Effects of convection on the removal of the multiplicity of stable states in one-dimensional vertical models

Here I develop a model of a radiative-convective atmosphere with both radiative and convective schemes highly simplified. The atmospheric absorption of radiation at selective wavelengths makes use of constant mass absorption coefficients in finite width spectral bands. The convective regime is introduced by using a prescribed lapse rate in the troposphere. The main novelty of the radiative-convective model developed here is that it is solved without using any angular approximation for the radiation field. The solution obtained in the purely radiation mode (i. e. with convection ignored) leads to multiple equilibria of stable states, being very similar to some results recently found in simple models of planetary atmospheres. However, the introduction of convective processes removes the multiple equilibria of stable states. This shows the importance of taking convective processes into account even for qualitative analyses of planetary atmosphere

What can ecosystems learn? Expanding evolutionary ecology with learning theory.

BACKGROUND: The structure and organisation of ecological interactions within an ecosystem is modified by the evolution and coevolution of the individual species it contains. Understanding how historical conditions have shaped this architecture is vital for understanding system responses to change at scales from the microbial upwards. However, in the absence of a group selection process, the collective behaviours and ecosystem functions exhibited by the whole community cannot be organised or adapted in a Darwinian sense. A long-standing open question thus persists: Are there alternative organising principles that enable us to understand and predict how the coevolution of the component species creates and maintains complex collective behaviours exhibited by the ecosystem as a whole? RESULTS: Here we answer this question by incorporating principles from connectionist learning, a previously unrelated discipline already using well-developed theories on how emergent behaviours arise in simple networks. Specifically, we show conditions where natural selection on ecological interactions is functionally equivalent to a simple type of connectionist learning, 'unsupervised learning', well-known in neural-network models of cognitive systems to produce many non-trivial collective behaviours. Accordingly, we find that a community can self-organise in a well-defined and non-trivial sense without selection at the community level; its organisation can be conditioned by past experience in the same sense as connectionist learning models habituate to stimuli. This conditioning drives the community to form a distributed ecological memory of multiple past states, causing the community to: a) converge to these states from any random initial composition; b) accurately restore historical compositions from small fragments; c) recover a state composition following disturbance; and d) to correctly classify ambiguous initial compositions according to their similarity to learned compositions. We examine how the formation of alternative stable states alters the community's response to changing environmental forcing, and we identify conditions under which the ecosystem exhibits hysteresis with potential for catastrophic regime shifts. CONCLUSIONS: This work highlights the potential of connectionist theory to expand our understanding of evo-eco dynamics and collective ecological behaviours. Within this framework we find that, despite not being a Darwinian unit, ecological communities can behave like connectionist learning systems, creating internal conditions that habituate to past environmental conditions and actively recalling those conditions. REVIEWERS: This article was reviewed by Prof. Ricard V Solé, Universitat Pompeu Fabra, Barcelona and Prof. Rob Knight, University of Colorado, Boulder.

Feedbacks between vegetation and disturbance processes promote long-term persistence of forest-grassland mosaics in south Brazil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Catastrophic regime shift in water reservoirs and São Paulo water supply crisis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ku-deficient yeast strains exhibit alternative states of silencing competence.

In Saccharomyces cerevisiae, efficient silencer function requires telomere proximity, i.e. compartments of the nucleoplasm enriched in silencing factors. Accordingly, silencers located far from telomeres function inefficiently. We show here that cells lacking yKu balance between two mitotically stable states of silencing competence. In one, a partial delocalization of telomeres and silencing factors throughout the nucleoplasm correlates with enhanced silencing at a non-telomeric locus, while in the other, telomeres retain their focal pattern of distribution and there is no repression at the non-telomeric locus, as observed in wild-type cells. The two states also differ in their level of residual telomeric silencing. These findings indicate the existence of a yKu-independent pathway of telomere clustering and Sir localization. Interestingly, this pathway appears to be under epigenetic control.

Precise calculations of the existence of multiple AMOC equilibria in coupled climate models Part I: equilibrium states

This study examines criteria for the existence of two stable states of the Atlantic Meridional Overturning Circulation (AMOC) using a combination of theory and simulations from a numerical coupled atmosphere–ocean climate model. By formulating a simple collection of state parameters and their relationships, the authors reconstruct the North Atlantic Deep Water (NADW) OFF state behavior under a varying external salt-flux forcing. This part (Part I) of the paper examines the steady-state solution, which gives insight into the mechanisms that sustain the NADW OFF state in this coupled model; Part II deals with the transient behavior predicted by the evolution equation. The nonlinear behavior of the Antarctic Intermediate Water (AAIW) reverse cell is critical to the OFF state. Higher Atlantic salinity leads both to a reduced AAIW reverse cell and to a greater vertical salinity gradient in the South Atlantic. The former tends to reduce Atlantic salt export to the Southern Ocean, while the latter tends to increases it. These competing effects produce a nonlinear response of Atlantic salinity and salt export to salt forcing, and the existence of maxima in these quantities. Thus the authors obtain a natural and accurate analytical saddle-node condition for the maximal surface salt flux for which a NADW OFF state exists. By contrast, the bistability indicator proposed by De Vries and Weber does not generally work in this model. It is applicable only when the effect of the AAIW reverse cell on the Atlantic salt budget is weak.

A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Challenges in the participatory assessment of sustainable management practices in dryland ecosystems under regime shifts

Regime shifts, defined as a radical and persistent reconfiguration of an ecosystem following a disturbance, have been acknowledged by scientists as a very important aspect of the dynamic of ecosystems. However, their consideration in land management planning remains marginal and limited to specific processes and systems. Current research focuses on mathematical modeling and statistical analysis of spatio-temporal data for specific environmental variables. These methods do not fulfill the needs of land managers, who are confronted with a multitude of processes and pressure types and require clear and simple strategies to prevent regime shift or to increase the resilience of their environment. The EU-FP7 CASCADE project is looking at regime shifts of dryland ecosystems in southern Europe and specifically focuses on rangeland and forest systems which are prone to various land degradation threats. One of the aims of the project is to evaluate the impact of different management practices on the dynamic of the environment in a participatory manner, including a multi-stakeholder evaluation of the state of the environment and of the management potential. To achieve this objective we have organized several stakeholder meetings and we have compiled a review of management practices using the WOCAT methodology, which enables merging scientific and land users knowledge. We highlight here the main challenges we have encountered in applying the notion of regime shift to real world socio-ecological systems and in translating related concepts such as tipping points, stable states, hysteresis and resilience to land managers, using concrete examples from CASCADE study sites. Secondly, we explore the advantages of including land users’ knowledge in the scientific understanding of regime shifts. Moreover, we discuss useful alternative concepts and lessons learnt that will allow us to build a participatory method for the assessment of resilient management practices in specific socio-ecological systems and to foster adaptive dryland management.

Beyond the Fragmentation Threshold Hypothesis: Regime Shifts in Biodiversity Across Fragmented Landscapes

Ecological systems are vulnerable to irreversible change when key system properties are pushed over thresholds, resulting in the loss of resilience and the precipitation of a regime shift. Perhaps the most important of such properties in human-modified landscapes is the total amount of remnant native vegetation. In a seminal study Andren proposed the existence of a fragmentation threshold in the total amount of remnant vegetation, below which landscape-scale connectivity is eroded and local species richness and abundance become dependent on patch size. Despite the fact that species patch-area effects have been a mainstay of conservation science there has yet to be a robust empirical evaluation of this hypothesis. Here we present and test a new conceptual model describing the mechanisms and consequences of biodiversity change in fragmented landscapes, identifying the fragmentation threshold as a first step in a positive feedback mechanism that has the capacity to impair ecological resilience, and drive a regime shift in biodiversity. The model considers that local extinction risk is defined by patch size, and immigration rates by landscape vegetation cover, and that the recovery from local species losses depends upon the landscape species pool. Using a unique dataset on the distribution of non-volant small mammals across replicate landscapes in the Atlantic forest of Brazil, we found strong evidence for our model predictions - that patch-area effects are evident only at intermediate levels of total forest cover, where landscape diversity is still high and opportunities for enhancing biodiversity through local management are greatest. Furthermore, high levels of forest loss can push native biota through an extinction filter, and result in the abrupt, landscape-wide loss of forest-specialist taxa, ecological resilience and management effectiveness. The proposed model links hitherto distinct theoretical approaches within a single framework, providing a powerful tool for analysing the potential effectiveness of management interventions.

Sigma phase morphologies in cast and aged super duplex stainless steel

Solution annealed and water quenched duplex and super duplex stainless steels are thermodynamically metastable systems at room temperature. These systems do not migrate spontaneously to a thermodynamically stable condition because an energy barrier separates the metastable and stable states. However, any heat input they receive, for example through isothermal treatment or through prolonged exposure to a voltaic arc in the welding process, cause them to reach a condition of stable equilibrium which, for super duplex stainless steels, means precipitation of intermetallic and carbide phases. These phases include the sigma phase, which is easily identified from its morphology, and its influence on the material`s impact strength. The purpose of this work was to ascertain how 2-hour isothermal heat treatments at 920 degrees C and 980 degrees C affect the microstructure of ASTM A890/A890M GR 6A super duplex stainless steel. The sigma phase morphologies were found to be influenced by these two aging temperatures, with the material showing a predominantly lacy microstructure when heat treated at 920 degrees C and block-shaped when heat treated at 980 degrees C. (C) 2009 Elsevier Inc. All rights reserved.

Coordinated transportation of a large object by a team of three robots

Dynamical systems theory in this work is used as a theoretical language and tool to design a distributed control architecture for a team of three robots that must transport a large object and simultaneously avoid collisions with either static or dynamic obstacles. The robots have no prior knowledge of the environment. The dynamics of behavior is defined over a state space of behavior variables, heading direction and path velocity. Task constraints are modeled as attractors (i.e. asymptotic stable states) of the behavioral dynamics. For each robot, these attractors are combined into a vector field that governs the behavior. By design the parameters are tuned so that the behavioral variables are always very close to the corresponding attractors. Thus the behavior of each robot is controlled by a time series of asymptotical stable states. Computer simulations support the validity of the dynamical model architecture.

Coordinated transportation of a large object by a team of two robots

In this paper dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for a team of two robots that must transport a large object and simultaneously avoid collisions with obstacles (either static or dynamic). This work extends the previous work with two robots (see [1] and [5]). However here we demonstrate that it’s possible to simplify the architecture presented in [1] and [5] and reach an equally stable global behavior. The robots have no prior knowledge of the environment. The dynamics of behavior is defined over a state space of behavior variables, heading direction and path velocity. Task constrains are modeled as attractors (i.e. asymptotic stable states) of a behavioral dynamics. For each robot, these attractors are combined into a vector field that governs the behavior. By design the parameters are tuned so that the behavioral variables are always very close to the corresponding attractors. Thus the behavior of each robot is controlled by a time series of asymptotic stable states. Computer simulations support the validity of the dynamical model architecture.

Object transportation by multiple mobile robots controlled by attractor dynamics: theory and implementation

Dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for teams of mobile robots, that must transport a large object and simultaneously avoid collisions with (either static or dynamic) obstacles. Here we demonstrate in simulations and implementations in real robots that it is possible to simplify the architectures presented in previous work and to extend the approach to teams of n robots. The robots have no prior knowledge of the environment. The motion of each robot is controlled by a time series of asymptotical stable states. The attractor dynamics permits the integration of information from various sources in a graded manner. As a result, the robots show a strikingly smooth an stable team behaviour.

Using attractor dynamics to generate decentralized motion control of two mobile robots transporting a long object in coordination

Dynamical systems theory is used here as a theoretical language and tool to design a distributed control architecture for a team of two mobile robots that must transport a long object and simultaneously avoid obstacles. In this approach the level of modeling is at the level of behaviors. A “dynamics” of behavior is defined over a state space of behavioral variables (heading direction and path velocity). The environment is also modeled in these terms by representing task constraints as attractors (i.e. asymptotically stable states) or reppelers (i.e. unstable states) of behavioral dynamics. For each robot attractors and repellers are combined into a vector field that governs the behavior. The resulting dynamical systems that generate the behavior of the robots may be nonlinear. By design the systems are tuned so that the behavioral variables are always very close to one attractor. Thus the behavior of each robot is controled by a time series of asymptotically stable states. Computer simulations support the validity of our dynamic model architectures.

The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.