The three-species problem: Incorporating competitive asymmetry and intransitivity in modern coexistence theory.

While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three-species competitive communities are a bridge to more-diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three-species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet-wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three-species competition outcomes.

Reciprocal inhibition and competitive hierarchy cause negative biodiversity-ecosystem function relationships.

The relationship between biodiversity and ecosystem function (BEF) captivates ecologists, but the factors responsible for the direction of this relationship remain unclear. While higher ecosystem functioning at higher biodiversity levels ('positive BEF') is not universal in nature, negative BEF relationships seem puzzlingly rare. Here, we develop a dynamical consumer-resource model inspired by microbial decomposer communities in pitcher plant leaves to investigate BEF. We manipulate microbial diversity via controlled colonization and measure their function as total ammonia production. We test how niche partitioning among bacteria and other ecological processes influence BEF in the leaves. We find that a negative BEF can emerge from reciprocal interspecific inhibition in ammonia production causing a negative complementarity effect, or from competitive hierarchies causing a negative selection effect. Absent these factors, a positive BEF was the typical outcome. Our findings provide a potential explanation for the rarity of negative BEF in empirical data.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly.

AbstractHow is trait diversity in a community apportioned between and within coevolving species? Disruptive selection may result in either a few species with large intraspecific trait variation (ITV) or many species with different mean traits but little ITV. Similar questions arise in spatially structured communities: heterogeneous environments could result in either a few species that exhibit local adaptation or many species with different mean traits but little local adaptation. To date, theory has been well-equipped to either include ITV or to dynamically determine the number of coexisting species, but not both. Here, we devise a theoretical framework that combines these facets and apply it to the above questions of how trait variation is apportioned within and between species in unstructured and structured populations, using two simple models of Lotka-Volterra competition. For unstructured communities, we find that as the breadth of the resource spectrum increases, ITV goes from being unimportant to crucial for characterizing the community. For spatially structured communities on two patches, we find no local adaptation, symmetric local adaptation, or asymmetric local adaptation, depending on how much the patches differ. Our framework provides a general approach to incorporate ITV in models of eco-evolutionary community assembly.

How public can public goods be? Environmental context shapes the evolutionary ecology of partially private goods.

The production of costly public goods (as distinct from metabolic byproducts) has largely been understood through the realization that spatial structure can minimize losses to non-producing "cheaters" by allowing for the positive assortment of producers. In well-mixed systems, where positive assortment is not possible, the stable production of public goods has been proposed to depend on lineages that become indispensable as the sole producers of those goods while their neighbors lose production capacity through genome streamlining (the Black Queen Hypothesis). Here, we develop consumer-resource models motivated by nitrogen-fixing, siderophore-producing bacteria that consider the role of colimitation in shaping eco-evolutionary dynamics. Our models demonstrate that in well-mixed environments, single "public goods" can only be ecologically and evolutionarily stable if they are partially privatized (i.e., if producers reserve a portion of the product pool for private use). Colimitation introduces the possibility of subsidy: strains producing a fully public good can exclude non-producing strains so long as the producing strain derives sufficient benefit from the production of a second partially private good. We derive a lower bound for the degree of privatization necessary for production to be advantageous, which depends on external resource concentrations. Highly privatized, low-investment goods, in environments where the good is limiting, are especially likely to be stably produced. Coexistence emerges more rarely in our mechanistic model of the external environment than in past phenomenological approaches. Broadly, we show that the viability of production depends critically on the environmental context (i.e., external resource concentrations), with production of shared resources favored in environments where a partially-privatized resource is scarce.

A general framework for species-abundance distributions: Linking traits and dispersal to explain commonness and rarity.

Species-abundance distributions (SADs) describe the spectrum of commonness and rarity in a community. Beyond the universal observation that most species are rare and only a few common, more-precise description of SAD shape is controversial. Furthermore, the mechanisms behind SADs and how they vary along environmental gradients remain unresolved. We lack a general, non-neutral theory of SADs. Here, we develop a trait-based framework, focusing on a local community coupled to the region by dispersal. The balance of immigration and exclusion determines abundances, which vary over orders-of-magnitude. The local trait-abundance distribution (TAD) reflects a transformation of the regional TAD. The left-tail of the SAD depends on scaling exponents of the exclusion function and the regional species pool. More-complex local dynamics can lead to multimodal TADs and SADs. Connecting SADs with trait-based ecological theory provides a way to generate more-testable hypotheses on the controls over commonness and rarity in communities.

Perennial, but not annual legumes synergistically benefit from infection with arbuscular mycorrhizal fungi and rhizobia: a meta-analysis.

Many plant species simultaneously interact with multiple symbionts, which can, but do not always, generate synergistic benefits for their host. We ask if plant life history (i.e. annual vs perennial) can play an important role in the outcomes of the tripartite symbiosis of legumes, arbuscular mycorrhizal fungi (AMF), and rhizobia. We performed a meta-analysis of 88 studies examining outcomes of legume-AMF-rhizobia interactions on plant and microbial growth. Perennial legumes associating with AMF and rhizobia grew larger than expected based on their response to either symbiont alone (i.e. their response to co-inoculation was synergistic). By contrast, annual legume growth with co-inoculation did not differ from additive expectations. AMF and rhizobia differentially increased phosphorus (P) and nitrogen (N) tissue concentration. Rhizobium nodulation increased with mycorrhizal fungi inoculation, but mycorrhizal fungi colonization did not increase with rhizobium inoculation. Microbial responses to co-infection were significantly correlated with synergisms in plant growth. Our work supports a balanced plant stoichiometry mechanism for synergistic benefits. We find that synergisms are in part driven by reinvestment in complementary symbionts, and that time-lags in realizing benefits of reinvestment may limit synergisms in annuals. Optimization of microbiome composition to maximize synergisms may be critical to productivity, particularly for perennial legumes.

Resource Competition and Host Feedbacks Underlie Regime Shifts in Gut Microbiota.

AbstractThe spread of an enteric pathogen in the human gut depends on many interacting factors, including pathogen exposure, diet, host gut environment, and host microbiota, but how these factors jointly influence infection outcomes remains poorly characterized. Here we develop a model of host-mediated resource competition between mutualistic and pathogenic taxa in the gut that aims to explain why similar hosts, exposed to the same pathogen, can have such different infection outcomes. Our model successfully reproduces several empirically observed phenomena related to transitions between healthy and infected states, including (1) the nonlinear relationship between pathogen inoculum size and infection persistence, (2) the elevated risk of chronic infection during or after treatment with broad-spectrum antibiotics, (3) the resolution of gut dysbiosis with fecal microbiota transplants, and (4) the potential protection from infection conferred by probiotics. We then use the model to explore how host-mediated interventions-namely, shifts in the supply rates of electron donors (e.g., dietary fiber) and respiratory electron acceptors (e.g., oxygen)-can potentially be used to direct gut community assembly. Our study demonstrates how resource competition and ecological feedbacks between the host and the gut microbiota can be critical determinants of human health outcomes. We identify several testable model predictions ready for experimental validation.

Microbial cross-feeding promotes multiple stable states and species coexistence, but also susceptibility to cheaters.

Mutualism, interspecific cooperation that yields reciprocal benefits, can promote species coexistence, enhancing biodiversity. As a specific form of mutualism, cross-feeding, where each of two mutualists produces a resource the other one needs, has been broadly studied. However, few theoretical studies have examined competition between cross-feeding mutualists and cheaters, who do not synthesize resources themselves. In this paper we study a model with two mutualists, a cheater, two micronutrients that are synthesized and exchanged by the mutualists, and one macronutrient that is only from external supply. We investigate the coexistence of the species in the framework of resource competition theory. In particular, we examine the effect of the mutualists' synthesis rates on their coexistence. In the absence of cheaters, multiple stable states occur if the synthesis rates are high, and higher synthesis rates increase the possibility that mutualists coexist. However, when the cheater is present, higher synthesis rates promote invasion by the cheater: If the cheater is superior on all three resources, it will either persist with at most one mutualist or even trigger extinction of all three species; if the cheater is only superior on the macronutrient, both mutualists may still coexist with the cheater. Our results provide a framework for further study on more complex mutualistic networks and real microbial communities.

Plant Strategies along Resource Gradients.

Plants present a variety of defensive strategies against herbivores, broadly classified into tolerance and resistance. Since resource availability can also limit plant growth, we expect plant allocation to resource acquisition and defense to vary along resource gradients. Yet, the conditions under which one defensive strategy is favored over the other are unclear. Here, we use an eco-evolutionary model to investigate plant adaptive allocation to resource acquisition, tolerance, and resistance along a resource gradient in a simple food web module inspired by plankton communities where plants compete for a single resource and are grazed on by a shared herbivore. We show that undefended, acquisition-specialist strategies dominate under low resource supplies. Conversely, high resource supplies, which lead to high herbivore abundance because of trophic transfers, result in either the dominance of very resistant strategies or coexistence between a completely resistant strategy and a fast-growing, tolerant one. We also explore the consequences of this adaptive allocation on species biomasses. Finally, we compare our predictions to a more traditional, density-independent optimization model. We show that density dependence mediated by resources and herbivores is the cause of the increase in plant resistance along the resource gradient, as the optimization model would instead have favored tolerance.

Facilitation- vs. competition-driven succession: the key role of resource-ratio.

Symbiotic nitrogen (N)-fixing plants are abundant during primary succession, as typical bedrocks lack available N. In turn, fixed N accumulates in soils through biomass turnover and recycling, favouring more nitrophilous organisms. Yet, it is unclear how this facilitation mechanism interacts with competition for other limiting nutrients such as phosphorus (P) and how this affects succession. Here, we introduce a resource-explicit, community assembly model of N-fixing species and analyze successional trajectories along resource availability gradients using contemporary niche theory. We show that facilitation-driven succession occurs under low N and high enough P availabilities, and is characterised by autogenic ecosystem development and relatively ordered trajectories. We show that late facilitation-driven succession is sensitive to catastrophic shifts, highlighting the need to invoke other mechanisms to explain ecosystem stability near the climax. Put together with competition-driven succession, these results lead to an enriched version of Tilman's resource-ratio theory of succession.

Integrating community assembly and biodiversity to better understand ecosystem function: the Community Assembly and the Functioning of Ecosystems (CAFE) approach.

The research of a generation of ecologists was catalysed by the recognition that the number and identity of species in communities influences the functioning of ecosystems. The relationship between biodiversity and ecosystem functioning (BEF) is most often examined by controlling species richness and randomising community composition. In natural systems, biodiversity changes are often part of a bigger community assembly dynamic. Therefore, focusing on community assembly and the functioning of ecosystems (CAFE), by integrating both species richness and composition through species gains, losses and changes in abundance, will better reveal how community changes affect ecosystem function. We synthesise the BEF and CAFE perspectives using an ecological application of the Price equation, which partitions the contributions of richness and composition to function. Using empirical examples, we show how the CAFE approach reveals important contributions of composition to function. These examples show how changes in species richness and composition driven by environmental perturbations can work in concert or antagonistically to influence ecosystem function. Considering how communities change in an integrative fashion, rather than focusing on one axis of community structure at a time, will improve our ability to anticipate and predict changes in ecosystem function.

Geometrical envelopes: Extending graphical contemporary niche theory to communities and eco-evolutionary dynamics.

Contemporary niche theory is a powerful structuring framework in theoretical ecology. First developed in the context of resource competition, it has been extended to encompass other types of regulating factors such as shared predators, parasites or inhibitors. A central component of contemporary niche theory is a graphical approach popularized by Tilman that illustrates the different outcomes of competition along environmental gradients, like coexistence and competitive exclusion. These food web modules have been used to address species sorting in community ecology, as well as adaptation and coexistence on eco-evolutionary time scales in adaptive dynamics. Yet, the associated graphical approach has been underused so far in the evolutionary context. In this paper, we provide a rigorous approach to extend this graphical method to a continuum of interacting strategies, using the geometrical concept of the envelope. Not only does this approach provide community and eco-evolutionary bifurcation diagrams along environmental gradients, it also sheds light on the similarities and differences between those two perspectives. Adaptive dynamics naturally merges with this ecological framework, with a close correspondence between the classification of singular strategies and the geometrical properties of the envelope. Finally, this approach provides an integrative tool to study adaptation between levels of organization, from the individual to the ecosystem.

Entanglement entropy for the long-range Ising chain in a transverse field.

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi-long-range order, and one dominated by the long-range interaction, with long-range Néel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central charges. In the phase with quasi-long-range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.