Arend Hintze

Scaling metagenome sequence assembly with probabilistic de Bruijn graphs

Deep sequencing has enabled the investigation of a wide range of environmental microbial ecosystems, but the high memory requirements for 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 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.

Evolution of Complex Modular Biological Networks

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 gene pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor gene 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.

Impact of epistasis and pleiotropy on evolutionary adaptation

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.

Integrated Information Increases with Fitness in the Evolution of Animats

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.

Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything

Zero-determinant 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 (coercive strategies), or else to set the ratio between the player’s and their opponent’s expected payoff (extortionate strategies). Here we show that zero-determinant strategies are at most weakly dominant, are not evolutionarily stable, and will instead evolve into less coercive strategies. We show that zero-determinant strategies with an informational advantage over other players that allows them to recognize each other 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.

Predator confusion is sufficient to evolve swarming behaviour

Swarming behaviours in animals have been extensively studied owing 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 favour 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 behaviour in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predators visual field, favouring 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 predators consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint—predator confusion—could have pervasive evolutionary effects on prey behaviour, predator sensory mechanisms and the ecological interactions between predators and prey.

Sequence dependence of isothermal DNA amplification via EXPAR.

Isothermal nucleic acid amplification is becoming increasingly important for molecular diagnostics. Therefore, new computational tools are needed to facilitate assay design. In the isothermal EXPonential Amplification Reaction (EXPAR), template sequences with similar thermodynamic characteristics perform very differently. To understand what causes this variability, we characterized the performance of 384 template sequences, and used this data to develop two computational methods to predict EXPAR template performance based on sequence: a position weight matrix approach with support vector machine classifier, and RELIEF attribute evaluation with Naïve Bayes classification. The methods identified well and poorly performing EXPAR templates with 67–70% sensitivity and 77–80% specificity. We combined these methods into a computational tool that can accelerate new assay design by ruling out likely poor performers. Furthermore, our data suggest that variability in template performance is linked to specific sequence motifs. Cytidine, a pyrimidine base, is over-represented in certain positions of well-performing templates. Guanosine and adenosine, both purine bases, are over-represented in similar regions of poorly performing templates, frequently as GA or AG dimers. Since polymerases have a higher affinity for purine oligonucleotides, polymerase binding to GA-rich regions of a single-stranded DNA template may promote non-specific amplification in EXPAR and other nucleic acid amplification reactions.

Evolutionary game theory using agent-based methods.

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.

The evolution of representation in simple cognitive networks

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 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 agents long-term adaptive success.

Critical Dynamics in the Evolution of Stochastic Strategies for the Iterated Prisoner's Dilemma

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 Prisoners Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoners 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 as mutation rate, replacement rate, and memory, all of which affect a players ability to predict an opponents behavior. These results imply that in populations of players that can use previous decisions to plan future ones, cooperation depends critically on whether the players can rely on facing the same strategies that they have adapted to. Defection, on the other hand, is the optimal adaptive response in environments that change so quickly that the information gathered from previous plays cannot usefully be integrated for a response.