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

Degree of intervality of food webs: From body-size data to models

In food webs, the degree of intervality of consumers' diets is an indicator of the number of dimensions that are necessary to determine the niche of a species. Previous studies modeling food-web structure have shown that real networks are compatible with a high degree of diet contiguity. However, current models are also compatible with the opposite, namely that species' diets have relatively low contiguity. This is particularly true when one takes species' body size as a proxy for niche value, in which case the indeterminacy of diet contiguities provided by current models can be large. We propose a model that enables us to narrow down the range of possible values of diet contiguity. According to this model, we find that diet contiguity not only can be high, but must be high when species are ranked in ascending order of body size.This work was supported by a James S. Mc Donnell Foundation Research Award (R.G.), European Union Grant PIRG-GA-2010-277166 (R.G.), Spanish Ministerio de Ciencia e Innovación (MICINN) Grants FIS2009-13370-C02-01 A.A.), FIS2010-18639 (R.G.), PRODIEVO, and FIS2011-27569 (J.A.C.), Comunidad de Madrid Grant MODELICO-CM (J.A.C.) and by Generalitat de Catalunya 2009-SGR-838 (A.A.).Publicad

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

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

A fundamental-measure density functional for mixtures of parallel hard cylinders

We obtain a fundamental measure density functional for mixtures of parallel hard cylinders. To this purpose we first generalize to multicomponent mixtures the fundamental measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of these authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.Comment: 19 pages, 4 figure

Species assembly in model ecosystems, II: Results of the assembly process

In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.Comment: 14 pages, 13 figures. Revised versio

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

A signal of competitive dominance in mid-latitude herbaceous plant communities

Understanding the main determinants of species coexistence across space and time is a central question in ecology. However, ecologists still know little about the scales and conditions at which biotic interactions matter and how these interact with the environment to structure species assemblages. Here we use recent theoretical developments to analyse plant distribution and trait data across Europe and find that plant height clustering is related to both evapotranspiration (ET) and gross primary productivity. This clustering is a signal of interspecies competition between plants, which is most evident in mid-latitude ecoregions, where conditions for growth (reflected in actual ET rates and gross primary productivities) are optimal. Away from this optimum, climate severity probably overrides the effect of competition, or other interactions become increasingly important. Our approach bridges the gap between species-rich competition theories and large-scale species distribution data analysisThis work was funded by the Spanish ‘Ministerio de Economía y Competitividad’ under the projects CGL2012-39964 and CGL2015-69043-P (D.A. and J.A.C.), by the Spanish ‘Ministerio de Ciencia, Innovación y Universidades’ under the project PGC2018-096577-B-I00 (D.A. and J.A.C.), and the Ramón y Cajal Fellowship program (RYC-2010-06545, D.A.). J.A.C. acknowledges partial financial support from the Department of Applied Mathematics (Universidad Politécnica de Madrid). S.C. acknowledges financial support from Banco Santander through grant no. PR87/19-2258

Disentangling categorical relationships through a graph of co-occurrences

The mesoscopic structure of complex networks has proven a powerful level of description to understand the linchpins of the system represented by the network. Nevertheless, themapping of a series of relationships between elements, in terms of a graph, is sometimes not straightforward. Given that all the information we would extract using complex network tools depend on this initial graph, it is mandatory to preprocess the data to build it on in the most accurate manner. Here we propose a procedure to build a network, attending only to statistically significant relations between constituents. We use a paradigmatic example of word associations to show the development of our approach. Analyzing the modular structure of the obtained network we are able to disentangle categorical relations, disambiguating words with success that is comparable to the best algorithms designed to the same end.We acknowledge financia support through Grant No. FIS2009-13364-C02-01, Holopedia (Grant No. TIN2010-21128-C02-01), MOSAICO (Grant No. FIS2006-01485), PRODIEVO (Grant No. FIS2011-22449), and Complexity-NET RESINEE, all of them from Ministerio de Educación y Ciencia in Spain, as well as support from Research Networks MODELICO-CM (Grant No. S2009/ESP-1691) and MA2VICMR (Grant No. S2009/TIC-1542) from Comunidad de Madrid, and Network 2009-SGR-838 from Generalitat de Catalunya