List of abstracts

List of Abstracts

Jeff Arnoldi - Invasion fitness, indirect feedbacks and alternative stable states in ecological community models

(Joint work with Matthieu Barbier, Guyri Barabas, Ruth Kelly, Andrew L Jackson and Guy Bunin).

In Lotka-Volterra models, there is at most one stable state per species composition. This means that shifts between alternative states must involve extinctions and, importantly, invasions by species previously excluded from the community.

Many facets of ecological theory rely on the analysis of invasion processes,  and general approaches exist to understand the early stages of an invasion. However, predicting the long-term transformations of communities following an invasion remains an open problem. 

Here I will explain some recent progress in that direction, applicable to arbitrarily complex community models, from few competing phenotypes to large nonlinear food webs. 

Whether a species can invade is controlled by its invasion fitness, which depends on environmental conditions and direct interactions with resident species. But whether this invasion will cause significant transformations, such as extinctions or a regime shift, depends on a specific measure of indirect feedbacks that can involve the entire resident community. Applying this metric to random Lotka-Volterra models, we can investigate how the complexity, specialization and asymmetry of invader-resident and resident-resident interactions affects the severity of invasion impacts. This approach also hints at ways to characterise a phase transition in large random lotka-Volterra models, from criticality to a glass phase presenting ageing processes along alternative stable states.

Matthieu Barbier - How random are these grasses? Understanding low- and high-dimensional structures in empirical species interactions

Sufficiently random and heterogeneous interactions do not allow all species to coexist, but how far do we need to stray from randomness to understand real communities of coexisting species?

In a wide region of parameters, Lotka-Volterra dynamics will cause some species to go extinct until an equilibrium is reached. The surviving community can contain many species, but their characteristics and interactions must have some nonrandom features. We find that these nonrandom features are minimal correlations: the smallest deviation from randomness that permits coexistence.

We infer species interactions in grassland competition experiments, and show that correlations in these interactions match our predictions quantitatively, supporting the idea that the interactions are close to random, yet biased by coexistence.

To extend this reasoning to more complex ecological networks, such as food webs, we must also consider how macroscopic structures will alter these results. This invites new mathematical inquiries into deterministic perturbations of random matrices, and ecological questions of identifying these macrostructures in empirical data.

Ugo Bastolla - Structural stability of ecological interactions

In this talk we address through analytical approximations and numerical simulations the question of which type of ecological interactions are more favourable to the structural stability of model ecosystems and the maintenance of their biodiversity. We find that the answer depends on the connectance and the overlap (sometimes called nestedness) of the ecological networks, and discuss which regime could be more representative of real ecosystems.

Barbara Bauer - Elemental fluxes in spatial models with multiple resources and consumers

Barbara Bauer, iDiv- German Centre for Integrative Biodiversity Reseach Halle-Jena-Leipzig

Recently there has been increasing attention on describing the flow of elements, besides energy, between compartments in complex food webs to better understand the role of species diversity and composition in global nutrient cycles. In my talk I focus my attention to the elemental fluxes at the base of the food web, namely the uptake of mineral nutrients by plants. I will first briefly review and compare the general features of the numerous existing models of consumer-resource systems. While the majority of theoretical studies focus on perfectly substitutable resources, I will include models of non-substitutable (essential) resources in the comparison as they are especially (but not only) relevant in the context of resource uptake by primary producers. I show preliminary results of simulations where relative availabilities of different types of resources are varied in space and consumers vary in their trait values. I end with a discussion on how coexistence patterns under different simulation settings could be linked to spatial patterns in resource uptake.

Giulio Biroli - Multiple Equilibria, Chaos and Aging Dynamics in Large Interacting Ecosystems

I will focus on Lotka-Volterra equations, which provide a general model to study large assemblies of strongly interacting degrees of freedom in many different fields: biology, economy and in particular ecology. I will present our analysis of the generalised Lotka-Volterra model of ecological communities formed by a large number of species and focus in particular on two different phases that emerge: when interactions are symmetric we find a regime characterized by an exponential number of multiple equilibria, all poised at the edge of stability for a large number of species. For non-symmetric interactions, this phase is replaced by a chaotic one or a dynamical aging regime depending on the presence of migration from the mainland. I will also briefly present the theoretical methods we used: dynamical mean-field theory and relationships with spin-glass physics. 

Guy Bunin - Dynamics of high-diversity communities: A tale of two phases

In high-diversity communities, species interactions can produce a number of distinct dynamical behaviors. Here we contrast two such dynamical regimes. In one, species interactions drive the entire community into a persistent chaotic state. In another, the dynamics are robustly directional, meaning that the state of a system can be characterized by a function that increases in time. Both regimes are profoundly affected by adding a spatial dimension, modeled here as a meta-community. In the former, space stabilizes the chaotic behavior for very long times, even in a finite population and without inducing extinctions. These fluctuating states enable dramatically more species to coexist than at equilibrium in the very same system. In the later, the system admits many alternative community states, that are able to expand in space, forming (exact or approximate) copies of themselves. This leads to community-level selection, in analogy with Darwinian selection, with the increasing function acting as a fitness.

Ursula Gaedke - Improving the realism of predator-prey and food web models to understand complex plankton food web dynamics

Ursula Gaedke, Alice Boit, Ruben Ceulemans, Elias Ehrlich, Toni Klauschies, Nadja Kath, Katrin Tirok, Ellen van Velzen & Christian Guill

In the context of climate change research we confronted numerically solved, high dimensional differential equation models with comprehensive long-term, high-frequency observations of a complex lake plankton food web. Initially, data and model results deviated fundamentally although the model food web structure was based on measurements and its stability was much higher than that of a random-matrix model. Among others, model realism could be enhanced by improving the representation of respiratory losses (e.g. activity vs. basal respiration). In addition, the properties (traits) of individuals and populations such as constant maximum growth and grazing rates are not static. Rather, organisms can adjust such trait values to ambient conditions. We show that this has far reaching consequences for the structure and dynamics of food webs and can lead to so-called biomass-trait feedback cycles or eco-evolutionary dynamics. For example, under high predation pressure the prey likely develops defence mechanisms that stabilize prey biomasses and let the predators decline. Subsequently, ubiquitous trade-offs between e.g. growth and defence increase the fitness of undefended prey, which eventually lets the predator biomass increase again. Biomass and trait dynamics get even more complex when the predators develop a counter defence against the prey defence, leading potentially to out-of-phase or even reversed predator-prey cycles. We provide examples how such adaptive processes cause a food web rewiring, impact system dynamics and improve model realism. Furthermore, we show that modelling at least three trophic levels is essential for accurately capturing the seasonal trait shifts seen in the empirical data. Finally, we highlight the importance of nutrient recycling as an additional interaction pathway in food webs by demonstrating how accounting for nutrients retained in consumer biomass affects system dynamics.

Mathew Leibold - Emerging frontiers in biodiversity ecology – generalizing Lotka-Volterra models at realistic biodiversity scales.

Community ecology is in a dramatic state of development with the advent of important new concepts and analytical tools as well as exciting progress in theory.  This includes approaches that can transfer insights from our basic theories, such as Lotka-Volterra for pairwise species interactions, to the study of realistically biodiverse biotas.  From an empiricists point of view, the challenge is to find the ways to integrate this emerging theory with empirical approaches that can allow us to both test and apply these ideas.  To promote thinking about this integration, I will try to identify some of the challenges ahead for the theory and to identify some critical experiments and data-analytic methods that may help in the evaluation and application of these insights.  The challenges include thinking about processes that are not normally addressed in L-V modeling such as drift, dispersal, and rapid evolution, and linking the predictions of the theory to emerging statistical methods that address these issues within the context of broader issues in ecology such as metacommunities and environmental change. 

Mylène Maïda - Tutorial on random matrix theory

Abstract : I will review mathematical results on the spectrum of random matrices, that may be relevant for the study of large dimensional Lotka-Volterra systems. Some of these results are now classical for people working in random matrix theory, others are more advanced.   I will also present some models that are still not fully understood mathematically  but may be of interest for theoretical ecology.

Christian Mazza - Feasibility of equilibria in large ecosystems

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems.

Axel Rossberg and Jacob O'Sullivan - Hurray! - Ecological structural instability is everywhere

A central mechanism shaping the phenomenology of large random Lotka-Volterra models is ecological structural instability: when the interaction matrix of the extant set of species has eigenvalues in the vicinity of zero, a community becomes highly sensitive to press perturbations and species easily go extinct. This leads to self-organization of these communities in states at the edge of structural instability. In more realistic community models, such self-organisation can be demonstrated as well, inviting the question what it plays in nature. Indeed, we will discuss evidence that structural instability is the mechanism underlying a wide range of patterns long known to ecologists. These include biodiversity patterns in space, time and across trophic levels and phenomena related to indirect interactions and the question whether ecological communities ever attain equilibria or not. Based on this evidence we must thus conclude that, just as the Lotka-Volterra models we all study, most natural communities spontaneously self-organization in states at the edge of structural instability.

Alix Sauve - On parameterising large seasonal food webs

Dynamic food web models are essential to predicting the response of ecosystems to perturbations such as predator culling or resource disruption, but are only as good as their parameterisation. However, dynamic models are notoriously difficult to parameterise. Current approaches meet the challenge for simple predator-prey systems to medium-sized food webs. Yet, they are inadequate to the modelling of large food webs in fluctuating environments: allometric scaling of predator-prey interactions makes similarly-sized species prone to extinction while biomass flow approaches are restricted to steady-state ecosystems.

Adequately parameterising large terrestrial food webs of temperate and arctic environments requires to deal both with many species of similar sizes and a strongly seasonal environment. Drawing on theoretical studies on small predator-prey modules, I will present a general and flexible workflow which implements food web seasonality into dynamical models (non-autonomous coupled ODE systems).

Applying this framework to a case study, the food web of the Bialowieza forest (Poland), and thus building on decades of wildlife survey, produces high persistence levels in spite of massive apparent competition and a quantitative match to observed biomasses. With these promising results, such a framework initiates the modelling of large communities undergoing temporal forcing, which is required to investigate their response to changing environments.

Carlos Servan - Trait dimensionality effects on model ecological communities

Abstract: In recent years there has been an increased interest in the use of functional traits as a basis for explaining community ecology patterns. Typically, in this framework, each species is associated with a set of trait values which then determine how the species behave in the community. In this work, we use the functional traits perspective to study the effects of trait dimensionality on community patterns. We consider a set of n interacting species whose dynamics are governed by Generalized Lotka-Volterra equations(GLV). To incorporate the effects of traits we assign each species a trait vector of length k and model the interaction matrix as the covariance matrix between these trait vectors. Assuming that the trait vectors are sampled independently from a Gaussian distribution we derive exact formulas for community properties such as the distribution of the number of coexisting species and the total biomass of the system. Extensions of these results to the introduction of correlations among traits will also be discussed.

Lewi Stone - When Google meets Lotka-Volterra

Abstract : T.B.A.