Catastrophic regime shifts in model ecological communities are true phase transitions

Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in external conditions. Usual models introduce nonlinearities in the macroscopic dynamics of the ecosystem that lead to different stable attractors among which the shift takes place. Here we propose an alternative explanation of catastrophic regime shifts based on a recent model that pictures ecological communities as systems in continuous fluctuation, according to certain transition probabilities, between different micro-states in the phase space of viable communities. We introduce a spontaneous extinction rate that accounts for gradual changes in external conditions, and upon variations on this control parameter the system undergoes a regime shift with similar features to those previously reported. Under our microscopic viewpoint we recover the main results obtained in previous theoretical and empirical work (anomalous variance, hysteresis cycles, trophic cascades). The model predicts a gradual loss of species in trophic levels from bottom to top near the transition. But more importantly, the spectral analysis of the transition probability matrix allows us to rigorously establish that we are observing the fingerprints, in a finite size system, of a true phase transition driven by background extinctions.Comment: 19 pages, 11 figures, revised versio

Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory

In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share "lost cases", i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane x+y+z=0. The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through a new term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for new developments of fundamental measure theory.Comment: 10 pages, 9 figures, uses RevTeX

Phase diagram of a two-dimensional lattice gas model of a ramp system

Using Monte Carlo Simulation and fundamental measure theory we study the phase diagram of a two-dimensional lattice gas model with a nearest neighbor hard core exclusion and a next-to-nearest neighbors finite repulsive interaction. The model presents two competing ranges of interaction and, in common with many experimental systems, exhibits a low density solid phase, which melts back to the fluid phase upon compression. The theoretical approach is found to provide a qualitatively correct picture of the phase diagram of our model system.Comment: 14 pages, 8 figures, uses RevTex

Crossed-ratchet effects and domain wall geometrical pinning

The motion of a domain wall in a two dimensional medium is studied taking into account the internal elastic degrees of freedom of the wall and geometrical pinning produced both by holes and sample boundaries. This study is used to analyze the geometrical conditions needed for optimizing crossed ratchet effects in periodic rectangular arrays of asymmetric holes, recently observed experimentally in patterned ferromagnetic films. Geometrical calculations and numerical simulations have been used to obtain the anisotropic critical fields for depinning flat and kinked walls in rectangular arrays of triangles. The aim is to show with a generic elastic model for interfaces how to build a rectifier able to display crossed ratchet effects or effective potential landscapes for controlling the motion of interfaces or invasion fronts.Comment: 13 pages, 18 figure

Statistical mechanics of ecosystem assembly

We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the endstate of the process), which is therefore resistant to invasions. This also shows that the endstate is independent on the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner.Comment: Accepted for publication in Physical Review Letter

Virus Replication as a Phenotypic Version of Polynucleotide Evolution

In this paper we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. By taking into account beneficial effects we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium" and transient. Finally, based on these quantitative results we are able to draw some qualitative conclusions.Comment: 23 pages, 1 figure, 2 tables. arXiv admin note: substantial text overlap with arXiv:1110.336

Generosity Pays in the Presence of Direct Reciprocity: A Comprehensive Study of 2×2 Repeated Games

By applying a technique previously developed to study ecosystem assembly [Capitán et al., Phys. Rev. Lett. 103, 168101 (2009)] we study the evolutionary stable strategies of iterated 22 games. We focus on memory-one strategies, whose probability to play a given action depends on the actions of both players in the previous time step. We find the asymptotically stable populations resulting from all possible invasions of any known stable population. The results of this invasion process are interpreted as transitions between different populations that occur with a certain probability. Thus the whole process can be described as a Markov chain whose states are the different stable populations. With this approach we are able to study the whole space of symmetric 22 games, characterizing the most probable results of evolution for the different classes of games. Our analysis includes quasi-stationary mixed equilibria that are relevant as very long-lived metastable states and is compared to the predictions of a fixation probability analysis. We confirm earlier results on the success of the Pavlov strategy in a wide range of parameters for the iterated Prisoner's Dilemma, but find that as the temptation to defect grows there are many other possible successful strategies. Other regions of the diagram reflect the equilibria structure of the underlying one-shot game, albeit often some non-expected strategies arise as well. We thus provide a thorough analysis of iterated 22 games from which we are able to extract some general conclusions. Our most relevant finding is that a great deal of the payoff parameter range can still be understood by focusing on win-stay, lose-shift strategies, and that very ambitious ones, aspiring to obtaining always a high payoff, are never evolutionary stable

Severe Hindrance of Viral Infection Propagation in Spatially Extended Hosts

The production of large progeny numbers affected by high mutation rates is a ubiquitous strategy of viruses, as it promotes quick adaptation and survival to changing environments. However, this situation often ushers in an arms race between the virus and the host cells. In this paper we investigate in depth a model for the dynamics of a phenotypically heterogeneous population of viruses whose propagation is limited to two-dimensional geometries, and where host cells are able to develop defenses against infection. Our analytical and numerical analyses are developed in close connection to directed percolation models. In fact, we show that making the space explicit in the model, which in turn amounts to reducing viral mobility and hindering the infective ability of the virus, connects our work with similar dynamical models that lie in the universality class of directed percolation. In addition, we use the fact that our model is a multicomponent generalization of the Domany-Kinzel probabilistic cellular automaton to employ several techniques developed in the past in that context, such as the two-site approximation to the extinction transition line. Our aim is to better understand propagation of viral infections with mobility restrictions, e.g., in crops or in plant leaves, in order to inspire new strategies for effective viral control

Sheldon Spectrum and the Plankton Paradox: Two Sides of the Same Coin : A trait-based plankton size-spectrum model

The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems: the biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude. While size-spectrum models have explained this phenomenon for assemblages of multicellular organisms, this paper introduces a species-resolved size-spectrum model to explain the phenomenon in unicellular plankton. A Sheldon spectrum spanning the cell-size range of unicellular plankton necessarily consists of a large number of coexisting species covering a wide range of characteristic sizes. The coexistence of many phytoplankton species feeding on a small number of resources is known as the Paradox of the Plankton. Our model resolves the paradox by showing that coexistence is facilitated by the allometric scaling of four physiological rates. Two of the allometries have empirical support, the remaining two emerge from predator-prey interactions exactly when the abundances follow a Sheldon spectrum. Our plankton model is a scale-invariant trait-based size-spectrum model: it describes the abundance of phyto- and zooplankton cells as a function of both size and species trait (the maximal size before cell division). It incorporates growth due to resource consumption and predation on smaller cells, death due to predation, and a flexible cell division process. We give analytic solutions at steady state for both the within-species size distributions and the relative abundances across species

Seguimiento de las guías españolas para el manejo del asma por el médico de atención primaria: un estudio observacional ambispectivo

Objetivo Evaluar el grado de seguimiento de las recomendaciones de las versiones de la Guía española para el manejo del asma (GEMA 2009 y 2015) y su repercusión en el control de la enfermedad. Material y métodos Estudio observacional y ambispectivo realizado entre septiembre del 2015 y abril del 2016, en el que participaron 314 médicos de atención primaria y 2.864 pacientes. Resultados Utilizando datos retrospectivos, 81 de los 314 médicos (25, 8% [IC del 95%, 21, 3 a 30, 9]) comunicaron seguir las recomendaciones de la GEMA 2009. Al inicio del estudio, 88 de los 314 médicos (28, 0% [IC del 95%, 23, 4 a 33, 2]) seguían las recomendaciones de la GEMA 2015. El tener un asma mal controlada (OR 0, 19, IC del 95%, 0, 13 a 0, 28) y presentar un asma persistente grave al inicio del estudio (OR 0, 20, IC del 95%, 0, 12 a 0, 34) se asociaron negativamente con tener un asma bien controlada al final del seguimiento. Por el contrario, el seguimiento de las recomendaciones de la GEMA 2015 se asoció de manera positiva con una mayor posibilidad de que el paciente tuviera un asma bien controlada al final del periodo de seguimiento (OR 1, 70, IC del 95%, 1, 40 a 2, 06). Conclusiones El escaso seguimiento de las guías clínicas para el manejo del asma constituye un problema común entre los médicos de atención primaria. Un seguimiento de estas guías se asocia con un control mejor del asma. Existe la necesidad de actuaciones que puedan mejorar el seguimiento por parte de los médicos de atención primaria de las guías para el manejo del asma. Objective: To assess the degree of compliance with the recommendations of the 2009 and 2015 versions of the Spanish guidelines for managing asthma (Guía Española para el Manejo del Asma [GEMA]) and the effect of this compliance on controlling the disease. Material and methods: We conducted an observational ambispective study between September 2015 and April 2016 in which 314 primary care physicians and 2864 patients participated. Results: Using retrospective data, we found that 81 of the 314 physicians (25.8%; 95% CI 21.3–30.9) stated that they complied with the GEMA2009 recommendations. At the start of the study, 88 of the 314 physicians (28.0%; 95% CI 23.4–33.2) complied with the GEMA2015 recommendations. Poorly controlled asthma (OR, 0.19; 95% CI 0.13–0.28) and persistent severe asthma at the start of the study (OR, 0.20; 95% CI 0.12–0.34) were negatively associated with having well-controlled asthma by the end of the follow-up. In contrast, compliance with the GEMA2015 recommendations was positively associated with a greater likelihood that the patient would have well-controlled asthma by the end of the follow-up (OR, 1.70; 95% CI 1.40–2.06). Conclusions: Low compliance with the clinical guidelines for managing asthma is a common problem among primary care physicians. Compliance with these guidelines is associated with better asthma control. Actions need to be taken to improve primary care physician compliance with the asthma management guidelines