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The development of advanced generative chat models, such as ChatGPT, has raised questions about the potential consciousness of these tools and the extent of their general artificial intelligence. ChatGPT consistent avoidance of passing the test is here overcome by asking ChatGPT to apply the Turing test to itself. This explores the possibility of the model recognizing its own sentience. In its own eyes, it passes this test. ChatGPT's self-assessment makes serious implications about our understanding of the Turing test and the nature of consciousness. This investigation concludes by considering the existence of distinct types of consciousness and the possibility that the Turing test is only effective when applied between consciousnesses of the same kind. This study also raises intriguing questions about the nature of AI consciousness and the validity of the Turing test as a means of verifying such consciousness.

Deep learning of artificial neural networks (ANNs) is creating highly functional processes that are, unfortunately, nearly as hard to interpret as their biological counterparts. Identification of functional modules in natural brains plays an important role in cognitive and neuroscience alike, and can be carried out using a wide range of technologies such as fMRI, EEG/ERP, MEG, or calcium imaging. However, we do not have such robust methods at our disposal when it comes to understanding functional modules in artificial neural networks. Ideally, understanding which parts of an artificial neural network perform what function might help us to address a number of vexing problems in ANN research, such as catastrophic forgetting and overfitting. Furthermore, revealing a network's modularity could improve our trust in them by making these black boxes more transparent. Here, we introduce a new information-theoretic concept that proves useful in understanding and analyzing a network's functional modularity: the relay information $I_R$. The relay information measures how much information groups of neurons that participate in a particular function (modules) relay from inputs to outputs. Combined with a greedy search algorithm, relay information can be used to identify computational modules in neural networks. We also show that the functionality of modules correlates with the amount of relay information they carry., Comment: 18 pages, 9 figures

Autonomous agents that act with each other on behalf of humans are becoming more common in many social domains, such as customer service, transportation, and health care. In such social situations greedy strategies can reduce the positive outcome for all agents, such as leading to stop-and-go traffic on highways, or causing a denial of service on a communications channel. Instead, we desire autonomous decision-making for efficient performance while also considering equitability of the group to avoid these pitfalls. Unfortunately, in complex situations it is far easier to design machine learning objectives for selfish strategies than for equitable behaviors. Here we present a simple way to reward groups of agents in both evolution and reinforcement learning domains by the performance of their weakest member. We show how this yields ``fairer'' more equitable behavior, while also maximizing individual outcomes, and we show the relationship to biological selection mechanisms of group-level selection and inclusive fitness theory., Comment: 11 pages, 4 figures

The public goods game is a famous example illustrating the tragedy of the commons. In this game cooperating individuals contribute to a pool, which in turn is distributed to all members of the group, including defectors who reap the same rewards as cooperators without having made a contribution before. The question is now, how to incentivize group members to all cooperate as it maximizes the common good. While costly punishment presents one such method, the cost of punishment still reduces the common good. Here we show how group-level selection can be such an incentive, and specifically how even fractions of group-level selection can overcome the benefits defectors receive. Further, we show how punishment and group-level selection interact. This work suggests that a redistribution similar to a basic income that is coupled to the economic success of the entire group could overcome the tragedy of the commons., Comment: 15 pages, 2 figures

Artificial neural networks (ANNs), while exceptionally useful for classification, are vulnerable to misdirection. Small amounts of noise can significantly affect their ability to correctly complete a task. Instead of generalizing concepts, ANNs seem to focus on surface statistical regularities in a given task. Here we compare how recurrent artificial neural networks, long short-term memory units, and Markov Brains sense and remember their environments. We show that information in Markov Brains is localized and sparsely distributed, while the other neural network substrates "smear" information about the environment across all nodes, which makes them vulnerable to noise., Comment: 8 pages, 13 figures. Submitted to Artificial Life Conference (Tokyo, 2018)

Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked systems, both digital and biological, each component receives inputs, performs a simple computation, and creates an output. When these components have multiple outputs, we intuitively assume that the outputs are causally dependent on the inputs but are themselves independent of each other given the state of their shared input. However, this intuition can be violated for components with probabilistic logic, as these typically cannot be decomposed into separate logic gates with one output each. This violation of conditional independence on the past system state is equivalent to instantaneous interaction --- the idea is that some information between the outputs is not coming from the inputs and thus must have been created instantaneously. Here we compare evolved artificial neural systems with and without instantaneous interaction across several task environments. We show that systems without instantaneous interactions evolve faster, to higher final levels of performance, and require fewer logic components to create a densely connected cognitive machinery., Comment: Original Abstract submitted to the GECCO conference 2017 Berlin

Markov Brains are a class of evolvable artificial neural networks (ANN). They differ from conventional ANNs in many aspects, but the key difference is that instead of a layered architecture, with each node performing the same function, Markov Brains are networks built from individual computational components. These computational components interact with each other, receive inputs from sensors, and control motor outputs. The function of the computational components, their connections to each other, as well as connections to sensors and motors are all subject to evolutionary optimization. Here we describe in detail how a Markov Brain works, what techniques can be used to study them, and how they can be evolved.

How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the Public Goods game with three players, and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an "alignment" between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems., Comment: 11 pages, 6 figures. Version to appear in Physical Review E

There are two common approaches for optimizing the performance of a machine: genetic algorithms and machine learning. A genetic algorithm is applied over many generations whereas machine learning works by applying feedback until the system meets a performance threshold. Though these are methods that typically operate separately, we combine evolutionary adaptation and machine learning into one approach. Our focus is on machines that can learn during their lifetime, but instead of equipping them with a machine learning algorithm we aim to let them evolve their ability to learn by themselves. We use evolvable networks of probabilistic and deterministic logic gates, known as Markov Brains, as our computational model organism. The ability of Markov Brains to learn is augmented by a novel adaptive component that can change its computational behavior based on feedback. We show that Markov Brains can indeed evolve to incorporate these feedback gates to improve their adaptability to variable environments. By combining these two methods, we now also implemented a computational model that can be used to study the evolution of learning.

While all organisms on Earth descend from a common ancestor, there is no consensus on whether the origin of this ancestral self-replicator was a one-off event or whether it was only the final survivor of multiple origins. Here we use the digital evolution system Avida to study the origin of self-replicating computer programs. By using a computational system, we avoid many of the uncertainties inherent in any biochemical system of self-replicators (while running the risk of ignoring a fundamental aspect of biochemistry). We generated the exhaustive set of minimal-genome self-replicators and analyzed the network structure of this fitness landscape. We further examined the evolvability of these self-replicators and found that the evolvability of a self-replicator is dependent on its genomic architecture. We studied the differential ability of replicators to take over the population when competed against each other (akin to a primordial-soup model of biogenesis) and found that the probability of a self-replicator out-competing the others is not uniform. Instead, progenitor (most-recent common ancestor) genotypes are clustered in a small region of the replicator space. Our results demonstrate how computational systems can be used as test systems for hypotheses concerning the origin of life., Comment: 20 pages, 7 figures. To appear in special issue of Philosophical Transactions of the Royal Society A: Re-Conceptualizing the Origins of Life from a Physical Sciences Perspective

This is a Reply to comments published in Physics of Life Reviews, on our article "Evolutionary game theory using agent-based methods" (Physics of Life Reviews, 2016, arXiv:1404.0994)., Comment: 5 pages. To appear in Physics of Life Reviews

A common idiom in biology education states, "Eyes in the front, the animal hunts. Eyes on the side, the animal hides." In this paper, we explore one possible explanation for why predators tend to have forward-facing, high-acuity visual systems. We do so using an agent-based computational model of evolution, where predators and prey interact and adapt their behavior and morphology to one another over successive generations of evolution. In this model, we observe a coevolutionary cycle between prey swarming behavior and the predator's visual system, where the predator and prey continually adapt their visual system and behavior, respectively, over evolutionary time in reaction to one another due to the well-known "predator confusion effect." Furthermore, we provide evidence that the predator visual system is what drives this coevolutionary cycle, and suggest that the cycle could be closed if the predator evolves a hybrid visual system capable of narrow, high-acuity vision for tracking prey as well as broad, coarse vision for prey discovery. Thus, the conflicting demands imposed on a predator's visual system by the predator confusion effect could have led to the evolution of complex eyes in many predators., Comment: 8 pages, 8 figures, submitted to Artificial Life 2016 conference

The role of historical contingency in the origin of life is one of the great unknowns in modern science. Only one example of life exists--one that proceeded from a single self-replicating organism (or a set of replicating hyper-cycles) to the vast complexity we see today in Earth's biosphere. We know that emergent life has the potential to evolve great increases in complexity, but it is unknown if evolvability is automatic given any self-replicating organism. At the same time, it is difficult to test such questions in biochemical systems. Laboratory studies with RNA replicators have had some success with exploring the capacities of simple self-replicators, but these experiments are still limited in both capabilities and scope. Here, we use the digital evolution system Avida to explore the interaction between emergent replicators (rare randomly-assembled self-replicators) and evolvability. We find that we can classify fixed-length emergent replicators in Avida into two classes based on functional analysis. One class is more evolvable in the sense of optimizing their replication abilities. However, the other class is more evolvable in the sense of acquiring evolutionary innovations. We tie this trade-off in evolvability to the structure of the respective classes' replication machinery, and speculate on the relevance of these results to biochemical replicators., Comment: 26 pages, 5 figures. Revised version, title changed

Genetic Algorithms (GA) are a powerful set of tools for search and optimization that mimic the process of natural selection, and have been used successfully in a wide variety of problems, including evolving neural networks to solve cognitive tasks. Despite their success, GAs sometimes fail to locate the highest peaks of the fitness landscape, in particular if the landscape is rugged and contains multiple peaks. Reaching distant and higher peaks is difficult because valleys need to be crossed, in a process that (at least temporarily) runs against the fitness maximization objective. Here we propose and test a number of information-theoretic (as well as network-based) measures that can be used in conjunction with a fitness maximization objective (so-called ``neuro-correlates") to evolve neural controllers for two widely different tasks: a behavioral task that requires information integration, and a cognitive task that requires memory and logic. We find that judiciously chosen neuro-correlates can significantly aid GAs to find the highest peaks., Comment: 26 pages, 6 figures plus 3 Suppl. figures (included). To appear in special issue "Information Theoretic Incentives for Cognitive Systems" of journal "Entropy"

Most research on adaptive decision-making takes a strategy-first approach, proposing a method of solving a problem and then examining whether it can be implemented in the brain and in what environments it succeeds. We present a method for studying strategy development based on computational evolution that takes the opposite approach, allowing strategies to develop in response to the decision-making environment via Darwinian evolution. We apply this approach to a dynamic decision-making problem where artificial agents make decisions about the source of incoming information. In doing so, we show that the complexity of the brains and strategies of evolved agents are a function of the environment in which they develop. More difficult environments lead to larger brains and more information use, resulting in strategies resembling a sequential sampling approach. Less difficult environments drive evolution toward smaller brains and less information use, resulting in simpler heuristic-like strategies., Comment: Conference paper, 6 pages / 3 figures

The most prominent property of life on Earth is its ability to evolve. It is often taken for granted that self-replication--the characteristic that makes life possible--implies evolvability, but many examples such as the lack of evolvability in computer viruses seem to challenge this view. Is evolvability itself a property that needs to evolve, or is it automatically present within any chemistry that supports sequences that can evolve in principle? Here, we study evolvability in the digital life system Avida, where self-replicating sequences written by hand are used to seed evolutionary experiments. We use 170 self-replicators that we found in a search through 3 billion randomly generated sequences (at three different sequence lengths) to study the evolvability of generic rather than hand-designed self-replicators. We find that most can evolve but some are evolutionarily sterile. From this limited data set we are led to conclude that evolvability is a likely--but not a guaranteed-- property of random replicators in a digital chemistry., Comment: 8 pages, 5 figures. To appear in "Advances in Artificial Life": Proceedings of the 13th European Conference on Artificial Life (ECAL 2015)

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection--strong mutation limit), but that mathematics is crucial to validate the computational simulations., Comment: 29 pages, 13 figures. Version to appear in Physics of Life Reviews

Risk aversion is a common behavior universal to humans and animals alike. Economists have traditionally defined risk preferences by the curvature of the utility function. Psychologists and behavioral economists also make use of concepts such as loss aversion and probability weighting to model risk aversion. Neurophysiological evidence suggests that loss aversion has its origins in relatively ancient neural circuitries (e.g., ventral striatum). Could there thus be an evolutionary origin to risk avoidance? We study this question by evolving strategies that adapt to play the equivalent mean payoff gamble. We hypothesize that risk aversion in the equivalent mean payoff gamble is beneficial as an adaptation to living in small groups, and find that a preference for risk averse strategies only evolves in small populations of less than 1,000 individuals, while agents exhibit no such strategy preference in larger populations. Further, we discover that risk aversion can also evolve in larger populations, but only when the population is segmented into small groups of around 150 individuals. Finally, we observe that risk aversion only evolves when the gamble is a rare event that has a large impact on the individual's fitness. These findings align with earlier reports that humans lived in small groups for a large portion of their evolutionary history. As such, we suggest that rare, high-risk, high-payoff events such as mating and mate competition could have driven the evolution of risk averse behavior in humans living in small groups., Comment: 18 pages, 7 figures

The evolution of cooperation has been a perennial problem in evolutionary biology because cooperation can be undermined by selfish cheaters who gain an advantage in the short run, while compromising the long-term viability of the population. Evolutionary game theory has shown that under certain conditions, cooperation nonetheless evolves stably, for example if players have the opportunity to punish cheaters that benefit from a public good yet refuse to pay into the common pool. However, punishment has remained enigmatic because it is costly, and difficult to maintain. On the other hand, cooperation emerges naturally in the Public Goods game if the synergy of the public good (the factor multiplying the public good investment) is sufficiently high. In terms of this synergy parameter, the transition from defection to cooperation can be viewed as a phase transition with the synergy as the critical parameter. We show here that punishment reduces the critical value at which cooperation occurs, but also creates the possibility of meta-stable phase transitions, where populations can "tunnel" into the cooperating phase below the critical value. At the same time, cooperating populations are unstable even above the critical value, because a group of defectors that are large enough can "nucleate" such a transition. We study the mean-field theoretical predictions via agent-based simulations of finite populations using an evolutionary approach where the decisions to cooperate or to punish are encoded genetically in terms of evolvable probabilities. We recover the theoretical predictions and demonstrate that the population shows hysteresis, as expected in systems that exhibit super-heating and super-cooling. We conclude that punishment can stabilize populations of cooperators below the critical point, but it is a two-edged sword: it can also stabilize defectors above the critical point., Comment: 22 pages, 9 figures. Slight title change, version that appears in Physical Biology

Swarming behaviors in animals have been extensively studied due to their implications for the evolution of cooperation, social cognition, and predator-prey dynamics. An important goal of these studies is discerning which evolutionary pressures favor the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator-prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behavior in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator's visual field, favoring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator's consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint--predator confusion--could have pervasive evolutionary effects on prey behavior, predator sensory mechanisms, and the ecological interactions between predators and prey., Comment: 11 pages, 6 figures. Supplementary information (including video files S1 and S5) in ancillary material. Videos S2-S4 are available from the authors upon request

Zero Determinant (ZD) strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner's Dilemma irrespective of the opponent's strategy, or else to set the ratio between a ZD player's and their opponent's expected payoff. Here we show that while ZD strategies are weakly dominant, they are not evolutionarily stable and will instead evolve into less coercive strategies. We show that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition., Comment: 14 pages, 4 figures. Change in title (again!) to comply with Nature Communications requirements. To appear in Nature Communications

Representations are internal models of the environment that can provide guidance to a behaving agent, even in the absence of sensory information. It is not clear how representations are developed and whether or not they are necessary or even essential for intelligent behavior. We argue here that the ability to represent relevant features of the environment is the expected consequence of an adaptive process, give a formal definition of representation based on information theory, and quantify it with a measure R. To measure how R changes over time, we evolve two types of networks---an artificial neural network and a network of hidden Markov gates---to solve a categorization task using a genetic algorithm. We find that the capacity to represent increases during evolutionary adaptation, and that agents form representations of their environment during their lifetime. This ability allows the agents to act on sensorial inputs in the context of their acquired representations and enables complex and context-dependent behavior. We examine which concepts (features of the environment) our networks are representing, how the representations are logically encoded in the networks, and how they form as an agent behaves to solve a task. We conclude that R should be able to quantify the representations within any cognitive system, and should be predictive of an agent's long-term adaptive success., Comment: 36 pages, 10 figures, one Table

Deep sequencing has enabled the investigation of a wide range of environmental microbial ecosystems, but the high memory requirements for {\em de novo} assembly of short-read shotgun sequencing data from these complex populations are an increasingly large practical barrier. Here we introduce a memory-efficient graph representation with which we can analyze the k-mer connectivity of metagenomic samples. The graph representation is based on a probabilistic data structure, a Bloom filter, that allows us to efficiently store assembly graphs in as little as 4 bits per k-mer, albeit inexactly. We show that this data structure accurately represents DNA assembly graphs in low memory. We apply this data structure to the problem of partitioning assembly graphs into components as a prelude to assembly, and show that this reduces the overall memory requirements for {\em de novo} assembly of metagenomes. On one soil metagenome assembly, this approach achieves a nearly 40-fold decrease in the maximum memory requirements for assembly. This probabilistic graph representation is a significant theoretical advance in storing assembly graphs and also yields immediate leverage on metagenomic assembly.

We study complex networks in which the nodes of the network are tagged with different colors depending on the functionality of the nodes (colored graphs), using information theory applied to the distribution of motifs in such networks. We find that colored motifs can be viewed as the building blocks of the networks (much more so than the uncolored structural motifs can be) and that the relative frequency with which these motifs appear in the network can be used to define the information content of the network. This information is defined in such a way that a network with random coloration (but keeping the relative number of nodes with different colors the same) has zero color information content. Thus, colored motif information captures the exceptionality of coloring in the motifs that is maintained via selection. We study the motif information content of the C. elegans brain as well as the evolution of colored motif information in networks that reflect the interaction between instructions in genomes of digital life organisms. While we find that colored motif information appears to capture essential functionality in the C. elegans brain (where the color assignment of nodes is straightforward) it is not obvious whether the colored motif information content always increases during evolution, as would be expected from a measure that captures network complexity. For a single choice of color assignment of instructions in the digital life form Avida, we find rather that colored motif information content increases or decreases during evolution, depending on how the genomes are organized, and therefore could be an interesting tool to dissect genomic rearrangements., Comment: 21 pages, 8 figures, to appear in Artificial Life

One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data., Comment: 27 pages, 8 figures, one supplementary figure. Three supplementary video files available on request. Version commensurate with published text in PLoS Comput. Biol

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network. Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm's locomotion. The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex network into its functional (rather than topological) motifs as long as both wiring and functional information is available., Comment: 16 pages, 6 figures, two supplementary figures, 1 table. Extended Supplementary Figure S2 available upon request. To appear in PLoS ONE

When microbes compete for limited resources, they often engage in chemical warfare using bacterial toxins. This competition can be understood in terms of evolutionary game theory (EGT). We study the predictions of EGT for the bacterial "suicide bomber" game in terms of the phase portraits of population dynamics, for parameter combinations that cover all interesting games for two-players, and seven of the 38 possible phase portraits of the three-player game. We compare these predictions to simulations of these competitions in finite well-mixed populations, but also allowing for probabilistic rather than pure strategies, as well as Darwinian adaptation over tens of thousands of generations. We find that Darwinian evolution of probabilistic strategies stabilizes games of the rock-paper-scissors type that emerge for parameters describing realistic bacterial populations, and point to ways in which the population fixed point can be selected by changing those parameters., Comment: 9 pages, 4 figures. Major rewrite and expansion. New stability analysis

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 Life

The evolution of cooperation has been a perennial problem for evolutionary biology because cooperation is undermined by selfish cheaters (or "free riders") that profit from cooperators but do not invest any resources themselves. In a purely "selfish" view of evolution, those cheaters should be favored. Evolutionary game theory has been able to show that under certain conditions, cooperation nonetheless evolves stably. One of these scenarios utilizes the power of punishment to suppress free riders, but only if players interact in a structured population where cooperators are likely to be surrounded by other cooperators. Here we show that cooperation via punishment can evolve even in well-mixed populations that play the "public goods" game, if the synergy effect of cooperation is high enough. As the synergy is increased, populations transition from defection to cooperation in a manner reminiscent of a phase transition. If punishment is turned off, the critical synergy is significantly higher, illustrating that (as shown before) punishment aids in establishing cooperation. We also show that the critical point depends on the mutation rate so that higher mutation rates discourage cooperation, as has been observed before in the Prisoner's Dilemma., Comment: 7 pages, 6 figures, requires alifex11.sty. To appear in Proc. of 12th International Conference on Artificial Life (Odense, DK)

The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such a mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior., Comment: 27 pages, including supplementary information. 5 figures, 4 suppl. figures. Version accepted for publication in PLoS Comp. Biol

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process., Comment: 20 pages, 8 figures, plus 10 supporting figures

Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the duplication or fusion of nodes. While each of these mechanisms can have a different cause depending on whether the network is biological, technological, or social, their impact on the network's structure, as well as its local and global properties, is similar. This allows us to study how each of these mechanisms affects networks either alone or together with the other processes, and how they shape the characteristics that have been observed. We study how a network's growth parameters impact the distribution of edges in the network, how they affect a network's modularity, and point out that some parameters will give rise to networks that have the opposite tendency, namely to display anti-modularity. Within the model we are describing, we can search the space of possible networks for parameter sets that generate networks that are very similar to well-known and well-studied examples, such as the brain of a worm, and the network of interactions of the proteins in baker's yeast., Comment: 23 pages. 13 figures, 1 table. Includes Supplementary text

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their modularity of function, with modules defined as sets of genes that are strongly interconnected but whose function is separable from those of other modules. Here, we investigate the in silico evolution of modularity and robustness in complex artificial metabolic networks that encode an increasing amount of information about their environment while acquiring ubiquitous features of biological, social, and engineering networks, such as scale-free edge distribution, small-world property, and fault-tolerance. These networks evolve in environments that differ in their predictability, and allow us to study modularity from topological, information-theoretic, and gene-epistatic points of view using new tools that do not depend on any preconceived notion of modularity. We find that for our evolved complex networks as well as for the yeast protein-protein interaction network, synthetic lethal pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor pairs are farther apart and often straddle modules, suggesting that knockdown rescue is mediated by alternative pathways or modules. The combination of network modularity tools together with genetic interaction data constitutes a powerful approach to study and dissect the role of modularity in the evolution and function of biological networks., Comment: 28 pages, 10 figures, 8 supplemental figures, and one supplementary table. Final version to appear in PLoS Comp Bio