Serguei Saavedra

On the structural stability of mutualistic systems

Introduction Several major developments in theoretical ecology have relied on either dynamical stability or numerical simulations, but oftentimes, they have found contradictory results. This is partly a result of not rigorously checking either the assumption that a steady state is feasible—meaning, all species have constant and positive abundances—or the dependence of results to model parameterization. Here, we extend the concept of structural stability to community ecology in order to account for these two problems. Specifically, we studied the set of conditions leading to the stable coexistence of all species within a community. This shifts the question from asking whether we can find a feasible equilibrium point for a fixed set of parameter values, to asking how large is the range of parameter values that are compatible with the stable coexistence of all species. The architecture of plant-animal mutualistic networks modulates the range of conditions leading to the stable coexistence of all species. The area of the different domains represents the structural stability of a model of mutualistic communities with a given network architecture. The nested networks observed in nature—illustrated here by the network at the bottom—lead to a maximum structural stability. Rationale We begin by disentangling the conditions of global stability from the conditions of feasibility of a steady state in ecological systems. To quantify the domain of stable coexistence, we first find its center (the structural vector of intrinsic growth rates). Next, we determine the boundaries of such a domain by quantifying the amount of variation from the structural vector tolerated before one species goes extinct. Through this two-step approach, we disentangle the effects of the size of the feasibility domain from how close a solution is to its boundary, which is at the heart of previous contradictory results. We illustrate our method by exploring how the observed architecture of mutualistic networks between plants and their pollinators or seed dispersers affects their domain of stable coexistence. Results First, we determined the network architecture that maximizes the structural stability of mutualistic systems. This corresponds to networks with a maximal level of nestedness, a small trade-off between the number and intensity of interactions a species has, and a high level of mutualistic strength within the constraints of global stability. Second, we found that the large majority of observed mutualistic networks are close to this optimum network architecture, maximizing the range of parameters that are compatible with species coexistence. Conclusion Structural stability has played a major role in several fields such as evolutionary developmental biology, in which it has brought the view that some morphological structures are more common than others because they are compatible with a wider range of developmental conditions. In community ecology, structural stability is the sort of framework needed to study the consequences of global environmental change—by definition, large and directional—on species coexistence. Structural stability will serve to assess both the range of variability a given community can withstand and why some community patterns are more widespread than others. A structural approach to species interactions What determines the stability of ecological networks? Rohr et al. devised a conceptual approach to study interactions between species that emphasizes the role of network structure (see the Perspective by Pawar). Using the example of mutualistic networks of communities of plants and their pollinator species, they show how the structure of networks can determine the persistence of the interactions. Network structures and architectures observed in nature intrinsically match the most stable solution. This approach has promise for application to questions of ecological community stability under global change. Science, this issue 10.1126/science.1253497; see also p. 383 In ecology, structural stability influences the range of perturbations mutualistic networks can withstand. [Also see Perspective by Pawar] In theoretical ecology, traditional studies based on dynamical stability and numerical simulations have not found a unified answer to the effect of network architecture on community persistence. Here, we introduce a mathematical framework based on the concept of structural stability to explain such a disparity of results. We investigated the range of conditions necessary for the stable coexistence of all species in mutualistic systems. We show that the apparently contradictory conclusions reached by previous studies arise as a consequence of overseeing either the necessary conditions for persistence or its dependence on model parameterization. We show that observed network architectures maximize the range of conditions for species coexistence. We discuss the applicability of structural stability to study other types of interspecific interactions.

Seasonal species interactions minimize the impact of species turnover on the likelihood of community persistence

Many of the observed species interactions embedded in ecological communities are not permanent, but are characterized by temporal changes that are observed along with abiotic and biotic variations. While work has been done describing and quantifying these changes, little is known about their consequences for species coexistence. Here, we investigate the extent to which changes of species composition impact the likelihood of persistence of the predator-prey community in the highly seasonal Białowieza Primeval Forest (northeast Poland), and the extent to which seasonal changes of species interactions (predator diet) modulate the expected impact. This likelihood is estimated extending recent developments on the study of structural stability in ecological communities. We find that the observed species turnover strongly varies the likelihood of community persistence between summer and winter. Importantly, we demonstrate that the observed seasonal interaction changes minimize the variation in the likelihood of persistence associated with species turnover across the year. We find that these community dynamics can be explained as the coupling of individual species to their environment by minimizing both the variation in persistence conditions and the interaction changes between seasons. Our results provide a homeostatic explanation for seasonal species interactions and suggest that monitoring the association of interactions changes with the level of variation in community dynamics can provide a good indicator of the response of species to environmental pressures.

Nested species interactions promote feasibility over stability during the assembly of a pollinator community

Abstract The foundational concepts behind the persistence of ecological communities have been based on two ecological properties: dynamical stability and feasibility. The former is typically regarded as the capacity of a community to return to an original equilibrium state after a perturbation in species abundances and is usually linked to the strength of interspecific interactions. The latter is the capacity to sustain positive abundances on all its constituent species and is linked to both interspecific interactions and species demographic characteristics. Over the last 40 years, theoretical research in ecology has emphasized the search for conditions leading to the dynamical stability of ecological communities, while the conditions leading to feasibility have been overlooked. However, thus far, we have no evidence of whether species interactions are more conditioned by the communitys need to be stable or feasible. Here, we introduce novel quantitative methods and use empirical data to investigate the consequences of species interactions on the dynamical stability and feasibility of mutualistic communities. First, we demonstrate that the more nested the species interactions in a community are, the lower the mutualistic strength that the community can tolerate without losing dynamical stability. Second, we show that high feasibility in a community can be reached either with high mutualistic strength or with highly nested species interactions. Third, we find that during the assembly process of a seasonal pollinator community located at The Zackenberg Research Station (northeastern Greenland), a high feasibility is reached through the nested species interactions established between newcomer and resident species. Our findings imply that nested mutualistic communities promote feasibility over stability, which may suggest that the former can be key for community persistence.

How structurally stable are global socioeconomic systems

The stability analysis of socioeconomic systems has been centred on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. Therefore, a key stability question that has been under-investigated is how strongly the conditions of a system itself can change before the system moves to a qualitatively different behaviour, i.e. how structurally stable the systems is. Here, we introduce a framework to investigate the structural stability of socioeconomic systems formed by a network of interactions among agents competing for resources. We measure the structural stability of the system as the range of conditions in the distribution and availability of resources compatible with the qualitative behaviour in which all the constituent agents can be self-sustained across time. To illustrate our framework, we study an empirical representation of the global socioeconomic system formed by countries sharing and competing for multinational companies used as proxy for resources. We demonstrate that the structural stability of the system is inversely associated with the level of competition and the level of heterogeneity in the distribution of resources. Importantly, we show that the qualitative behaviour of the observed global socioeconomic system is highly sensitive to changes in the distribution of resources. We believe that this work provides a methodological basis to develop sustainable strategies for socioeconomic systems subject to constantly changing conditions.

Persist or Produce: A Community Trade-Off Tuned by Species Evenness

Understanding the effects of biodiversity on community persistence and productivity is key to managing both natural and production systems. Because rare species face greater danger of extinction, species evenness, a measure of how similar abundances are across species in a community, is seen as a key component of biodiversity. However, previous studies have failed to find a consistent association of species evenness with species survival and biomass production. Here we provide a theoretical framework for the relationship among these three elements. We demonstrate that the lack of consistent outcomes is not an idiosyncratic artifact of different studies but can be unified under one common framework. Applying a niche theory approach, we confirm that under demographic stochasticity evenness is a general indicator of the risk of future species extinctions in a community, in accordance with the majority of empirical studies. In contrast, evenness cannot be used as a direct indicator of the level of biomass production in a community. When a single species dominates, as expressed by the constraints imposed by the population dynamics, biomass production depends on the niche position of the dominating species and can increase or decrease with evenness. We demonstrate that high species evenness and an intermediate level of biomass production is the configuration that maximizes the average species survival probability in response to demographic stochasticity.

Estimating the effect of the reorganization of interactions on the adaptability of species to changing environments

A major challenge in community ecology is to understand how species respond to environmental changes. Previous studies have shown that the reorganization of interactions among co-occurring species can modulate their chances to adapt to novel environmental conditions. Moreover, empirical evidence has shown that these ecological dynamics typically facilitate the persistence of groups of species rather than entire communities. However, so far, we have no systematic methodology to identify those groups of species with the highest or lowest chances to adapt to new environments through a reorganization of their interactions. Yet, this could prove extremely valuable for developing new conservation strategies. Here, we introduce a theoretical framework to estimate the effect of the reorganization of interactions on the adaptability of a group of species, within a community, to novel environmental conditions. We introduce the concept of the adaptation space of a group of species based on a feasibility analysis of a population dynamics model. We define the adaptation space of a group as the set of environmental conditions that can be made compatible with its persistence thorough the reorganization of interactions among species within the group. The larger the adaptation space of a group, the larger its likelihood to adapt to a novel environment. We show that the interactions in the community outside a group can act as structural constraints and be used to quantitatively compare the size of the adaptation space among different groups of species within a community. To test our theoretical framework, we perform a data analysis on several pairs of natural and artificially perturbed ecological communities. Overall, we find that the groups of species present in both control and perturbed communities are among the ones with the largest adaptation space. We believe that the results derived from our framework point out towards new directions to understand and estimate the adaptability of species to changing environments.

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.

Towards the Integration of Niche and Network Theories

The quest for understanding how species interactions modulate diversity has progressed by theoretical and empirical advances following niche and network theories. Yet, niche studies have been limited to describe coexistence within tropic levels despite incorporating information about multi-trophic interactions. Network approaches could address this limitation, but they have ignored the structure of species interactions within trophic levels. Here we call for the integration of niche and network theories to reach new frontiers of knowledge exploring how interactions within and across trophic levels promote species coexistence. This integration is possible due to the strong parallelisms in the historical development, ecological concepts, and associated mathematical tools of both theories. We provide a guideline to integrate this framework with observational and experimental studies.

Comparing species interaction networks along environmental gradients: Networks along environmental gradients

Knowledge of species composition and their interactions, in the form of interaction networks, is required to understand processes shaping their distribution over time and space. As such, comparing ecological networks along environmental gradients represents a promising new research avenue to understand the organization of life. Variation in the position and intensity of links within networks along environmental gradients may be driven by turnover in species composition, by variation in species abundances and by abiotic influences on species interactions. While investigating changes in species composition has a long tradition, so far only a limited number of studies have examined changes in species interactions between networks, often with differing approaches. Here, we review studies investigating variation in network structures along environmental gradients, highlighting how methodological decisions about standardization can influence their conclusions. Due to their complexity, variation among ecological networks is frequently studied using properties that summarize the distribution or topology of interactions such as number of links, connectance, or modularity. These properties can either be compared directly or using a procedure of standardization. While measures of network structure can be directly related to changes along environmental gradients, standardization is frequently used to facilitate interpretation of variation in network properties by controlling for some co‐variables, or via null models. Null models allow comparing the deviation of empirical networks from random expectations and are expected to provide a more mechanistic understanding of the factors shaping ecological networks when they are coupled with functional traits. As an illustration, we compare approaches to quantify the role of trait matching in driving the structure of plant–hummingbird mutualistic networks, i.e. a direct comparison, standardized by null models and hypothesis‐based metaweb. Overall, our analysis warns against a comparison of studies that rely on distinct forms of standardization, as they are likely to highlight different signals. Fostering a better understanding of the analytical tools available and the signal they detect will help produce deeper insights into how and why ecological networks vary along environmental gradients.

Reorganization of interaction networks modulates the persistence of species in late successional stages

Ecological interaction networks constantly reorganize as interspecific interactions change across successional stages and environmental gradients. This reorganization can also be associated with the extent to which species change their preference for types of niches available in their local sites. Despite the pervasiveness of these interaction changes, previous studies have revealed that network reorganizations have a minimal or insignificant effect on global descriptors of network architecture, such as connectance, modularity and nestedness. However, little is known about whether these reorganizations may have an effect on community dynamics and composition. To answer the question above, we study the multi-year dynamics and reorganization of plant-herbivore interaction networks across secondary successional stages of a tropical dry forest. We develop new quantitative tools based on a structural stability approach to estimate the potential impact of network reorganization on species persistence. Then, we investigate whether this impact can explain the likelihood of persistence of herbivore species in the observed communities. We find that resident (early-arriving) herbivore species increase their likelihood of persistence across time and successional stages. Importantly, we demonstrate that, in late successional stages, the reorganization of interactions among resident species has a strong inhibitory effect on the likelihood of persistence of colonizing (late-arriving) herbivores. These findings support earlier predictions suggesting that, in mature communities, changes of species interactions can act as community-control mechanisms (also known as priority effects). Furthermore, our results illustrate that the dynamics and composition of ecological communities cannot be fully understood without attention to their reorganization processes, despite the invariability of global network properties.