Ecological networks. On the structural stability of mutualistic systems

Estimating genus-specific effects of non-native honey bees and urbanization on wild bee communities: A case study in Maryland, United States

Non-native species have the potential to detrimentally affect native species through resource competition, disease transmission, and other forms of antagonism. The western honey bee (Apis mellifera) is one such species that has been widely introduced beyond its native range for hundreds of years. There are strong concerns in the United States, and other countries, about the strain that high-density, managed honey bee populations could pose to already imperiled wild bee communities. While there is some experimental evidence of honey bees competing with wild bees for resources, few studies have connected landscape-scale honey bee apiary density with down-stream consequences for wild bee communities. Here, using a dataset from Maryland, US and joint species distribution models, we provide the largest scale, most phylogenetically resolved assessment of non-native honey bee density effects on wild bee abundance to date. As beekeeping in Maryland primarily consists of urban beekeeping, we also assessed the relative impact of developed land on wild bee communities. Six of the 33 wild bee genera we assessed showed a high probability (> 90 %) of a negative association with apiary density and/or developed land. These bees were primarily late-season, specialist genera (several long-horned genera represented) or small, ground nesting, season-long foragers (including several sweat bee genera). Conversely, developed land was associated with an increase in relative abundance for some genera including invasive Anthidium and other urban garden-associated genera. We discuss several avenues to ameliorate potentially detrimental effects of beekeeping and urbanization on the most imperiled wild bee groups. We additionally offer methodological insights based on sampling efficiency of different methods (hand netting, pan trapping, vane trapping), highlighting large variation in effect sizes across genera. The magnitude of sampling effect was very high, relative to the observed ecological effects, demonstrating the importance of integrated sampling, particularly for multi-species or community level assessments.

Soil microbial influences over coexistence potential in multispecies plant communities in a subtropical forest

Soil microbes have long been recognized to substantially affect the coexistence of pairwise plant species across terrestrial ecosystems. However, projecting their impacts on the coexistence of multispecies plant systems remains a pressing challenge. To address this challenge, we conducted a greenhouse experiment with 540 seedlings of five tree species in a subtropical forest in China and evaluated microbial effects on multispecies coexistence using the structural method, which quantifies how the structure of species interactions influences the likelihood for multiple species to persist. Specifically, we grew seedlings alone or with competitors in different microbial contexts and fitted individual biomass to a population dynamic model to calculate intra- and interspecific interaction strength with and without soil microbes. We then used these interaction structures to calculate two metrics of multispecies coexistence, structural niche differences (which promote coexistence) and structural fitness differences (which drive exclusion), for all possible communities comprising two to five plant species. We found that soil microbes generally increased both the structural niche and fitness differences across all communities, with a much stronger effect on structural fitness differences. A further examination of functional traits between plant species pairs found that trait differences are stronger predictors of structural niche differences than of structural fitness differences, and that soil microbes have the potential to change trait-mediated plant interactions. Our findings underscore that soil microbes strongly influence the coexistence of multispecies plant systems, and also add to the experimental evidence that the influence is more on fitness differences rather than on niche differences.

The development of ecological systems along paths of least resistance

A long-standing question in biology is whether there are common principles that characterize the development of ecological systems (the appearance of a group of taxa), regardless of organismal diversity and environmental context.1,2,3,4,5,6,7,8,9,10,11 Classic ecological theory holds that these systems develop following a sequenced, orderly process that generally proceeds from fast-growing to slow-growing taxa and depends on life-history trade-offs.2,12,13 However, it is also possible that this developmental order is simply the path with the least environmental resistance for survival of the component species and hence favored by probability alone. Here, we use theory and data to show that the order from fast- to slow-growing taxa is the most likely developmental path for diverse systems when local taxon interactions self-organize in light of environmental resistance. First, we demonstrate theoretically that a sequenced development is more likely than a simultaneous one, at least until the number of iterations becomes so large as to be ecologically implausible. We then show that greater diversity of taxa and life histories improves the likelihood of a sequenced order from fast- to slow-growing taxa. Using data from bacterial and metazoan systems,14,15,16,17,18,19 we present empirical evidence that the developmental order of ecological systems moves along the paths of least environmental resistance. The capacity of simple principles to explain the trend in the developmental order of diverse ecological systems paves the way to an enhanced understanding of collective features of life.

Plant diversity increases diversity and network complexity rather than alters community assembly processes of leaf-associated fungi in a subtropical forest

Plant diversity significantly impacts ecosystem processes and functions, yet its influence on the community assembly of leaf fungi remains poorly understood. In this study, we investigated leaf epiphytic and endophytic fungal communities in a Chinese subtropical tree species richness experiment, ranging from 1 to 16 species, using amplicon sequencing to target the internal transcribed spacer 1 region of the rDNA. We found that the community assembly of epiphytic and endophytic fungi was predominantly governed by stochastic processes, with a higher contribution of dispersal limitation on epiphytic than on endophytic fungal communities but a higher contribution of selection on endophytic than on epiphytic fungal communities. The plant-epiphytic fungus interaction network was more complex (e.g., more highly connected and strongly nested but less specialized and modularized) than the plant-endophytic fungus interaction network. Additionally, tree species richness was positively correlated with the network complexity and diversity of epiphytic (α-, β- and γ-diversity) and endophytic (β- and γ-diversity) fungi, but was not associated with the contribution of the stochastic and deterministic processes on the community assembly of epiphytic and endophytic fungi. This study highlights that tree species diversity enhances the diversity and network complexity, rather than alters the ecological processes in community assembly of leaf-associated fungi.

The Interplay of Binary and Quantitative Structure on the Stability of Mutualistic Networks

Understanding how the structure of biological systems impacts their resilience (broadly defined) is a recurring question across multiple levels of biological organization. In ecology, considerable effort has been devoted to understanding how the structure of interactions between species in ecological networks is linked to different broad resilience outcomes, especially local stability. Still, nearly all of that work has focused on interaction structure in presence-absence terms and has not investigated quantitative structure, i.e., the arrangement of interaction strengths in ecological networks. We investigated how the interplay between binary and quantitative structure impacts stability in mutualistic interaction networks (those in which species interactions are mutually beneficial), using community matrix approaches. We additionally examined the effects of network complexity and within-guild competition for context. In terms of structure, we focused on understanding the stability impacts of nestedness, a structure in which more-specialized species interact with smaller subsets of the same species that more-generalized species interact with. Most mutualistic networks in nature display binary nestedness, which is puzzling because both binary and quantitative nestedness are known to be destabilizing on their own. We found that quantitative network structure has important consequences for local stability. In more-complex networks, binary-nested structures were the most stable configurations, depending on the quantitative structures, but which quantitative structure was stabilizing depended on network complexity and competitive context. As complexity increases and in the absence of within-guild competition, the most stable configurations have a nested binary structure with a complementary (i.e., anti-nested) quantitative structure. In the presence of within-guild competition, however, the most stable networks are those with a nested binary structure and a nested quantitative structure. In other words, the impact of interaction overlap on community persistence is dependent on the competitive context. These results help to explain the prevalence of binary-nested structures in nature and underscore the need for future empirical work on quantitative structure.

Response of bacterial ecological and functional properties to anthropogenic interventions during maturation of mine sand soil

Soil formation is a complex process that starts from the biological development. The ecological principles and biological function in soil are of great importance, whereas their response to anthropogenic intervention has been poorly understood. In this study, a 150-day microcosmic experiment was conducted with the addition of sludge and/or fermented wood chips (FWC) to promote the soil maturation. The results showed that, compared to the control (natural development without anthropogenic intervention), sludge, FWC, and their combination increased the availability of carbon, nitrogen, and potassium, and promoted the soil aggregation. They also enhanced the cellulase activity, microbial biomass carbon (MBC) and bacterial diversity, indicating that anthropogenic interventions promoted the maturation of sand soil. Molecular ecology network and functional analyses indicated that soil maturation was accomplished with the enhancement of ecosystem functionality and stability. Specifically, sludge promoted a transition in bacterial community function from denitrification to nitrification, facilitated the degradation of easily degradable organic matter, and enhanced the autotrophic nutritional mode. FWC facilitated the transition of bacterial function from denitrification to ammonification, promoted the degradation of recalcitrant organic matter, and simultaneously enhanced both autotrophic and heterotrophic nutritional modes. Although both sludge and FWC promoted the soil functionality, they showed distinct mechanistic actions, with sludge enhancing the physical structure, and FWC altering chemical composition. It is also worth emphasizing that sludge and FWC exhibited a synergistic effect in promoting biological development and ecosystem stability, thereby providing an effective avenue for soil maturation.

The structure of bacteria-fungi bipartite networks along elevational gradients in contrasting climates

Climate change is altering species distribution and modifying interactions in microbial communities. Understanding microbial community structure and their interactions is crucial to interpreting ecosystem responses to climate change. Here, we examined the assemblages of stream bacteria and fungi, and the associations between the two groups along elevational gradients in two regions with contrasting precipitation and temperature, that is the Galong and Qilian mountains of the Tibetan Plateau. In the wetter and warmer region, the species richness significantly increased and decreased with elevation for bacteria and fungi, respectively, while were nonsignificant in the drier and colder region. Their bipartite network structure was also different by showing significant increases in connectance and nestedness towards higher elevations only in the wetter and warmer region. In addition, these correlation network structure generally exhibited similar positive association with species richness in the wetter and warmer region and the drier and colder region. In the wetter and warmer region, climatic change along elevation was more important in determining connectance and nestedness, whereas microbial species richness exerted a stronger influence on network structure and robustness in the drier and colder region. These findings indicate substantial forthcoming changes in microbial diversity and network structure in warming climates, especially in wetter and warmer regions on Earth, advancing the understanding of microbial bipartite interactions' response to climate change.

Stability, resilience and eco-evolutionary feedbacks of mutualistic networks to rising temperature

Ecological networks comprising of mutualistic interactions can suddenly transition to undesirable states, such as collapse, due to small changes in environmental conditions such as a rise in local environmental temperature. However, little is known about the capacity of such interaction networks to adapt to a rise in temperature and the occurrence of critical transitions. Here, combining quantitative genetics and mutualistic dynamics in an eco-evolutionary framework, we evaluated the stability and resilience of mutualistic networks to critical transitions as environmental temperature increases. Specifically, we modelled the dynamics of an optimum trait that determined the tolerance of species to local environmental temperature as well as to species interaction. We then evaluated the impact of individual trait variation and evolutionary dynamics on the stability of feasible equilibria, the occurrence of threshold temperatures at which community collapses, and the abruptness of such community collapses. We found that mutualistic network architecture, that is the size of the community and the arrangement of species interactions, interacted with evolutionary dynamics to impact the onset of network collapses. Some networks had more capacity to track the rise in temperatures than others and thereby increased the threshold temperature at which the networks collapsed. However, such a result was modulated by the amount of heritable trait variation species exhibited, with high trait variation in the mean optimum phenotypic trait increasing the environmental temperature at which networks collapsed. Furthermore, trait variation not only increased the onset of temperatures at which networks collapsed but also increased the local stability of feasible equilibria. Our study argued that mutualistic network architecture interacts with species evolutionary dynamics and increases the capacity of networks to adapt to changes in temperature and thereby delayed the occurrence of community collapses.

Exploring spatial segregation induced by competition avoidance as driving mechanism for emergent coexistence in microbial communities

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models, and we consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

Structural dynamics of plant-pollinator mutualistic networks

The discourse surrounding the structural organization of mutualistic interactions mostly revolves around modularity and nestedness. The former is known to enhance the stability of communities, while the latter is related to their feasibility, albeit compromising the stability. However, it has recently been shown that the joint emergence of these structures poses challenges that can eventually lead to limitations in the dynamic properties of mutualistic communities. We hypothesize that considering compound arrangements-modules with internal nested organization-can offer valuable insights in this debate. We analyze the temporal structural dynamics of 20 plant-pollinator interaction networks and observe large structural variability throughout the year. Compound structures are particularly prevalent during the peak of the pollination season, often coexisting with nested and modular arrangements in varying degrees. Motivated by these empirical findings, we synthetically investigate the dynamics of the structural patterns across two control parameters-community size and connectance levels-mimicking the progression of the pollination season. Our analysis reveals contrasting impacts on the stability and feasibility of these mutualistic communities. We characterize the consistent relationship between network structure and stability, which follows a monotonic pattern. But, in terms of feasibility, we observe nonlinear relationships. Compound structures exhibit a favorable balance between stability and feasibility, particularly in mid-sized ecological communities, suggesting they may effectively navigate the simultaneous requirements of stability and feasibility. These findings may indicate that the assembly process of mutualistic communities is driven by a delicate balance among multiple properties, rather than the dominance of a single one.

Scaling approaches and macroecology provide a foundation for assessing ecological resilience in the Anthropocene

In the Anthropocene, intensifying ecological disturbances pose significant challenges to our predictive capabilities for ecosystem responses. Macroecology-which focuses on emergent statistical patterns in ecological systems-unveils consistent regularities in the organization of biodiversity and ecosystems. These regularities appear in terms of abundance, body size, geographical range, species interaction networks, or the flux of matter and energy. This paper argues for moving beyond qualitative resilience metaphors, such as the 'ball and cup', towards a more quantitative macroecological framework. We suggest a conceptual and theoretical basis for ecological resilience that integrates macroecology with a stochastic diffusion approximation constrained by principles of biological symmetry. This approach provides an alternative novel framework for studying ecological resilience in the Anthropocene. We demonstrate how our framework can effectively quantify the impacts of major disturbances and their extensive ecological ramifications. We further show how biological scaling insights can help quantify the consequences of major disturbances, emphasizing their cascading ecological impacts. The nature of these impacts prompts a re-evaluation of our understanding of resilience. Emphasis on regularities of ecological assemblages can help illuminate resilience dynamics and offer a novel basis to predict and manage the impacts of disturbance in the Anthropocene more efficiently. This article is part of the theme issue 'Ecological novelty and planetary stewardship: biodiversity dynamics in a transforming biosphere'.

Structural stability of invasion graphs for Lotka-Volterra systems

In this paper, we study in detail the structure of the global attractor for the Lotka-Volterra system with a Volterra-Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.

Parameter Sensitivity of Transient Community Dynamics

AbstractTransient dynamics have always intrigued ecologists, but current rapid environmental change (inducing transients even in previously undisturbed systems) has highlighted their importance more than ever. Here, I introduce a method for analyzing the sensitivity of transient ecological dynamics to parameter perturbations. The question the method answers is: how would the community dynamics have unfolded for some time horizon had the parameters been slightly different? I apply the method to three empirically parameterized models: competition between native forbs and exotic grasses in California, a host-parasitoid system, and an experimental chemostat predator-prey model. These applications showcase the ecological insights one can gain from models using transient sensitivity analysis. First, one can find parameters and their combinations whose perturbations disproportionately affect a system. Second, one can identify particular windows of time during which the predicted deviation from the unperturbed trajectories is especially large and utilize this information for management purposes. Third, there is an inverse relationship between transient and long-term sensitivities whenever the interacting populations are ecologically similar; paradoxically, the smaller the immediate response of the system, the more extreme its long-term response will be.

Multitrophic Higher-Order Interactions Modulate Species Persistence

AbstractEcologists increasingly recognize that interactions between two species can be affected by the density of a third species. How these higher-order interactions (HOIs) affect species persistence remains poorly understood. To explore the effect of HOIs stemming from multiple trophic layers on a plant community composition, we experimentally built a mesocosm with three plants and three pollinator species arranged in a fully nested and modified network structure. We estimated pairwise interactions among plants and between plants and pollinators, as well as HOIs initiated by a plant or a pollinator affecting plant species pairs. Using a structuralist approach, we evaluated the consequences of the statistically supported HOIs on the persistence probability of each of the three competing plant species and their combinations. HOIs substantially redistribute the strength and sign of pairwise interactions between plant species, promoting the opportunities for multispecies communities to persist compared with a non-HOI scenario. However, the physical elimination of a plant-pollinator link in the modified network structure promotes changes in per capita pairwise interactions and HOIs, resulting in a single-species community. Our study provides empirical evidence of the joint importance of HOIs and network structure in determining species persistence within diverse communities.

A taxonomy of multiple stable states in complex ecological communities

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing "diversity-stability debate." Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions among populations with sublinear growth do not lead to exclusion, as occurs with logistic growth, but instead promote stability at higher diversity. Our model realigns theory with classic observations and predicts large-scale macroecological patterns. However, it makes an unsettling prediction: Biodiversity loss may accelerate the destabilization of ecosystems.

Both local stability and dispersal contribute to metacommunity sensitivity to asynchronous habitat availability

The stability of isolated communities depends on the complexity of their foodwebs. However, it remains unclear how local stability interacts with dispersal in multitrophic metacommunities to shape biodiversity patterns. This lack of understanding is deeper in the more realistic frame of landscapes that exhibit non-trivial and time-varying structures. Therefore, in this study, we aim to evaluate the influence of local stabilizing factors versus dispersal in determining the sensitivity of metacommunity biodiversity to increasing asynchrony of site availability. Additionally, we assess the role of foodweb complexity and landscape structure as modulating factors. To accomplish our goals we developed a model based on random matrices for local communities, which are linked by stochastic dispersal over explicit dynamic landscapes. We ran numerical simulations and computed the effect sizes of foodweb temperature, self-limitation, dispersal ability, and all pairwise combinations, on the sensitivity of biodiversity to landscape asynchrony. In our experiments we explored gradients of species richness, foodweb connectance, number of sites, and landscape modularity. Our results showed that asynchrony among site availability periods reduced α -diversity and increased β -diversity. Asynchrony increased γ -diversity at high dispersal rates. Both local and regional stabilizing factors determined the sensitivity of metacommunities to landscape asynchrony. Local factors were more influential in landscapes with fewer sites and lower modularity, as well as in metacommunities composed of complex foodwebs. This research offers insights into the dynamics of metacommunities in dynamic landscapes, providing valuable knowledge about the interplay between local and regional factors in shaping ecological stability and species persistence.

Interaction network rewiring and species' contributions to community-scale flexibility

The architecture of species interaction networks is a key factor determining the stability of ecological communities. However, the fact that ecological network architecture can change through time is often overlooked in discussions on community-level processes, despite its theoretical importance. By compiling a time-series community dataset involving 50 spider species and 974 Hexapoda prey species/strains, we quantified the extent to which the architecture of predator-prey interaction networks could shift across time points. We then developed a framework for finding species that could increase the flexibility of the interaction network architecture. Those "network coordinator" species are expected to promote the persistence of species-rich ecological communities by buffering perturbations in communities. Although spiders are often considered as generalist predators, their contributions to network flexibility vary greatly among species. We also found that detritivorous prey species can be cores of interaction rewiring, dynamically interlinking below-ground and above-ground community dynamics. We further found that the predator-prey interactions between those network coordinators differed from those highlighted in the standard network-analytical framework assuming static topology. Analyses of network coordinators will add a new dimension to our understanding of species coexistence mechanisms and provide platforms for systematically prioritizing species in terms of their potential contributions in ecosystem conservation and restoration.

Interaction network structure explains species' temporal persistence in empirical plant-pollinator communities

Despite clear evidence that some pollinator populations are declining, our ability to predict pollinator communities prone to collapse or species at risk of local extinction is remarkably poor. Here, we develop a model grounded in the structuralist approach that allows us to draw sound predictions regarding the temporal persistence of species in mutualistic networks. Using high-resolution data from a six-year study following 12 independent plant-pollinator communities, we confirm that pollinator species with more persistent populations in the field are theoretically predicted to tolerate a larger range of environmental changes. Persistent communities are not necessarily more diverse, but are generally located in larger habitat patches, and present a distinctive combination of generalist and specialist species resulting in a more nested structure, as predicted by previous theoretical work. Hence, pollinator interactions directly inform about their ability to persist, opening the door to use theoretically informed models to predict species' fate within the ongoing global change.

Plant interaction networks reveal the limits of our understanding of diversity maintenance

Species interactions are key drivers of biodiversity and ecosystem stability. Current theoretical frameworks for understanding the role of interactions make many assumptions which unfortunately, do not always hold in natural, diverse communities. This mismatch extends to annual plants, a common model system for studying coexistence, where interactions are typically averaged across environmental conditions and transitive competitive hierarchies are assumed to dominate. We quantify interaction networks for a community of annual wildflowers in Western Australia across a natural shade gradient at local scales. Whilst competition dominated, intraspecific and interspecific facilitation were widespread in all shade categories. Interaction strengths and directions varied substantially despite close spatial proximity and similar levels of local species richness, with most species interacting in different ways under different environmental conditions. Contrary to expectations, all networks were predominantly intransitive. These findings encourage us to rethink how we conceive of and categorize the mechanisms driving biodiversity in plant systems.

Coexistence mechanism of ecological specialists and generalists based on a network dimension reduction method

As an ecological strategy for species coexistence, some species adapt to a wide range of habitats, while others specialize in particular environments. Such 'generalists' and 'specialists' achieve normal ecological balance through a complex network of interactions between species. However, the role of these interactions in maintaining the coexistence of generalist and specialist species has not been elucidated within a general theoretical framework. Here, we analyze the ecological mechanism for the coexistence of specialist and generalist species in a class of mutualistic and competitive interaction ecosystems based on the network dimension reduction method. We find that ecological specialists and generalists can be identified based on the number of their respective interactions. We also find, using real-world empirical network simulations, that the removal of ecological generalists can lead to the collapse of local ecosystems, which is rarely observed with the loss of ecological specialists.

Horizontal gene transfer is predicted to overcome the diversity limit of competing microbial species

Natural microbial ecosystems harbor substantial diversity of competing species. Explaining such diversity is challenging, because in classic theories it is extremely infeasible for a large community of competing species to stably coexist in homogeneous environments. One important aspect mostly overlooked in these theories, however, is that microbes commonly share genetic materials with their neighbors through horizontal gene transfer (HGT), which enables the dynamic change of species growth rates due to the fitness effects of the mobile genetic elements (MGEs). Here, we establish a framework of species competition by accounting for the dynamic gene flow among competing microbes. Combining theoretical derivation and numerical simulations, we show that in many conditions HGT can surprisingly overcome the biodiversity limit predicted by the classic model and allow the coexistence of many competitors, by enabling dynamic neutrality of competing species. In contrast with the static neutrality proposed by previous theories, the diversity maintained by HGT is highly stable against random perturbations of microbial fitness. Our work highlights the importance of considering gene flow when addressing fundamental ecological questions in the world of microbes and has broad implications for the design and engineering of complex microbial consortia.

On the limits to invasion prediction using coexistence outcomes

The dynamics of ecological communities in nature are typically characterized by probabilistic processes involving invasion dynamics. Because of technical challenges, however, the majority of theoretical and experimental studies have focused on coexistence dynamics. Therefore, it has become central to understand the extent to which coexistence outcomes can be used to predict analogous invasion outcomes relevant to systems in nature. Here, we study the limits to this predictability under a geometric and probabilistic Lotka-Volterra framework. We show that while individual survival probability in coexistence dynamics can be fairly closely translated into invader colonization probability in invasion dynamics, the translation is less precise between community persistence and community augmentation, and worse between exclusion probability and replacement probability. These results provide a guiding and testable theoretical framework regarding the translatability of outcomes between coexistence and invasion outcomes when communities are represented by Lotka-Volterra dynamics under environmental uncertainty.

Robustness versus productivity during evolutionary community assembly: short-term synergies and long-term trade-offs

The realization that evolutionary feedbacks need to be considered to fully grasp ecological dynamics has sparked interest in the effect of evolution on community properties like coexistence and productivity. However, little is known about the evolution of community robustness and productivity along diversification processes in species-rich systems. We leverage the recent structural approach to coexistence together with adaptive dynamics to study such properties and their relationships in a general trait-based model of competition on a niche axis. We show that the effects of coevolution on coexistence are two-fold and contrasting depending on the time scale considered. In the short term, evolution of niche differentiation strengthens coexistence, while long-term diversification leads to niche packing and decreased robustness. Moreover, we find that coevolved communities tend to be on average more robust and more productive than non-evolutionary assemblages. We illustrate how our theoretical predictions echo in observed empirical patterns and the implications of our results for empiricists and applied ecologists. We suggest that some of our results such as the improved robustness of Evolutionarily Stable Communities could be tested experimentally in suitable model systems.

Using individual-based trait frequency distributions to forecast plant-pollinator network responses to environmental change

Determining how and why organisms interact is fundamental to understanding ecosystem responses to future environmental change. To assess the impact on plant-pollinator interactions, recent studies have examined how the effects of environmental change on individual interactions accumulate to generate species-level responses. Here, we review recent developments in using plant-pollinator networks of interacting individuals along with their functional traits, where individuals are nested within species nodes. We highlight how these individual-level, trait-based networks connect intraspecific trait variation (as frequency distributions of multiple traits) with dynamic responses within plant-pollinator communities. This approach can better explain interaction plasticity, and changes to interaction probabilities and network structure over spatiotemporal or other environmental gradients. We argue that only through appreciating such trait-based interaction plasticity can we accurately forecast the potential vulnerability of interactions to future environmental change. We follow this with general guidance on how future studies can collect and analyse high-resolution interaction and trait data, with the hope of improving predictions of future plant-pollinator network responses for targeted and effective conservation.

Microbial collaborations and conflicts: unraveling interactions in the gut ecosystem

The human gut microbiota constitutes a vast and complex community of microorganisms. The myriad of microorganisms present in the intestinal tract exhibits highly intricate interactions, which play a crucial role in maintaining the stability and balance of the gut microbial ecosystem. These interactions, in turn, influence the overall health of the host. The mammalian gut microbes have evolved a wide range of mechanisms to suppress or even eliminate their competitors for nutrients and space. Simultaneously, extensive cooperative interactions exist among different microbes to optimize resource utilization and enhance their own fitness. This review will focus on the competitive mechanisms among members of the gut microorganisms and discuss key modes of actions, including bacterial secretion systems, bacteriocins, membrane vesicles (MVs) etc. Additionally, we will summarize the current knowledge of the often-overlooked positive interactions within the gut microbiota, and showcase representative machineries. This information will serve as a reference for better understanding the complex interactions occurring within the mammalian gut environment. Understanding the interaction dynamics of competition and cooperation within the gut microbiota is crucial to unraveling the ecology of the mammalian gut microbial communities. Targeted interventions aimed at modulating these interactions may offer potential therapeutic strategies for disease conditions.

How collectively integrated are ecological communities?

Beyond abiotic conditions, do population dynamics mostly depend on a species' direct predators, preys and conspecifics? Or can indirect feedback that ripples across the whole community be equally important? Determining where ecological communities sit on the spectrum between these two characterizations requires a metric able to capture the difference between them. Here we show that the spectral radius of a community's interaction matrix provides such a metric, thus a measure of ecological collectivity, which is accessible from imperfect knowledge of biotic interactions and related to observable signatures. This measure of collectivity integrates existing approaches to complexity, interaction structure and indirect interactions. Our work thus provides an original perspective on the question of to what degree communities are more than loose collections of species or simple interaction motifs and explains when pragmatic reductionist approaches ought to suffice or fail when applied to ecological communities.

Landscape quantifies the intermediate state and transition dynamics in ecological networks

Understanding the ecological mechanisms associated with the collapse and restoration is especially critical in promoting harmonious coexistence between humans and nature. So far, it remains challenging to elucidate the mechanisms of stochastic dynamical transitions for ecological systems. Using an example of plant-pollinator network, we quantified the energy landscape of ecological system. The landscape displays multiple attractors characterizing the high, low and intermediate abundance stable states. Interestingly, we detected the intermediate states under pollinator decline, and demonstrated the indispensable role of the intermediate state in state transitions. From the landscape, we define the barrier height (BH) as a global quantity to evaluate the transition feasibility. We propose that the BH can serve as a new early-warning signal (EWS) for upcoming catastrophic breakdown, which provides an earlier and more accurate warning signal than traditional metrics based on time series. Our results promote developing better management strategies to achieve environmental sustainability.

Stochastic model corrections for reduced Lotka-Volterra models exhibiting mutual, commensal, competitive, and predatory interactions

We explore model-form error and how to correct it in systems of ordinary differential equations. In particular, we focus on the Lotka-Volterra equations, which are used broadly in fields such as ecology, biology, economics, chemistry, and physics. Accounting for every object and their complex interactions with a complete model often becomes infeasible, thereby requiring reduced models. However, reduced models may omit vital relationships, resulting in discrepancies between reduced model predictions and observations from the true system. In this work, we propose a model correction framework for decreasing such discrepancies. Specifically, we embed a stochastic enrichment operator into the reduced model's system of equations. The enrichment operator is theory-informed, calibrated with observations from the complete model, and extended to extrapolative combinations of parameters and initial conditions. The complete model involves N species, while the reduced and enriched models only track M Collapse

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Affiliation(s)

R Bandy Department of Computer Science, University of Colorado Boulder, Boulder, Colorado 80309, USA
R Morrison Department of Computer Science, University of Colorado Boulder, Boulder, Colorado 80309, USA

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Rate-induced tipping in complex high-dimensional ecological networks

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Towards a general modeling framework of resource competition in cognitive development

The current paper presents an integrated formal model of typical and atypical development based on the mechanisms of mutualism and resource competition. The mutualistic network model is extended with the dynamics of competition for limited resources, such as time and environmental factors. The proposed model generates patterns that resemble established phenomena in cognitive development: the positive manifold, developmental phases, developmental delays and lack of early indicators in atypical development, developmental regression, and "quasi-autism" caused by extreme environmental deprivation. The presented modeling framework fits a general movement towards formal theory construction in psychology. The model is easy to replicate and develop further, and we offer several avenues for future work.

Five fundamental ways in which complex food webs may spiral out of control

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these 'delayed negative feedbacks' may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large-scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food-web patterns are sufficient to prevent abrupt, large-scale transitions under global environmental change.

Time delays modulate the stability of complex ecosystems

What drives the stability, or instability, of complex ecosystems? This question sits at the heart of community ecology and has motivated a large body of theoretical work exploring how community properties shape ecosystem dynamics. However, the overwhelming majority of current theory assumes that species interactions are instantaneous, meaning that changes in the abundance of one species will lead to immediate changes in the abundances of its partners. In practice, time delays in how species respond to one another are widespread across ecological contexts, yet the impact of these delays on ecosystems remains unclear. Here we derive a new body of theory to comprehensively study the impact of time delays on ecological stability. We find that time delays are important for ecosystem stability. Large delays are typically destabilizing but, surprisingly, short delays can substantially increase community stability. Moreover, in stark contrast to delay-free systems, delays dictate that communities with more abundant species can be less stable than ones with less abundant species. Finally, we show that delays fundamentally shift how species interactions impact ecosystem stability, with communities of mixed interaction types becoming the most stable class of ecosystem. Our work demonstrates that time delays can be critical for the stability of complex ecosystems.

A spatially structured mathematical model of the gut microbiome reveals factors that increase community stability

Given the importance of gut microbial communities for human health, we may want to ensure their stability in terms of species composition and function. Here, we built a mathematical model of a simplified gut composed of two connected patches where species and metabolites can flow from an upstream patch, allowing upstream species to affect downstream species' growth. First, we found that communities in our model are more stable if they assemble through species invasion over time compared to combining a set of species from the start. Second, downstream communities are more stable when species invade the downstream patch less frequently than the upstream patch. Finally, upstream species that have positive effects on downstream species can further increase downstream community stability. Despite it being quite abstract, our model may inform future research on designing more stable microbial communities or increasing the stability of existing ones.

Stability of human gut microbiome: Comparison of ecological modelling and observational approaches

The gut microbiome plays a pivotal role in the human body, and perturbations in its composition have been linked to various disorders. Stability is an essential property of a healthy human gut microbiome, which allows it to maintain its functional richness under the external influences. This property has been explored through two distinct methodologies - mathematical modelling based on ecological principles and statistical analysis drawn from observations in interventional studies. Here we conducted a meta-analysis aimed to compare the two approaches utilising the data from 9 interventional and time series studies encompassing 3512 gut microbiome profiles obtained via 16S rRNA gene sequencing. By employing the previously published compositional Lotka-Volterra method, we modelled the dynamics of the microbial community and evaluated ecological stability measures. These measures were compared to those based on observed microbiome changes. There was a substantial correlation between the outcomes of the two approaches. Particularly, local stability assessed within the ecological paradigm was positively correlated with observational stability measures accounting for the compositional nature of microbiome data. Additionally, we were able to reproduce the previously reported inverse relationship between the community's robustness to microorganism loss and local stability, attributed to the distinct impacts of coefficient characterising the network decomposition on these two stability assessments. Our findings demonstrate harmonisation between the ecological and observational approaches to microbiome analysis, advancing the understanding of healthy gut microbiome concept. This paves the way to develop efficient microbiome-targeting interventions for disease prevention and treatment.

Emergent coexistence in multispecies microbial communities

Understanding the mechanisms that maintain microbial biodiversity is a critical aspiration in ecology. Past work on microbial coexistence has largely focused on species pairs, but it is unclear whether pairwise coexistence in isolation is required for coexistence in a multispecies community. To address this question, we conducted hundreds of pairwise competition experiments among the stably coexisting members of 12 different enrichment communities in vitro. To determine the outcomes of these experiments, we developed an automated image analysis pipeline to quantify species abundances. We found that competitive exclusion was the most common outcome, and it was strongly hierarchical and transitive. Because many species that coexist within a stable multispecies community fail to coexist in pairwise co-culture under identical conditions, we concluded that multispecies coexistence is an emergent phenomenon. This work highlights the importance of community context for understanding the origins of coexistence in complex ecosystems.

Relationships of temperature and biodiversity with stability of natural aquatic food webs

Temperature and biodiversity changes occur in concert, but their joint effects on ecological stability of natural food webs are unknown. Here, we assess these relationships in 19 planktonic food webs. We estimate stability as structural stability (using the volume contraction rate) and temporal stability (using the temporal variation of species abundances). Warmer temperatures were associated with lower structural and temporal stability, while biodiversity had no consistent effects on either stability property. While species richness was associated with lower structural stability and higher temporal stability, Simpson diversity was associated with higher temporal stability. The responses of structural stability were linked to disproportionate contributions from two trophic groups (predators and consumers), while the responses of temporal stability were linked both to synchrony of all species within the food web and distinctive contributions from three trophic groups (predators, consumers, and producers). Our results suggest that, in natural ecosystems, warmer temperatures can erode ecosystem stability, while biodiversity changes may not have consistent effects.

Evading tipping points in socio-mutualistic networks via structure mediated optimal strategy

The threat of large-scale pollinator decline is increasing globally under stress from multiple anthropogenic pressures. Traditional approaches have focused on managing endangered species at an individual level, in which the effect of complex interactions such as mutualism and competition are amiss. Here, we develop a coupled socio-mutualistic network model that captures the change in pollinator dynamics with human conservation opinion in a deteriorating environment. We show that the application of social norm (or conservation) at the pollinator nodes is fit to prevent sudden community collapse in representative networks of varied topology. Whilst primitive strategies have focused on regulating abundance as a mitigation strategy, the role of network structure has been largely overlooked. Here, we develop a novel network structure-mediated conservation strategy to find the optimal set of nodes on which norm implementation successfully prevents community collapse. We find that networks of intermediate nestedness require conservation at a minimum number of nodes to prevent a community collapse. We claim the robustness of the optimal conservation strategy (OCS) after validation on several simulated and empirical networks of varied complexity against a broad range of system parameters. Dynamical analysis of the reduced model shows that incorporating social norms allows the pollinator abundance to grow that would have otherwise crossed a tipping point and undergo extinction. Together, this novel means OCS provides a potential plan of action for conserving plant-pollinator networks bridging the gap between research in mutualistic networks and conservation ecology.

Facilitative interaction networks in experimental microbial community dynamics

Facilitative interactions between microbial species are ubiquitous in various types of ecosystems on the Earth. Therefore, inferring how entangled webs of interspecific interactions shift through time in microbial ecosystems is an essential step for understanding ecological processes driving microbiome dynamics. By compiling shotgun metagenomic sequencing data of an experimental microbial community, we examined how the architectural features of facilitative interaction networks could change through time. A metabolic modeling approach for estimating dependence between microbial genomes (species) allowed us to infer the network structure of potential facilitative interactions at 13 time points through the 110-day monitoring of experimental microbiomes. We then found that positive feedback loops, which were theoretically predicted to promote cascade breakdown of ecological communities, existed within the inferred networks of metabolic interactions prior to the drastic community-compositional shift observed in the microbiome time-series. We further applied "directed-graph" analyses to pinpoint potential keystone species located at the "upper stream" positions of such feedback loops. These analyses on facilitative interactions will help us understand key mechanisms causing catastrophic shifts in microbial community structure.

Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities

Theory posits that the persistence of species in ecological communities is shaped by their interactions within and across trophic guilds. However, we lack empirical evaluations of how the structure, strength and sign of biotic interactions drive the potential to coexist in diverse multi-trophic communities. Here, we model community feasibility domains, a theoretically informed measure of multi-species coexistence probability, from grassland communities comprising more than 45 species on average from three trophic guilds (plants, pollinators and herbivores). Contrary to our hypothesis, increasing community complexity, measured either as the number of guilds or community richness, did not decrease community feasibility. Rather, we observed that high degrees of species self-regulation and niche partitioning allow for maintaining larger levels of community feasibility and higher species persistence in more diverse communities. Our results show that biotic interactions within and across guilds are not random in nature and both structures significantly contribute to maintaining multi-trophic diversity.

Rigorous Criteria for the Collapse of Nonlinear Cooperative Networks

Many real-world complex systems, when hitting a tipping point, undergo irreversible sudden shifts that can eventually take a great toll on humanity and the natural world, such as ecosystem collapses, disease outbreaks, etc. Previous work has adopted approximations to predict the tipping points, but due to the nature of nonlinearity, this may lead to unexpected errors in predicting real-world systems. Here we obtain the rigorous bounds of the tipping points for general nonlinear cooperative networks. Our results offer two rigorous criteria that determine the collapse and survival of such a system. These two criteria are decided by the combined effect of dynamical parameters and interaction topology.

Intraspecific variation in species interactions promotes the feasibility of mutualistic assemblages

Patterns of resource use observed at the species level emerge from the way individuals exploit the range of available resources. Hence, accounting for interindividual differences in resource use, such as pollinator use by plants, is essential to advance our understanding of community assembly and persistence. By using finely resolved data on plant-pollinator interactions, we evaluated how interindividual plant variation in pollinator use scales up to affect community structure and dynamics. All co-occurring plant species comprised specialists interacting with proper subsets of pollinators that visited generalists, and differences in interaction patterns were driven by among-individual trait variation. Furthermore, the nested structure and feasibility of plant-pollinator communities were maximised at higher levels of interindividual plant variation in traits and pollinator use. Our study sheds light on how pervasive properties of community structure arise from individual-level processes and contributes to elucidate the importance of preserving intraspecific variation in traits and resource use within populations.

Nitrogen enrichment and foliar fungal pathogens affect the mechanisms of multispecies plant coexistence

Changes in resources (e.g. nitrogen) and enemies (e.g. foliar pathogens) are key drivers of plant diversity and composition. However, their effects have not been connected to the niche and fitness differences that determine multispecies coexistence. Here, we combined a structuralist theoretical approach with a detailed grassland experiment factorially applying nitrogen addition and foliar fungal pathogen suppression to evaluate the joint effect of nitrogen and pathogens on niche and fitness differences, across a gradient from two to six interacting species. Nitrogen addition and pathogen suppression modified species interaction strengths and intrinsic growth rates, leading to reduced multispecies fitness differences. However, contrary to expected, we also observed that they promote stabilising niche differences. Although these modifications did not substantially alter species richness, they predicted major changes in community composition. Indirect interactions between species explained these community changes in smaller assemblages (three and four species) but lost importance in favour of direct pairwise interactions when more species were involved (five and six). Altogether, our work shows that explicitly considering the number of interacting species is critical for better understanding the direct and indirect processes by which nitrogen enrichment and pathogen communities shape coexistence in grasslands.

Forest edges increase pollinator network robustness to extinction with declining area

Edge effects often exacerbate the negative effects of habitat loss on biodiversity. In forested ecosystems, however, many pollinators actually prefer open sunny conditions created by edge disturbances. We tested the hypothesis that forest edges have a positive buffering effect on plant-pollinator interaction networks in the face of declining forest area. In a fragmented land-bridge island system, we recorded ~20,000 plant-pollinator interactions on 41 islands over 3 yr. We show that plant richness and floral resources decline with decreasing forest area at both interior and edge sites, but edges maintain 10-fold higher pollinator abundance and richness regardless of area loss. Edge networks contain highly specialized species, with higher nestedness and lower modularity than interior networks, maintaining high robustness to extinction following area loss while forest interior networks collapse. Anthropogenic forest edges benefit community diversity and network robustness to extinction in the absence of natural gap-phase dynamics in small degraded forest remnants.

The stability and collapse of marine ecosystems during the Permian-Triassic mass extinction

The history of Earth's biodiversity is punctuated episodically by mass extinctions. These are characterized by major declines of taxon richness, but the accompanying ecological collapse has rarely been evaluated quantitatively. The Permian-Triassic mass extinction (PTME; ∼252 mya), as the greatest known extinction, permanently altered marine ecosystems and paved the way for the transition from Paleozoic to Mesozoic evolutionary faunas. Thus, the PTME offers a window into the relationship between taxon richness and ecological dynamics of ecosystems during a severe extinction. However, the accompanying ecological collapse through the PTME has not been evaluated in detail. Here, using food-web models and a marine paleocommunity dataset spanning the PTME, we show that after the first extinction phase, community stability decreased only slightly despite the loss of more than half of taxonomic diversity, while community stability significantly decreased in the second phase. Thus, taxonomic and ecological changes were unequivocally decoupled, with species richness declining severely ∼61 ka earlier than the collapse of marine ecosystem stability, implying that in major catastrophes, a biodiversity crash may be the harbinger of a more devastating ecosystem collapse.

Rising temperature drives tipping points in mutualistic networks

The effect of climate warming on species' physiological parameters, including growth rate, mortality rate and handling time, is well established from empirical data. However, with an alarming rise in global temperature more than ever, predicting the interactive influence of these changes on mutualistic communities remains uncertain. Using 139 real plant-pollinator networks sampled across the globe and a modelling approach, we study the impact of species' individual thermal responses on mutualistic communities. We show that at low mutualistic strength plant-pollinator networks are at potential risk of rapid transitions at higher temperatures. Evidently, generalist species play a critical role in guiding tipping points in mutualistic networks. Further, we derive stability criteria for the networks in a range of temperatures using a two-dimensional reduced model. We identify network structures that can ascertain the delay of a community collapse. Until the end of this century, on account of increasing climate warming many real mutualistic networks are likely to be under the threat of sudden collapse, and we frame strategies to mitigate this. Together, our results indicate that knowing individual species' thermal responses and network structure can improve predictions for communities facing rapid transitions.

Stability of multi-layer ecosystems

Community structure is reported to play a critical role in ecosystem stability, which indicates the ability of a system to return to equilibrium after perturbations. However, current studies rely on the assumption that the community consists of only a single-layer structure. In practice, multi-layer structures are common in ecosystems, e.g. the distributions of both microorganisms in strata and fish in the ocean usually stratify into multi-layer structures. Here we use multi-layer networks to model species interactions within each layer and between different layers, and study the stability of multi-layer ecosystems under different interaction types. We show that competitive interactions within each layer have a more substantial stabilizing effect in multi-layer ecosystems relative to their impact in single-layer ecosystems. Surprisingly, between different layers, we find that competition between species destabilizes the ecosystem. We further provide a theoretical analysis of the stability of multi-layer ecosystems and confirm the robustness of our findings for different connectances between layers, numbers of species in each layer, and numbers of layers. Our work provides a general framework for investigating the stability of multi-layer ecosystems and uncovers the double-sided role of competitive interactions in the stability of multi-layer ecosystems.