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28-29 Oct 2024 Champs-sur-Marne (France)
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List of abstracts + slides
Allesina Stefano TITLE : Robust coexistence in ecological competitive communities ABSTRACT : The notions of intraspecific competition and population self-regulation play a central role in ecological theory, leading to foundational concepts such as limiting similarity and niche differentiation. They also are crucial for coexistence: for example, May showed that ecological dynamics around a "feasible" equilibrium can be stabilized by imposing sufficiently strong self-regulation on all populations. For large random systems, the transition from instability to stability is sharp, and achieved beyond a critical value of intraspecific competition d > dS. Here we document a similar transition from unfeasible to feasible equilibria. We derive results for general Lotka-Volterra systems and then apply these methods to the case of systems with random interactions, for which several results are available. We can generalize, refine and strengthen previous findings, showing that the existence of a feasible state is guaranteed whenever d > dF. We compute the probability of feasibility for a community of n populations given the level of intraspecific competition d for different model formulations, and show that the transition to feasibility is smooth, contrary to what found for stability. We explore the relationship between the two critical levels, dS and dF, and determine that, for large random ecological communities dominated by competition, dF > dS, that is, the existence of a feasible equilibrium implies its stability. This means that non-equilibrium coexistence via limit cycles or chaos is never observed in these large ecological systems. Dynamics always converge to an equilibrium in which a set of competitors robustly coexist, such that the community can recover from perturbations, be assembled from the bottom-up, and is resistant to invasions. Azaele Sandro TITLE : How do non-Gaussian interactions drive patterns and coexistence in large ecosystems? ABSTRACT : In the exploration of theoretical ecology, the Generalized Lotka-Volterra (GLV) equations stand as a pivotal model, in which species interactions are fixed over time and heterogeneous. Current approaches postulate that for large, disordered GLV systems, species abundances are dictated by the mean and variance of interaction distributions. Yet, this assumption does not hold up against the backdrop of empirical ecological communities, where deviations from such universality are observed. We will introduce a generalized dynamical mean field theory tailored for non-Gaussian interactions, with applicability extending well beyond the GLV model. We find that the solutions of the new equations are influenced by the full range of cumulants of the interaction distribution. We will delve into the implications of these results, showing how to derive more realistic patterns. The framework allows to deduce some statistical properties of microscopic interactions from the observable macroscopic distribution of species densities. Our findings are also able to elucidate the effects of sparse interactions, at least in some regions of the parameter space. We will also illustrate the patterns that emerge when species’ interactions randomly change on temporal scales that are comparable to the dynamics of the populations (annealed disorder).
TITLE : Some stochastic functional responses in ecology ABSTRACT : Functional responses describe the rate at which interactions occur in various living or chemical systems, particularly in predator-prey dynamics. Our focus is on deriving these responses from individual-based models. We aim to understand the scales at which such approximations hold, allowing for reliable predictions in population dynamics, while also quantifying the inherent fluctuations/heterogeneity due to the stochastic nature of the foraging process. We will relax some of the common assumptions typically made in deriving macroscopic functional responses, such as the absence of memory and simplification of the spatial structure. This is based on works in collaboration with Sylvain Billiard, Geoffroy Berthelot, Jean René Chazottes, and Bertrand Cloez.
TITLE : Tackling the profusion vs novelty issue : Punctuated evolution by simple inflation of a random matrix ABSTRACT : The picture of punctuated evolution has regained popularity and was proposed to account for the evolutionary dynamics in a number of fields beyond biology [1]. In the economic sphere, for instance, the vision in separate « sectors » does not render the series of « disruptions » that we experiment through successive innovations (from the refrigerator to the smartphone). There are not many works relating this aspect of growth/speciation/novelty/profusion with random matrices. For instance, R.M. May famous approach on stability of large system has not spawned into means of addressing “punctuations”. I have proposed that a “matrix inflation” process can perform this task [2,3]. The idea is that any operator M acting on a vector V (of species abundances of similar ones) in the time-discrete form V(t+1)=M V(t) reaches, if M is fixed, the eigenvector W of largest eigenvalue module of the (non-Hermitian) matrix M. If “novelties” are introduced in the form of a random set of one extra line and column to M, inflating its size by one every few time steps for instance, “quakes” disrupt the stasis of the quiet convergence to W as soon as another vector W’ wins the competition of eigenvalues with W, both evolving under the “inflation process”. We shall document this idea more thoroughly based on our recent attempts [2,3]. A small real-world system that provides a basic example is the flourishing one of journal scientific publications. The statistics of stasis durations will be another piece of interest. A more daunting perspective is to wonder if, equipped with a model of profusion + diversification that, in the case of human economy, ignores the planetary limits, some sensible hints on “deflation” can be devised and if they carry any meaning for societies. [1] On the multiscale dynamics of punctuated evolution, Duran-Nebreda, Salva et al., Trends in Ecology & Evolution, Volume 39, Issue 8, 734 – 744 (2024) [2] H. Benisty, "Evolutionary behaviour of 'inflating' random real matrices for economy or biology: stasis statistics of vector iterations upon growth", J. Phys. Complex, vol.3, pp 025006, 2022. [3] H. Benisty, "Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices", Entropy vol. 25, pp.1507, 2023. https://doi.org/10.3390/e25111507
Bieg Carling TITLE : Ecological structure and function in variable environments ABSTRACT : While ecological theory has made significant strides towards understanding the structure and function of nature’s complex networks of interactions, food webs have historically been modeled under greatly simplified temporal and spatial assumptions. Notably, global change is altering more than the average conditions that organisms experience; the regular and repeating fluctuations that define environments (e.g., diurnal and seasonal rhythms), and the less-predictable patterns superimposed upon these cycles are also changing. This alarmingly leaves us with an ecosystem theory that is not yet prepared to interpret the impacts of global change. Across simple interaction structures, I will discuss how changes in regular (e.g., periodic) fluctuations under global change can drive noise-driven states that would not be predicted from deterministic theory. As a step towards mechanistically understanding these seemingly counterintuitive non-equilibrium effects, I will show how geometric characteristics (i.e., models’ deterministic skeletons) allow us to unpack interactions between local and non-local dynamics driving these outcomes. Specifically focusing on the role of periodic environments in mediating competitive interactions, I use a simple analytical solution to describe how temporal asymmetries in species’ growth and competition can exacerbate the magnitude of counterintuitive effects and result in unexpected local extinction of certain species. Importantly, the seasonal patterns and species’ trade-offs that magnify these results are biologically realistic, therefore providing important insight into the implications for the maintenance of biodiversity under global change. Altogether, global change may have seemingly unexpected – yet potentially predictable – effects on ecological structure and function if we understand the relationship between environmental variation and key biotic responses.
TITLE : Quantifying metapopulation persistence across varying spatial networks. ABSTRACT : Habitat fragmentation, caused by natural phenomena and human land use, is a major driver of biodiversity loss. Metapopulation models help to understand the persistence of species through colonization and extinction in fragmented habitats. Traditionally, these models use a metric called metapopulation capacity, derived from network properties, to assess species persistence, but they often overlook the temporal dynamics of habitats.
Recently, ecologists have begun to use multilayer networks as a mathematical tool for representing temporal networks. In particular, multilayer networks are well suited for studying temporal networks in the case of metapopulation dynamics. Using methods borrowed from the physics of Markov processes and epidemiology, we recover criteria for metapopulation capacity in the case of temporal networks, allowing the assessment of species persistence over time and the development of strategies to mitigate habitat fragmentation. This new metric, which is similar to metapopulation capacity and considers network structure from a temporal perspective, may represent a turning point in the analysis of species persistence in a changing habitat. It provides a single framework that ecologists can use and is consistent with recent literature on multilayer networks with a strong theoretical focus.
TITLE : Persistence and coexistence of species in spatial networks ABSTRACT : A classic result in community ecology is that dispersal between patches (e.g. islands, forest fragments) promotes local biodiversity in those patches. However, the mechanisms causing this result are not well understood. Available patch-occupancy models predict the fraction of patches a given species occupies, but either only consider a single species, or imply extinction of all species across all patches in absence of dispersal. Available simulation models are more realistic but have been impossible to mathematically analyse beyond species pairs, making it unclear how general their simulation results really are. During my talk, I will present new results that shed light on the effect of dispersal on local biodiversity. I will show how the assumption of small dispersal leads to an analytical treatment of an otherwise impalpable model. A first analysis focuses on the species level, showing how dispersal, local species interactions, and the size of the spatial network (i.e. the number of patches) jointly influence persistence. Interestingly, the effect of local interactions is fully captured by the focal species invasion growth rate, a main variable of interest in modern coexistence theory. A second analysis focus on the community level, introducing the idea of community-level patch occupancy: the fraction of patches occupied by all species and thus the community as a whole. I show how patch occupancy is intimately linked to feasibility, another key concept in coexistence theory. I end by showing how our predictions of patch occupancy match simulations, relaxing all our assumptions.
TITLE : Exploring the role of groups for functioning and ecosystem management in ecological communities ABSTRACT: Ecological processes in food webs depend on species interactions. By identifying broad-scaled interaction patterns, important information on species' ecological roles may be revealed. Here, we use stochastic block models, in ecology known as the group model, to address two research questions. First, we examine how spatial resolution and proximity influence group structure in a spatially divided food web. We test how the group structure in the sub-networks differ depending on 1) the regional metaweb to subregions and 2) subregion to subregion. Our results show that species ecological roles vary depending on fine-scaled differences in the patterns of interactions, and that local network characteristics are important to consider. However, given the stochastic nature of the method group structures of the same food web can differ between multiple model runs; a single best partition may miss relevant information, and a consensus solution may blur complementary communities. Therefore, the second question we address it is how reliable the identified partitions are. We analyze the solution landscape while searching for the optimal partitioning of species using a set of food webs. We aim to explain the differences between solutions and what they entail, structurally and ecologically. Our results show that the overall general group structures remain intact across different iterations, with some important exceptions.
Hachem Walid TITLE : Distribution of the equilibrium of a large Lotka-Volterra system through an Approximate Message Passing approach ABSTRACT : We have recently used the Approximate Message Passing (AMP) algorithms to evaluate the asymptotic distribution of the globally stable equilibrium vector of a large Lotka-Volterra system when this vector exists and when the interaction matrix is random. The most general interaction matrix model we deal with is the matrix model of elliptical type, non necessarily Gaussian, and with a sparse random profile. The large dimensional distribution of the equilibrium is shown to be a mixture of a large number of Gaussians, which parameters are characterized through a system of implicit equations.
Loeuille Nicolas TITLE : Implications of eco-evolutionary dynamics for the structure and functioning of ecological networks ABSTRACT : In the past decades, various empirical and theoretical works have highlighted how the stability and functioning of ecological networks do not simply emerge from their diversity, but also depend on their structure and architecture. Such structures are affected by ecological dynamics (eg, species colonization and extinction), but also depend on the trait distributions of interacting species and on their (co)evolutionary dynamics. In this talk, I will first question which phenotypic traits are suitable for understanding the eco-evolutionary dynamics of ecological networks. I will then present a few models in which the structure of either unipartite or bipartite, mutualistic or antagonistic networks emerge from simple evolutionary dynamics. I will discuss how emerging structures compare to our empirical knowledge of ecological networks, and their implications for network functioning and stability. Finally, given the accumulating empirical evidence of fast evolutionary dynamics in response to current global changes, I will discuss whether such evolutionary dynamics favors resilience and coexistence within ecological networks.
TITLE : Evolution of dormancy in the context of complex ecological dynamics ABSTRACT : Dormancy is usually understood as a strategy for coping with extrinsically variable environments, but intrinsic population fluctuations also create conditions where dormancy is adaptive. By analyzing simple population models, we show that, very generally, population fluctuations favor the evolution of dormancy, but dormancy stabilizes population dynamics. This sets up a feedback loop that can enable the coexistence of alternative dormancy strategies. Over longer timescales, we find that evolution of dormancy to an evolutionary stable state can drive populations to the edge of stability, where dynamics are only weakly stabilized. We also consider how these conclusions apply in more complex community contexts, where the type and organization of interspecific interactions mediates the stabilizing effect of dormancy. Our results suggest that complex dynamics such as chaos and high-amplitude population cycles are highly vulnerable to invasion and subsequent stabilization by dormancy, potentially explaining their rarity. At the same time, the propensity of ecological dynamics to fluctuate may be an underappreciated driver of the evolution of dormancy.
Ros Valentina TITLE : The multiple equilibria of many-species ecosystems: how many, how stable, how relevant? ABSTRACT : In an attempt to understand the complex dynamics of ecosystems, recently there has been quite a lot of interest in the study of high-dimensional dynamical systems describing many species interacting randomly, possibly in a non-reciprocal (asymmetric) way. These systems of equations generally exhibit a transition in the strength of the variability of the interactions: when the variability is weak, the dynamics quickly settle into a stationary state, converging to a unique equilibrium configuration; when the variability is high, the dynamics keep fluctuating, exhibiting signatures of progressive slowing down or chaos. This dynamical transition is expected to be concomitant with the emergence of “glassiness”, intended here as the sudden explosion in the number of possible equilibrium configurations of the dynamical equations. In this talk, I will focus on a prototypical dynamical system with all-to-all random interactions, the so-called random Generalized Lotka-Volterra equations. I will discuss how to explicitly compute the number of equilibrium configurations and characterize their properties. I will focus in particular on the case of non- reciprocal interactions between the species, which render the system non-conservative, thereby ruling out some standard approaches developed in the field of glasses to treat conservative systems with randomness.
Rossberg Axel TITLE : More recent evidence for self-organised ecological structural instability in nature ABSTRACT : Ecological Structural Instability (ESI) denotes a high sensitivity of ecological communities to press perturbations emerging at high species richness, a limit to robust co-existence, resulting from the amplification of indirect interactions between species. Since the monograph “Food Webs and Biodiversity: Foundation, Model, Data” suggested in 2013 that natural ecological communities self-organise into states close to the onset of ESI, this theory has gained support along several independent lines of evidence. Because measuring interactions in the field is difficult, this evidence relies heavily on comparisons of the emergent phenomenology of self-organised ESI, found in mathematical models, with field observations. Here I will discuss our recent solutions of the asymmetric random Lotka-Volterra competition assembly model and the Locally Saturated Patch Occupancy Model to discuss how the excellent fit of these models to data supports the theory of self-organised ESI. I will point to opportunities to synthesise these results with other ongoing work in mathematical community ecology.
TITLE : Species diversity, food web structure and the temporal stability of ecosystems: bridging the gap between theory and data? ABSTRACT : The consequences of diversity and food web structure on the stability of ecological communities have been debated for more than 5 decades. While the understanding of the relation between diversity and the stability of properties at community and ecosystem levels has gained from joint empirical, experimental and theoretical insights, the question of the relation between food web structure and stability has received almost exclusively theoretical attention. The lack of empirical studies on this issue is partly due to the fact that theoretical studies are often disconnected from the stability of natural ecosystems, and to the difficulty of describing and manipulating food web structure in the field. Here I will present the results of two joint studies, one based on a theoretical food web model and the other on the data analysis of time-series of fish communities, aiming to investigate in parallel the relations between diversity, food web structure and the stability of community-level properties.
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