Detecting and interpreting higher-order interactions in ecological communities

Fluctuation-Dependent Coexistence of Stage-Structured Species

AbstractModern coexistence theory is a dominant framework for understanding how environmental fluctuations promote species coexistence. However, assessing fluctuation-dependent mechanisms of coexistence in empirical systems-in which species have diverse life histories and environment-competition relationships-has remained challenging for many ecologists. To help empiricists and theoreticians alike build intuition for the role of fluctuation-dependent mechanisms across systems and environments, we explore how two stage-structured life histories-perennial and seedbanking annuals-differ in competition with a nonseedbanking annual across three environmental scenarios. Our scenarios delineate how species partition resources within and among years and whether competition is most intense during favorable or unfavorable periods. We use this work to link differences in vital rates and interaction strengths to patterns and mechanisms of coexistence. Fluctuation-dependent mechanisms of coexistence can be equally important for perennial species with an adult "storage" stage as for seedbanking annuals. However, coexistence outcomes differentiate between these two stage-structured strategies based on whether they experience stronger or weaker competition in favorable environments. This work sets the stage for applying coexistence theory and fluctuation-dependent partitioning frameworks to perennial and mixed stage-structure communities, facilitating understanding of how environmental variation drives species dynamics across a broader range of systems.

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.

Changes in flowering phenology with altered rainfall and the potential community impacts in an annual grassland

PREMISE

Shifts in the timing of life history events, or phenology, have been recorded across many taxa and biomes in response to global change. These phenological changes are often studied in a single species context, but considering the community context is essential for anticipating the cascading effects on biotic interactions that are likely to occur. Focusing on an annual grassland plant community, we examined how experimental changes in precipitation affect flowering phenology in a community context and explore the implications of these shifts for competitive interactions and species coexistence.

METHODS

We experimentally manipulated rainfall with rainout shelters and recorded detailed flowering phenology data for seven annual species including two grasses and five forbs. We assessed how their first and peak flowering days were affected by changes in rainfall and explored how flowering overlap between competing species changed.

RESULTS

Changes in rainfall shifted flowering phenology of some species, but sensitivity differed among neighboring species. Four of the seven species studied started and/or peaked flowering earlier in response to reduced water availability. The idiosyncratic shifts in flowering phenology have the potential to alter existing temporal dynamics that may be maintaining coexistence, such as temporal separation of resource-use among neighbors.

CONCLUSIONS

Our results show how species-specific phenological consequences of global change can impact community dynamics and competition between neighboring plants and warrant future research.

A Continuum From Positive to Negative Interactions Drives Plant Species' Performance in a Diverse Community

With many species interacting in nature, determining which interactions describe community dynamics is nontrivial. By applying a computational modeling approach to an extensive field survey, we assessed the importance of interactions from plants (both inter- and intra-specific), pollinators and insect herbivores on plant performance (i.e., viable seed production). We compared the inclusion of interaction effects as aggregate guild-level terms versus terms specific to taxonomic groups. We found that a continuum from positive to negative interactions, containing mostly guild-level effects and a few strong taxonomic-specific effects, was sufficient to describe plant performance. While interactions with herbivores and intraspecific plants varied from weakly negative to weakly positive, heterospecific plants mainly promoted competition and pollinators facilitated plants. The consistency of these empirical findings over 3 years suggests that including the guild-level effects and a few taxonomic-specific groups rather than all pairwise and high-order interactions, can be sufficient for accurately describing species variation in plant performance across natural 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.

Similar Conditions With Opposite Effects: Predation-Risk Effects on Prey Abundance Are Highly Contingent

Experiments have shown that predation-risk effects on prey fitness can be highly contingent on environmental conditions, suggesting a potential difficulty in generalizing risk effects on prey abundance in natural settings. Rather than study the influence of a particular controlled factor, we examine the problem with a novel approach. We examined the influence of risk effects in multiple experiments performed under similar study conditions. Any differences in the experiments would typically be deemed incidental, that is, they would not be given attention in methodology, nor be presented as factors affecting results or inferences. Therefore, any differences in the magnitude and direction of risk effects among experiments would indicate that risk effects on prey population abundance are strongly influenced by context in natural communities. The multiple experiments were conducted under similar conditions, objectives, measurables and implementation, and captured much of the complexity of natural systems (e.g., they were performed with diverse prey assemblages (≥ 11 taxa) over multiple prey generations). Our results highlight the potentially profound context dependence of risk effects: risk effects on the density of some zooplankton species varied between a significant negative effect in one experiment to a significant positive effect in another, whereas other species showed significant negative or positive effects in one experiment and no effect in another. We review mechanisms that could underlie risk effects having opposite effects on the same prey. Our findings illustrate that risk effects observed in one study may not hold, even for the same species in the same system.

Stability of Ecological Systems: A Theoretical Review

The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on the theoretical frameworks for analyzing the stability of ecological systems. Notably, we survey various stability notions, including linear stability, sign stability, diagonal stability, D-stability, total stability, sector stability, and structural stability. For each of these stability notions, we examine necessary or sufficient conditions for achieving such stability and demonstrate the intricate interplay of these conditions on the network structures of ecological systems. We further discuss the stability of ecological systems with higher-order interactions.

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.

Consequences of Local Conspecific Density Effects for Plant Diversity and Community Dynamics

Conspecific density dependence (CDD) in plant populations is widespread, most likely caused by local-scale biotic interactions, and has potentially important implications for biodiversity, community composition, and ecosystem processes. However, progress in this important area of ecology has been hindered by differing viewpoints on CDD across subfields in ecology, lack of synthesis across CDD-related frameworks, and misunderstandings about how empirical measurements of local CDD fit within the context of broader ecological theories on community assembly and diversity maintenance. Here, we propose a conceptual synthesis of local-scale CDD and its causes, including species-specific antagonistic and mutualistic interactions. First, we compare and clarify different uses of CDD and related concepts across subfields within ecology. We suggest the use of local stabilizing/destabilizing CDD to refer to the scenario where local conspecific density effects are more negative/positive than heterospecific effects. Second, we discuss different mechanisms for local stabilizing and destabilizing CDD, how those mechanisms are interrelated, and how they cut across several fields of study within ecology. Third, we place local stabilizing/destabilizing CDD within the context of broader ecological theories and discuss implications and challenges related to scaling up the effects of local CDD on populations, communities, and metacommunities. The ultimate goal of this synthesis is to provide a conceptual roadmap for researchers studying local CDD and its implications for population and community dynamics.

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.

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.

Trophic tug-of-war: Coexistence mechanisms within and across trophic levels

Ecological communities encompass rich diversity across multiple trophic levels. While modern coexistence theory has been widely applied to understand community assembly, its traditional formalism only allows assembly within a single trophic level. Here, using an expanded definition of niche and fitness differences applicable to multitrophic communities, we study how diversity within and across trophic levels affects species coexistence. If each trophic level is analysed separately, both lower- and higher trophic levels are governed by the same coexistence mechanisms. In contrast, if the multitrophic community is analysed as a whole, different trophic levels are governed by different coexistence mechanisms: coexistence at lower trophic levels is predominantly limited by fitness differences, whereas coexistence at higher trophic levels is predominantly limited by niche differences. This dichotomy in coexistence mechanisms is supported by theoretical derivations, simulations of phenomenological and trait-based models, and a case study of a primeval forest ecosystem. Our work provides a general and testable prediction of coexistence mechanism operating in multitrophic communities.

Positive associations fuel soil biodiversity and ecological networks worldwide

Microbial interactions are key to maintaining soil biodiversity. However, whether negative or positive associations govern the soil microbial system at a global scale remains virtually unknown, limiting our understanding of how microbes interact to support soil biodiversity and functions. Here, we explored ecological networks among multitrophic soil organisms involving bacteria, protists, fungi, and invertebrates in a global soil survey across 20 regions of the planet and found that positive associations among both pairs and triads of soil taxa governed global soil microbial networks. We further revealed that soil networks with greater levels of positive associations supported larger soil biodiversity and resulted in lower network fragility to withstand potential perturbations of species losses. Our study provides unique evidence of the widespread positive associations between soil organisms and their crucial role in maintaining the multitrophic structure of soil biodiversity worldwide.

Bridging theory and experiments of priority effects

Priority effects play a key role in structuring natural communities, but considerable confusion remains about how they affect different ecological systems. Synthesizing previous studies, we show that this confusion arises because the mechanisms driving priority and the temporal scale at which they operate differ among studies, leading to divergent outcomes in species interactions and biodiversity patterns. We suggest grouping priority effects into two functional categories based on their mechanisms: frequency-dependent priority effects that arise from positive frequency dependence, and trait-dependent priority effects that arise from time-dependent changes in interacting traits. Through easy quantification of these categories from experiments, we can construct community models representing diverse biological mechanisms and interactions with priority effects, therefore better predicting their consequences across ecosystems.

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.

Uncovering the metabolic pathway of novel Burkholderia sp. for efficient triclosan degradation and implication: Insight from exogenous bioaugmentation and toxicity pressure

Triclosan (TCS), a synthetic and broad-spectrum antimicrobial agent, is frequently detected in various environmental matrices. A novel TCS degrading bacterial strain, Burkholderia sp. L303, was isolated from local activated sludge. The strain could metabolically degrade TCS up to 8 mg/L, and optimal conditions for TCS degradation were at temperature of 35 °C, pH 7, and an increased inoculum size. During TCS degradation, several intermediates were identified, with the initial degradation occurring mainly through hydroxylation of aromatic ring, followed by dechlorination. Further intermediates such as 2-chlorohydroquinone, 4-chlorocatechol, and 4-chlorophenol were produced via ether bond fission and C-C bond cleavage, which could be further transformed into unchlorinated compounds, ultimately resulting in the complete stoichiometric free chloride release. Bioaugmentation of strain L303 in non-sterile river water demonstrated better degradation than in sterile water. Further exploration of the microbial communities provided insights into the composition and succession of the microbial communities under the TCS stress as well as during the TCS biodegradation process in real water samples, the key microorganisms involved in TCS biodegradation or showing resistance to the TCS toxicity, and the changes in microbial diversity related to exogenous bioaugmentation, TCS input, and TCS elimination. These findings shed light on the metabolic degradation pathway of TCS and highlight the significance of microbial communities in the bioremediation of TCS-contaminated environments.

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.

Experimental evidence for a hidden network of higher-order interactions in a diverse arthropod community

Transcending pairwise interactions in ecological networks remains a challenge.^1,2,3,4,5 Higher-order interactions (HOIs), the modulation of a pairwise interaction by a third species,⁶ are thought to play a particularly important role in stabilizing coexistence and maintaining species diversity.^{7,8,9,10,11,12} However, HOIs have so far only been demonstrated in models^{9,10,11,12,13,14} or isolated experimental systems including only a few interacting species.^7,8,15 Their ubiquity and importance at a community level in the real world remain unknown. We hypothesized that a complex network of HOIs could be constantly modifying pairwise interactions and shaping ecological communities and that consequently the outcome of pairwise interactions would be a product of many influences from distinct sources. Using field experiments, we tested how multiple interactions within a diverse arthropod community associated with the tropical shrub Baccharis dracunculifolia D.C. (Asteraceae) were modified by the removal of ant species or live or hatched insect galls (a non-trophic engineering effect) of the dominant galler species. We revealed an extensive hidden network of HOIs modifying each other and the "visible" pairwise interactions. Most pairwise interactions were affected indirectly by the manipulation of non-interacting taxonomic groups. The pervasiveness of these interaction modifications challenges pairwise approaches to understanding interaction outcomes and could shift our thinking about the structure and persistence of ecological communities. Investigating coexistence mechanisms involving interaction modulation by HOIs may be key to elucidating the underlying causes of the stability and persistence of ecological communities.

Small rainfall changes drive substantial changes in plant coexistence

Although precipitation patterns have long been known to shape plant distributions1, the effect of changing climate on the interactions of species and therefore community composition is far less understood2,3. Here, we explored how changes in precipitation alter competitive dynamics via direct effects on individual species, as well as by the changing strength of competitive interactions between species, using an annual grassland community in California. We grew plants under ambient and reduced precipitation in the field to parameterize a competition model4 with which we quantified the stabilizing niche and fitness differences that determine species coexistence in each rainfall regime. We show that reduced precipitation had little direct effect on species grown alone, but it qualitatively shifted predicted competitive outcomes for 10 of 15 species pairs. In addition, species pairs that were functionally more similar were less likely to experience altered outcomes, indicating that functionally diverse communities may be most threatened by changing interactions. Our results highlight how important it is to account for changes to species interactions when predicting species and community response to global change.

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.