How to discriminate easily between Directed-percolation and Manna scaling

Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e. transitions in the so-called Manna or C-DP class. Even if it is clearly established that these constitute two different universality classes, most of their universal features (exponents, moment ratios, scaling functions,...) are very similar, making it difficult to discriminate numerically between them. Nevertheless, as illustrated here, the two classes behave in a rather different way upon introducing a physical boundary or wall. Taking advantage of this, we propose a simple and fast method to discriminate between these two universality classes. This is particularly helpful in solving some existing discrepancies in self-organized critical systems as sandpiles.Comment: 7 Pages, 4 Figure

Evolutionary comparison between viral lysis rate and latent period

Marine viruses shape the structure of the microbial community. They are, thus, a key determinant of the most important biogeochemical cycles in the planet. Therefore, a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems. The infection cycle, for example, is indistinctly modeled in two very different ways. In one representation, the process is described including explicitly a fixed delay between infection and offspring release. In the other, the offspring are released at exponentially distributed times according to a fixed release rate. By considering obvious quantitative differences pointed out in the past, the latter description is widely used as a simplification of the former. However, it is still unclear how the dichotomy "delay versus rate description" affects long-term predictions of host-virus interaction models. Here, we study the ecological and evolutionary implications of using one or the other approaches, applied to marine microbes. To this end, we use mathematical and eco-evolutionary computational analysis. We show that the rate model exhibits improved competitive abilities from both ecological and evolutionary perspectives in steady environments. However, rate-based descriptions can fail to describe properly long-term microbe-virus interactions. Moreover, additional information about trade-offs between life-history traits is needed in order to choose the most reliable representation for oceanic bacteriophage dynamics. This result affects deeply most of the marine ecosystem models that include viruses, especially when used to answer evolutionary questions.Comment: to appear in J. Theor. Bio

Ecological and evolutionary consequences of viral plasticity

Viruses use the host machinery to replicate, and their performance thus depends on the host’s physiological state. For bacteriophages, this link between host and viral performance has been characterized empirically and with intracellular theories. Such theories are too detailed to be included in models that study host-phage interactions in the long term, which hinders our understanding of systems that range from pathogens infecting gut bacteria to marine phage shaping the oceans. Here, we combined data and models to study the short-and long-term consequences that host physiology has on bacteriophage performance. We compiled data showing the dependence of lytic-phage traits on host growth rate (referred to as viral phenotypic plasticity) to deduce simple expressions that represent such plasticity. Including these expressions in a standard host-phage model allowed us to understand mechanistically how viral plasticity affects emergent evolutionary strategies and the population dynamics associated with different environmental scenarios including, for example, nutrient pulses or host starvation. Moreover, we show that plasticity on the offspring number drives the phage ecological and evolutionary dynamics by reinforcing feedbacks between host, virus, and environment. Standard models neglect viral plasticity, which therefore handicaps their predictive ability in realistic scenarios. Our results highlight the importance of viral plasticity to unravel host-phage interactions and the need of laboratory and field experiments to characterize viral plastic responses across systems

Cusps, self-organization, and absorbing states

Elastic interfaces embedded in (quenched) random media exhibit meta-stability and stick-slip dynamics. These non-trivial dynamical features have been shown to be associated with cusp singularities of the coarse-grained disorder correlator. Here we show that annealed systems with many absorbing states and a conservation law but no quenched disorder exhibit identical cusps. On the other hand, similar non-conserved systems in the directed percolation class, are also shown to exhibit cusps, but of a different type. These results are obtained both by a recent method to explicitly measure disorder correlators and by defining an alternative new protocol, inspired by self-organized criticality, which opens the door to easily accessible experimental realizations.Comment: 4 pages, 2 figures. Accepted in Phys. Rev. E: Rapid Communication

Boundary-induced heterogeneous absorbing states

We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.Comment: 8 pages, 2 figure

Evolution in the Debian GNU/Linux software network : analogies and differences with gene regulatory networks

Biological networks exhibit intricate architectures deemed to be crucial for their functionality. In particular, gene regulatory networks, which play a key role in information processing in the cell, display non-trivial architectural features such as scale-free degree distributions, high modularity and low average distance between connected genes. Such networks result from complex evolutionary and adaptive processes difficult to track down empirically. On the other hand, there exists detailed information on the developmental (or evolutionary) stages of open-software networks that result from self-organized growth across versions. Here, we study the evolution of the Debian GNU/Linux software network, focusing on the changes of key structural and statistical features over time. Our results show that evolution has led to a network structure in which the out-degree distribution is scale-free and the in-degree distribution is a stretched exponential. In addition, while modularity, directionality of information flow, and average distance between elements grew, vulnerability decreased over time. These features resemble closely those currently shown by gene regulatory networks, suggesting the existence of common adaptive pathways for the architectural design of information-processing networks. Differences in other hierarchical aspects point to system-specific solutions to similar evolutionary challenges

Evolution of a Modular Software Network

"Evolution behaves like a tinkerer" (Francois Jacob, Science, 1977). Software systems provide a unique opportunity to understand biological processes using concepts from network theory. The Debian GNU/Linux operating system allows us to explore the evolution of a complex network in a novel way. The modular design detected during its growth is based on the reuse of existing code in order to minimize costs during programming. The increase of modularity experienced by the system over time has not counterbalanced the increase in incompatibilities between software packages within modules. This negative effect is far from being a failure of design. A random process of package installation shows that the higher the modularity the larger the fraction of packages working properly in a local computer. The decrease in the relative number of conflicts between packages from different modules avoids a failure in the functionality of one package spreading throughout the entire system. Some potential analogies with the evolutionary and ecological processes determining the structure of ecological networks of interacting species are discussed.Comment: To appear in PNA

Quenched disorder forbids discontinuous transitions in nonequilibrium low-dimensional systems

Quenched disorder affects significantly the behavior of phase transitions. The Imry-Ma-Aizenman-Wehr-Berker argument prohibits first-order or discontinuous transitions and their concomitant phase coexistence in low-dimensional equilibrium systems in the presence of random fields. Instead, discontinuous transitions become rounded or even continuous once disorder is introduced. Here we show that phase coexistence and first-order phase transitions are also precluded in nonequilibrium low-dimensional systems with quenched disorder: discontinuous transitions in two-dimensional systems with absorbing states become continuous in the presence of quenched disorder. We also study the universal features of this disorder-induced criticality and find them to be compatible with the universality class of the directed percolation with quenched disorder. Thus, we conclude that first-order transitions do not exist in low-dimensional disordered systems, not even in genuinely nonequilibrium systems with absorbing states

Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality

We elucidate a long-standing puzzle about the non-equilibrium universality classes describing self-organized criticality in sandpile models. We show that depinning transitions of linear interfaces in random media and absorbing phase transitions (with a conserved non-diffusive field) are two equivalent languages to describe sandpile criticality. This is so despite the fact that local roughening properties can be radically different in the two pictures, as explained here. Experimental implications of our work as well as promising paths for future theoretical investigations are also discussed.Comment: 4 pages. 2 Figure

Inferring Long-term Dynamics of Ecological Communities Using Combinatorics

In an increasingly changing world, predicting the fate of species across the globe has become a major concern. Understanding how the population dynamics of various species and communities will unfold requires predictive tools that experimental data alone can not capture. Here, we introduce our combinatorial framework, Widespread Ecological Networks and their Dynamical Signatures (WENDyS) which, using data on the relative strengths of interactions and growth rates within a community of species predicts all possible long-term outcomes of the community. To this end, WENDyS partitions the multidimensional parameter space (formed by the strengths of interactions and growth rates) into a finite number of regions, each corresponding to a unique set of coarse population dynamics. Thus, WENDyS ultimately creates a library of all possible outcomes for the community. On the one hand, our framework avoids the typical ``parameter sweeps'' that have become ubiquitous across other forms of mathematical modeling, which can be computationally expensive for ecologically realistic models and examples. On the other hand, WENDyS opens the opportunity for interdisciplinary teams to use standard experimental data (i.e., strengths of interactions and growth rates) to filter down the possible end states of a community. To demonstrate the latter, here we present a case study from the Indonesian Coral Reef. We analyze how different interactions between anemone and anemonefish species lead to alternative stable states for the coral reef community, and how competition can increase the chance of exclusion for one or more species. WENDyS, thus, can be used to anticipate ecological outcomes and test the effectiveness of management (e.g., conservation) strategies.Comment: 25 pages, 9 figure