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1. Dispersal is a central life history trait that affects the ecological and evolutionary dynamics of populations and communities. The recent use of experimental evolution for the study of dispersal is a promising avenue for demonstrating valuable proofs of concept, bringing insight into alternative dispersal strategies and tradeoffs, and testing the repeatability of evolutionary outcomes. 2. Practical constraints restrict experimental evolution studies of dispersal to a set of typically small, short-lived organisms reared in artificial laboratory conditions. Here, we argue that despite these restrictions, inferences from these studies can reinforce links between theoretical predictions and empirical observations and advance our understanding of the eco-evolutionary consequences of dispersal. 3. We illustrate how applying an integrative framework of theory, experimental evolution and natural systems can improve our understanding of dispersal evolution under more complex and realistic biological scenarios, such as the role of biotic interactions and complex dispersal syndromes.

Microbe-mediated transformations of arsenic (As) often require As to be taken up into cells prior to enzymatic reaction. Despite the importance of these microbial reactions for As speciation and toxicity, understanding of how As bioavailability and uptake are regulated by aspects of extracellular water chemistry, notably dissolved organic matter (DOM), remains limited. Whole-cell biosensors utilizing fluorescent proteins are increasingly used for high-throughput quantification of the bioavailable fraction of As in water. Here, we present a mathematical framework for interpreting the time series of biosensor fluorescence as a measure of As uptake kinetics, which we used to evaluate the effects of different forms of DOM on uptake of trivalent arsenite. We found that thiol-containing organic compounds significantly inhibited uptake of arsenite into cells, possibly through the formation of aqueous complexes between arsenite and thiol ligands. While there was no evidence for competitive interactions between arsenite and low-molecular-weight neutral molecules (urea, glycine, and glyceraldehyde) for uptake through the aquaglyceroporin channel GlpF, which mediates transport of arsenite across cell membranes, there was evidence that labile DOM fractions may inhibit arsenite uptake through a catabolite repression-like mechanism. The observation of significant inhibition of arsenite uptake at DOM/As ratios commonly encountered in wetland pore waters suggests that DOM may be an important control on the microbial uptake of arsenite in the environment, with aspects of DOM quality playing an important role in the extent of inhibition. IMPORTANCE The speciation and toxicity of arsenic in environments like rice paddy soils and groundwater aquifers are controlled by microbe-mediated reactions. These reactions often require As to be taken up into cells prior to enzymatic reaction, but there is limited understanding of how microbial arsenic uptake is affected by variations in water chemistry. In this study, we explored the effect of dissolved organic matter (DOM) quantity and quality on microbial As uptake, with a focus on the role of thiol functional groups that are well known to form aqueous complexes with arsenic. We developed a quantitative framework for interpreting fluorescence time series from whole-cell biosensors and used this technique to evaluate effects of DOM on the rates of microbial arsenic uptake. We show that thiol-containing compounds significantly decrease rates of As uptake into microbial cells at environmentally relevant DOM/As ratios, revealing the importance of DOM quality in regulating arsenic uptake, and subsequent biotransformation, in the environment.

Microbial communities are ubiquitous and play crucial roles in many natural processes. Despite their importance for the environment, industry and human health, there are still many aspects of microbial community dynamics that we do not understand quantitatively. Recent experiments have shown that the structure and composition of microbial communities are intertwined with the metabolism of the species that inhabit them, suggesting that properties at the intracellular level such as the allocation of cellular proteomic resources must be taken into account when describing microbial communities with a population dynamics approach. In this work, we reconsider one of the theoretical frameworks most commonly used to model population dynamics in competitive ecosystems, MacArthur’s consumer-resource model, in light of experimental evidence showing how proteome allocation affects microbial growth. This new framework allows us to describe community dynamics at an intermediate level of complexity between classical consumer-resource models and biochemical models of microbial metabolism, accounting for temporally-varying proteome allocation subject to constraints on growth and protein synthesis in the presence of multiple resources, while preserving analytical insight into the dynamics of the system. We first show with a simple experiment that proteome allocation needs to be accounted for to properly understand the dynamics of even the simplest microbial community, i.e. two bacterial strains competing for one common resource. Then, we study our consumer-proteome-resource model analytically and numerically to determine the conditions that allow multiple species to coexist in systems with arbitrary numbers of species and resources.

Aquatic microbial communities contribute fundamentally to biogeochemical transformations in natural ecosystems, and disruption of these communities can lead to ecological disasters such as harmful algal blooms. Microbial communities are highly dynamic, and their composition and function are tightly controlled by the biophysical (e.g., light, fluid flow, and temperature) and biochemical (e.g., chemical gradients and cell concentration) parameters of the surrounding environment. Due to the large number of environmental factors involved, a systematic understanding of the microbial community-environment interactions is lacking. In this article, we show that microfluidic platforms present a unique opportunity to recreate well-defined environmental factors in a laboratory setting in a high throughput way, enabling quantitative studies of microbial communities that are amenable to theoretical modeling. The focus of this article is on aquatic microbial communities, but the microfluidic and mathematical models discussed here can be readily applied to investigate other microbiomes.

Significance Empirical laws predicting metabolic rates of a species by its average body mass neglect intraspecies variability arising from the range of physiologically feasible rates and phenotypic heterogeneity. We describe an exploratory experimental test of a theory that explicitly accounts for such variations. We show, by single-cell joint measurements of mass and uptake rates, how marginal distributions of mass and rates collapse onto a common master distribution for species spanning 3 orders of magnitude in cell volume. These results demonstrate the potential of a generalized scaling theory that goes beyond population averages to incorporate within-species variation., Kleiber’s law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber’s law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber’s law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber’s law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR. (C) 2018 The Authors. Published by Elsevier Ltd.

Antagonistic interactions are widespread in the microbial world and affect microbial evolutionary dynamics. Natural microbial communities often display spatial structure, which affects biological interactions, but much of what we know about microbial warfare comes from laboratory studies of well-mixed communities. To overcome this limitation, we manipulated two killer strains of the budding yeast Saccharomyces cerevisiae, expressing different toxins, to independently control the rate at which they released their toxins. We developed mathematical models that predict the experimental dynamics of competition between toxin-producing strains in both well-mixed and spatially structured populations. In both situations, we experimentally verified theory’s prediction that a stronger antagonist can invade a weaker one only if the initial invading population exceeds a critical frequency or size. Finally, we found that toxin-resistant cells and weaker killers arose in spatially structured competitions between toxin-producing strains, suggesting that adaptive evolution can affect the outcome of microbial antagonism in spatial settings.

Microbial communities are ubiquitous and play crucial roles in many natural processes. Despite their importance for the environment, industry and human health, there are still many aspects of microbial community dynamics that we do not understand quantitatively. Recent experiments have shown that the metabolism of species in a community is intertwined with its composition, suggesting that properties at the intracellular level such as the allocation of cellular proteomic resources must be taken into account when describing microbial communities with a population dynamics approach. In this work we reconsider one of the theoretical frameworks most commonly used to model population dynamics in competitive ecosystems, MacArthur’s consumer-resource model, in light of experimental evidence showing how pro-teome allocation affects microbial growth. This new framework allows us to describe community dynamics at an intermediate level of complexity between classical consumer-resource models and biochemical models of microbial metabolism, accounting for temporally-varying proteome allocation subject to constraints on growth and protein synthesis in the presence of multiple resources, while preserving analytical insight into the dynamics of the system. We first show experimentally that proteome allocation needs to be accounted for to properly understand the dynamics of even the simplest microbial community, i.e. two bacterial strains competing for one common resource. We then study the model analytically and numerically to determine the conditions that allow multiple species to coexist in systems with arbitrary numbers of species and resources.

Significance Microbes often live in dense populations such as colonies and biofilms. We show that the success and extinction of yeast strains within a growing colony are determined by a combination of their relative fitness and the forces exerted by proliferating cells on their neighbors. These physical interactions prolong the survival of less-fit strains at the growing frontier of the colony and slow down the colony’s takeover by fitter strains. This reduction in the power of natural selection favors the maintenance of genetic diversity in environments in which the strains’ relative growth rates vary with time. Growth-induced physical interactions may thus favor the maintenance of drug-resistant cells, which are typically less fit than nonresistant cells, within dense microbial populations., Microbial populations often assemble in dense populations in which proliferating individuals exert mechanical forces on the nearby cells. Here, we use yeast strains whose doubling times depend differently on temperature to show that physical interactions among cells affect the competition between different genotypes in growing yeast colonies. Our experiments demonstrate that these physical interactions have two related effects: they cause the prolonged survival of slower-growing strains at the actively-growing frontier of the colony and cause faster-growing strains to increase their frequency more slowly than expected in the absence of physical interactions. These effects also promote the survival of slower-growing strains and the maintenance of genetic diversity in colonies grown in time-varying environments. A continuum model inspired by overdamped hydrodynamics reproduces the experiments and predicts that the strength of natural selection depends on the width of the actively growing layer at the colony frontier. We verify these predictions experimentally. The reduced power of natural selection observed here may favor the maintenance of drug-resistant cells in microbial populations and could explain the apparent neutrality of interclone competition within tumors.

Bacteria are able to adapt to different environments by changing their “metabolic strategies”, i.e. the ways in which they uptake available resources from the environment. For example, in a celebrated experiment Jacques Monod showed that bacteria cultured in media containing two different sugars consume them sequentially, resulting in bi-phasic growth curves called “diauxic shifts”. From the theoretical point of view, microbial communities are commonly described using MacArthur’s consumer-resource model, which describes the population dynamics of species competing for a given set of resources. In this model, however, metabolic strategies are treated as constant parameters. Here, we introduce adaptive metabolic strategies in the framework of consumer-resource models, allowing the strategies to evolve to maximize each species’ relative fitness. By doing so, we are able to describe quantitatively, and without invoking any specific molecular mechanisms for the metabolism of the microbial species, growth curves of the baker’s yeastSaccharomyces cerevisiaemeasured in a controlled experimental set-up, with galactose as the primary carbon source. We also show that metabolic adaptation enables the community to self-organize, allowing species to coexist even in the presence of few resources, and to respond optimally to a time-dependent environment. A connection between the Competitive Exclusion Principle and the metabolic theory of ecology is also discussed.

Phototaxis, the process through which motile organisms direct their swimming toward or away from light, is implicated in key ecological phenomena (including algal blooms and diel vertical migration) that shape the distribution, diversity, and productivity of phytoplankton and thus energy transfer to higher trophic levels in aquatic ecosystems. Phototaxis also finds important applications in biofuel reactors and microbiopropellers and is argued to serve as a benchmark for the study of biological invasions in heterogeneous environments owing to the ease of generating stochastic light fields. Despite its ecological and technological relevance, an experimentally tested, general theoretical model of phototaxis seems unavailable to date. Here, we present accurate measurements of the behavior of the alga Euglena gracilis when exposed to controlled light fields. Analysis of E. gracilis' phototactic accumulation dynamics over a broad range of light intensities proves that the classic Keller-Segel mathematical framework for taxis provides an accurate description of both positive and negative phototaxis only when phototactic sensitivity is modeled by a generalized "receptor law," a specific nonlinear response function to light intensity that drives algae toward beneficial light conditions and away from harmful ones. The proposed phototactic model captures the temporal dynamics of both cells' accumulation toward light sources and their dispersion upon light cessation. The model could thus be of use in integrating models of vertical phytoplankton migrations in marine and freshwater ecosystems, and in the design of bioreactors.

Taylor's law (TL) states that the variance $V$ of a non-negative random variable is a power function of its mean $M$, i.e. $V=a M^b$. The ubiquitous empirical verification of TL, typically displaying sample exponents $b \simeq 2$, suggests a context-independent mechanism. However, theoretical studies of population dynamics predict a broad range of values of $b$. Here, we explain this apparent contradiction by using large deviations theory to derive a generalized TL in terms of sample and populations exponents $b_{jk}$ for the scaling of the $k$-th vs the $j$-th cumulant (conventional TL is recovered for $b=b_{12}$), with the sample exponent found to depend predictably on the number of observed samples. Thus, for finite numbers of observations one observes sample exponents $b_{jk}\simeq k/j$ (thus $b\simeq2$) independently of population exponents. Empirical analyses on two datasets support our theoretical results., Comment: 41 pages, 10 figures, 6 tables

Biological dispersal shapes species’ distribution and affects their coexistence. The spread of organisms governs the dynamics of invasive species, the spread of pathogens, and the shifts in species ranges due to climate or environmental change. Despite its relevance for fundamental ecological processes, however, replicated experimentation on biological dispersal is lacking, and current assessments point at inherent limitations to predictability, even in the simplest ecological settings. In contrast, we show, by replicated experimentation on the spread of the ciliate Tetrahymena sp. in linear landscapes, that information on local unconstrained movement and reproduction allows us to predict reliably the existence and speed of traveling waves of invasion at the macroscopic scale. Furthermore, a theoretical approach introducing demographic stochasticity in the Fisher–Kolmogorov framework of reaction–diffusion processes captures the observed fluctuations in range expansions. Therefore, predictability of the key features of biological dispersal overcomes the inherent biological stochasticity. Our results establish a causal link from the short-term individual level to the long-term, broad-scale population patterns and may be generalized, possibly providing a general predictive framework for biological invasions in natural environments.

Habitat fragmentation and land use changes are causing major biodiversity losses. Connectivity of the landscape or environmental conditions alone can shape biodiversity patterns. In nature however local habitat characteristics are often intrinsically linked to a specific connectivity. Such a link is evident in riverine ecosystems where hierarchical dendritic structures command related scaling on habitat capacity. We experimentally disentangled the effect of local habitat capacity (i.e. the patch size) and dendritic connectivity on biodiversity in aquatic microcosm metacommunities by suitably arranging patch sizes within river like networks. Overall more connected communities that occupy a central position in the network exhibited higher species richness irrespective of patch size arrangement. High regional evenness in community composition was found only in landscapes preserving geomorphological scaling properties of patch sizes. In these landscapes some of the rarer species sustained regionally more abundant populations better tracking their own niche requirements compared to landscapes with homogeneous patch size or landscapes with spatially uncorrelated patch size. Our analysis suggests that altering the natural link between dendritic connectivity and patch size strongly affects community composition and population persistence at multiple scales. The experimental results are demonstrating a principle that can be tested in theoretical metacommunity models and eventually be projected to real riverine ecosystems. © 2013 by The University of Chicago.

Classical models of biological invasions assess species spread in homogeneous landscapes by assuming constant growth rates and random local movement. Mounting evidence suggests, however, that demographic stochasticity, environmental heterogeneity and non-random movement of individuals affect considerably the spread dynamics. Here, we show that the dynamics of biological invasions are controlled by the spatial heterogeneity of the resource distribution. We show theoretically that increasing the landscape resource autocorrelation length causes a reduction in the average speed of species spread. Demographic stochasticity plays a key role in the slowdown, which is streghtened when individuals can actively move towards resources. The reduction in the front propagation speed is verified in laboratory microcosm experiments with the flagellated protistEuglena gracilisby comparing spread in habitats characterized by different resource heterogeneity. Our theoretical and experimental findings highlight the need to account for the intrinsic stochasticity of population dynamics to describe spread in spatially extended landscapes, which are inevitably characterized by heterogeneous spatial distributions of resources controlling vital rates. Our work identifies the resource autocorrelation length as a key modulator and a simple measure of landscape susceptibility to biological invasions, with implications for predicting the characters of biological invasions within naturally heterogeneous environmental corridors.

1. Natural communities commonly contain many different species and functional groups, and multiple types of species interactions act simultaneously, such as competition, predation, commensalism or mutualism. However, experimental and theoretical investigations have generally been limited by focusing on one type of interaction at a time or by a lack of a common methodological and conceptual approach to measure species interactions. 2. We compared four methods to measure and express species interactions. These approaches are, with increasing degree of model complexity, an extinction-based model, a relative yield model and two generalized Lotka-Volterra (LV) models. All four approaches have been individually applied in different fields of community ecology, but rarely integrated. We provide an overview of the definitions, assumptions and data needed for the specific methods and apply them to empirical data by experimentally deriving the interaction matrices among 11 protist and rotifer species, belonging to three functional groups. Furthermore, we compare their advantages and limitations to predict multispecies community dynamics and ecosystem functioning. 3. The relative yield method is, in terms of final biomass production, the best method in predicting the 11-species community dynamics from the pairwise competition experiments. The LV model, which is considering equilibrium among the species, suffers from experimental constraints given the strict equilibrium assumption, and this may be rarely satisfied in ecological communities. 4. We show how simulations of a LV stochastic community model, derived from an empirical interaction matrix, can be used to predict multispecies community dynamics across multiple functional groups. 5.Our work unites available tools to measure species interactions under one framework. This improves our ability to make management-oriented predictions of species coexistence/extinction and to compare ecosystem processes across study systems.

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.

We reinvestigate the Deterministic Lattice Gas introduced as a paradigmatic model of the 1/f spectra (Phys. Rev. Lett. V26, 3103 (1990)) arising according to the Self-Organized Criticality scenario. We demonstrate that the density fluctuations exhibit an unexpected dependence on systems size and relate the finding to effective Langevin equations. The low density behavior is controlled by the critical properties of the gas at the absorbing state phase transition. We also show that the Deterministic Lattice Gas is in the Manna universality class of absorbing state phase transitions. This is in contrast to expectations in the literature which suggested that the entirely deterministic nature of the dynamics would put the model in a different universality class. To our knowledge this is the first fully deterministic member of the Manna universality class., 8 pages, 12 figures. Changes in the new version: Reference list has been corrected

Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide. To model the effects of this increase, it is crucial to understand whether possible self-organized patterns are inherent in the global road network structure. Here, we use the largest updated database comprising all major roads on the Earth, together with global urban and cropland inventories, to suggest that road length distributions within croplands are indistinguishable from urban ones, once rescaled to account for the difference in mean road length. Such similarity extends to road length distributions within urban or agricultural domains of a given area. We find two distinct regimes for the scaling of the mean road length with the associated area, holding in general at small and at large values of the latter. In suitably large urban and cropland domains, we find that mean and total road lengths increase linearly with their domain area, differently from earlier suggestions. Scaling regimes suggest that simple and universal mechanisms regulate urban and cropland road expansion at the global scale. As such, our findings bear implications for global road infrastructure growth based on land-use change and for planning policies sustaining urban expansions.

Unveiling the mechanisms that promote coexistence in biological communities is a fundamental problem in ecology. Stable coexistence of many species is commonly observed in natural communities. Most of these natural communities, however, are composed of species from multiple trophic and functional groups, while theory and experiments on coexistence have been focusing on functionally similar species. Here, we investigated how functional diversity affects the stability of species coexistence and productivity in multispecies communities by characterizing experimentally all pairwise species interactions in a pool of 11 species of eukaryotes (10 protists and one rotifer) belonging to three different functional groups. Species within the same functional group showed stronger competitive interactions compared to among-functional group interactions. This often led to competitive exclusion between species that had higher functional relatedness, but only at low levels of species richness. Communities with higher functional diversity resulted in increased species coexistence and community biomass production. Our experimental findings and the results of a stochastic model tailored to the experimental interaction matrix suggest the emergence of strong stabilizing forces when species from different functional groups interact in a homogeneous environment. By combining theoretical analysis with experiments we could also disentangle the relationship between species richness and functional diversity, showing that functional diversity per se is a crucial driver of productivity and stability in multispecies community.

Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked had been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such framework is consistent with the stationary state statistics of a broad class of resource-limited community dynamics models, regardless of parametrization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations., Comment: S.Z. and A.G. contributed equally to this work