scholarly journals The cavity method for community ecology

2017 ◽  
Author(s):  
Matthieu Barbier ◽  
Jean-François Arnoldi

AbstractThis article is addressed to researchers and students in theoretical ecology, as an introduction to “disordered systems” approaches from statistical physics, and how they can help understand large ecological communities. We discuss the relevance of these approaches, and how they fit within the broader landscape of models in community ecology. We focus on a remarkably simple technique, the cavity method, which allows to derive the equilibrium properties of Lotka-Volterra systems. We present its predictions, the new intuitions it suggests, and its technical underpinnings. We also discuss a number of new results concerning possible extensions, including different functional responses and community structures.

Author(s):  
Lenka Zdeborová

Statistical physics of hard optimization problemsOptimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.


Author(s):  
L. de Arcangelis ◽  
E. Lippiello ◽  
M. Pica Ciamarra ◽  
A. Sarracino

The frictional properties of disordered systems are affected by external perturbations. These perturbations usually weaken the system by reducing the macroscopic friction coefficient. This friction reduction is of particular interest in the case of disordered systems composed of granular particles confined between two plates, as this is a simple model of seismic fault. Indeed, in the geophysical context frictional weakening could explain the unexpected weakness of some faults, as well as earthquake remote triggering. In this manuscript, we review recent results concerning the response of confined granular systems to external perturbations, considering the different mechanisms by which the perturbation could weaken a system, the relevance of the frictional reduction to earthquakes, as well as discussing the intriguing scenario whereby the weakening is not monotonic in the perturbation frequency, so that a re-entrant transition is observed, as the system first enters a fluidized state and then returns to a frictional state. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.


Author(s):  
John P. DeLong

Predator-prey interactions form an essential part of ecological communities, determining the flow of energy from autotrophs to top predators. The rate of predation is a key regulator of that energy flow, and that rate is determined by the functional response. Functional responses themselves are emergent ecological phenomena – they reflect morphology, behavior, and physiology of both predator and prey and are both outcomes of evolution and the source of additional evolution. The functional response is thus a concept that connects many aspects of biology from behavioral ecology to eco-evolutionary dynamics to food webs, and as a result, the functional response is the key to an integrative science of predatory ecology. In this book, I provide a synthesis of research on functional responses, starting with the basics. I then break the functional response down into foraging components and connect these to the traits and behaviors that connect species in food webs. I conclude that contrary to appearances, we know very little about functional responses, and additional work is necessary for us to understand how environmental change and management will impact ecological systems


Ecology ◽  
2012 ◽  
Author(s):  
Herman A. Verhoef

At the beginning of the 20th century there was much debate about the “nature” of communities. The driving question was whether the community was a self-organized system of co-occurring species or simply a haphazard collection of populations with minimal functional integration. At that time, two extreme views dominated the discussion: one view considered a community as a superorganism, the member species of which were tightly bound together by interactions that contributed to repeatable patterns of species abundance in space and time. This concept led to the assumption that communities are fundamental entities, to be classified as the Linnaean taxonomy of species. Frederick E. Clements was one of the leading proponents of this approach, and his view became known as the organismic concept of communities. This assumes a common evolutionary history for the integrated species. The opposite view was the individualistic continuum concept, advocated by H. A. Gleason. His focus was on the traits of individual species that allow each to live within specific habitats or geographical ranges. In this view a community is an assemblage of populations of different species whose traits allow persisting in a prescribed area. The spatial boundaries are not sharp, and the species composition can change considerably. Consequently, it was discussed whether ecological communities were sufficiently coherent entities to be considered appropriate study objects. Later, consensus was reached: that properties of communities are of central interest in ecology, regardless of their integrity and coherence. From the 1950s and 1960s onward, the discussion was dominated by the deterministic outcome of local interactions between species and their environments and the building of this into models of communities. This approach, indicated as “traditional community ecology,” led to a morass of theoretical models, without being able to provide general principles about many-species communities. Early-21st-century approaches to bringing general patterns into community ecology concern (1) the metacommunity approach, (2) the functional trait approach, (3) evolutionary community ecology, and (4) the four fundamental processes. The metacommunity approach implicitly recognizes and studies the important role of spatiotemporal dynamics. In the functional trait approach, four themes are focused upon: traits, environmental gradients, the interaction milieu, and performance currencies. This functional, trait-focused approach should have a better prospect of understanding the effects of global changes. Evolutionary community ecology is an approach in which the combination of community ecology and evolutionary biology will lead to a better understanding of the complexity of communities and populations. The four fundamental processes are selection, drift, speciation, and dispersal. This approach concerns an organizational scheme for community ecology, based on these four processes to describe all existing specific models and frameworks, in order to make general statements about process–pattern connections.


2019 ◽  
Vol 16 (151) ◽  
pp. 20180747
Author(s):  
Bernat Bramon Mora ◽  
Giulio V. Dalla Riva ◽  
Daniel B. Stouffer

Null models have become a crucial tool for understanding structure within incidence matrices across multiple biological contexts. For example, they have been widely used for the study of ecological and biogeographic questions, testing hypotheses regarding patterns of community assembly, species co-occurrence and biodiversity. However, to our knowledge we remain without a general and flexible approach to study the mechanisms explaining such structures. Here, we provide a method for generating ‘correlation-informed’ null models, which combine the classic concept of null models and tools from community ecology, like joint statistical modelling. Generally, this model allows us to assess whether the information encoded within any given correlation matrix is predictive for explaining structural patterns observed within an incidence matrix. To demonstrate its utility, we apply our approach to two different case studies that represent examples of common scenarios encountered in community ecology. First, we use a phylogenetically informed null model to detect a strong evolutionary fingerprint within empirically observed food webs, reflecting key differences in the impact of shared evolutionary history when shaping the interactions of predators or prey. Second, we use multiple informed null models to identify which factors determine structural patterns of species assemblages, focusing in on the study of nestedness and the influence of site size, isolation, species range and species richness. In addition to offering a versatile way to study the mechanisms shaping the structure of any incidence matrix, including those describing ecological communities, our approach can also be adapted further to test even more sophisticated hypotheses.


2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Silvio Franz ◽  
Giorgio Parisi ◽  
Maxime Sevelev ◽  
Pierfrancesco Urbani ◽  
Francesco Zamponi

Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.


Sign in / Sign up

Export Citation Format

Share Document