Structure-based identification of sensor species for anticipating critical transitions

Ecological systems can undergo sudden, catastrophic changes known as critical transitions. Anticipating these critical transitions remains challenging in systems with many species because the associated early warning signals can be weakly present or even absent in some species, depending on the system dynamics. Therefore, our limited knowledge of ecological dynamics may suggest that it is hard to identify those species in the system that display early warning signals. Here, we show that, in mutualistic ecological systems, it is possible to identify species that early anticipate critical transitions by knowing only the system structure—that is, the network topology of plant–animal interactions. Specifically, we leverage the mathematical theory of structural observability of dynamical systems to identify a minimum set of “sensor species,” whose measurement guarantees that we can infer changes in the abundance of all other species. Importantly, such a minimum set of sensor species can be identified by using the system structure only. We analyzed the performance of such minimum sets of sensor species for detecting early warnings using a large dataset of empirical plant–pollinator and seed-dispersal networks. We found that species that are more likely to be sensors tend to anticipate earlier critical transitions than other species. Our results underscore how knowing the structure of multispecies systems can improve our ability to anticipate critical transitions.

A Multi–Membrane System to Study the Effects of Physical and Metabolic Interactions in Microbial Co-Cultures and Consortia

Continuous cell-to-cell contact between different species is a general feature of all natural environments. However, almost all research is conducted on single-species cultures, reflecting a biotechnological bias and problems associated with the complexities of reproducibly growing and controlling multispecies systems. Consequently, biotic stress due to the presence of other species remains poorly understood. In this context, understanding the effects of physical contact between species when compared to metabolic contact alone is one of the first steps to unravelling the mechanisms that underpin microbial ecological interactions. The current technologies to study the effects of cell-to-cell contact present disadvantages, such as the inefficient or discontinuous exchange of metabolites when preventing contact between species. This paper presents and characterizes a novel bioreactor system that uses ceramic membranes to create a “multi-membrane” compartmentalized system whereby two or more species can be co-cultured without the mixing of the species, while ensuring the efficient sharing of all of the media components. The system operates continuously, thereby avoiding the discontinuities that characterize other systems, which either have to use hourly backwashes to clean their membranes, or have to change the direction of the flow between compartments. This study evaluates the movement of metabolites across the membrane in co-cultures of yeast, microalgae and bacterial species, and monitors the movement of the metabolites produced during co-culturing. These results show that the multi-membrane system proposed in this study represents an effective system for studying the effects of cell-to-cell contact in microbial consortia. The system can also be adapted for various biotechnological purposes, such as the production of metabolites when more than one species is required for such a process.

Metapopulation capacity determines food chain length in fragmented landscapes

Metapopulation capacity provides an analytic tool to quantify the impact of landscape configuration on metapopulation persistence, which has proven powerful in biological conservation. Yet surprisingly few efforts have been made to apply this approach to multispecies systems. Here, we extend metapopulation capacity theory to predict the persistence of trophically interacting species. Our results demonstrate that metapopulation capacity could be used to predict the persistence of trophic systems such as prey–predator pairs and food chains in fragmented landscapes. In particular, we derive explicit predictions for food chain length as a function of metapopulation capacity, top-down control, and population dynamical parameters. Under certain assumptions, we show that the fraction of empty patches for the basal species provides a useful indicator to predict the length of food chains that a fragmented landscape can support and confirm this prediction for a host–parasitoid interaction. We further show that the impact of habitat changes on biodiversity can be predicted from changes in metapopulation capacity or approximately by changes in the fraction of empty patches. Our study provides an important step toward a spatially explicit theory of trophic metacommunities and a useful tool for predicting their responses to habitat changes.

Coexistence holes characterize the assembly and disassembly of multispecies systems

A central goal of life science has been to understand the limits of species coexistence. However, we know surprisingly little about the structure of species coexistence below such limits, and how it affects the assembly and disassembly of ecological systems. Here we introduce a novel hypergraph-based formalism that fully captures the structure of coexistence in multispecies systems. Our formalism uncovers that, below its limits, coexistence in ecological systems has ubiquitous discontinuities that we call “coexistence holes.” These coexistence holes do not occur arbitrarily but tend to obey patterns that make them predictable. We provide direct evidence showing that the biotic and abiotic constraints of empirical systems produce an over-representation of coexistence holes. By highlighting discontinuities in the form of coexistence holes, our work provides a new platform to uncover the order and structure of the assembly and disassembly of ecological systems.

Models for large ecological communities—a random matrix approach

Lotka and Volterra were among the first to attempt to mathematize the dynamics of interacting populations. While their work had a profound influence on ecology, leading to many of the results that were covered in the preceding chapters, their approach is difficult to generalize to the case of many interacting species. When the number of species in a community is sufficiently large, there is little hope of obtaining analytical results by carefully studying the system of dynamical equations describing their interactions. Here, we introduce an approach based on the theory of random matrices that exploits the very large number of species to derive cogent mathematical results. We review basic concepts in random matrix theory by illustrating their applications to the study of multispecies systems. We introduce tools that can be used to yield new insights into community ecology and conclude with a list of open problems.