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.

Protection promotes energetically efficient structures in marine communities.

The sustainability of marine communities is critical for supporting many biophysical processes that provide ecosystem services that promote human well-being. It is expected that anthropogenic disturbances such as climate change and human activities will tend to create less energetically-efficient ecosystems that support less biomass per unit energy flow. It is debated, however, whether this expected development should translate into bottom-heavy (with small basal species being the most abundant) or top-heavy communities (where more biomass is supported at higher trophic levels with species having larger body sizes). Here, we combine ecological theory and empirical data to demonstrate that full marine protection promotes shifts towards top-heavy energetically-efficient structures in marine communities. First, we use metabolic scaling theory to show that protected communities are expected to display stronger top-heavy structures than disturbed communities. Similarly, we show theoretically that communities with high energy transfer efficiency display stronger top-heavy structures than communities with low transfer efficiency. Next, we use empirical structures observed within fully protected marine areas compared to disturbed areas that vary in stress from thermal events and adjacent human activity. Using a nonparametric causal-inference analysis, we find a strong, positive, causal effect between full marine protection and stronger top-heavy structures. Our work corroborates ecological theory on community development and provides a quantitative framework to study the potential restorative effects of different candidate strategies on protected areas.

Assembly archetypes in ecological communities.

An instrumental discovery in comparative and developmental biology is the existence of assembly archetypes that synthesize the vast diversity of organisms' body plans-from legs and wings to human arms-into simple, interpretable and general design principles. Here, we combine a novel mathematical formalism based on category theory with experimental data to show that similar 'assembly archetypes' exist at the larger organization scale of ecological communities when assembling a species pool across diverse environmental contexts, particularly when species interactions are highly structured. We applied our formalism to clinical data discovering two assembly archetypes that differentiate between healthy and unhealthy human gut microbiota. The concept of assembly archetypes and the methods to synthesize them can pave the way to discovering the general assembly principles of the ecological communities we observe in nature.

Understanding the state-dependent impact of species correlated responses on community sensitivity to perturbations.

Understanding how communities respond to perturbations requires us to consider not only changes in the abundance of individual species but also correlated changes that can emerge through interspecific effects. However, our knowledge of this phenomenon is mostly constrained to situations where interspecific effects are fixed. Here, we introduce a framework to disentangle the impact of species correlated responses on community sensitivity to perturbations when interspecific effects change over time due to cyclic or chaotic population dynamics. We partition the volume expansion rate of perturbed abundances (community sensitivity) into contributions of individual species and of species correlated responses by converting the time-varying Jacobian matrix containing interspecific effects into a time-varying covariance matrix. Using population dynamics models, we demonstrate that species correlated responses change considerably across time and continuously alternate between reducing and having no impact on community sensitivity. Importantly, these alternating impacts depend on the abundance of particular species and can be detected even from noisy time series. We showcase our framework using two experimental predator-prey time series and find that the impact of species correlated responses is modulated by prey abundance-as theoretically expected. Our results provide new insights into how and when species interactions can dampen community sensitivity when abundances fluctuate over time.

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.

Ranking species based on sensitivity to perturbations under non-equilibrium community dynamics.

Managing ecological communities requires fast detection of species that are sensitive to perturbations. Yet, the focus on recovery to equilibrium has prevented us from assessing species responses to perturbations when abundances fluctuate over time. Here, we introduce two data-driven approaches (expected sensitivity and eigenvector rankings) based on the time-varying Jacobian matrix to rank species over time according to their sensitivity to perturbations on abundances. Using several population dynamics models, we demonstrate that we can infer these rankings from time-series data to predict the order of species sensitivities. We find that the most sensitive species are not always the ones with the most rapidly changing or lowest abundance, which are typical criteria used to monitor populations. Finally, using two empirical time series, we show that sensitive species tend to be harder to forecast. Our results suggest that incorporating information on species interactions can improve how we manage communities out of equilibrium.

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.

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.

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'.

Untangling the complexity of priority effects in multispecies communities.

The history of species immigration can dictate how species interact in local communities, thereby causing historical contingency in community assembly. Since immigration history is rarely known, these historical influences, or priority effects, pose a major challenge in predicting community assembly. Here, we provide a graph-based, non-parametric, theoretical framework for understanding the predictability of community assembly as affected by priority effects. To develop this framework, we first show that the diversity of possible priority effects increases super-exponentially with the number of species. We then point out that, despite this diversity, the consequences of priority effects for multispecies communities can be classified into four basic types, each of which reduces community predictability: alternative stable states, alternative transient paths, compositional cycles and the lack of escapes from compositional cycles to stable states. Using a neural network, we show that this classification of priority effects enables accurate explanation of community predictability, particularly when each species immigrates repeatedly. We also demonstrate the empirical utility of our theoretical framework by applying it to two experimentally derived assembly graphs of algal and ciliate communities. Based on these analyses, we discuss how the framework proposed here can help guide experimental investigation of the predictability of history-dependent community assembly.

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.

Impact of colonization history on the composition of ecological systems.

Observational studies of ecological systems have shown that different species compositions can arise from distinct species arrival orders during community assembly-also known as colonization history. The presence of multiple interior equilibria in the positive orthant of the state space of the population dynamics will naturally lead to history dependency of the final state. However, it is still unclear whether and under which conditions colonization history will dominate community composition in the absence of multiple interior equilibria. Here, by considering that only one species can invade at a time and there are no recurrent invasions, we show clear evidence that the colonization history can have a big impact on the composition of ecological systems even in the absence of multiple interior equilibria. In particular, we first derive two simple rules to determine whether the composition of a community will depend on its colonization history in the absence of multiple interior equilibria and recurrent invasions. Then we apply them to communities governed by generalized Lotka-Volterra (gLV) dynamics and propose a numerical scheme to measure the probability of colonization history dependence. Finally, we show, via numerical simulations, that for gLV dynamics with a single interior equilibrium, the probability that community composition is dominated by colonization history increases monotonically with community size, network connectivity, and the variation of intrinsic growth rates across species. These results reveal that in the absence of multiple interior equilibria and recurrent invasions, community composition is a probabilistic process mediated by ecological dynamics via the interspecific variation and the size of regional pools.

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.

Observed Ecological Communities Are Formed by Species Combinations That Are among the Most Likely to Persist under Changing Environments.

AbstractDespite the rich biodiversity found in nature, it is unclear to what extent some combinations of interacting species, while conceivable in a given place and time, may never be realized. Yet solving this problem is important for understanding the role of randomness and predictability in the assembly of ecological communities. Here we show that the specific combinations of interacting species that emerge from the ecological dynamics within regional species pools are not all equally likely to be seen; rather, they are among the most likely to persist under changing environments. First, we use niche-based competition matrices and Lotka-Volterra models to demonstrate that realized combinations of interacting species are more likely to persist under random parameter perturbations than the majority of potential combinations with the same number of species that could have been formed from the regional pool. We then corroborate our theoretical results using a 10-year observational study, recording 88 plant-herbivore communities across three different forest successional stages. By inferring and validating plant-mediated communities of competing herbivore species, we find that observed combinations of herbivores have an expected probability of species persistence higher than half of all potential combinations. Our findings open up the opportunity to establish a formal probabilistic and predictive understanding of the composition of ecological 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.

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.