Self-organized instability in complex ecosystems

Fundamental constraints to the logic of living systems

It has been argued that the historical nature of evolution makes it a highly path-dependent process. Under this view, the outcome of evolutionary dynamics could have resulted in organisms with different forms and functions. At the same time, there is ample evidence that convergence and constraints strongly limit the domain of the potential design principles that evolution can achieve. Are these limitations relevant in shaping the fabric of the possible? Here, we argue that fundamental constraints are associated with the logic of living matter. We illustrate this idea by considering the thermodynamic properties of living systems, the linear nature of molecular information, the cellular nature of the building blocks of life, multicellularity and development, the threshold nature of computations in cognitive systems and the discrete nature of the architecture of ecosystems. In all these examples, we present available evidence and suggest potential avenues towards a well-defined theoretical formulation.

Modeling tumors as complex ecosystems

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: multiple cell populations, each with different phenotypic signatures, coexist within a tumor and its metastases. Like species in an ecosystem, cancer populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity or predict its consequences. Here, we propose that the generalized Lotka-Volterra model (GLV), a standard tool to describe species-rich ecological communities, provides a suitable framework to model the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties provide a new understanding of the disease. We discuss potential extensions of the model and their application to phenotypic plasticity, cancer-immune interactions, and metastatic growth. Our work outlines a set of questions and a road map for further research in cancer ecology.

The role of trophic, mutualistic, and competitive interactions in an industrial symbiosis process implementation: an ecological network perspective

For both government and private institutions, the development of collaboration networks becomes an element of great importance for the implementation of related policies such as the circular economy and sustainable practices in manufacturing. Despite the above, such initiatives have not received as much attention in literature but have been decisive as both public and private initiatives. Initiatives in Latin America do not escape this scenario, especially in the creation of conditions that allow the promotion of approaches such as industrial symbiosis. In this way, the present research is aimed at identifying the role of trophic, mutualistic, and competitive interactions in an industrial symbiosis process implementation. A network analysis model is used to achieve this purpose. This technique allows us to know the degree of importance of the different actors that are part of a network, as well as the factors that determine the implementation of initiatives such as industrial symbiosis. Among the results are that empirical findings confirm the presence of trophic interactions that enhance resource efficiency, mutualistic interactions fostering collaboration and synergy, and competitive interactions promoting efficiency and dynamism. Additionally, a green culture, business size, and innovation activities are revealed as influential factors amplifying network dynamics.

Modeling tumors as species-rich ecological communities

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

Anthropogenic activities mediate stratification and stability of microbial communities in freshwater sediments

BACKGROUND

Freshwater sediment microbes are crucial decomposers that play a key role in regulating biogeochemical cycles and greenhouse gas emissions. They often exhibit a highly ordered structure along depth profiles. This stratification not only reflects redox effects but also provides valuable insights into historical transitions, as sediments serve as important archives for tracing environmental history. The Anthropocene, a candidate geological epoch, has recently garnered significant attention. However, the human impact on sediment zonation under the cover of natural redox niches remains poorly understood. Dam construction stands as one of the most far-reaching anthropogenic modifications of aquatic ecosystems. Here we attempted to identify the ecological imprint of damming on freshwater sediment microbiome.

RESULTS

We conducted a year-round survey on the sediment profiles of Lake Chaohu, a large shallow lake in China. Through depth-discrete shotgun metagenomics, metataxonomics, and geophysiochemical analyses, we unveiled a unique prokaryotic hierarchy shaped by the interplay of redox regime and historical damming (labeled by the 137Cs peak in AD 1963). Dam-induced initial differentiation was further amplified by nitrogen and methane metabolism, forming an abrupt transition governing nitrate-methane metabolic interaction and gaseous methane sequestration depth. Using a random forest algorithm, we identified damming-sensitive taxa that possess distinctive metabolic strategies, including energy-saving mechanisms, unique motility behavior, and deep-environment preferences. Moreover, null model analysis showed that damming altered microbial community assembly, from a selection-oriented deterministic process above to a more stochastic, dispersal-limited one below. Temporal investigation unveiled the rapid transition zone as an ecotone, characterized by high species richness, low community stability, and emergent stochasticity. Path analysis revealed the observed emergent stochasticity primarily came from the high metabolic flexibility, which potentially contributed to both ecological and statistical neutralities.

CONCLUSIONS

We delineate a picture in which dam-induced modifications in nutrient availability and sedimentation rates impact microbial metabolic activities and generate great changes in the community structure, assembly, and stability of the freshwater sediment microbiome. These findings reflect profound ecological and biogeochemical ramifications of human-Earth system interactions and help re-examine the mainstream views on the formation of sediment microbial stratification. Video Abstract.

Biodiversity transformations in the global ocean: A climate change and conservation management perspective

Understanding the biological diversity of different communities and evaluating the risks to biological sustainability in a time of rapid environmental change is a key challenge for providing an adapting management approach for biodiversity transformations in the ocean linked to human well-being. (Photo credit: Andrea Belgrano).

Single Seed Microbiota: Assembly and Transmission from Parent Plant to Seedling

The seed acts as the primary inoculum source for the plant microbiota. Understanding the processes involved in its assembly and dynamics during germination and seedling emergence has the potential to allow for the improvement of crop establishment. Changes in the bacterial community structure were tracked in 1,000 individual seeds that were collected throughout seed developments of beans and radishes. Seeds were associated with a dominant bacterial taxon that represented more than 75% of all reads. The identity of this taxon was highly variable between the plants and within the seeds of the same plant. We identified selection as the main ecological process governing the succession of dominant taxa during seed filling and maturation. In a second step, we evaluated the seedling transmission of seed-borne taxa in 160 individual plants. While the initial bacterial abundance on seeds was not a good predictor of seedling transmission, the identities of the seed-borne taxa modified the phenotypes of seedlings. Overall, this work revealed that individual seeds are colonized by a few bacterial taxa of highly variable identity, which appears to be important for the early stages of plant development. IMPORTANCE Seeds are key components of plant fitness and are central to the sustainability of the agri-food system. Both the seed quality for food consumption and the seed vigor in agricultural settings can be influenced by the seed microbiota. Understanding the ecological processes involved in seed microbiota assembly will inform future practices for promoting the presence of important seed microorganisms for plant health and productivity. Our results highlighted that seeds were associated with one dominant bacterial taxon of variable taxonomic identity. This variety of dominant taxa was due to (i) spatial heterogeneity between and within plants and (ii) primary succession during seed development. According to neutral models, selection was the main driver of microbial community assembly for both plant species.

Emergent phases of ecological diversity and dynamics mapped in microcosms

From tropical forests to gut microbiomes, ecological communities host notably high numbers of coexisting species. Beyond high biodiversity, communities exhibit a range of complex dynamics that are difficult to explain under a unified framework. Using bacterial microcosms, we performed a direct test of theory predicting that simple community-level features dictate emergent behaviors of communities. As either the number of species or the strength of interactions increases, we show that microbial ecosystems transition between three distinct dynamical phases, from a stable equilibrium in which all species coexist to partial coexistence to emergence of persistent fluctuations in species abundances, in the order predicted by theory. Under fixed conditions, high biodiversity and fluctuations reinforce each other. Our results demonstrate predictable emergent patterns of diversity and dynamics in ecological communities.

Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities

Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants-the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case-the "unified neutral theory of biodiversity." Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration-extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.

Fast growth can counteract antibiotic susceptibility in shaping microbial community resilience to antibiotics

SignificanceAntibiotic exposure stands among the most used interventions to drive microbial communities away from undesired states. How the ecology of microbial communities shapes their recovery-e.g., posttreatment shifts toward Clostridioides difficile infections in the gut-after antibiotic exposure is poorly understood. We study community response to antibiotics using a model community that can reach two alternative states. Guided by theory, our experiments show that microbial growth following antibiotic exposure can counteract antibiotic susceptibility in driving transitions between alternative community states. This makes it possible to reverse the outcome of antibiotic exposure through modifying growth dynamics, including cooperative growth, of community members. Our research highlights the relevance of simple ecological models to better understand the long-term effects of antibiotic treatment.

The virota and its transkingdom interactions in the healthy infant gut

SignificanceMicrobes colonizing the infant gut during the first year(s) of life play an important role in immune system development. We show that after birth the (nearly) sterile gut is rapidly colonized by bacteria and their viruses (phages), which often show a strong cooccurrence. Most viruses infecting the infant do not cause clinical signs and their numbers strongly increase after day-care entrance. The infant diet is clearly reflected by identification of plant-infecting viruses, whereas fungi and parasites are not part of a stable gut microbiota. These temporal high-resolution baseline data about the gut colonization process will be valuable for further investigations of pathogenic viruses, dynamics between phages and their bacterial host, as well as studies investigating infants with a disturbed microbiota.

Temperature increase drives critical slowing down of fish ecosystems

Fish ecosystems perform ecological functions that are critically important for the sustainability of marine ecosystems, such as global food security and carbon stock. During the 21st century, significant global warming caused by climate change has created pressing challenges for fish ecosystems that threaten species existence and global ecosystem health. Here, we study a coastal fish community in Maizuru Bay, Japan, and investigate the relationships between fluctuations of ST, abundance-based species interactions and salient fish biodiversity. Observations show that a local 20% increase in temperature from 2002 to 2014 underpins a long-term reduction in fish diversity (∼25%) played out by some native and invasive species (e.g. Chinese wrasse) becoming exceedingly abundant; this causes a large decay in commercially valuable species (e.g. Japanese anchovy) coupled to an increase in ecological productivity. The fish community is analyzed considering five temperature ranges to understand its atemporal seasonal sensitivity to ST changes, and long-term trends. An optimal information flow model is used to reconstruct species interaction networks that emerge as topologically different for distinct temperature ranges and species dynamics. Networks for low temperatures are more scale-free compared to ones for intermediate (15-20°C) temperatures in which the fish ecosystem experiences a first-order phase transition in interactions from locally stable to metastable and globally unstable for high temperatures states as suggested by abundance-spectrum transitions. The dynamic dominant eigenvalue of species interactions shows increasing instability for competitive species (spiking in summer due to intermediate-season critical transitions) leading to enhanced community variability and critical slowing down despite higher time-point resilience. Native competitive species whose abundance is distributed more exponentially have the highest total directed interactions and are keystone species (e.g. Wrasse and Horse mackerel) for the most salient links with cooperative decaying species. Competitive species, with higher eco-climatic memory and synchronization, are the most affected by temperature and play an important role in maintaining fish ecosystem stability via multitrophic cascades (via cooperative-competitive species imbalance), and as bioindicators of change. More climate-fitted species follow temperature increase causing larger divergence divergence between competitive and cooperative species. Decreasing dominant eigenvalues and lower relative network optimality for warmer oceans indicate fishery more attracted toward persistent oscillatory states, yet unpredictable, with lower cooperation, diversity and fish stock despite the increase in community abundance due to non-commercial and venomous species. We emphasize how changes in species interaction organization, primarily affected by temperature fluctuations, are the backbone of biodiversity dynamics and yet for functional diversity in contrast to taxonomic richness. Abundance and richness manifest gradual shifts while interactions show sudden shift. The work provides data-driven tools for analyzing and monitoring fish ecosystems under the pressure of global warming or other stressors. Abundance and interaction patterns derived by network-based analyses proved useful to assess ecosystem susceptibility and effective change, and formulate predictive dynamic information for science-based fishery policy aimed to maintain marine ecosystems stable and sustainable.

Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

Microbial communities found in nature are composed of many rare species and few abundant ones, as reflected by their heavy-tailed abundance distributions. How a large number of species can coexist in those complex communities and why they are dominated by rare species is still not fully understood. We show how heavy-tailed distributions arise as an emergent property from large communities with many interacting species in population-level models. To do so, we rely on generalized Lotka-Volterra models for which we introduce a global maximal capacity. This maximal capacity accounts for the fact that communities are limited by available resources and space. In a parallel ad hoc approach, we obtain heavy-tailed abundance distributions from logistic models, without interactions, through specific distributions of the parameters. We expect both mechanisms, interactions between many species and specific parameter distributions, to be relevant to explain the observed heavy tails.

Persistence of functional microbiota composition across generations

Holobionts are defined as a host and its microbiota, however, only a fraction of the bacteria are inherited vertically and thus coevolve with the host. The "it's the song, not the singer" theory proposes that functional traits, instead of taxonomical microbiota composition, could be preserved across generations if interspecies interaction patterns perpetuate themselves. We tested conservation of functional composition across generations using zooplankton, mosquito, and plant datasets. Then, we tested if there is a change of functional microbiota composition over time within a generation in human datasets. Finally, we simulated microbiota communities to investigate if (pairwise) interactions can lead to multiple stable community compositions. Our results suggest that the vertically transmitted microbiota starts a predictable change of functions performed by the microbiota over time, whose robustness depends on the arrival of diverse migrants. This succession culminates in a stable functional composition state. The results suggest that the host-microbiota interaction and higher order interactions in general have an important contribution to the robustness of the final community. If the proposed mechanism proves to be valid for a diverse array of host species, this would support the concept of holobionts being used as units of selection, including animal breeding, suggesting this has a wider applicability.

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.

Stochastic logistic models reproduce experimental time series of microbial communities

We analyze properties of experimental microbial time series, from plankton and the human microbiome, and investigate whether stochastic generalized Lotka-Volterra models could reproduce those properties. We show that this is the case when the noise term is large and a linear function of the species abundance, while the strength of the self-interactions varies over multiple orders of magnitude. We stress the fact that all the observed stochastic properties can be obtained from a logistic model, that is, without interactions, even the niche character of the experimental time series. Linear noise is associated with growth rate stochasticity, which is related to changes in the environment. This suggests that fluctuations in the sparsely sampled experimental time series may be caused by extrinsic sources.

Slow Waves in Cortical Slices: How Spontaneous Activity is Shaped by Laminar Structure

Cortical slow oscillations (SO) of neural activity spontaneously emerge and propagate during deep sleep and anesthesia and are also expressed in isolated brain slices and cortical slabs. We lack full understanding of how SO integrate the different structural levels underlying local excitability of cell assemblies and their mutual interaction. Here, we focus on ongoing slow waves (SWs) in cortical slices reconstructed from a 16-electrode array designed to probe the neuronal activity at multiple spatial scales. In spite of the variable propagation patterns observed, we reproducibly found a smooth strip of loci leading the SW fronts, overlapping cortical layers 4 and 5, along which Up states were the longest and displayed the highest firing rate. Propagation modes were uncorrelated in time, signaling a memoryless generation of SWs. All these features could be modeled by a multimodular large-scale network of spiking neurons with a specific balance between local and intermodular connectivity. Modules work as relaxation oscillators with a weakly stable Down state and a peak of local excitability to model layers 4 and 5. These conditions allow for both optimal sensitivity to the network structure and richness of propagation modes, both of which are potential substrates for dynamic flexibility in more general contexts.

Signatures of ecological processes in microbial community time series

BACKGROUND

Growth rates, interactions between community members, stochasticity, and immigration are important drivers of microbial community dynamics. In sequencing data analysis, such as network construction and community model parameterization, we make implicit assumptions about the nature of these drivers and thereby restrict model outcome. Despite apparent risk of methodological bias, the validity of the assumptions is rarely tested, as comprehensive procedures are lacking. Here, we propose a classification scheme to determine the processes that gave rise to the observed time series and to enable better model selection.

RESULTS

We implemented a three-step classification scheme in R that first determines whether dependence between successive time steps (temporal structure) is present in the time series and then assesses with a recently developed neutrality test whether interactions between species are required for the dynamics. If the first and second tests confirm the presence of temporal structure and interactions, then parameters for interaction models are estimated. To quantify the importance of temporal structure, we compute the noise-type profile of the community, which ranges from black in case of strong dependency to white in the absence of any dependency. We applied this scheme to simulated time series generated with the Dirichlet-multinomial (DM) distribution, Hubbell's neutral model, the generalized Lotka-Volterra model and its discrete variant (the Ricker model), and a self-organized instability model, as well as to human stool microbiota time series. The noise-type profiles for all but DM data clearly indicated distinctive structures. The neutrality test correctly classified all but DM and neutral time series as non-neutral. The procedure reliably identified time series for which interaction inference was suitable. Both tests were required, as we demonstrated that all structured time series, including those generated with the neutral model, achieved a moderate to high goodness of fit to the Ricker model.

CONCLUSIONS

We present a fast and robust scheme to classify community structure and to assess the prevalence of interactions directly from microbial time series data. The procedure not only serves to determine ecological drivers of microbial dynamics, but also to guide selection of appropriate community models for prediction and follow-up analysis.

Ecological communities with Lotka-Volterra dynamics

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

Coordination Dynamics in Cognitive Neuroscience

Many researchers and clinicians in cognitive neuroscience hold to a modular view of cognitive function in which the cerebral cortex operates by the activation of areas with circumscribed elementary cognitive functions. Yet an ongoing paradigm shift to a dynamic network perspective is underway. This new viewpoint treats cortical function as arising from the coordination dynamics within and between cortical regions. Cortical coordination dynamics arises due to the unidirectional influences imposed on a cortical area by inputs from other areas that project to it, combined with the projection reciprocity that characterizes cortical connectivity and gives rise to reentrant processing. As a result, cortical dynamics exhibits both segregative and integrative tendencies and gives rise to both cooperative and competitive relations within and between cortical areas that are hypothesized to underlie the emergence of cognition in brains.

An exploration of the relationships between microalgae biomass growth and related environmental variables

Algal community plays critical roles as the primary producer and as a major biotic component in the nutrient/energy cycle in aquatic ecosystems. The potential of fresh water algal biomass to mitigate global problems of food and energy and its significance as a carbon sink have been recognized. In this study, with a view to decreasing the cost of producing algal biomass for various purposes, the natural medium of unsupplemented freshwater was applied to mimic the real world to produce algal biomass. The relevant physicochemical variables in the improvised algal growth environment were analyzed and monitored, to investigate the algal growth mechanism. The simple regression analysis showed the applicability of the unsupplemented natural medium with sufficient natural nutrition for algal biomass production. The multiple linear analyses explained the complexity of the mimicked freshwater mixed-algal community in the laboratory. The laboratory results obtained in the present study also provide better insights that improve our understanding of the natural algal growth characteristics.

Language extinction and linguistic fronts

Language diversity has become greatly endangered in the past centuries owing to processes of language shift from indigenous languages to other languages that are seen as socially and economically more advantageous, resulting in the death or doom of minority languages. In this paper, we define a new language competition model that can describe the historical decline of minority languages in competition with more advantageous languages. We then implement this non-spatial model as an interaction term in a reaction–diffusion system to model the evolution of the two competing languages. We use the results to estimate the speed at which the more advantageous language spreads geographically, resulting in the shrinkage of the area of dominance of the minority language. We compare the results from our model with the observed retreat in the area of influence of the Welsh language in the UK, obtaining a good agreement between the model and the observed data.

The dynamics of assembling food webs

Community assembly is central to ecology, yet ecologists have amassed little quantitative information about how food webs assemble. Theory holds that colonisation rate is a primary driver of community assembly. We present new data from a mesocosm experiment to test the hypothesis that colonisation rate also determines the assembly dynamics of food webs. By manipulating colonisation rate and measuring webs through time, we show how colonisation rate governs structural changes during assembly. Webs experiencing different colonisation rates had stable topologies despite significant species turnover, suggesting that some features of network architecture emerge early and change little through assembly. But webs experiencing low colonisation rates showed less variation in the magnitudes of trophic fluxes, and were less likely to develop coupled fast and slow resource channels--a common feature of published webs. Our results reveal that food web structure develops according to repeatable trajectories that are strongly influenced by colonisation rate.

Emergence of structural patterns in neutral trophic networks

Interaction networks are central elements of ecological systems and have very complex structures. Historically, much effort has focused on niche-mediated processes to explain these structures, while an emerging consensus posits that both niche and neutral mechanisms simultaneously shape many features of ecological communities. However, the study of interaction networks still lacks a comprehensive neutral theory. Here we present a neutral model of predator-prey interactions and analyze the structural characteristics of the simulated networks. We find that connectance values (complexity) and complexity-diversity relationships of neutral networks are close to those observed in empirical bipartite networks. High nestedness and low modularity values observed in neutral networks fall in the range of those from empirical antagonist bipartite networks. Our results suggest that, as an alternative to niche-mediated processes that induce incompatibility between species ("niche forbidden links"), neutral processes create "neutral forbidden links" due to uneven species abundance distributions and the low probability of interaction between rare species. Neutral trophic networks must be seen as the missing endpoint of a continuum from niche to purely stochastic approaches of community organization.

Spatial effects on species persistence and implications for biodiversity

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time, and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species persistence times, defined as the time spans between local colonizations and extinctions in a given geographic region. Empirical distributions pertaining to two different taxa, breeding birds and herbaceous plants, analyzed in a framework that accounts for the finiteness of the observational period exhibit power-law scaling limited by a cutoff determined by the rate of emergence of new species. In spite of the differences between taxa and spatial scales of analysis, the scaling exponents are statistically indistinguishable from each other and significantly different from those predicted by existing models. We theoretically investigate how the scaling features depend on the structure of the spatial interaction network and show that the empirical scaling exponents are reproduced once a two-dimensional isotropic texture is used, regardless of the details of the ecological interactions. The framework developed here also allows to link the cutoff time scale with the spatial scale of analysis, and the persistence-time distribution to the species-area relationship. We conclude that the inherent coherence obtained between spatial and temporal macroecological patterns points at a seemingly general feature of the dynamical evolution of ecosystems.

Simple model of recovery dynamics after mass extinction

Biotic recoveries following mass extinctions are characterized by a complex set of dynamics, including the rebuilding of whole ecologies from low-diversity assemblages of survivors and opportunistic species. Three broad classes of diversity dynamics during recovery have been suggested: an immediate linear response, a logistic recovery, and a simple positive feedback pattern of species interaction. Here we present a simple model of recovery which generates these three scenarios via differences in the extent of species interactions, thus capturing the dynamical logic of the recovery pattern. The model results indicate that the lag time to biotic recovery increases significantly as biotic interactions become more important in the recovery process.

Diversity, competition, extinction: the ecophysics of language change

As indicated early by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of information exchanges and communicative constraints in groups of agents under selective scenarios. These models have been very helpful in providing a rationale on how complex forms of communication emerge under evolutionary pressures. However, other patterns of large-scale organization can be described using mathematical methods ignoring communicative traits. These approaches consider shorter time scales and have been developed by exploiting both theoretical ecology and statistical physics methods. The models are reviewed here and include extinction, invasion, origination, spatial organization, coexistence and diversity as key concepts and are very simple in their defining rules. Such simplicity is used in order to catch the most fundamental laws of organization and those universal ingredients responsible for qualitative traits. The similarities between observed and predicted patterns indicate that an ecological theory of language is emerging, supporting (on a quantitative basis) its ecological nature, although key differences are also present. Here, we critically review some recent advances and outline their implications and limitations as well as highlight problems for future research.

Origin of Pareto-like spatial distributions in ecosystems

Recent studies of cluster distribution in various ecosystems revealed Pareto statistics for the size of spatial colonies. These results were supported by cellular automata simulations that yield robust criticality for endogenous pattern formation based on positive feedback. We show that this patch statistics is a manifestation of the law of proportionate effect. Mapping the stochastic model to a Markov birth-death process, the transition rates are shown to scale linearly with cluster size. This mapping provides a connection between patch statistics and the dynamics of the ecosystem; the "first passage time" for different colonies emerges as a powerful tool that discriminates between endogenous and exogenous clustering mechanisms. Imminent catastrophic shifts (such as desertification) manifest themselves in a drastic change of the stability properties of spatial colonies.

Rank abundance relations in evolutionary dynamics of random replicators

We present a nonequilibrium statistical mechanics description of rank abundance relations (RAR) in random community models of ecology. Specifically, we study a multispecies replicator system with quenched random interaction matrices. We here consider symmetric interactions as well as asymmetric and antisymmetric cases. RARs are obtained analytically via a generating functional analysis, describing fixed-point states of the system in terms of a small set of order parameters, and in dependence on the symmetry or otherwise of interactions and on the productivity of the community. Our work is an extension of Tokita [Phys. Rev. Lett. 93, 178102 (2004)], where the case of symmetric interactions was considered within an equilibrium setup. The species abundance distribution in our model come out as truncated normal distributions or transformations thereof and, in some case, are similar to left-skewed distributions observed in ecology. We also discuss the interaction structure of the resulting food-web of stable species at stationarity, cases of heterogeneous cooperation pressures as well as effects of finite system size and of higher-order interactions.

Reconciling empirical ecology with neutral community models

Neutral community models embody the idea that individuals are ecologically equivalent, having equal fitness over all environmental conditions, and describe how the spatial dynamics and speciation of such individuals can produce a wide range of patterns of distribution, diversity, and abundance. Neutral models have been controversial, provoking a rush of tests and comments. The debate has been spurred by the suggestion that we should test mechanisms. However, the mechanisms and the spatial scales of interest have never clearly been described, and consequently, the tests have often been only peripherally relevant. At least two mechanisms are present in spatially structured neutral models. Dispersal limitation causes clumping of a species, which increases the strength of intraspecific competition and reduces the strength of interspecific competition. This may prolong coexistence and enhance local and regional diversity. Speciation is present in some neutral models and gives a donor-controlled input of new species, many of which remain rare or are short lived, but which directly add to species diversity. Spatial scale is an important consideration in neutral models. Ecological equivalence and equal fitness have implicit spatial scales because dispersal limitation and its emergent effects operate at population levels, and populations and communities are defined at a chosen spatial scale in recent neutral models; equality is measured relative to a metacommunity, and this necessitates defining the spatial scale of that metacommunity. Furthermore, dispersal has its own scales. Thorough empirical tests of neutral models will require both tests of mechanisms and pattern-producing ability, and will involve coupling theoretical models and experiments.

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.