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.

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.

Metapopulation persistence can be inferred from incomplete surveys.

Habitat destruction and fragmentation are principal causes of species loss. While a local population might go extinct, a metapopulation-populations inhabiting habitat patches connected by dispersal-can persist regionally by recolonizing empty patches. To assess metapopulation persistence, two widely adopted indicators in conservation management are metapopulation capacity and patch importance. However, we face a fundamental limitation in that assessing metapopulation persistence requires that we survey or sample all the patches in a landscape: often these surveys are logistically challenging to conduct and repeat, which raises the question whether we can learn enough about the metapopulation persistence from an incomplete survey. Here, we provide a robust statistical approach to infer metapopulation capacity and patch importance by sampling a portion of all patches. We provided analytic arguments on why the metapopulation capacity and patch importance can be well predicted from sub-samples of habitat patches. Full-factorial simulations with more complex models corroborate our analytic predictions. We applied our model to an empirical metapopulation of mangrove hummingbirds (Amazilia boucardi). On the basis of our statistical framework, we provide some sampling suggestion for monitoring metapopulation persistence. Our approach allows for rapid and effective inference of metapopulation persistence from incomplete patch surveys.

Generalism drives abundance: A computational causal discovery approach.

A ubiquitous pattern in ecological systems is that more abundant species tend to be more generalist; that is, they interact with more species or can occur in wider range of habitats. However, there is no consensus on whether generalism drives abundance (a selection process) or abundance drives generalism (a drift process). As it is difficult to conduct direct experiments to solve this chicken-and-egg dilemma, previous studies have used a causal discovery method based on formal logic and have found that abundance drives generalism. Here, we refine this method by correcting its bias regarding skewed distributions, and employ two other independent causal discovery methods based on nonparametric regression and on information theory, respectively. Contrary to previous work, all three independent methods strongly indicate that generalism drives abundance when applied to datasets on plant-hummingbird communities and reef fishes. Furthermore, we find that selection processes are more important than drift processes in structuring multispecies systems when the environment is variable. Our results showcase the power of the computational causal discovery approach to aid ecological research.

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.

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.

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.

Telling ecological networks apart by their structure: An environment-dependent approach.

The network architecture of an ecological community describes the structure of species interactions established in a given place and time. It has been suggested that this architecture presents unique features for each type of ecological interaction: e.g., nested and modular architectures would correspond to mutualistic and antagonistic interactions, respectively. Recently, Michalska-Smith and Allesina (2019) proposed a computational challenge to test whether it is indeed possible to differentiate ecological interactions based on network architecture. Contrary to the expectation, they found that this differentiation is practically impossible, moving the question to why it is not possible to differentiate ecological interactions based on their network architecture alone. Here, we show that this differentiation becomes possible by adding the local environmental information where the networks were sampled. We show that this can be explained by the fact that environmental conditions are a confounder of ecological interactions and network architecture. That is, the lack of association between network architecture and type of ecological interactions changes by conditioning on the local environmental conditions. Additionally, we find that environmental conditions are linked to the stability of ecological networks, but the direction of this effect depends on the type of interaction network. This suggests that the association between ecological interactions and network architectures exists, but cannot be fully understood without attention to the environmental conditions acting upon them.

Towards a Probabilistic Understanding About the Context-Dependency of Species Interactions.

Observational and experimental studies have shown that an interaction class between two species (be it mutualistic, competitive, antagonistic, or neutral) may switch to a different class, depending on the biotic and abiotic factors within which species are observed. This complexity arising from the evidence of context-dependencies has underscored a difficulty in establishing a systematic analysis about the extent to which species interactions are expected to switch in nature and experiments. Here, we propose an overarching theoretical framework, by integrating probabilistic and structural approaches, to establish null expectations about switches of interaction classes across environmental contexts. This integration provides a systematic platform upon which it is possible to establish new hypotheses, clear predictions, and quantifiable expectations about the context-dependency of species interactions.

On the Consequences of the Interdependence of Stabilizing and Equalizing Mechanisms.

We present an overlooked but important property of modern coexistence theory (MCT), along with two key new results and their consequences. The overlooked property is that stabilizing mechanisms (increasing species' niche differences) and equalizing mechanisms (reducing species' fitness differences) have two distinct sets of meanings within MCT: one in a two-species context and another in a general multispecies context. We demonstrate that the two-species framework is not a special case of the multispecies one, and therefore these two parallel frameworks must be studied independently. Our first result is that, using the two-species framework and mechanistic consumer-resource models, stabilizing and equalizing mechanisms exhibit complex interdependence, such that changing one will simultaneously change the other. Furthermore, the nature and direction of this simultaneous change sensitively depend on model parameters. The second result states that while MCT is often seen as bridging niche and neutral modes of coexistence by building a niche-neutrality continuum, the interdependence between stabilizing and equalizing mechanisms acts to break this continuum under almost any biologically relevant circumstance. We conclude that the complex entanglement of stabilizing and equalizing terms makes their impact on coexistence difficult to understand, but by seeing them as aggregated effects (rather than underlying causes) of coexistence, we may increase our understanding of ecological dynamics.

Beware z-scores.

Song, Rohr, and Saavedra (2017) have proposed a methodology to compare network properties across systems with different sizes and constraints, in response to the fact that z-scores cannot be used for such purposes. Simmons, Hoeppke, and Sutherland (2019) have shown that part of the methodology can be improved. Here, we show that all previous results hold and are strengthened by the new methodology.

Rethinking the importance of the structure of ecological networks under an environment-dependent framework.

A major quest in network and community ecology has been centered on understanding the importance of structural patterns in species interaction networks-the synthesis of who interacts with whom in a given location and time. In the past decades, much effort has been devoted to infer the importance of a particular structure by its capacity to tolerate an external perturbation on its structure or dynamics. Here, we demonstrate that such a perspective leads to inconsistent conclusions. That is, the importance of a network structure changes as a function of the external perturbations acting on a community at any given point in time. Thus, we discuss a research agenda to investigate the relative importance of the structure of ecological networks under an environment-dependent framework. We hypothesize that only by studying systematically the link between network structure and community dynamics under an environment-dependent framework, we can uncover the limits at which communities can tolerate environmental changes.

Structural stability as a consistent predictor of phenological events.

The timing of the first and last seasonal appearance of a species in a community typically follows a pattern that is governed by temporal factors. While it has been shown that changes in the environment are linked to phenological changes, the direction of this link appears elusive and context-dependent. Thus, finding consistent predictors of phenological events is of central importance for a better assessment of expected changes in the temporal dynamics of ecological communities. Here we introduce a measure of structural stability derived from species interaction networks as an estimator of the expected range of environmental conditions compatible with the existence of a community. We test this measure as a predictor of changes in species richness recorded on a daily basis in a high-arctic plant-pollinator community during two spring seasons. We find that our measure of structural stability is the only consistent predictor of changes in species richness among different ecological and environmental variables. Our findings suggest that measures based on the notion of structural stability can synthesize the expected variation of environmental conditions tolerated by a community, and explain more consistently the phenological changes observed in ecological communities.

Structural changes within trophic levels are constrained by within-family assembly rules at lower trophic levels.

Historical contingency broadly refers to the proposition that even random historical events can constrain the ecological and evolutionary pathways of organisms and that of entire communities. Focusing on communities, these pathways can be reflected into specific structural changes within and across trophic levels - how species interact with and affect each other - which has important consequences for species coexistence. Using the registry of the last 2000 years of plant introductions and their novel herbivores encountered in Central Europe, we find that the order of arrival of closely related (but not of distantly related) plant species constrained the structural changes within the trophic level formed by herbivore species across the observation period. Because it is difficult for field and lab experiments to be conducted over hundreds of years to record and replay the assembly history of a community, our study provides an alternative to understand how structural changes have occurred across extensive periods of time.

A guideline to study the feasibility domain of multi-trophic and changing ecological communities.

The feasibility domain of an ecological community can be described by the set of environmental abiotic and biotic conditions under which all co-occurring and interacting species in a given site and time can have positive abundances. Mathematically, the feasibility domain corresponds to the parameter space compatible with positive (feasible) solutions at equilibrium for all the state variables in a system under a given model of population dynamics. Under specific dynamics, the existence of a feasible equilibrium is a necessary condition for species persistence regardless of whether the feasible equilibrium is dynamically stable or not. Thus, the size of the feasibility domain can also be used as an indicator of the tolerance of a community to random environmental variations. This has motivated a rich research agenda to estimate the feasibility domain of ecological communities. However, these methodologies typically assume that species interactions are static, or that input and output energy flows on each trophic level are unconstrained. Yet, this is different to how communities behave in nature. Here, we present a step-by-step quantitative guideline providing illustrative examples, computational code, and mathematical proofs to study systematically the feasibility domain of ecological communities under changes of interspecific interactions and subject to different constraints on the trophic energy flows. This guideline covers multi-trophic communities that can be formed by any type of interspecific interactions. Importantly, we show that the relative size of the feasibility domain can significantly change as a function of the biological information taken into consideration. We believe that the availability of these methods can allow us to increase our understanding about the limits at which ecological communities may no longer tolerate further environmental perturbations, and can facilitate a stronger integration of theoretical and empirical research.

Will a small randomly assembled community be feasible and stable?

How likely is it that few species can randomly assemble into a feasible and stable community? Some studies have answered that as long as the community is feasible, it will nearly always be stable. In contrast, other studies have answered that the likelihood is almost null. Here, we show that the origin of this debate has been the underestimation of the association of the parameter space of intrinsic growth rates with the feasibility and stability properties of small randomly-assembled communities. In particular, we demonstrate that not all parameterizations and sampling distributions of intrinsic growth rates lead to the same probabilities of stability and feasibility, which could mistakenly lead to under- or overestimate the stability properties of feasible communities. Additionally, we find that stability imposes a filtering of species abundances "towards" more even distributions in small feasible randomly-assembled communities. This indicates that the stability of feasible communities is inherently linked to the starting distribution of species abundances, a characteristic that many times has been ignored, but should be incorporated in manageable lab and field experiments. Overall, the return to this debate is a central reminder that a more systematic exploration of the feasible parameter space is necessary to derive general conclusions about the stability properties of ecological communities.

Why are some plant-pollinator networks more nested than others?

Empirical studies have found that the mutualistic interactions forming the structure of plant-pollinator networks are typically more nested than expected by chance alone. Additionally, theoretical studies have shown a positive association between the nested structure of mutualistic networks and community persistence. Yet, it has been shown that some plant-pollinator networks may be more nested than others, raising the interesting question of which factors are responsible for such enhanced nested structure. It has been argued that ordered network structures may increase the persistence of ecological communities under less predictable environments. This suggests that nested structures of plant-pollinator networks could be more advantageous under highly seasonal environments. While several studies have investigated the link between nestedness and various environmental variables, unfortunately, there has been no unified answer to validate these predictions. Here, we move from the problem of describing network structures to the problem of comparing network structures. We develop comparative statistics, and apply them to investigate the association between the nested structure of 59 plant-pollinator networks and the temperature seasonality present in their locations. We demonstrate that higher levels of nestedness are associated with a higher temperature seasonality. We show that the previous lack of agreement came from an extended practice of using standardized measures of nestedness that cannot be compared across different networks. Importantly, our observations complement theory showing that more nested network structures can increase the range of environmental conditions compatible with species coexistence in mutualistic systems, also known as structural stability. This increase in nestedness should be more advantageous and occur more often in locations subject to random environmental perturbations, which could be driven by highly changing or seasonal environments. This synthesis of theory and observations could prove relevant for a better understanding of the ecological processes driving the assembly and persistence of ecological communities.