Structural forecasting of species persistence under changing environments

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.

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

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

Structured community transitions explain the switching capacity of microbial systems

Microbial systems appear to exhibit a relatively high switching capacity of moving back and forth among few dominant communities (taxon memberships). While this switching behavior has been mainly attributed to random environmental factors, it remains unclear the extent to which internal community dynamics affect the switching capacity of microbial systems. Here, we integrate ecological theory and empirical data to demonstrate that structured community transitions increase the dependency of future communities on the current taxon membership, enhancing the switching capacity of microbial systems. Following a structuralist approach, we propose that each community is feasible within a unique domain in environmental parameter space. Then, structured transitions between any two communities can happen with probability proportional to the size of their feasibility domains and inversely proportional to their distance in environmental parameter space-which can be treated as a special case of the gravity model. We detect two broad classes of systems with structured transitions: one class where switching capacity is high across a wide range of community sizes and another class where switching capacity is high only inside a narrow size range. We corroborate our theory using temporal data of gut and oral microbiota (belonging to class 1) as well as vaginal and ocean microbiota (belonging to class 2). These results reveal that the topology of feasibility domains in environmental parameter space is a relevant property to understand the changing behavior of microbial systems. This knowledge can be potentially used to understand the relevant community size at which internal dynamics can be operating in microbial systems.

On the limits to invasion prediction using coexistence outcomes

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

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

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

Structural asymmetry in biotic interactions as a tool to understand and predict ecological persistence

A universal feature of ecological systems is that species do not interact with others with the same sign and strength. Yet, the consequences of this asymmetry in biotic interactions for the short- and long-term persistence of individual species and entire communities remains unclear. Here, we develop a set of metrics to evaluate how asymmetric interactions among species translate to asymmetries in their individual vulnerability to extinction under changing environmental conditions. These metrics, which solve previous limitations of how to independently quantify the size from the shape of the so-called feasibility domain, provide rigorous advances to understand simultaneously why some species and communities present more opportunities to persist than others. We further demonstrate that our shape-related metrics are useful to predict short-term changes in species' relative abundances during 7 years in a Mediterranean grassland. Our approach is designed to be applied to any ecological system regardless of the number of species and type of interactions. With it, we show that is possible to obtain both mechanistic and predictive information on ecological persistence for individual species and entire communities, paving the way for a stronger integration of theoretical and empirical research.

Mean species responses predict effects of environmental change on coexistence

Environmental change research is plagued by the curse of dimensionality: the number of communities at risk and the number of environmental drivers are both large. This raises the pressing question if a general understanding of ecological effects is achievable. Here, we show evidence that this is indeed possible. Using theoretical and simulation-based evidence for bi- and tritrophic communities, we show that environmental change effects on coexistence are proportional to mean species responses and depend on how trophic levels on average interact prior to environmental change. We then benchmark our findings using relevant cases of environmental change, showing that means of temperature optima and of species sensitivities to pollution predict concomitant effects on coexistence. Finally, we demonstrate how to apply our theory to the analysis of field data, finding support for effects of land use change on coexistence in natural invertebrate communities.

Rapid monitoring of ecological persistence

Effective conservation of ecological communities requires accurate and up-to-date information about whether species are persisting or declining to extinction. The persistence of an ecological community is supported by its underlying network of species interactions. While the persistence of the network supporting the whole community is the most relevant scale for conservation, in practice, only small subsets of these networks can be monitored. There is therefore an urgent need to establish links between the small snapshots of data conservationists can collect, and the "big picture" conclusions about ecosystem health demanded by policymakers, scientists, and societies. Here, we show that the persistence of small subnetworks (motifs) in isolation-that is, their persistence when considered separately from the larger network of which they are a part-is a reliable probabilistic indicator of the persistence of the network as a whole. Our methods show that it is easier to detect if an ecological community is not persistent than if it is persistent, allowing for rapid detection of extinction risk in endangered systems. Our results also justify the common practice of predicting ecological persistence from incomplete surveys by simulating the population dynamics of sampled subnetworks. Empirically, we show that our theoretical predictions are supported by data on invaded networks in restored and unrestored areas, even in the presence of environmental variability. Our work suggests that coordinated action to aggregate information from incomplete sampling can provide a means to rapidly assess the persistence of entire ecological networks and the expected success of restoration strategies.

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

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

Understanding the impact of third-party species on pairwise coexistence

The persistence of virtually every single species depends on both the presence of other species and the specific environmental conditions in a given location. Because in natural settings many of these conditions are unknown, research has been centered on finding the fraction of possible conditions (probability) leading to species coexistence. The focus has been on the persistence probability of an entire multispecies community (formed of either two or more species). However, the methodological and philosophical question has always been whether we can observe the entire community and, if not, what the conditions are under which an observed subset of the community can persist as part of a larger multispecies system. Here, we derive long-term (using analytical calculations) and short-term (using simulations and experimental data) system-level indicators of the effect of third-party species on the coexistence probability of a pair (or subset) of species under unknown environmental conditions. We demonstrate that the fraction of conditions incompatible with the possible coexistence of a pair of species tends to become vanishingly small within systems of increasing numbers of species. Yet, the probability of pairwise coexistence in isolation remains approximately the expected probability of pairwise coexistence in more diverse assemblages. In addition, we found that when third-party species tend to reduce (resp. increase) the coexistence probability of a pair, they tend to exhibit slower (resp. faster) rates of competitive exclusion. Long-term and short-term effects of the remaining third-party species on all possible specific pairs in a system are not equally distributed, but these differences can be mapped and anticipated under environmental uncertainty.

It is debated whether the frequency with which two species coexist in isolation or within a single environmental context is representative of their coexistence expectation within larger multispecies systems and across different environmental conditions. Here, using analytical calculations, simulations, and experimental data, we show why and how third-party species can provide the opportunity for pairwise coexistence regardless of whether a pair of species can coexist in isolation across different environmental conditions. However, we show that this opportunity is not homogeneously granted across all pairs within the same system. We provide a framework to understand and map the long-term and short-term effects that third-party species have on the coexistence of each possible subset in a multispecies system.

Multispecies coexistence in fragmented landscapes

Spatial dynamics have long been recognized as an important driver of biodiversity. However, our understanding of species' coexistence under realistic landscape configurations has been limited by lack of adequate analytical tools. To fill this gap, we develop a spatially explicit metacommunity model of multiple competing species and derive analytical criteria for their coexistence in fragmented heterogeneous landscapes. Specifically, we propose measures of niche and fitness differences for metacommunities, which clarify how spatial dynamics and habitat configuration interact with local competition to determine coexistence of species. We parameterize our model with a Bayesian approach using a 36-y time-series dataset of three Daphnia species in a rockpool metacommunity covering >500 patches. Our results illustrate the emergence of interspecific variation in extinction and recolonization processes, including their dependencies on habitat size and environmental temperature. We find that such interspecific variation contributes to the coexistence of Daphnia species by reducing fitness differences and increasing niche differences. Additionally, our parameterized model allows separating the effects of habitat destruction and temperature change on species extinction. By integrating coexistence theory and metacommunity theory, our study provides platforms to increase our understanding of species' coexistence in fragmented heterogeneous landscapes and the response of biodiversity to environmental changes.

State-Space-Based Framework for Predicting Microbial Interaction Variability in Wastewater Treatment Plants

Substantial attempts have been made to control microbial communities for environmental integrity, biosystem performance, and human health. However, it is difficult to manipulate microbial communities in practice due to the varying and nonlinear nature of interspecific interaction networks. Here, we develop a manifold-based framework to investigate the patterns of microbial interaction variability in wastewater treatment plants using manifold geometric properties and design a simple control strategy to manipulate the microbes in nonlinear communities. We validate our framework using the readily available and nonsequential microbiome profiles of wastewater treatment plants. Our results show that some microbes in the activated sludge and anammox communities display deterministic rival or cooperative relationships and constitute a stable subnetwork within the whole nonlinear community network. We further use a simulation to demonstrate that these microbes can be used to drive a microbe in a target direction regardless of the community dynamics. Overall, our framework can provide a time-efficient solution to select effective control inputs for reliable manipulation in varying microbial networks, opening up new possibilities across a range of biological fields, including wastewater treatment plants.

Towards a system-level causative knowledge of pollinator communities

Pollination plays a central role in both crop production and maintaining biodiversity. However, habitat loss, pesticides, invasive species and larger environmental fluctuations are contributing to a dramatic decline of pollinators worldwide. Different management solutions require knowledge of how ecological communities will respond following interventions. Yet, anticipating the response of these systems to interventions remains extremely challenging due to the unpredictable nature of ecological communities, whose nonlinear behaviour depends on the specific details of species interactions and the various unknown or unmeasured confounding factors. Here, we propose that this knowledge can be derived by following a probabilistic systems analysis rooted on non-parametric causal inference. The main outcome of this analysis is to estimate the extent to which a hypothesized cause can increase or decrease the probability that a given effect happens without making assumptions about the form of the cause-effect relationship. We discuss a road map for how this analysis can be accomplished with the aim of increasing our system-level causative knowledge of natural communities. This article is part of the theme issue 'Natural processes influencing pollinator health: from chemistry to landscapes'.

Fine scale prediction of ecological community composition using a two-step sequential Machine Learning ensemble

Prediction is one of the last frontiers in ecology. Indeed, predicting fine-scale species composition in natural systems is a complex challenge as multiple abiotic and biotic processes operate simultaneously to determine local species abundances. On the one hand, species intrinsic performance and their tolerance limits to different abiotic pressures modulate species abundances. On the other hand, there is growing recognition that species interactions play an equally important role in limiting or promoting such abundances within ecological communities. Here, we present a joint effort between ecologists and data scientists to use data-driven models to predict species abundances using reasonably easy to obtain data. We propose a sequential data-driven modeling approach that in a first step predicts the potential species abundances based on abiotic variables, and in a second step uses these predictions to model the realized abundances once accounting for species competition. Using a curated data set over five years we predict fine-scale species abundances in a highly diverse annual plant community. Our models show a remarkable spatial predictive accuracy using only easy-to-measure variables in the field, yet such predictive power is lost when temporal dynamics are taken into account. This result suggests that predicting future abundances requires longer time series analysis to capture enough variability. In addition, we show that these data-driven models can also suggest how to improve mechanistic models by adding missing variables that affect species performance such as particular soil conditions (e.g. carbonate availability in our case). Robust models for predicting fine-scale species composition informed by the mechanistic understanding of the underlying abiotic and biotic processes can be a pivotal tool for conservation, especially given the human-induced rapid environmental changes we are experiencing. This objective can be achieved by promoting the knowledge gained with classic modelling approaches in ecology and recently developed data-driven models.

The spatial configuration of biotic interactions shapes coexistence-area relationships in an annual plant community

The increase of species richness with area is a universal phenomenon on Earth. However, this observation contrasts with our poor understanding of how these species-area relationships (SARs) emerge from the collective effects of area, spatial heterogeneity, and local interactions. By combining a structuralist approach with five years of empirical observations in a highly-diverse Mediterranean grassland, we show that spatial heterogeneity plays a little role in the accumulation of species richness with area in our system. Instead, as we increase the sampled area more species combinations are realized, and they coexist mainly due to direct pairwise interactions rather than by changes in single-species dominance or by indirect interactions. We also identify a small set of transient species with small population sizes that are consistently found across spatial scales. These findings empirically support the importance of the architecture of species interactions together with stochastic events for driving coexistence- and species-area relationships.

Understanding the emergence of contingent and deterministic exclusion in multispecies communities

Competitive exclusion can be classified as deterministic or as historically contingent. While competitive exclusion is common in nature, it has remained unclear when multispecies communities formed by more than two species should be dominated by deterministic or contingent exclusion. Here, we take a fully parameterised model of an empirical competitive system between invasive annual and native perennial plant species to explain both the emergence and sources of competitive exclusion in multispecies communities. Using a structural approach to understand the range of parameters promoting deterministic and contingent exclusions, we then find heuristic theoretical support for the following three general conclusions. First, we find that the life-history of perennial species increases the probability of observing contingent exclusion by increasing their effective intrinsic growth rates. Second, we find that the probability of observing contingent exclusion increases with weaker intraspecific competition, and not with the level of hierarchical competition. Third, we find a shift from contingent exclusion to deterministic exclusion with increasing numbers of competing species. Our work provides a heuristic framework to increase our understanding about the predictability of species persistence within multispecies communities.

Generalizing game-changing species across microbial communities

Microbes form multispecies communities that play essential roles in our environment and health. Not surprisingly, there is an increasing need for understanding if certain invader species will modify a given microbial community, producing either a desired or undesired change in the observed collection of resident species. However, the complex interactions that species can establish between each other and the diverse external factors underlying their dynamics have made constructing such understanding context-specific. Here we integrate tractable theoretical systems with tractable experimental systems to find general conditions under which non-resident species can change the collection of resident communities-game-changing species. We show that non-resident colonizers are more likely to be game-changers than transients, whereas game-changers are more likely to suppress than to promote resident species. Importantly, we find general heuristic rules for game-changers under controlled environments by integrating mutual invasibility theory with in vitro experimental systems, and general heuristic rules under changing environments by integrating structuralist theory with in vivo experimental systems. Despite the strong context-dependency of microbial communities, our work shows that under an appropriate integration of tractable theoretical and experimental systems, it is possible to unveil regularities that can then be potentially extended to understand the behavior of complex natural communities.

Coexistence holes characterize the assembly and disassembly of multispecies systems

A central goal of ecological research has been to understand the limits on the maximum number of species that can coexist under given constraints. However, we know little about the assembly and disassembly processes under which a community can reach such a maximum number, or whether this number is in fact attainable in practice. This limitation is partly due to the challenge of performing experimental work and partly due to the lack of a formalism under which one can systematically study such processes. Here, we introduce a formalism based on algebraic topology and homology theory to study the space of species coexistence formed by a given pool of species. We show that this space is characterized by ubiquitous discontinuities that we call coexistence holes (that is, empty spaces surrounded by filled space). Using theoretical and experimental systems, we provide direct evidence showing that these coexistence holes do not occur arbitrarily-their diversity is constrained by the internal structure of species interactions and their frequency can be explained by the external factors acting on these systems. Our work suggests that the assembly and disassembly of ecological systems is a discontinuous process that tends to obey regularities.

Experimental evidence of the importance of multitrophic structure for species persistence

Ecological theory predicts that species interactions embedded in multitrophic networks shape the opportunities for species to persist. However, the lack of experimental support of this prediction has limited our understanding of how species interactions occurring within and across trophic levels simultaneously regulate the maintenance of biodiversity. Here, we integrate a mathematical approach and detailed experiments in plant-pollinator communities to demonstrate the need to jointly account for species interactions within and across trophic levels when estimating the ability of species to persist. Within the plant trophic level, we show that the persistence probability of plant species increases when introducing the effects of plant-pollinator interactions. Across trophic levels, we show that the persistence probabilities of both plants and pollinators exhibit idiosyncratic changes when experimentally manipulating the multitrophic structure. Importantly, these idiosyncratic effects are not recovered by traditional simulations. Our work provides tractable experimental and theoretical platforms upon which it is possible to investigate the multitrophic factors affecting species persistence in ecological communities.

Merging dynamical and structural indicators to measure resilience in multispecies systems

Resilience is broadly understood as the ability of an ecological system to resist and recover from perturbations acting on species abundances and on the system's structure. However, one of the main problems in assessing resilience is to understand the extent to which measures of recovery and resistance provide complementary information about a system. While recovery from abundance perturbations has a strong tradition under the analysis of dynamical stability, it is unclear whether this same formalism can be used to measure resistance to structural perturbations (e.g. perturbations to model parameters). Here, we provide a framework grounded on dynamical and structural stability in Lotka-Volterra systems to link recovery from small perturbations on species abundances (i.e. dynamical indicators) with resistance to parameter perturbations of any magnitude (i.e. structural indicators). We use theoretical and experimental multispecies systems to show that the faster the recovery from abundance perturbations, the higher the resistance to parameter perturbations. We first use theoretical systems to show that the return rate along the slowest direction after a small random abundance perturbation (what we call full recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before losing any species (what we call full resistance). We also show that the return rate along the second fastest direction after a small random abundance perturbation (what we call partial recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before at most one species survives (what we call partial resistance). Then, we use a dataset of experimental microbial systems to confirm our theoretical expectations and to demonstrate that full and partial components of resilience are complementary. Our findings reveal that we can obtain the same level of information about resilience by measuring either a dynamical (i.e. recovery) or a structural (i.e. resistance) indicator. Irrespective of the chosen indicator (dynamical or structural), our results show that we can obtain additional information by separating the indicator into its full and partial components. We believe these results can motivate new theoretical approaches and empirical analyses to increase our understanding about risk in ecological systems.

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.