The mechanistic basis for higher-order interactions and non-additivity in competitive communities

When Do Trait-Based Higher Order Interactions and Individual Variation Promote Robust Species Coexistence?

Models on the effects of individual variation often focus on pairwise interactions, but communities could harbor both pairwise and higher order interactions (HOIs). Theoretical studies on HOIs, where a third species modulates pairwise species competition, tend to assign them at random, even though they could be mediated and structured by one-dimensional traits. Here, we consider two different classes of models of both pairwise and higher order trait-mediated interactions: competition alleviated by increasing trait distance, and hierarchical competition where species higher in the hierarchy exert more competition on those lower and vice versa. Combining these models with evolutionary dynamics based on quantitative genetics, we compare their impact on species diversity, community pattern, and robustness of coexistence. Regardless of individual variation, trait-mediated HOIs generally do not promote and often hinder species coexistence, but there are some notable exceptions to this. We present an analytical argument to make sense of these results and argue that while the effects of trait-based HOIs on diversity may appear confusing on the surface, we can understand what outcome to expect in any given scenario by looking at the shape of the effective interaction kernel that arises from the joint action of pairwise and HOI terms. In addition, we find that (i) communities structured by competitive trait hierarchies are highly vulnerable to external perturbations, regardless of HOIs, and (ii) trait-based HOIs with distance-dependent competition create the most robust communities, with minimal impact from individual variation, and (iii) both individual variation and HOIs consistently lead to a more even distribution of species traits than would occur by chance. These findings suggest that trait-mediated HOIs foster coexistence only under special conditions, raising the question of whether HOIs must involve multiple traits to positively affect coexistence in competitive communities.

Heterogeneous K-core percolation on hypergraphs

In complex systems, there are pairwise and multiple interactions among elements, which can be described as hypergraphs. K-core percolation is widely utilized in the investigation of the robustness of systems subject to random or targeted attacks. However, the robustness of nodes usually correlates with their characteristics, such as degree, and exhibits heterogeneity while lacking a theoretical study on the K-core percolation on a hypergraph. To this end, we constructed a hyperedge K-core percolation model that introduces heterogeneity parameters to divide the active hyperedges into two parts, where hyperedges are inactive unless they have a certain number of active nodes. In the stage of pruning process, when the number of active nodes contained in a hyperedge is less than its set value, it will be pruned, which will result in the deletion of other hyperedges and ultimately trigger cascading failures. We studied the magnitude of the giant connected component and the percolation threshold of the model by mapping a random hypergraph to a factor graph. Subsequently, we conducted a large number of simulation experiments, and the theoretical values matched well with the simulated values. The heterogeneity parameters of the proposed model have a significant impact on the magnitude of the giant connected component and the type of phase transition in the network. We found that decreasing the value of heterogeneity parameters renders the network more fragile, while increasing the value of heterogeneity parameters makes it more resilient under random attacks. Meanwhile, as the heterogeneity parameter decreases to 0, it may cause a change in the nature of network phase transition, and the network shows a hybrid transition.

Effects of Phylogeny on Coexistence in Model Communities

AbstractSpecies' interactions are shaped by their traits. Thus, we expect traits-in particular, trait (dis)similarity-to play a central role in determining whether a particular set of species coexists. Traits are, in turn, the outcome of an eco-evolutionary process summarized by a phylogenetic tree. Therefore, the phylogenetic tree associated with a set of species should carry information about the dynamics and assembly properties of the community. Many studies have highlighted the potentially complex ways in which this phylogenetic information is translated into species' ecological properties. However, much less emphasis has been placed on developing clear, quantitative expectations for community properties under a particular hypothesis. To address this gap, we couple a simple model of trait evolution on a phylogenetic tree with Lotka-Volterra community dynamics. This allows us to derive properties of a community of coexisting species as a function of the number of traits, tree topology, and the size of the species pool. Our analysis highlights how phylogenies, through traits, affect the coexistence of a set of species. Together, these results provide much-needed baseline expectations for the ways in which evolutionary history, summarized by phylogeny, is reflected in the size and structure of ecological communities.

Modification speed alters stability of ecological higher-order interaction networks

Higher-order interactions (HOIs) have the potential to greatly increase our understanding of ecological interaction networks beyond what is possible with established models that usually consider only pairwise interactions between organisms. While equilibrium values of such HOI-based models have been studied, the dynamics of these models and the stability of their equilibria remain underexplored. Here we present a novel investigation on the effect of the onset speed of a higher-order interaction. In particular, we study the stability of the equilibrium of all configurations of a three-species interaction network, including transitive as well as intransitive ones. We show that the HOI onset speed has a dramatic effect on the evolution and stability of the ecological network, with significant structural changes compared to commonly used HOI extensions or pairwise networks. Changes in the HOI onset speed from fast to slow can reverse the stability of the interaction network. The evolution of the system also affects the equilibrium that will be reached, influenced by the HOI onset speed. This implies that the HOI onset speed is an important determinant in the dynamics of ecological systems, and including it in models of ecological networks can improve our understanding thereof.

Calibrated Ecosystem Models Cannot Predict the Consequences of Conservation Management Decisions

Ecosystem models are often used to predict the consequences of management interventions in applied ecology and conservation. These models are often high-dimensional and nonlinear, yet limited data are available to calibrate or validate them. Consequently, their utility as decision-support tools is unclear. In this paper, we calibrate ecosystem models to time series data from 110 different experimental microcosm ecosystems, each containing three to five interacting species. Then, we assess their ability to predict the consequences of management interventions. Our results show that for each time series dataset, multiple divergent parameter sets offer equivalent, good fits. However, these models have poor predictive accuracy when forecasting future dynamics or when predicting how the ecosystem will respond to management intervention. Closer inspection reveals that the models fail because calibration cannot determine the nature of the interspecific interactions. Our findings question whether ecosystem models can support applied ecological decision-making when calibrated against real-world datasets.

Arbuscular mycorrhizal fungi equalize differences in plant fitness and facilitate plant species coexistence through niche differentiation

Mycorrhizal fungi are essential to the establishment of the vast majority of plant species but are often conceptualized with contradictory roles in plant community assembly. On the one hand, host-specific mycorrhizal fungi may allow a plant to be competitively dominant by enhancing growth. On the other hand, host-specific mycorrhizal fungi with different functional capabilities may increase nutrient niche partitioning, allowing plant species to coexist. Here, to resolve the balance of these two contradictory forces, we used a controlled greenhouse study to manipulate the presence of two main types of mycorrhizal fungus, ectomycorrhizal fungi and arbuscular mycorrhizal fungi, and used a range of conspecific and heterospecific competitor densities to investigate the role of mycorrhizal fungi in plant competition and coexistence. We find that the presence of arbuscular mycorrhizal fungi equalizes fitness differences between plants and stabilizes competition to create conditions for host species coexistence. Our results show how below-ground mutualisms can shift outcomes of plant competition and that a holistic view of plant communities that incorporates their mycorrhizal partners is important in predicting plant community dynamics.

Hypernetwork modeling and topology of high-order interactions for complex systems

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.

How combined pairwise and higher-order interactions shape transient dynamics

Understanding how species interactions shape biodiversity is a core challenge in ecology. While much focus has been on long-term stability, there is rising interest in transient dynamics-the short-lived periods when ecosystems respond to disturbances and adjust toward stability. These transitions are crucial for predicting ecosystem reactions and guiding effective conservation. Our study introduces a model that uses convex combinations to blend pairwise and higher-order interactions (HOIs), offering a more realistic view of natural ecosystems. We find that pairwise interactions slow the journey to stability, while HOIs speed it up. Employing global stability analysis and numerical simulations, we establish that as the proportion of HOIs increases, mean transient times exhibit a significant reduction, thereby underscoring the essential role of HOIs in enhancing biodiversity stabilization. Our results reveal a robust correlation between the most negative real part of the eigenvalues of the Jacobian matrix associated with the linearized system at the coexistence equilibrium and the mean transient times. This indicates that a more negative leading eigenvalue correlates with accelerated convergence to stable coexistence abundances. This insight is vital for comprehending ecosystem resilience and recovery, emphasizing the key role of HOIs in promoting stabilization. Amid growing interest in transient dynamics and its implications for biodiversity and ecological stability, our study enhances the understanding of how species interactions affect both transient and long-term ecosystem behavior. By addressing a critical gap in ecological theory and offering a practical framework for ecosystem management, our work advances knowledge of transient dynamics, ultimately informing effective conservation strategies.

Detecting Nonadditive Biotic Interactions and Assessing Their Biological Relevance among Temperate Rainforest Trees

AbstractInteractions between and within abiotic and biotic processes generate nonadditive density-dependent effects on species performance that can vary in strength or direction across environments. If ignored, nonadditivities can lead to inaccurate predictions of species responses to environmental and compositional changes. While there are increasing empirical efforts to test the constancy of pairwise biotic interactions along environmental and compositional gradients, few assess both simultaneously. Using a nationwide forest inventory that spans broad ambient temperature and moisture gradients throughout New Zealand, we address this gap by analyzing the diameter growth of six focal tree species as a function of neighbor densities and climate, as well as neighbor × climate and neighbor × neighbor statistical interactions. The most complex model featuring all interaction terms had the highest predictive accuracy. Compared with climate variables, biotic interactions typically had stronger effects on diameter growth, especially when subjected to nonadditivities from local climatic conditions and the density of intermediary species. Furthermore, statistically strong (or weak) nonadditivities could be biologically irrelevant (or significant) depending on whether a species pair typically interacted under average or more extreme conditions. Our study highlights the importance of considering both the statistical potential and the biological relevance of nonadditive biotic interactions when assessing species performance under global change.

Biobased short chain fatty acid production - Exploring microbial community dynamics and metabolic networks through kinetic and microbial modeling approaches

In recent years, there has been growing interest in harnessing anaerobic digestion technology for resource recovery from waste streams. This approach has evolved beyond its traditional role in energy generation to encompass the production of valuable carboxylic acids, especially volatile fatty acids (VFAs) like acetic acid, propionic acid, and butyric acid. VFAs hold great potential for various industries and biobased applications due to their versatile properties. Despite increasing global demand, over 90% of VFAs are currently produced synthetically from petrochemicals. Realizing the potential of large-scale biobased VFA production from waste streams offers significant eco-friendly opportunities but comes with several key challenges. These include low VFA production yields, unstable acid compositions, complex and expensive purification methods, and post-processing needs. Among these, production yield and acid composition stand out as the most critical obstacles impacting economic viability and competitiveness. This paper seeks to offer a comprehensive view of combining complementary modeling approaches, including kinetic and microbial modeling, to understand the workings of microbial communities and metabolic pathways in VFA production, enhance production efficiency, and regulate acid profiles through the integration of omics and bioreactor data.

Food web context modifies predator foraging and weakens trophic interaction strength

Trophic interaction modifications (TIM) are widespread in natural systems and occur when a third species indirectly alters the strength of a trophic interaction. Past studies have focused on documenting the existence and magnitude of TIMs; however, the underlying processes and long-term consequences remain elusive. To address this gap, we experimentally quantified the density-dependent effect of a third species on a predator's functional response. We conducted short-term experiments with ciliate communities composed of a predator, prey and non-consumable 'modifier' species. In both communities, increasing modifier density weakened the trophic interaction strength, due to a negative effect on the predator's space clearance rate. Simulated long-term dynamics indicate quantitative differences between models that account for TIMs or include only pairwise interactions. Our study demonstrates that TIMs are important to understand and predict community dynamics and highlights the need to move beyond focal species pairs to understand the consequences of species interactions in communities.

Global epistasis and the emergence of function in microbial consortia

The many functions of microbial communities emerge from a complex web of interactions between organisms and their environment. This poses a significant obstacle to engineering microbial consortia, hindering our ability to harness the potential of microorganisms for biotechnological applications. In this study, we demonstrate that the collective effect of ecological interactions between microbes in a community can be captured by simple statistical models that predict how adding a new species to a community will affect its function. These predictive models mirror the patterns of global epistasis reported in genetics, and they can be quantitatively interpreted in terms of pairwise interactions between community members. Our results illuminate an unexplored path to quantitatively predicting the function of microbial consortia from their composition, paving the way to optimizing desirable community properties and bringing the tasks of predicting biological function at the genetic, organismal, and ecological scales under the same quantitative formalism.

When can higher-order interactions produce stable coexistence?

Most ecological models are based on the assumption that species interact in pairs. Diverse communities, however, can have higher-order interactions, in which two or more species jointly impact the growth of a third species. A pitfall of the common pairwise approach is that it misses the higher-order interactions potentially responsible for maintaining natural diversity. Here, we explore the stability properties of systems where higher-order interactions guarantee that a specified set of abundances is a feasible equilibrium of the dynamics. Even these higher-order interactions which lead to equilibria do not necessarily produce stable coexistence. Instead, these systems are more likely to be stable when the pairwise interactions are weak or facilitative. Correlations between the pairwise and higher-order interactions, however, do permit robust coexistence even in diverse systems. Our work not only reveals the challenges in generating stable coexistence through higher-order interactions but also uncovers interaction patterns that can enable diversity.

Higher-order species interactions cause time-dependent niche and fitness differences: Experimental evidence in plant-feeding arthropods

Species interact in different ways, including competition, facilitation and predation. These interactions can be non-linear or higher order and may depend on time or species densities. Although these higher-order interactions are virtually ubiquitous, they remain poorly understood, as they are challenging both theoretically and empirically. We propose to adapt niche and fitness differences from modern coexistence theory and apply them to species interactions over time. As such, they may not merely inform about coexistence, but provide a deeper understanding of how species interactions change. Here, we investigated how the exploitation of a biotic resource (plant) by phytophagous arthropods affects their interactions. We performed monoculture and competition experiments to fit a generalized additive mixed model to the empirical data, which allowed us to calculate niche and fitness differences. We found that species switch between different types of interactions over time, including intra- and interspecific facilitation, and strong and weak competition.

Time-dependent interaction modification generated from plant-soil feedback

Pairwise interactions between species can be modified by other community members, leading to emergent dynamics contingent on community composition. Despite the prevalence of such higher-order interactions, little is known about how they are linked to the timing and order of species' arrival. We generate population dynamics from a mechanistic plant-soil feedback model, then apply a general theoretical framework to show that the modification of a pairwise interaction by a third plant depends on its germination phenology. These time-dependent interaction modifications emerge from concurrent changes in plant and microbe populations and are strengthened by higher overlap between plants' associated microbiomes. The interaction between this overlap and the specificity of microbiomes further determines plant coexistence. Our framework is widely applicable to mechanisms in other systems from which similar time-dependent interaction modifications can emerge, highlighting the need to integrate temporal shifts of species interactions to predict the emergent dynamics of natural communities.

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.

Matrix community models for ecology and evolution

Ecological communities are shaped by biotic interactions as well as environmental forces, and both must be incorporated to obtain models capable of forecasting realistic community dynamics. Many community models first specify pairwise biotic interactions and then secondarily examine how extrinsic factors such as abiotic conditions affect species abundances. A disadvantage of this approach is that the species interactions themselves are often environment and context specific, making parameterization difficult. We propose an alternative approach, matrix community models (MCMs), which are sets of matrix population models linked by an assumption of aggregate density dependence. MCMs incorporate detailed species autecology but are neutral with respect to pairwise species interactions, instead allowing interactions to be revealed within the model structure. These model-revealed species interactions, including competitive exclusion, facilitation, and interference competition, shape the distribution and abundance of species within communities and generate empirically testable predictions about species interactions. We develop a framework for building MCMs using vital rates in a stochastic, multispecies framework. Single-species matrix population models are connected via an assumption of aggregate density dependence, pairwise species interactions are estimated with sensitivity analysis, and community trajectories are analyzed under different environmental regimes using standard statistical tools and network analysis. MCMs have the advantage that pairwise species interactions need not be specified a priori, and that mechanistic demographic-environment linkages permit forecasting of community dynamics under novel, non-stationary environmental regimes. A challenge is that species' autecological vital rates, such as fecundity, growth and survivorship, must be measured under a diverse range of environmental conditions to parameterize the models. We illustrate the approach with examples and discuss prospects for future theoretical and empirical developments.

The existence and strength of higher order interactions is sensitive to environmental context

One strategy for understanding the dynamics of any complex system, such as a community of competing species, is to study the dynamics of parts of the system in isolation. Ecological communities can be decomposed into single species, and pairs of interacting species. This reductionist strategy assumes that whole-community dynamics are predictable and explainable from knowledge of the dynamics of single species and pairs of species. This assumption will be violated if higher order interactions (HOIs) are strong. Theory predicts that HOIs should be common. But it is difficult to detect HOIs, and to infer their long-term consequences for species coexistence, solely from short-term data. I conducted a protist microcosm experiment to test for HOIs among competing bacterivorous ciliates, and test the sensitivity of HOIs to environmental context. I grew three competing ciliate species in all possible combinations at each of two resource enrichment levels, and used the population dynamic data from the one- and two-species treatments to parameterize a competition model at each enrichment level. I then compared the predictions of the parameterized model to the dynamics of the whole community (three-species treatment). I found that the existence, and thus strength, of HOIs was environment dependent. I found a strong HOI at low enrichment, which enabled the persistence of a species that would otherwise have been competitively excluded. At high enrichment, three-species dynamics could be predicted from a parameterized model of one- and two-species dynamics, provided that the model accounted for nonlinear intraspecific density dependence. The results provide one of the first rigorous demonstrations of the long-term consequences of HOIs for species coexistence, and demonstrate the context dependence of HOIs. HOIs create difficult challenges for predicting and explaining species coexistence in nature.

Microbial interactions in theory and practice: when are measurements compatible with models?

Most predictive models of ecosystem dynamics are based on interactions between organisms: their influence on each other's growth and death. We review here how theoretical approaches are used to extract interaction measurements from experimental data in microbiology, particularly focusing on the generalised Lotka-Volterra (gLV) framework. Though widely used, we argue that the gLV model should be avoided for estimating interactions in batch culture - the most common, simplest and cheapest in vitro approach to culturing microbes. Fortunately, alternative approaches offer a way out of this conundrum. Firstly, on the experimental side, alternatives such as the serial-transfer and chemostat systems more closely match the theoretical assumptions of the gLV model. Secondly, on the theoretical side, explicit organism-environment interaction models can be used to study the dynamics of batch-culture systems. We hope that our recommendations will increase the tractability of microbial model systems for experimentalists and theoreticians alike.

Connecting higher-order interactions with ecological stability in experimental aquatic food webs

Community ecology is built on theories that represent the strength of interactions between species as pairwise links. Higher-order interactions (HOIs) occur when a species changes the pairwise interaction between a focal pair. Recent theoretical work has highlighted the stabilizing role of HOIs for large, simulated communities, yet it remains unclear how important higher-order effects are in real communities. Here, we used experimental communities of aquatic protists to examine the relationship between HOIs and stability (as measured by the persistence of a species in a community). We cultured a focal pair of consumers in the presence of additional competitors and a predator and collected time series data of their abundances. We then fitted competition models with and without HOIs to measure interaction strength between the focal pair across different community compositions. We used survival analysis to measure the persistence of individual species. We found evidence that additional species positively affected persistence of the focal species and that HOIs were present in most of our communities. However, persistence was only linked to HOIs for one of the focal species. Our results vindicate community ecology theory positing that species interactions may deviate from assumptions of pairwise interactions, opening avenues to consider possible consequences for coexistence and stability.

Mechanistic Models of Trophic Interactions: Opportunities for Species Richness and Challenges for Modern Coexistence Theory

AbstractMany potential mechanisms promote species coexistence, but we know little about their relative importance. To compare multiple mechanisms, we modeled a two-trophic planktonic food web based on mechanistic species interactions and empirically measured species traits. We simulated thousands of possible communities under realistic and altered interaction strengths to assess the relative importance of three potential drivers of phytoplankton and zooplankton species richness: resource-mediated coexistence mechanisms, predator-prey interactions, and trait trade-offs. Next, we computed niche and fitness differences of competing zooplankton to obtain a deeper understanding of how these mechanisms determine species richness. We found that predator-prey interactions were the most important driver of phytoplankton and zooplankton species richness and that large zooplankton fitness differences were associated with low species richness, but zooplankton niche differences were not associated with species richness. However, for many communities we could not apply modern coexistence theory to compute niche and fitness differences of zooplankton because of conceptual issues with the invasion growth rates arising from trophic interactions. We therefore need to expand modern coexistence theory to fully investigate multitrophic-level communities.

Universal gut microbial relationships in the gut microbiome of wild baboons

Ecological relationships between bacteria mediate the services that gut microbiomes provide to their hosts. Knowing the overall direction and strength of these relationships is essential to learn how ecology scales up to affect microbiome assembly, dynamics, and host health. However, whether bacterial relationships are generalizable across hosts or personalized to individual hosts is debated. Here, we apply a robust, multinomial logistic-normal modeling framework to extensive time series data (5534 samples from 56 baboon hosts over 13 years) to infer thousands of correlations in bacterial abundance in individual baboons and test the degree to which bacterial abundance correlations are 'universal'. We also compare these patterns to two human data sets. We find that, most bacterial correlations are weak, negative, and universal across hosts, such that shared correlation patterns dominate over host-specific correlations by almost twofold. Further, taxon pairs that had inconsistent correlation signs (either positive or negative) in different hosts always had weak correlations within hosts. From the host perspective, host pairs with the most similar bacterial correlation patterns also had similar microbiome taxonomic compositions and tended to be genetic relatives. Compared to humans, universality in baboons was similar to that in human infants, and stronger than one data set from human adults. Bacterial families that showed universal correlations in human infants were often universal in baboons. Together, our work contributes new tools for analyzing the universality of bacterial associations across hosts, with implications for microbiome personalization, community assembly, and stability, and for designing microbiome interventions to improve host health.

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

The temperature dependence of microbial community respiration is amplified by changes in species interactions

Respiratory release of CO2 by microorganisms is one of the main components of the global carbon cycle. However, there are large uncertainties regarding the effects of climate warming on the respiration of microbial communities, owing to a lack of mechanistic, empirically tested theory that incorporates dynamic species interactions. We present a general mathematical model which predicts that thermal sensitivity of microbial community respiration increases as species interactions change from competition to facilitation (for example, commensalism, cooperation and mutualism). This is because facilitation disproportionately increases positive feedback between the thermal sensitivities of species-level metabolic and biomass accumulation rates at warmer temperatures. We experimentally validate our theoretical predictions in a community of eight bacterial taxa and show that a shift from competition to facilitation, after a month of co-adaptation, caused a 60% increase in the thermal sensitivity of respiration relative to de novo assembled communities that had not co-adapted. We propose that rapid changes in species interactions can substantially change the temperature dependence of microbial community respiration, which should be accounted for in future climate-carbon cycle models.

Predator-mediated diversity of stream fish assemblages in a boreal river basin, China

Predator-prey interactions are critical for understanding species composition and community assembly; however, there is still limited research on whether and how the prey species composition or community assembly in natural communities are mediated by predators. To address this question, we performed a field investigation to examine the influence of the presence of Lutra lutra on the diversity of fish communities of the Hunchun River Basin, Jilin Province, China. Our results indicate that L. lutra, as a potential umbrella species and generalist predator in the stream ecosystem, promotes the coexistence of a vast variety of fish taxa, which emphasizes the importance of top-down control in the ecological community. We suggest that L. lutra regulates the fish community assembly likely through the stochastic process. Although this was a pilot study regarding predator-prey interactions, the results highlight the effects of predators on the prey community assembly, and emphasize the role of predators on the maintenance of biodiversity and ecosystem function. Future conservation decisions involving ecosystem biodiversity should require the inclusion of predation intensity. The inclusion of scientific research and protection of umbrella species would thus constitute an additional and important step in biodiversity conservation.

Coexistence in diverse communities with higher-order interactions

A central assumption in most ecological models is that the interactions in a community operate only between pairs of species. However, two species may interactively affect the growth of a focal species. Although interactions among three or more species, called higher-order interactions, have the potential to modify our theoretical understanding of coexistence, ecologists lack clear expectations for how these interactions shape community structure. Here we analytically predict and numerically confirm how the variability and strength of higher-order interactions affect species coexistence. We found that as higher-order interaction strengths became more variable across species, fewer species could coexist, echoing the behavior of pairwise models. If interspecific higher-order interactions became too harmful relative to self-regulation, coexistence in diverse communities was destabilized, but coexistence was also lost when these interactions were too weak and mutualistic higher-order effects became prevalent. This behavior depended on the functional form of the interactions as the destabilizing effects of the mutualistic higher-order interactions were ameliorated when their strength saturated with species' densities. Last, we showed that more species-rich communities structured by higher-order interactions lose species more readily than their species-poor counterparts, generalizing classic results for community stability. Our work provides needed theoretical expectations for how higher-order interactions impact species coexistence in diverse communities.

Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions

The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel perspective for understanding the influence of higher-order interactions on the evolution of social phenotypes. Our simple model yields a prosperous outlook to demonstrate the impact of perturbations on intransitive competitive higher-order interactions. Using a mathematical technique, we show how alone the perturbed interaction network can quickly determine the coexistence equilibrium of competing species instead of solving a large system of ordinary differential equations. It is possible to split the system into multiple feasible cluster states depending on the number of perturbations. Our analysis also reveals that the ratio between the unperturbed and perturbed species is inversely proportional to the amount of employed perturbation. Our results suggest that nonlinear dynamical systems and interaction topologies can be interplayed to comprehend species' coexistence under adverse conditions. Particularly, our findings signify that less competition between two species increases their abundance and outperforms others.

LiDAR Reveals the Process of Vision-Mediated Predator–Prey Relationships

Exploring the processes of interspecific relationships is crucial to understanding the mechanisms of biodiversity maintenance. Visually detecting interspecies relationships of large mammals is limited by the reconstruction accuracy of the environmental structure and the timely detection of animal behavior. Hence, we used backpack laser scanning (BLS) to reconstruct the high-resolution three-dimensional environmental structure to simulate the process of a predator approaching its prey, indicating that predator tigers would reduce their visibility by changing their behavior. Wild boars will nibble off about 5m of branches around the nest in order to create better visibility around the nest, adopting an anti-predation strategy to detect possible predators in advance. Our study not only points out how predator–prey relationships are affected by visibility as the environment mediates it, but also provides an operable framework for exploring interspecific relationships from a more complex dimension. Finally, this study provides a new perspective for exploring the mechanisms of biodiversity maintenance.

Detecting and interpreting higher-order interactions in ecological communities

When species simultaneously compete with two or more species of competitor, higher-order interactions (HOIs) can lead to emergent properties not present when species interact in isolated pairs. To extend ecological theory to multi-competitor communities, ecologists must confront the challenges of measuring and interpreting HOIs in models of competition fit to data from nature. Such efforts are hindered by the fact that different studies use different definitions, and these definitions have unclear relationships to one another. Here, we propose a distinction between 'soft' HOIs, which identify possible interaction modification by competitors, and 'hard' HOIs, which identify interactions uniquely emerging in systems with three or more competitors. We show how these two classes of HOI differ in their motivation and interpretation, as well as the tests one uses to identify them in models fit to data. We then show how to operationalise this structure of definitions by analysing the results of a simulated competition experiment underlain by a consumer resource model. In the course of doing so, we clarify the challenges of interpreting HOIs in nature, and suggest a more precise framing of this research endeavour to catalyse further investigations.

Linking Reactive Oxygen Species (ROS) to Abiotic and Biotic Feedbacks in Plant Microbiomes: The Dose Makes the Poison

In nature, plants develop in complex, adaptive environments. Plants must therefore respond efficiently to environmental stressors to maintain homeostasis and enhance their fitness. Although many coordinated processes remain integral for achieving homeostasis and driving plant development, reactive oxygen species (ROS) function as critical, fast-acting orchestrators that link abiotic and biotic responses to plant homeostasis and development. In addition to the suite of enzymatic and non-enzymatic ROS processing pathways that plants possess, they also rely on their microbiota to buffer and maintain the oxidative window needed to balance anabolic and catabolic processes. Strong evidence has been communicated recently that links ROS regulation to the aggregated function(s) of commensal microbiota and plant-growth-promoting microbes. To date, many reports have put forth insightful syntheses that either detail ROS regulation across plant development (independent of plant microbiota) or examine abiotic–biotic feedbacks in plant microbiomes (independent of clear emphases on ROS regulation). Here we provide a novel synthesis that incorporates recent findings regarding ROS and plant development in the context of both microbiota regulation and plant-associated microbes. Specifically, we discuss various roles of ROS across plant development to strengthen the links between plant microbiome functioning and ROS regulation for both basic and applied research aims.

Network structure of resource use and niche overlap within the endophytic microbiome

Endophytes often have dramatic effects on their host plants. Characterizing the relationships among members of these communities has focused on identifying the effects of single microbes on their host, but has generally overlooked interactions among the myriad microbes in natural communities as well as potential higher-order interactions. Network analyses offer a powerful means for characterizing patterns of interaction among microbial members of the phytobiome that may be crucial to mediating its assembly and function. We sampled twelve endophytic communities, comparing patterns of niche overlap between coexisting bacteria and fungi to evaluate the effect of nutrient supplementation on local and global competitive network structure. We found that, despite differences in the degree distribution, there were few significant differences in the global network structure of niche-overlap networks following persistent nutrient amendment. Likewise, we found idiosyncratic and weak evidence for higher-order interactions regardless of nutrient treatment. This work provides a first-time characterization of niche-overlap network structure in endophytic communities and serves as a framework for higher-resolution analyses of microbial interaction networks as a consequence and a cause of ecological variation in microbiome function.

The genus Caulobacter and its role in plant microbiomes

Recent omics approaches have revealed the prevalent microbial taxa that constitute the microbiome of various plant species. Across global scales and environmental conditions, strains belonging to the bacterial genus Caulobacter have consistently been found in association with various plant species. Aligned with agroecological relevance and biotechnological advances, many scientific communications have demonstrated that several Caulobacter strains (spanning several Caulobacter species) harbor the potential to enhance plant biomass for various plant species ranging from Arabidopsis to Citrullus and Zea mays. In the past several years, co-occurrence data have driven mechanistically resolved communications about select Caulobacter-plant interactions. Given the long-standing history of Caulobacter as a model organism for cell cycle regulation, genetic studies, and the prevalence of Caulobacter species in various plant microbiomes, the genus Caulobacter offers researchers a unique opportunity to leverage for investigating plant-microbe interactions and realizing targeted biotechnological applications. In this review, recent developments regarding Caulobacter-plant interactions are presented in terms of model utility for future biotechnological investigations.

Non-additive biotic interactions improve predictions of tropical tree growth and impact community size structure

Growth in individual size or biomass is a key demographic component in population models, with wide-ranging applications from quantifying species performance across abiotic or biotic conditions to assessing landscape-level dynamics under global change. In forest ecology, the responses of tree growth to biotic interactions are widely held to be crucial for understanding forest diversity, function, and structure. To date, most studies on plant-plant interactions only examine the additive competitive or facilitative interactions between species pairs; however, there is increasing evidence of non-additive, higher-order interactions (HOIs) impacting species demographic rates. When HOIs are present, the dynamics of a multispecies community cannot be fully understood or accurately predicted solely from pairwise outcomes because of how additional species "interfere" with the direct, pairwise interactions. Such HOIs should be particularly prevalent when species show non-linear functional responses to resource availability and resource-acquisition traits themselves are density dependent. With this in mind, we used data from a tropical secondary forest-a system that fulfills both of these conditions-to build an ontogenetic diameter growth model for individuals across 10 woody-plant species. We allowed both direct and indirect interactions within communities to influence the species-specific growth parameters in a generalized Lotka-Volterra model. Specifically, indirect interactions entered the model as higher-order quadratic terms, i.e., non-additive effects of conspecific and heterospecific neighbor size on the focal individual's growth. For the whole community and for four out of 10 focal species, the model that included HOIs had more statistical support than the model that included only direct interactions, despite the former containing a far greater number of parameters. HOIs had comparable effect sizes to direct interactions, and tended to further reduce the diameter growth rates of most species beyond what direct interactions had already reduced. In a simulation of successional stand dynamics, the inclusion of HOIs led to rank swaps in species' diameter hierarchies, even when community-level size distributions remained qualitatively similar. Our study highlights the implications, and discusses possible mechanisms, of non-additive density dependence in highly diverse and light-competitive tropical forests.

Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

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

Species richness increases fitness differences, but does not affect niche differences

A key question in ecology is what limits species richness. Modern coexistence theory presents the persistence of species as a balance between niche differences and fitness differences that favour and hamper coexistence, respectively. With most applications focusing on species pairs, however, we know little about if and how this balance changes with species richness. Here, we apply recently developed definitions of niche and fitness differences, based on invasion analysis, to multispecies communities. We present the first mathematical proof that, for invariant average interaction strengths, the average fitness difference among species increases with richness, while the average niche difference stays constant. Extensive simulations with more complex models and analyses of empirical data confirmed these mathematical results. Combined, our work suggests that, as species accumulate in ecosystems, ever-increasing fitness differences will at some point exceed constant niche differences, limiting species richness. Our results contribute to a better understanding of coexistence multispecies communities.

Towards a deeper understanding of microbial communities: integrating experimental data with dynamic models

Microbial communities and their functions are shaped by complex networks of interactions among microbes and with their environment. While the critical roles microbial communities play in numerous environments have become increasingly appreciated, we have a very limited understanding of their interactions and how these interactions combine to generate community-level behaviors. This knowledge gap hinders our ability to predict community responses to perturbations and to design interventions that manipulate these communities to our benefit. Dynamic models are promising tools to address these questions. We review existing modeling techniques to construct dynamic models of microbial communities at different scales and suggest ways to leverage multiple types of models and data to facilitate our understanding and engineering of microbial communities.

Emergent Shapes of Trait-Based Competition Functions from Resource-Based Models: A Gaussian Is Not Normal in Plant Communities

AbstractIn community ecology, it is widely assumed that organisms with similar traits compete more intensely with one another for resources. This assumption is often encoded into theory and empirical tests via a unimodal competition function, which predicts that per capita competitive effect declines with separation in traits. Yet it remains unknown how well this function represents the true effect of traits on competitive outcomes, especially for long-lived plant communities, where lifetime fitness is difficult to estimate. Here, we evaluate the shape of competition functions embedded in two resource-based (RB) models, wherein plants compete for shared, essential resources. In the first RB model individuals compete for two essential nutrients, and in the second they compete for light in a size-based successional setting. We compared the shapes of the competition functions that emerged from interactions within these RB models to the unimodal function and others shapes commonly applied. In few instances did the trait-based competition function emerging from the RB model even vaguely resemble any of the shapes previously used. The mismatch between these two approaches suggests that theory derived using fixed competition functions based on trait separation may not apply well to plant systems, where individuals compete for shared resources. The more promising path will be to model depletion of resources by populations in relation to their traits, with its consequences for fitness landscapes and competitive exclusion.

Natural enemies have inconsistent impacts on the coexistence of competing species

The role of natural enemies in promoting coexistence of competing species has generated substantial debate. Modern coexistence theory provides a detailed framework to investigate this topic, but there have been remarkably few empirical applications to the impact of natural enemies. We tested experimentally the capacity for a generalist enemy to promote coexistence of competing insect species, and the extent to which any impact can be predicted by trade-offs between reproductive rate and susceptibility to natural enemies. We used experimental mesocosms to conduct a fully factorial pairwise competition experiment for six rainforest Drosophila species, with and without a generalist pupal parasitoid. We then parameterised models of competition and examined the coexistence of each pair of Drosophila species within the framework of modern coexistence theory. We found idiosyncratic impacts of parasitism on pairwise coexistence, mediated through changes in fitness differences, not niche differences. There was no evidence of an overall reproductive rate-susceptibility trade-off. Pairwise reproductive rate-susceptibility relationships were not useful shortcuts for predicting the impact of parasitism on coexistence. Our results exemplify the value of modern coexistence theory in multi-trophic contexts and the importance of contextualising the impact of generalist natural enemies to determine their impact. In the set of species investigated, competition was affected by the higher trophic level, but the overall impact on coexistence cannot be easily predicted just from knowledge of relative susceptibility. Methodologically, our Bayesian approach highlights issues with the separability of model parameters within modern coexistence theory and shows how using the full posterior parameter distribution improves inferences. This method should be widely applicable for understanding species coexistence in a range of systems.

Beyond direct neighbourhood effects: higher-order interactions improve modelling and predicting tree survival and growth

It is known that biotic interactions are the key to species coexistence and maintenance of species diversity. Traditional studies focus overwhelmingly on pairwise interactions between organisms, ignoring complex higher-order interactions (HOIs). In this study, we present a novel method of calculating individual-level HOIs for trees, and use this method to test the importance of size- and distance-dependent individual-level HOIs to tree performance in a 25-ha temperate forest dynamic plot. We found that full HOI-inclusive models improved our ability to model and predict the survival and growth of trees, providing empirical evidence that HOIs strongly influence tree performance in this temperate forest. Specifically, assessed HOIs mitigate the competitive direct effects of neighbours on survival and growth of focal trees. Our study lays a foundation for future investigations of the prevalence and relative importance of HOIs in global forests and their impact on species diversity.

Identifying "Useful" Fitness Models: Balancing the Benefits of Added Complexity with Realistic Data Requirements in Models of Individual Plant Fitness

AbstractDirect species interactions are commonly included in individual fitness models used for coexistence and local diversity modeling. Though widely considered important for such models, direct interactions alone are often insufficient for accurately predicting fitness, coexistence, or diversity outcomes. Incorporating higher-order interactions (HOIs) can lead to more accurate individual fitness models but also adds many model terms, which can quickly result in model overfitting. We explore approaches for balancing the trade-off between tractability and model accuracy that occurs when HOIs are added to individual fitness models. To do this, we compare models parameterized with data from annual plant communities in Australia and Spain, varying in the extent of information included about the focal and neighbor species. The best-performing models for both data sets were those that grouped neighbors based on origin status and life form, a grouping approach that reduced the number of model parameters substantially while retaining important ecological information about direct interactions and HOIs. Results suggest that the specific identity of focal or neighbor species is not necessary for building well-performing fitness models that include HOIs. In fact, grouping neighbors by even basic functional information seems sufficient to maximize model accuracy, an important outcome for the practical use of HOI-inclusive fitness models.

Hidden layers of density dependence in consumer feeding rates

Functional responses relate a consumer's feeding rates to variation in its abiotic and biotic environment, providing insight into consumer behaviour and fitness, and underpinning population and food-web dynamics. Despite their broad relevance and long-standing history, we show here that the types of density dependence found in classic resource- and consumer-dependent functional-response models equate to strong and often untenable assumptions about the independence of processes underlying feeding rates. We first demonstrate mathematically how to quantify non-independence between feeding and consumer interference and between feeding on multiple resources. We then analyse two large collections of functional-response data sets to show that non-independence is pervasive and borne out in previously hidden forms of density dependence. Our results provide a new lens through which to view variation in consumer feeding rates and disentangle the biological underpinnings of species interactions in multi-species contexts.

Habitat loss alters effects of intransitive higher-order competition on biodiversity: a new metapopulation framework

Recent studies have suggested that intransitive competition, as opposed to hierarchical competition, allows more species to coexist. Furthermore, it is recognized that the prevalent paradigm, which assumes that species interactions are exclusively pairwise, may be insufficient. More importantly, whether and how habitat loss, a key driver of biodiversity loss, can alter these complex competition structures (and therefore species coexistence) remain unclear. We thus present a new, simple yet comprehensive metapopulation framework that can account for any competition pattern and more complex higher-order interactions (HOIs) among species. We find that competitive intransitivity increases community diversity and that HOIs generally enhance this effect. Essentially, intransitivity promotes species richness by preventing the dominance of a few species, unlike the hierarchical competition, while HOIs facilitate species coexistence through stabilizing community fluctuations. However, variation in species' vital rates and habitat loss can weaken or even reverse such higher-order effects, as their interaction can lead to a more rapid decline in competitive intransitivity under HOIs. Thus, it is essential to correctly identify the most appropriate interaction model for a given system before models are used to inform conservation efforts. Overall, our simple model framework provides a more parsimonious explanation for biodiversity maintenance than the existing theory.

gauseR: Simple methods for fitting Lotka-Volterra models describing Gause's "Struggle for Existence"

Point 1: The ecological models of Alfred J. Lotka and Vito Volterra have had an enormous impact on ecology over the past century. Some of the earliest-and clearest-experimental tests of these models were famously conducted by Georgy Gause in the 1930s. Although well known, the data from these experiments are not widely available and are often difficult to analyze using standard statistical and computational tools. Point 2: Here, we introduce the gauseR package, a collection of tools for fitting Lotka-Volterra models to time series data of one or more species. The package includes several methods for parameter estimation and optimization, and includes 42 datasets from Gause's species interaction experiments and related work. Additionally, we include with this paper a short blog post discussing the historical importance of these data and models, and an R vignette with a walk-through introducing the package methods. The package is available for download at github.com/adamtclark/gauseR. Point 3: To demonstrate the package, we apply it to several classic experimental studies from Gause, as well as two other well-known datasets on multi-trophic dynamics on Isle Royale, and in spatially structured mite populations. In almost all cases, models fit observations closely and fitted parameter values make ecological sense. Point 4: Taken together, we hope that the methods, data, and analyses that we present here provide a simple and user-friendly way to interact with complex ecological data. We are optimistic that these methods will be especially useful to students and educators who are studying ecological dynamics, as well as researchers who would like a fast tool for basic analyses.

Ecological models: higher complexity in, higher feasibility out

Finding a compromise between tractability and realism has always been at the core of ecological modelling. The introduction of nonlinear functional responses in two-species models has reconciled part of this compromise. However, it remains unclear whether this compromise can be extended to multispecies models. Yet, answering this question is necessary in order to differentiate whether the explanatory power of a model comes from the general form of its polynomial or from a more realistic description of multispecies systems. Here, we study the probability of feasibility (the existence of at least one positive real equilibrium) in complex models by adding higher-order interactions and nonlinear functional responses to the linear Lotka-Volterra model. We characterize complexity by the number of free-equilibrium points generated by a model, which is a function of the polynomial degree and system's dimension. We show that the probability of generating a feasible system in a model is an increasing function of its complexity, regardless of the specific mechanism invoked. Furthermore, we find that the probability of feasibility in a model will exceed that of the linear Lotka-Volterra model when a minimum level of complexity is reached. Importantly, this minimum level is modulated by parameter restrictions, but can always be exceeded via increasing the polynomial degree or system's dimension. Our results reveal that conclusions regarding the relevance of mechanisms embedded in complex models must be evaluated in relation to the expected explanatory power of their polynomial forms.