Criticality and scaling in evolutionary ecology

Spatial food webs in the Barents Sea: atlantification and the reorganization of the trophic structure

Climate change affects ecosystems at several levels: by altering the spatial distribution of individual species, by locally rewiring interspecific interactions, and by reorganizing trophic networks at larger scales. The dynamics of marine food webs are becoming more and more sensitive to spatial processes and connections in the seascape. As a case study, we study the atlantification of the Barents Sea: we compare spatio-temporal subsystems at three levels: the identity of key organisms, critically important interactions and the entire food web. Network analysis offers quantitative measurements, including centrality indices, trophic similarity indices, a topological measure of interaction asymmetry and network-level measures. We found that atlantification alters the identity of key species (boreal demersals becoming hubs), results in strongly asymmetric interactions (dominated by haddock), changes the dominant regulation regime (from bottom-up to wasp-waist control) and makes the food web less modular. Since the results of food web analysis may be quite sensitive to network construction, the aggregation of food web data was explicitly studied to increase the robustness of food web analysis. We found that an alternative, mathematical aggregation algorithm better preserves some network properties (e.g. density) of the original, unaggregated network than the biologically inspired aggregation into functional groups. This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'.

Decadal-scale time series highlight the role of chronic disturbances in driving ecosystem collapse in the Anthropocene

Biome degradation characterizes the Anthropocene Epoch, and modern ecology is deeply involved with describing the changes underway. Most research has focused on the role of acute disturbances in causing conspicuous changes in ecosystem structure, which leads to an underappreciation of the chronic effects causing large changes through the cumulative effects of small perturbations over decades. Coral reefs epitomize this trend, because the changes in community structure are profound, yet the data to quantify these effects are usually insufficient to evaluate the relative roles of different disturbance types. Here, four decades of surveys from two coral reefs (9 and 14 m depth) off St. John, US Virgin Islands, are used to quantify the associations of acute and chronic events with the changes in benthic community structure. These reefs profoundly changed over 36 years, with coral death altering species assemblages to depress abundances of the ecologically important coral Orbicella spp. and elevating the coverage of macroalgae and crustose coralline algae/turf/bare space (CTB). Linear mixed models revealed the prominent role of chronic variation in temperature in accounting for changes in coverage of corals, macroalgae, and CTB, with rising temperature associated with increases in coral cover on the deep reef, and declines on the shallow reef. Hurricanes were also associated with declines in coral cover on the shallow reef, and increases on the deep reef. Multivariate analyses revealed strong associations between community structure and temperature, but weaker associations with hurricanes, bleaching, and diseases. These results highlight the overwhelming importance of chronically increasing temperature in altering the benthic community structure of Caribbean reefs.

The Major Features of Macroevolution

Evolutionary dynamics operating across deep time leave footprints in the shapes of phylogenetic trees. For the last several decades, researchers have used increasingly large and robust phylogenies to study the evolutionary history of individual clades and to investigate the causes of the glaring disparities in diversity among groups. Whereas typically not the focal point of individual clade-level studies, many researchers have remarked on recurrent patterns that have been observed across many different groups and at many different time scales. Whereas previous studies have documented various such regularities in topology and branch length distributions, they have typically focused on a single pattern and used a disparate collection (oftentimes, of quite variable reliability) of trees to assess it. Here we take advantage of modern megaphylogenies and unify previous disparate observations about the shapes embedded in the Tree of Life to create a catalog of the "major features of macroevolution." By characterizing such a large swath of subtrees in a consistent way, we hope to provide a set of phenomena that process-based macroevolutionary models of diversification ought to seek to explain.

Toward a cohesive understanding of ecological complexity

Ecological systems are quintessentially complex systems. Understanding and being able to predict phenomena typical of complex systems is, therefore, critical to progress in ecology and conservation amidst escalating global environmental change. However, myriad definitions of complexity and excessive reliance on conventional scientific approaches hamper conceptual advances and synthesis. Ecological complexity may be better understood by following the solid theoretical basis of complex system science (CSS). We review features of ecological systems described within CSS and conduct bibliometric and text mining analyses to characterize articles that refer to ecological complexity. Our analyses demonstrate that the study of complexity in ecology is a highly heterogeneous, global endeavor that is only weakly related to CSS. Current research trends are typically organized around basic theory, scaling, and macroecology. We leverage our review and the generalities identified in our analyses to suggest a more coherent and cohesive way forward in the study of complexity in ecology.

Book Review: On ecological networks and biological invasions

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Phase transitions in evolutionary dynamics

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

How critical is brain criticality?

Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.

Engineering self-organized criticality in living cells

Complex dynamical fluctuations, from intracellular noise, brain dynamics or computer traffic display bursting dynamics consistent with a critical state between order and disorder. Living close to the critical point has adaptive advantages and it has been conjectured that evolution could select these critical states. Is this the case of living cells? A system can poise itself close to the critical point by means of the so-called self-organized criticality (SOC). In this paper we present an engineered gene network displaying SOC behaviour. This is achieved by exploiting the saturation of the proteolytic degradation machinery in E. coli cells by means of a negative feedback loop that reduces congestion. Our critical motif is built from a two-gene circuit, where SOC can be successfully implemented. The potential implications for both cellular dynamics and behaviour are discussed.

Assessment of State Transition Dynamics of Coastal Wetlands in Northern Venice Lagoon, Italy

Coastal wetlands represent particularly valuable natural resources, characterized by the interaction between their geomorphological and biological components. Their adaptation to the changing conditions depends on the rate and extent of spatial and temporal processes and their response is still not fully understood. This work aims at detecting and improving the understanding of the transition dynamics on eco-geomorphological structures in a coastal wetland ecosystem. The approach could support sustainable habitat management improving the detection and optimizing the offer of Earth Observation (EO) products for coastal system monitoring. Such course of action will strengthen evidence-based policy making, surface biophysical data sovereignty and the Space Data downstream sector through remote sensing techniques thanks to the capability of investigating larger scale and short-to-long-term dynamics. The selected case study is the Lido basin (Venice Lagoon, Italy). Our methodology offers a support in the framework of nature-based solutions, allowing the identification of ecosystem-level indicators of the surface biophysical properties influencing stability and evolution of intertidal flats on which a conceptual model is implemented. Landsat satellite imagery is used to delineate the spatial and temporal variability of the main vegetation and sediment typologies in 1990–2011. Within this period, specific anthropic activities were carried out for morphological restoration and flood protection interventions. Specifically, the lower saltmarsh shows its more fragmented part in the Baccan islet, a residual sandy spit in front of the Lido inlet. The area covered by Sarcocornia-Limonium, that triggers sediment deposition, has fluctuated yearly, from a minimum coverage of 13% to a maximum of 50%. The second decade (2001–2009) is identified as the period with major changes of halophytic and Algae-Biofilm cover typologies distribution. The power law and related thresholds, representing the patch size frequency distribution, is an indicator of the ecosystem state transition dynamics. The approach, based on multi-temporal and spatial EO analysis, is scalable elsewhere, from regional to local-to-global scale, considering the variability of climate data and anthropogenic activities. The present research also supports sustainable habitat management, improving the detection, and optimizing the offer of EO products for coastal system monitoring.

Song Morphing by Humpback Whales: Cultural or Epiphenomenal?

Singing humpback whales (Megaptera noavaengliae) collectively and progressively change the sounds and patterns they produce within their songs throughout their lives. The dynamic modifications that humpback whales make to their songs are often cited as an impressive example of cultural transmission through vocal learning in a non-human. Some elements of song change challenge this interpretation, however, including: (1) singers often incrementally and progressively morph phrases within and across songs as time passes, with trajectories of change being comparable across multiple time scales; (2) acoustically isolated subpopulations singing similar songs morph the acoustic properties of songs in similar ways; and (3) complex sound patterns, including phrases, themes, and whole songs, recur across years and populations. These properties of song dynamics suggest that singing humpback whales may be modulating song features in response to local conditions and genetic predispositions rather than socially learning novel sound patterns by copying other singers. Experimental and observational tests of key predictions of these alternative hypotheses are critical to identifying how and why singing humpback whales constantly change their songs.

Scale-invariant topology and bursty branching of evolutionary trees emerge from niche construction

Phylogenetic trees describe both the evolutionary process and community diversity. Recent work has established that they exhibit scale-invariant topology, which quantifies the fact that their branching lies in between the two extreme cases of balanced binary trees and maximally unbalanced ones. In addition, the backbones of phylogenetic trees exhibit bursts of diversification on all timescales. Here, we present a simple, coarse-grained statistical model of niche construction coupled to speciation. Finite-size scaling analysis of the dynamics shows that the resultant phylogenetic tree topology is scale-invariant due to a singularity arising from large niche construction fluctuations that follow extinction events. The same model recapitulates the bursty pattern of diversification in time. These results show how dynamical scaling laws of phylogenetic trees on long timescales can reflect the indelible imprint of the interplay between ecological and evolutionary processes.

Collective learning from individual experiences and information transfer during group foraging

Living in groups brings benefits to many animals, such as protection against predators and an improved capacity for sensing and making decisions while searching for resources in uncertain environments. A body of studies has shown how collective behaviours within animal groups on the move can be useful for pooling information about the current state of the environment. The effects of interactions on collective motion have been mostly studied in models of agents with no memory. Thus, whether coordinated behaviours can emerge from individuals with memory and different foraging experiences is still poorly understood. By means of an agent-based model, we quantify how individual memory and information fluxes can contribute to improving the foraging success of a group in complex environments. In this context, we define collective learning as a coordinated change of behaviour within a group resulting from individual experiences and information transfer. We show that an initially scattered population of foragers visiting dispersed resources can gradually achieve cohesion and become selectively localized in space around the most salient resource sites. Coordination is lost when memory or information transfer among individuals is suppressed. The present modelling framework provides predictions for empirical studies of collective learning and could also find applications in swarm robotics and motivate new search algorithms based on reinforcement.

Invariance in ecological pattern

Background: The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common answers include maximum entropy, neutrality, and convergent outcome from different underlying biological processes.  Methods: This article proposes a more general answer based on the concept of invariance, the property by which a pattern remains the same after transformation. Invariance has a long tradition in physics. For example, general relativity emphasizes the need for the equations describing the laws of physics to have the same form in all frames of reference.  Results: By bringing this unifying invariance approach into ecology, we show that the log series pattern dominates when the consequences of processes acting on abundance are invariant to the addition or multiplication of abundance by a constant. The lognormal pattern dominates when the processes acting on net species growth rate obey rotational invariance (symmetry) with respect to the summing up of the individual component processes. Conclusions: Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches. First, invariance provides a simpler and more fundamental maximum entropy derivation of the log series distribution. Second, invariance provides a simple derivation of the key result from neutral theory: the log series at the metacommunity scale and a clearer form of the skewed lognormal at the local community scale. The invariance expressions are easy to understand because they uniquely describe the basic underlying components that shape pattern.

Universal scaling across biochemical networks on Earth

The application of network science to biology has advanced our understanding of the metabolism of individual organisms and the organization of ecosystems but has scarcely been applied to life at a planetary scale. To characterize planetary-scale biochemistry, we constructed biochemical networks using a global database of 28,146 annotated genomes and metagenomes and 8658 cataloged biochemical reactions. We uncover scaling laws governing biochemical diversity and network structure shared across levels of organization from individuals to ecosystems, to the biosphere as a whole. Comparing real biochemical reaction networks to random reaction networks reveals that the observed biological scaling is not a product of chemistry alone but instead emerges due to the particular structure of selected reactions commonly participating in living processes. We show that the topology of biochemical networks for the three domains of life is quantitatively distinguishable, with >80% accuracy in predicting evolutionary domain based on biochemical network size and average topology. Together, our results point to a deeper level of organization in biochemical networks than what has been understood so far.

Criticality Distinguishes the Ensemble of Biological Regulatory Networks

The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree ⟨K⟩ and mean bias in the logic functions ⟨p⟩, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.

On the networked architecture of genotype spaces and its critical effects on molecular evolution

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

Issues in data expansion in understanding criticality in biological systems

At the point of a second-order phase transition also termed as a critical point, systems display long-range order and their macroscopic behaviors are independent of the microscopic details making up the system. Due to these properties, it has long been speculated that biological systems that show similar behavior despite having very different microscopics, may be operating near a critical point. Recent methods in neuroscience are making it possible to explore whether criticality exists in neural networks. Despite being large in size, many datasets are only a minute sample of the neural system and methods have to be developed to expand these datasets to study criticality. In this work we develop an analytical method of expanding a dataset to the large N limit to make statements about the critical nature of the dataset. We show that different ways of expanding the dataset while keeping its variance and mean fixed yield different results regarding criticality. This hence casts doubts on the established procedures for deducing criticality of biological systems through expansion of finite-sized datasets.

Criticality predicts maximum irregularity in recurrent networks of excitatory nodes

A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of cerebral cortex operate at a critical regime, which is defined as a transition point between two phases of short lasting and chaotic activity. However, despite the fact that criticality brings about certain functional advantages for information processing, its supporting evidence is still far from conclusive, as it has been mostly based on power law scaling of size and durations of cascades of activity. Moreover, to what degree such hypothesis could explain some fundamental features of neural activity is still largely unknown. One of the most prevalent features of cortical activity in vivo is known to be spike irregularity of spike trains, which is measured in terms of the coefficient of variation (CV) larger than one. Here, using a minimal computational model of excitatory nodes, we show that irregular spiking (CV > 1) naturally emerges in a recurrent network operating at criticality. More importantly, we show that even at the presence of other sources of spike irregularity, being at criticality maximizes the mean coefficient of variation of neurons, thereby maximizing their spike irregularity. Furthermore, we also show that such a maximized irregularity results in maximum correlation between neuronal firing rates and their corresponding spike irregularity (measured in terms of CV). On the one hand, using a model in the universality class of directed percolation, we propose new hallmarks of criticality at single-unit level, which could be applicable to any network of excitable nodes. On the other hand, given the controversy of the neural criticality hypothesis, we discuss the limitation of this approach to neural systems and to what degree they support the criticality hypothesis in real neural networks. Finally, we discuss the limitations of applying our results to real networks and to what degree they support the criticality hypothesis.

Evolutionary fields can explain patterns of high-dimensional complexity in ecology

One of the properties that make ecological systems so unique is the range of complex behavioral patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to stochastic factors that have very high-degrees of freedom. Orthodox study of the evolution of these simple networks has generally been limited in its ability to explain complexity, since it restricts evolutionary adaptation to an inertia-free process with few degrees of freedom in which only gradual, moderately complex behaviors are possible. We propose a model inspired by particle-mediated field phenomena in classical physics in combination with fundamental concepts in adaptation, which suggests that small but high-dimensional chaotic dynamics near to the adaptive trait optimum could help explain complex properties shared by most ecological datasets, such as aperiodicity and pink, fractal noise spectra. By examining a simple predator-prey model and appealing to real ecological data, we show that this type of complexity could be easily confused for or confounded by stochasticity, especially when spurred on or amplified by stochastic factors that share variational and spectral properties with the underlying dynamics.

Punctuated equilibrium as an emergent process and its modified thermodynamic characterization

We address evolutionary dynamics and consider under which conditions the ecosystem interaction network allows punctuated equilibrium (i.e., alternation between hectic and quasi-stable phases). We focus on the links connecting various species and on the strength and sign of those links. For this study we consider the Tangled Nature model, which allows considerable flexibility and plasticity in the analysis of interspecies interactions. We find that it is necessary to have a proper balance of connectivity and interaction intensities so as to establish the kind of mutual cooperation and competition found in nature. It suggests evolutionary punctuated equilibrium as an emergent process, thus displaying features of complex systems. To explicitly demonstrate this fact we consider an extended form of thermodynamics, defining (for the present context) relevant out-of-equilibrium "collective" functions. We then show how to characterize the punctuated equilibrium through entropy-like and free energy-like quantities. Finally, from a close analogy to thermodynamic systems, we propose a protocol similar to simulated annealing. It is based on controlling the species' rate of mutation during the hectic periods, in this way enhancing the exploration of the genome space (similar to the known behavior of bacteria in stressful environments). This allows the system to more rapidly converge to long-duration quasi-stable phases.

Wing Shape Variation in the Taxonomic Recognition of Species of Diachlorus Osten-Sacken (Diptera: Tabanidae) from Colombia

We evaluated the directional asymmetry between right and left wings and quantified the intraspecific and interspecific variation of the wing shape of 601 specimens of the genus Diachlorus to determine to what extent the geometrical variation discriminates six species distributed in six protected areas of Colombia. Geometric analyses were performed, integrating Procrustes methods, principal component analyses, cluster analyses, linear and quadratic discriminant analyses, and evaluations of shape changes. In Diachlorus, left and right wings did not present significant asymmetry but a geometrical analysis was allowed for species identification and, in some cases, the origin of the specimens using the variation of wing shape; the best-assigned species was Diachlorus leticia Wilkerson & Fairchild, while the worst was Diachlorus jobbinsi Fairchild, which also had the highest intraspecific variation, while Diachlorus fuscistigma Lutz had the lowest variation. Diachlorus fuscistigma and Diachlorus leucotibialis Wilkerson & Fairchild were the most similar species, while D. leucotibialis and Diachlorus nuneztovari Fairchild & Ortiz were the most disimilar. The specimens with the most different wing shape belonged to Chocó (especially those of D. jobbinsi), the geographically farthest area from the others in the study; however, no correlation was observed between geometric and geographical distances. Linear discriminants were better than nonlinear (quadratic) discriminant analyses in predicting species membership, but the opposite was true for predicting area membership. Based on our data, we hypothesized that other species of Diachlorus could also be discriminated using geometric morphometry of the wing shape.

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

Dynamic landscapes: a model of context and contingency in evolution

Although the basic mechanics of evolution have been understood since Darwin, debate continues over whether macroevolutionary phenomena are driven by the fitness structure of genotype space or by ecological interaction. In this paper we propose a simple model capturing key features of fitness-landscape and ecological models of evolution. Our model describes evolutionary dynamics in a high-dimensional, structured genotype space with interspecies interaction. We find promising qualitative similarity with the empirical facts about macroevolution, including broadly distributed extinction sizes and realistic exploration of the genotype space. The abstraction of our model permits numerous applications beyond macroevolution, including protein and RNA evolution.

Scaling body size fluctuations

The size of an organism matters for its metabolic, growth, mortality, and other vital rates. Scale-free community size spectra (i.e., size distributions regardless of species) are routinely observed in natural ecosystems and are the product of intra- and interspecies regulation of the relative abundance of organisms of different sizes. Intra- and interspecies distributions of body sizes are thus major determinants of ecosystems' structure and function. We show experimentally that single-species mass distributions of unicellular eukaryotes covering different phyla exhibit both characteristic sizes and universal features over more than four orders of magnitude in mass. Remarkably, we find that the mean size of a species is sufficient to characterize its size distribution fully and that the latter has a universal form across all species. We show that an analytical physiological model accounts for the observed universality, which can be synthesized in a log-normal form for the intraspecies size distributions. We also propose how ecological and physiological processes should interact to produce scale-invariant community size spectra and discuss the implications of our results on allometric scaling laws involving body mass.

A journey from reductionist to systemic cell biology aboard the schooner Tara

In this essay I describe my personal journey from reductionist to systems cell biology and describe how this in turn led to a 3-year sea voyage to explore complex ocean communities. In describing this journey, I hope to convey some important principles that I gleaned along the way. I realized that cellular functions emerge from multiple molecular interactions and that new approaches borrowed from statistical physics are required to understand the emergence of such complex systems. Then I wondered how such interaction networks developed during evolution. Because life first evolved in the oceans, it became a natural thing to start looking at the small organisms that compose the plankton in the world's oceans, of which 98% are … individual cells—hence the Tara Oceans voyage, which finished on 31 March 2012 in Lorient, France, after a 60,000-mile around-the-world journey that collected more than 30,000 samples from 153 sampling stations.

Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics

Self-organized criticality purports to build multi-scaled structures out of local interactions. Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal scales. However, this apparent homogeneity can be misleading, especially as it spans more scales. Reducing biological processes to one power-law relationship neglects rich cascade dynamics. We review recent research into multifractality in executive-function cognitive tasks and propose that scaling reflects not criticality but instead interactions across multiple scales and among fluctuations of multiple sizes.

Eye movement dynamics and cognitive self-organization in typical and atypical development

This study analyzed distributions of Euclidean displacements in gaze (i.e. "gaze steps") to evaluate the degree of componential cognitive constraints on audio-visual speech perception tasks. Children performing these tasks exhibited distributions of gaze steps that were closest to power-law or lognormal distributions, suggesting a multiplicatively interactive, flexible, self-organizing cognitive system rather than a component-dominant stipulated cognitive structure. Younger children and children diagnosed with an autism spectrum disorder (ASD) exhibited distributions that were closer to power-law than lognormal, indicating a reduced degree of self-organized structure. The relative goodness of lognormal fit was also a significant predictor of ASD, suggesting that this type of analysis may point towards a promising diagnostic tool. These results lend further support to an interaction-dominant framework that casts cognitive processing and development in terms of self-organization instead of fixed components and show that these analytical methods are sensitive to important developmental and neuropsychological differences.

From physics to biology by extending criticality and symmetry breakings

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not "just" processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions.

Equation or algorithm: differences and choosing between them

The issue of whether formal reasoning or a computing-intensive approach is the most efficient manner to address scientific questions is the subject of some considerable debate and pertains not only to the nature of the phenomena and processes investigated by scientists, but also the nature of the equation and algorithm objects they use. Although algorithms and equations both rely on a common background of mathematical language and logic, they nevertheless possess some critical differences. They do not refer to the same level of symbolization, as equations are based on integrated concepts in a denotational manner, while algorithms specifically break down a complex problem into more elementary operations, in an operational manner. They may therefore be considered as suited to the representation of different phenomena. Specifically, algorithms are by nature sufficient to represent weak emergent phenomena, but not strong emergent patterns, while equations can do both. Finally, the choice between equations and algorithms are by nature sufficient to represent weak emergent phenomena, but not strong emergent patterns, while equations behave conversely. We propose a simplified classification of scientific issues for which both equation- and/or algorithm-based approaches can be envisaged, and discuss their respective pros and cons. We further discuss the complementary and sometimes conflicting uses of equations and algorithms in a context of ecological theory of metapopulation dynamics. We finally propose both conceptual and practical guidelines for choosing between the alternative approaches.

Toward a synthetic economic systems modeling tool for sustainable exploitation of ecosystems

Environmental resources that underpin the basic human needs of water, energy, and food are predicted to become in such short supply by 2050 that global security and the well-being of millions will be under threat. These natural commodities have been allowed to reach crisis levels of supply because of a failure of economic systems to sustain them. This is largely because there have been no means of integrating their exploitation into any economic model that effectively addresses ecological systemic failures in a way that provides an integrated ecological-economic tool that can monitor and evaluate market and policy targets. We review the reasons for this and recent attempts to address the problem while identifying outstanding issues. The key elements of a policy-oriented economic model that integrates ecosystem processes are described and form the basis of a proposed new synthesis approach. The approach is illustrated by an indicative case study that develops a simple model for rainfed and irrigated food production in the Murray-Darling basin of southeastern Australia.

Testing for criticality in ecosystem dynamics: the case of Amazonian rainforest and savanna fire

We test for two critical phenomena in Amazonian ecosystems: self-organized criticality (SOC) and critical transitions. SOC is often presented in the complex systems literature as a general explanation for scale invariance in nature. In particular, this mechanism is claimed to underlie the macroscopic structure and dynamics of terrestrial ecosystems. These would be inextricably linked to the action of fire, which is conceived as an endogenous ecological process. We show that Amazonian savanna fires display the scale-invariant features characteristic of SOC but do not display SOC. The same is true in Amazonian rainforests subject to moderate drought. These findings prove that there are other causes of scale invariance in ecosystems. In contrast, we do find evidence of a critical transition to a megafire regime under extreme drought in rainforests; this phenomenon is likely to determine the time scale of a possible loss of Amazonian rainforest caused by climate change.

Interpersonal pattern dynamics and adaptive behavior in multiagent neurobiological systems: conceptual model and data

Ecological dynamics characterizes adaptive behavior as an emergent, self-organizing property of interpersonal interactions in complex social systems. The authors conceptualize and investigate constraints on dynamics of decisions and actions in the multiagent system of team sports. They studied coadaptive interpersonal dynamics in rugby union to model potential control parameter and collective variable relations in attacker-defender dyads. A videogrammetry analysis revealed how some agents generated fluctuations by adapting displacement velocity to create phase transitions and destabilize dyadic subsystems near the try line. Agent interpersonal dynamics exhibited characteristics of chaotic attractors and informational constraints of rugby union boxed dyadic systems into a low dimensional attractor. Data suggests that decisions and actions of agents in sports teams may be characterized as emergent, self-organizing properties, governed by laws of dynamical systems at the ecological scale. Further research needs to generalize this conceptual model of adaptive behavior in performance to other multiagent populations.

Molecular evolution under fitness fluctuations

Molecular evolution is a stochastic process governed by fitness, mutations, and reproductive fluctuations in a population. Here, we study evolution where fitness itself is stochastic, with random switches in the direction of selection at individual genomic loci. As the correlation time of these fluctuations becomes larger than the diffusion time of mutations within the population, fitness changes from an annealed to a quenched random variable. We show that the rate of evolution has its maximum in the crossover regime, where both time scales are comparable. Adaptive evolution emerges in the quenched fitness regime (evidence for such fitness fluctuations has recently been found in genomic data). The joint statistical theory of reproductive and fitness fluctuations establishes a conceptual connection between evolutionary genetics and statistical physics of disordered systems.

Phase transitions and bistability in honeybee foraging dynamics

Many physical and biological systems display phase transitions, where a slight change in a parameter greatly changes the behavior of the system; and bistability, where for a certain range of this parameter either of two phases can be obtained, depending on initial conditions. We suggest the presence of these phenomena in a model of foraging honeybees. The eventual number of foragers depends in a complex way on the bee concentration and on the scouting rate. The results hold relevance for other multi-agent systems with potential jumps in system behavior or efficiency, depending on agent concentration.

Intrinsic and extrinsic causes of spatial variability across scales in a metacommunity

The relative importance of extrinsic and intrinsic causes of variability is among the oldest unresolved problems in ecology. However, the interaction between large-scale intrinsic variability in species abundance and environmental heterogeneity is still unknown. We use a metacommunity model with disturbance-recovery dynamics to resolve the interaction between scales of environmental heterogeneity, biotic processes and of intrinsic variability. We explain how population density increases with environmental variability only when its scale matches that of intrinsic patterns of abundance, through their ability to develop in heterogeneous environments. Succession dynamics reveals how the strength of local species interactions, through its control of intrinsic variability, can in turn control the scale of metapopulation response to environmental scales. Our results show that the environment and species density might fail to show any correlation despite their strong causal association. They more generally suggest that the spatial scale of ecological processes might not be sufficient to build a predictive framework for spatially heterogeneous habitats, including marine reserve networks.

Fitness declines in Tobacco etch virus upon serial bottleneck transfers

It has been well established that populations of RNA viruses transmitted throughout serial bottlenecks suffer from significant fitness declines as a consequence of the accumulation of deleterious mutations by the onset of Muller's ratchet. Bottlenecks are unavoidably linked to different steps of the infectious cycle of most plant RNA viruses, such as vector-mediated transmissions and systemic colonization of new leaves. Here we report evidence for fitness declines by the accumulation of deleterious mutations in the potyvirus Tobacco etch virus (TEV). TEV was inoculated into the nonsystemic host Chenopodium quinoa, and local lesions were isolated and used to initiate 20 independent mutation accumulation lineages. Weekly, a random lesion from each lineage was isolated and used to inoculate the next set of plants. At each transfer, the Malthusian growth rate was estimated. After 11 consecutive transfers, all lineages suffered significant fitness losses, and one even became extinct. The average rate of fitness decline was 5% per day. The average pattern of fitness decline was consistent with antagonistic epistasis between deleterious mutations, as postulated for antiredundant genomes. Temporal fitness fluctuations were not explained by random noise but reflected more complex underlying processes related to emergence and self-organization phenomena.

Comment on "A Keystone Mutualism Drives Pattern in a Power Function"

Vandermeer and Perfecto (Reports, 17 February 2006, p. 1000) reported a general power law pattern in the distribution of a common agricultural pest. However, there is an exact analytical solution for the expected cluster distribution under the proposed null model of density-independent growth in a patchy landscape. Reanalysis of the data shows that the system is not in a critical state but confirms the importance of a mutualism.