Ecological Networks over the Edge: Hypergraph Trait-Mediated Indirect Interaction (TMII) Structure.

Analyses of ecological network structure have yielded important insights into the functioning of complex ecological systems. However, such analyses almost universally omit non-pairwise interactions, many classes of which are crucial for system structure, function, and resilience. Hypergraphs are mathematical constructs capable of considering such interactions: we discuss their utility for studying ecological networks containing diverse interaction types, and associated challenges and strategies.

A 'crying wolf' game of interspecific kleptoparasitic mutualism.

We model a potentially mutualistic interaction between a species making antipredator alarm calls and a species which eavesdrops on those calls. Callers may or may not make deceptive alarm calls in order to kleptoparasitize food from eavesdroppers, which in turn may either heed or ignore all alarm calls. The two most likely outcomes in our model are either maximally deceptive callers and maximally trusting eavesdroppers, or persistently cycling strategy frequencies.

Lateral cascade of indirect effects in food webs with different types of adaptive behavior.

It is widely recognized that indirect effects due to adaptive behaviors can have important effects on food webs. One consequence may be to change how readily perturbations propagate through the web, because species' behaviors as well as densities may respond to perturbations. It is not well understood which types of behavior are more likely to facilitate versus inhibit propagation of disturbances through a food web, or how this might be affected by the shape of a food web or the patterns of interaction strengths within it.

Modifying modifiers: what happens when interspecific interactions interact?

1. The strength of the trophic link between any given pair of species in a food web is likely to depend on the presence and/or densities of other species in the community. How these trophic interaction modifications (TIMs) interact with one another to produce a net modifying effect is an important but under-explored issue.

Recycling‐mediated facilitation and coexistence based on plant size.

We introduce nutrient recycling into a model where competitors differ in the scale at which they perceive their environment. In a two-resource system with both external nutrient inputs and recycling, larger consumers ("integrators") often generate resource distributions that favor their smaller ("nonintegrator") competitors, and vice versa. This occurs because recycling of integrator biomass reduces between-patch resource heterogeneity, whereas recycling of nonintegrator biomass does not.

Control in mutualisms: combined implications of partner choice and bargaining roles.

When two species form a mutualistic association, the degree of control that each has over the interaction may be pivotal in determining the relative benefit each obtains. We incorporate the capacity for partner choice into a model of mutualism based on the exchange of goods and/or services, where one guild of mutualists plays the role of proposer (proposing a price at which the goods and/or services will be exchanged) and the other plays the role of responder (accepting or rejecting the deal). We show how the payoff structure in this scenario and other closely related ones correspond to the ultimatum and demand games of economics.

Competition among plant species that interact with their environment at different spatial scales.

Clonal plants that are physiologically integrated might perceive and interact with their environment at a coarser resolution than smaller, non-clonal competitors. We develop models to explore the implications of such scale asymmetries when species compete for multiple depletable resources that are heterogeneously distributed in space across two patches. Species are either 'non-integrators', whose growth in each patch depends on resource levels in that patch alone, or 'integrators', whose growth is equal between patches and depends on average resource levels across patches.

Interactive effects of builders and exploiters on environmental quality and the outcome of competition between the two.

The implications of spatial and temporal structure for the maintenance of mutualism, altruism, and niche construction or ecosystem engineering have been explored by many theoretical models. Part of what these models have shown is that organisms that give up some amount of potential short-term gain in order to improve the quality of their environment can, in a variety of scenarios, persist in the face of more exploitative competitors if structure in environmental quality allows the former to preferentially benefit from their investments. The models presented here consider the additional implications of interactions between competitors in their effects on their environment (recently documented in multiple systems).

Potential impacts of multiple partners on mycorrhizal community dynamics.

The significance of arbuscular mycorrhizal (AM) fungi in terrestrial ecosystems is widely acknowledged, but the causes and consequences of diversity in these fungi are not well understood. A recent frequency-dependent model suggests that dynamics within mycorrhizal mutualisms could promote the coexistence of at least two competing plant species and two competing fungal species within a community. Models are developed here in which simultaneous association with multiple partners may result in elevated or depressed fitness relative to association with either partner alone.