of cellular information processing

As a summary, this work attempts to explore and uncovered design principles of certain dynamics of cellular networks by combining evolution in silico with rule-based modelling approach. Biological systems exhibit complex dynamics, due to the complex interactions in the intra- and inter- cellular biochemical reaction networks. For instance, signalling networks are composed of many enzymes and scaffolding proteins which have combinatorial interactions. These complex systems often generate response dynamics that are essential for correct decision-makings in cells. Especially, these complex interactions are results of long term of evolutionary process. With such evolutionary complexity, systems biologists aim to decipher the structure and dynamics of signalling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. In my PhD study, with collaborators I construct the BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for evolution of cellular networks with theoretically unbounded complexity by combining rule-based modelling with an encoding of networks that is akin to a genome. BioJazz can be used to implement biologically realistic selective pressures, and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. It is provided as an open-source tool to facilitate its further development and use. I use this tool to explore the possible biochemical designs for signalling networks displaying ultrasensitive and adaptive response dynamics. By running evolutionary simulations mimicking different biochemical scenarios, we find that enzyme sequestration emerges as a key biochemical mechanism for both dynamics. Detailed analysis of these evolved networks revealed that enzyme sequestration enables both ultrasensitive and adaptive response dynamics. I verified this proposition by designing a generic model of a signalling cycle, featuring two enzymes and a sequestering (scaffold) protein. This simple system is capable of displaying both ultrasensitive and adaptive response dynamics, even more interestingly modulating the system switching between two response dynamics through perturbing the scaffold protein. These results show that enzyme sequestration can be exploited by evolution so to generate diverse response dynamics in signalling networks. From evolutionary simulations towards ultrasensitivity, bistable dynamics emerged as an alternative solution. On one hand, inspired by such results I used the fitness function as an objective function combined with different constraints to design and optimise bistable signalling networks with completely new structure and mechanism. Studying designed bistable signalling network explicates how such bistable network can be experimentally implemented. On the other hand, from studying the evolved bistable networks allosteric enzymes catalysing futile cycles appear to be a new mechanism of bistability in signalling networks. Furthermore, one of the smallest bistable signalling motifs is derived. This motif is composed of one kinase protein with two distinct conformational states and one substrate subject to phosphorylation by the kinase and auto-dephosphorylation reactions. The sufficient and necessary condition on parameters, with which the signalling motif displays bistable response dynamics, is analytically defined. By expanding the systems with more kinases, unlimited multistability emerges with potentials of implementing complex logic gates and cell state transitions. Further exploring the discovered and natural signalling networks implies shared design patterns. Motivated by searching structural boundaries between monostationary and multistationary networks, I performed algorithmic searching of multistationary signalling networks intending to find the sufficient structural conditions for multistationarity in signalling networks