Coexistence of many species under a random competition-colonization trade-off.

The competition-colonization (CC) trade-off is a well-studied coexistence mechanism for metacommunities. In this setting, it is believed that the coexistence of all species requires their traits to satisfy restrictive conditions limiting their similarity. To investigate whether diverse metacommunities can assemble in a CC trade-off model, we study their assembly from a probabilistic perspective. From a pool of species with parameters (corresponding to traits) sampled at random, we compute the probability that any number of species coexist and characterize the set of species that emerges through assembly. Remarkably, almost exactly half of the species in a large pool typically coexist, with no saturation as the size of the pool grows, and with little dependence on the underlying distribution of traits. Through a mix of analytical results and simulations, we show that this unlimited niche packing emerges as assembly actively moves communities toward overdispersed configurations in niche space. Our findings also apply to a realistic assembly scenario where species invade one at a time from a fixed regional pool. When diversity arises de novo in the metacommunity, richness still grows without bound, but more slowly. Together, our results suggest that the CC trade-off can support the robust emergence of diverse communities, even when coexistence of the full species pool is exceedingly unlikely.

Habitat Heterogeneity, Environmental Feedbacks, and Species Coexistence across Timescales.

AbstractClassic ecological theory explains species coexistence in variable environments. While spatial variation is often treated as an intrinsic feature of a landscape, it may be shaped and even generated by the resident community. All species modify their local environment to some extent, driving changes that can feed back to affect the composition and coexistence of the community, potentially over timescales very different from population dynamics. We introduce a simple nested modeling framework for community dynamics in heterogeneous environments, including the possible evolution of heterogeneity over time due to community-environment feedbacks. We use this model to derive analytical conditions for species coexistence in environments where heterogeneity is either fixed or shaped by feedbacks. Among other results, our approach reveals how dispersal and environmental specialization interact to shape realized patterns of habitat association and demonstrates that environmental feedbacks can tune landscape conditions to allow the stable coexistence of any number of species. Our flexible modeling framework helps explain feedback dynamics that arise in a wide range of ecosystems and offers a generic platform for exploring the interplay between species and landscape diversity.

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.

No robust multispecies coexistence in a canonical model of plant-soil feedbacks.

Plant-soil feedbacks (PSFs) are considered a key mechanism generating frequency-dependent dynamics in plant communities. Negative feedbacks, in particular, are often invoked to explain coexistence and the maintenance of diversity in species-rich communities. However, the primary modelling framework used to study PSFs considers only two plant species, and we lack clear theoretical expectations for how these complex interactions play out in communities with natural levels of diversity. Here, we extend this canonical model of PSFs to include an arbitrary number of plant species and analyse the dynamics. Surprisingly, we find that coexistence of more than two species is virtually impossible, suggesting that alternative theoretical frameworks are needed to describe feedbacks observed in diverse natural communities. Drawing on our analysis, we discuss future directions for PSF models and implications for experimental study of PSF-mediated coexistence in the field.

Metapopulations with habitat modification.

Across the tree of life, organisms modify their local environment, rendering it more or less hospitable for other species. Despite the ubiquity of these processes, simple models that can be used to develop intuitions about the consequences of widespread habitat modification are lacking. Here, we extend the classic Levins metapopulation model to a setting where each of n species can colonize patches connected by dispersal, and when patches are vacated via local extinction, they retain a "memory" of the previous occupant-modeling habitat modification. While this model can exhibit a wide range of dynamics, we draw several overarching conclusions about the effects of modification and memory. In particular, we find that any number of species may potentially coexist, provided that each is at a disadvantage when colonizing patches vacated by a conspecific. This notion is made precise through a quantitative stability condition, which provides a way to unify and formalize existing conceptual models. We also show that when patch memory facilitates coexistence, it generically induces a positive relationship between diversity and robustness (tolerance of disturbance). Our simple model provides a portable, tractable framework for studying systems where species modify and react to a shared landscape.

Local stability properties of complex, species-rich soil food webs with functional block structure.

Ecologists have long debated the properties that confer stability to complex, species-rich ecological networks. Species-level soil food webs are large and structured networks of central importance to ecosystem functioning. Here, we conducted an analysis of the stability properties of an up-to-date set of theoretical soil food web models that account both for realistic levels of species richness and the most recent views on the topological structure (who is connected to whom) of these food webs. The stability of the network was best explained by two factors: strong correlations between interaction strengths and the blocked, nonrandom trophic structure of the web. These two factors could stabilize our model food webs even at the high levels of species richness that are typically found in soil, and that would make random systems very unstable. Also, the stability of our soil food webs is well-approximated by the cascade model. This result suggests that stability could emerge from the hierarchical structure of the functional organization of the web. Our study shows that under the assumption of equilibrium and small perturbations, theoretical soil food webs possess a topological structure that allows them to be complex yet more locally stable than their random counterpart. In particular, results strongly support the general hypothesis that the stability of rich and complex soil food webs is mostly driven by correlations in interaction strength and the organization of the soil food web into functional groups. The implication is that in real-world food web, any force disrupting the functional structure and distribution pattern of interaction strengths (i.e., energy fluxes) of the soil food webs will destabilize the dynamics of the system, leading to species extinction and major changes in the relative abundances of species.

Tractable models of ecological assembly.

Ecological assembly is a fundamental and yet poorly understood process. Three main obstacles hinder the development of a theory of assembly, and when these issues are sidestepped by making strong assumptions, one can build an assembly graph in which nodes are ecological communities and edges are invasions shifting their composition. The graph can then be analysed directly, without the need to consider dynamics. To showcase this framework, we build and analyse assembly graphs for the competitive Lotka-Volterra model, showing that in these cases sequential assembly (in which species invade a community one at a time) can reach the same configurations found when starting the system with all species present at different initial conditions. We discuss how our results can advance our understanding of assembly both from an empirical and a theoretical point of view, informing the study of ecological restoration and the design of ecological communities.

Publisher Correction: Predicting coexistence in experimental ecological communities.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Predicting coexistence in experimental ecological communities.

The study of experimental communities is fundamental to the development of ecology. Yet, for most ecological systems, the number of experiments required to build, model or analyse the community vastly exceeds what is feasible using current methods. Here, we address this challenge by presenting a statistical approach that uses the results of a limited number of experiments to predict the outcomes (coexistence and species abundances) of all possible assemblages that can be formed from a given pool of species. Using three well-studied experimental systems-encompassing plants, protists, and algae with grazers-we show that this method predicts the results of unobserved experiments with high accuracy, while making no assumptions about the dynamics of the systems. These results demonstrate a fundamentally different way of building and quantifying experimental systems, requiring far fewer experiments than traditional study designs. By developing a scalable method for navigating large systems, this work provides an efficient approach to studying highly diverse experimental communities.

Transcriptome resilience predicts thermotolerance in Caenorhabditis elegans.

BACKGROUND: The detrimental effects of a short bout of stress can persist and potentially turn lethal, long after the return to normal conditions. Thermotolerance, which is the capacity of an organism to withstand relatively extreme temperatures, is influenced by the response during stress exposure, as well as the recovery process afterwards. While heat-shock response mechanisms have been studied intensively, predicting thermal tolerance remains a challenge. RESULTS: Here, we use the nematode Caenorhabditis elegans to measure transcriptional resilience to heat stress and predict thermotolerance. Using principal component analysis in combination with genome-wide gene expression profiles collected in three high-resolution time series during control, heat stress, and recovery conditions, we infer a quantitative scale capturing the extent of stress-induced transcriptome dynamics in a single value. This scale provides a basis for evaluating transcriptome resilience, defined here as the ability to depart from stress-expression dynamics during recovery. Independent replication across multiple highly divergent genotypes reveals that the transcriptional resilience parameter measured after a spike in temperature is quantitatively linked to long-term survival after heat stress. CONCLUSION: Our findings imply that thermotolerance is an intrinsic property that pre-determines long-term outcome of stress and can be predicted by the transcriptional resilience parameter. Inferring the transcriptional resilience parameters of higher organisms could aid in evaluating rehabilitation strategies after stresses such as disease and trauma.

Ecological networks: Pursuing the shortest path, however narrow and crooked.

Representing data as networks cuts across all sub-disciplines in ecology and evolutionary biology. Besides providing a compact representation of the interconnections between agents, network analysis allows the identification of especially important nodes, according to various metrics that often rely on the calculation of the shortest paths connecting any two nodes. While the interpretation of a shortest paths is straightforward in binary, unweighted networks, whenever weights are reported, the calculation could yield unexpected results. We analyzed 129 studies of ecological networks published in the last decade that use shortest paths, and discovered a methodological inaccuracy related to the edge weights used to calculate shortest paths (and related centrality measures), particularly in interaction networks. Specifically, 49% of the studies do not report sufficient information on the calculation to allow their replication, and 61% of the studies on weighted networks may contain errors in how shortest paths are calculated. Using toy models and empirical ecological data, we show how to transform the data prior to calculation and illustrate the pitfalls that need to be avoided. We conclude by proposing a five-point check-list to foster best-practices in the calculation and reporting of centrality measures in ecology and evolution studies.

Phenotypic variability promotes diversity and stability in competitive communities.

Intraspecific variation is at the core of evolutionary theory, and yet, from an ecological perspective, we have few robust expectations for how this variation should affect the dynamics of large communities. Here, by adapting an approach from evolutionary game theory, we show that the incorporation of phenotypic variability into competitive networks dramatically alters the dynamics across ecological timescales, stabilising the systems and buffering the communities against demographic perturbations. The beneficial effects of phenotypic variability are strongest when there are substantial differences among phenotypes and when phenotypes are inherited with moderately high fidelity; yet even low levels of variation lead to significant increases in diversity, stability, and robustness. By identifying a simple and ubiquitous stabilising force in competitive communities, this work contributes to our core understanding of how biological diversity is maintained in natural systems.

Telling ecological networks apart by their structure: A computational challenge.

Ecologists have been compiling ecological networks for over a century, detailing the interactions between species in a variety of ecosystems. To this end, they have built networks for mutualistic (e.g., pollination, seed dispersal) as well as antagonistic (e.g., herbivory, parasitism) interactions. The type of interaction being represented is believed to be reflected in the structure of the network, which would differ substantially between mutualistic and antagonistic networks. Here, we put this notion to the test by attempting to determine the type of interaction represented in a network based solely on its structure. We find that, although it is easy to separate different kinds of nonecological networks, ecological networks display much structural variation, making it difficult to distinguish between mutualistic and antagonistic interactions. We therefore frame the problem as a challenge for the community of scientists interested in computational biology and machine learning. We discuss the features a good solution to this problem should possess and the obstacles that need to be overcome to achieve this goal.

Reconciling empirical interactions and species coexistence.

Coexistence in ecological communities is governed largely by the nature and intensity of species interactions. Countless studies have proposed methods to infer these interactions from empirical data, yet models parameterised using such data often fail to recover observed coexistence patterns. Here, we propose a method to reconcile empirical parameterisations of community dynamics with species-abundance data, ensuring that the predicted equilibrium is consistent with the observed abundance distribution. To illustrate the approach, we explore two case studies: an experimental freshwater algal community and a long-term time series of displacement in an intertidal community. We demonstrate how our method helps recover observed coexistence patterns, capture the core dynamics of the system, and, in the latter case, predict the impacts of experimental extinctions. Collectively, these results demonstrate an intuitive approach for reconciling observed and empirical data, improving our ability to explore the links between species interactions and coexistence in natural systems.

Gene regulatory network stabilized by pervasive weak repressions: microRNA functions revealed by the May-Wigner theory.

Food web and gene regulatory networks (GRNs) are large biological networks, both of which can be analyzed using the May-Wigner theory. According to the theory, networks as large as mammalian GRNs would require dedicated gene products for stabilization. We propose that microRNAs (miRNAs) are those products. More than 30% of genes are repressed by miRNAs, but most repressions are too weak to have a phenotypic consequence. The theory shows that (i) weak repressions cumulatively enhance the stability of GRNs, and (ii) broad and weak repressions confer greater stability than a few strong ones. Hence, the diffuse actions of miRNAs in mammalian cells appear to function mainly in stabilizing GRNs. The postulated link between mRNA repression and GRN stability can be seen in a different light in yeast, which do not have miRNAs. Yeast cells rely on non-specific RNA nucleases to strongly degrade mRNAs for GRN stability. The strategy is suited to GRNs of small and rapidly dividing yeast cells, but not the larger mammalian cells. In conclusion, the May-Wigner theory, supplanting the analysis of small motifs, provides a mathematical solution to GRN stability, thus linking miRNAs explicitly to 'developmental canalization'.

Effect of population abundances on the stability of large random ecosystems.

Random matrix theory successfully connects the structure of interactions of large ecological communities to their ability to respond to perturbations. One of the most debated aspects of this approach is that so far studies have neglected the role of population abundances on stability. While species abundances are well studied and empirically accessible, studies on stability have so far failed to incorporate this information. Here we tackle this question by explicitly including population abundances in a random matrix framework. We derive an analytical formula that describes the spectrum of a large community matrix for arbitrary feasible species abundance distributions. The emerging picture is remarkably simple: while population abundances affect the rate to return to equilibrium after a perturbation, the stability of large ecosystems is uniquely determined by the interaction matrix. We confirm this result by showing that the likelihood of having a feasible and unstable solution in the Lotka-Volterra system of equations decreases exponentially with the number of species for stable interaction matrices.

Coexistence of many species in random ecosystems.

Rich ecosystems harbour thousands of species interacting in tangled networks encompassing predation, mutualism and competition. Such widespread biodiversity is puzzling, because in ecological models it is exceedingly improbable for large communities to stably coexist. One aspect rarely considered in these models, however, is that coexisting species in natural communities are a selected portion of a much larger pool, which has been pruned by population dynamics. Here we compute the distribution of the number of species that can coexist when we start from a pool of species interacting randomly, and show that even in this case we can observe rich, stable communities. Interestingly, our results show that, once stability conditions are met, network structure has very little influence on the level of biodiversity attained. Our results identify the main drivers responsible for widespread coexistence in natural communities, providing a baseline for determining which structural aspects of empirical communities promote or hinder coexistence.

Publisher Correction: Feasibility and coexistence of large ecological communities.

This corrects the article DOI: 10.1038/ncomms14389.

Network spandrels reflect ecological assembly.

Ecological networks that exhibit stable dynamics should theoretically persist longer than those that fluctuate wildly. Thus, network structures which are over-represented in natural systems are often hypothesised to be either a cause or consequence of ecological stability. Rarely considered, however, is that these network structures can also be by-products of the processes that determine how new species attempt to join the community. Using a simulation approach in tandem with key results from random matrix theory, we illustrate how historical assembly mechanisms alter the structure of ecological networks. We demonstrate that different community assembly scenarios can lead to the emergence of structures that are often interpreted as evidence of 'selection for stability'. However, by controlling for the underlying selection pressures, we show that these assembly artefacts-or spandrels-are completely unrelated to stability or selection, and are instead by-products of how new species are introduced into the system. We propose that these network-assembly spandrels are critically overlooked aspects of network theory and stability analysis, and we illustrate how a failure to adequately account for historical assembly can lead to incorrect inference about the causes and consequences of ecological stability.

Understanding the role of parasites in food webs using the group model.

Parasites are ubiquitous and have been shown to influence macroscopic measures of ecological network structure, such as connectance and robustness, as well as local structure, such as subgraph frequencies. Nevertheless, they are often under-represented in ecological studies due to their small size and often complex life cycles. We consider whether or not parasites play structurally unique roles in ecological networks; that is, can we distinguish parasites from other species using network structure alone? We partition the species in a community statistically using the group model, and we test whether or not parasites tend to cluster in their own groups, using a measure of "imbalance." We find that parasites form highly imbalanced groups, and that concomitant predation, in which a predator consumes a prey and its parasites, but not the number of interactions, improves the group model's ability to distinguish parasites from non-parasites. This work demonstrates that parasites and non-parasites interact in networks in statistically distinct ways, and that these differences are partly, but not entirely, due to the existence of concomitant predation.