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.

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.

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.

Structural forecasting of species persistence under changing environments.

The persistence of a species in a given place not only depends on its intrinsic capacity to consume and transform resources into offspring, but also on how changing environmental conditions affect its growth rate. However, the complexity of factors has typically taken us to choose between understanding and predicting the persistence of species. To tackle this limitation, we propose a probabilistic approach rooted on the statistical concepts of ensemble theory applied to statistical mechanics and on the mathematical concepts of structural stability applied to population dynamics models - what we call structural forecasting. We show how this new approach allows us to estimate a probability of persistence for single species in local communities; to understand and interpret this probability conditional on the information we have concerning a system; and to provide out-of-sample predictions of species persistence as good as the best experimental approaches without the need of extensive amounts of data.

The indirect paths to cascading effects of extinctions in mutualistic networks.

Biodiversity loss is a hallmark of our times, but predicting its consequences is challenging. Ecological interactions form complex networks with multiple direct and indirect paths through which the impacts of an extinction may propagate. Here we show that accounting for these multiple paths connecting species is necessary to predict how extinctions affect the integrity of ecological networks. Using an approach initially developed for the study of information flow, we estimate indirect effects in plant-pollinator networks and find that even those species with several direct interactions may have much of their influence over others through long indirect paths. Next, we perform extinction simulations in those networks and show that although traditional connectivity metrics fail in the prediction of coextinction patterns, accounting for indirect interaction paths allows predicting species' vulnerability to the cascading effects of an extinction event. Embracing the structural complexity of ecological systems contributes towards a more predictive ecology, which is of paramount importance amid the current biodiversity crisis.

Assessing the predictability of nonlinear dynamics under smooth parameter changes.

Short-term forecasts of nonlinear dynamics are important for risk-assessment studies and to inform sustainable decision-making for physical, biological and financial problems, among others. Generally, the accuracy of short-term forecasts depends upon two main factors: the capacity of learning algorithms to generalize well on unseen data and the intrinsic predictability of the dynamics. While generalization skills of learning algorithms can be assessed with well-established methods, estimating the predictability of the underlying nonlinear generating process from empirical time series remains a big challenge. Here, we show that, in changing environments, the predictability of nonlinear dynamics can be associated with the time-varying stability of the system with respect to smooth changes in model parameters, i.e. its local structural stability. Using synthetic data, we demonstrate that forecasts from locally structurally unstable states in smoothly changing environments can produce significantly large prediction errors, and we provide a systematic methodology to identify these states from data. Finally, we illustrate the practical applicability of our results using an empirical dataset. Overall, this study provides a framework to associate an uncertainty level with short-term forecasts made in smoothly changing environments.

The geographic mosaic of coevolution in mutualistic networks.

Ecological interactions shape adaptations through coevolution not only between pairs of species but also through entire multispecies assemblages. Local coevolution can then be further altered through spatial processes that have been formally partitioned in the geographic mosaic theory of coevolution. A major current challenge is to understand the spatial patterns of coadaptation that emerge across ecosystems through the interplay between gene flow and selection in networks of interacting species. Here, we combine a coevolutionary model, network theory, and empirical information on species interactions to investigate how gene flow and geographical variation in selection affect trait patterns in mutualistic networks. We show that gene flow has the surprising effect of favoring trait matching, especially among generalist species in species-rich networks typical of pollination and seed dispersal interactions. Using an analytical approximation of our model, we demonstrate that gene flow promotes trait matching by making the adaptive landscapes of different species more similar to each other. We use this result to show that the progressive loss of gene flow associated with habitat fragmentation may undermine coadaptation in mutualisms. Our results therefore provide predictions of how spatial processes shape the evolution of species-rich interactions and how the widespread fragmentation of natural landscapes may modify the coevolutionary process.

Unravelling Darwin's entangled bank: architecture and robustness of mutualistic networks with multiple interaction types.

Trying to unravel Darwin's entangled bank further, we describe the architecture of a network involving multiple forms of mutualism (pollination by animals, seed dispersal by birds and plant protection by ants) and evaluate whether this multi-network shows evidence of a structure that promotes robustness. We found that species differed strongly in their contributions to the organization of the multi-interaction network, and that only a few species contributed to the structuring of these patterns. Moreover, we observed that the multi-interaction networks did not enhance community robustness compared with each of the three independent mutualistic networks when analysed across a range of simulated scenarios of species extinction. By simulating the removal of highly interacting species, we observed that, overall, these species enhance network nestedness and robustness, but decrease modularity. We discuss how the organization of interlinked mutualistic networks may be essential for the maintenance of ecological communities, and therefore the long-term ecological and evolutionary dynamics of interactive, species-rich communities. We suggest that conserving these keystone mutualists and their interactions is crucial to the persistence of species-rich mutualistic assemblages, mainly because they support other species and shape the network organization.