Workshop Biostochastic Networks 2021

Speaker: Edouard Strickler (Inria Grand-Est and Université de Lorraine, Nancy, France)
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Abstract: We study a multi-group SIS (Susceptible - Infected - Susceptible) model in a finite size population. To take into account environmental variations, we assume that the rates of infection and cure can randomly switch into a finite number of possible values. When the size of the population goes to infinity, the process converge towards a system of switched ODE : a Piecewise Deterministic Markov 2 Process (PDMP). The aim of the talk is to show that the asymptotics of the extinction time and the quasi-stationary distribution of the process in large, but finite size population, depend heavily on the behaviour of the infinite population system (PDMP).

Speaker: Miguel Lurgi (Computational Ecology Lab. Swansea University. UK.)
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Abstract: Understanding the drivers of geographical variation in species distributions, and the resulting community structure, constitutes one of the grandest challenges in ecology. Geographical patterns of species richness and composition have been relatively well studied. Less is known about how the entire set of trophic and non-trophic ecological interactions, and the complex networks that they create by gluing species together in complex communities, change across geographical extents. Here, we compiled data of species composition and three types of ecological interactions occurring between species in rocky intertidal communities across a large spatial extent ( 970 km of shoreline) of central Chile, and analyzed the geographical variability in these multiplex networks (i.e., comprising several interaction types) of ecological interactions. We calculated nine network summary statistics common across interaction types, and additional network attributes specific to each of the dierent types of interactions. We then investigated potential environmental drivers of this multivariate network organization. These included variation in sea surface temperature and coastal upwelling, the main drivers of productivity in nearshore waters. Our results suggest that structural properties of multiplex ecological networks are aected by local species richness and modulated by factors inuencing productivity and environmental predictability. Our results show that non-trophic negative interactions are more sensitive to spatially structured temporal environmental variation than feeding relationships, with non-trophic positive interactions being the least labile to it. We also show that environmental eects are partly mediated through changes in species richness and partly through direct inuences on species interactions, probably associated to changes in environmental predictability and to bottom-up nutrient availability. Our findings highlight the need for a comprehensive picture of ecological interactions and their geographical variability if we are to predict potential eects of environmental changes on ecological communities.

Speaker: Nicolás Rivera (Universidad de Valparaíso)
Abstract: In this talk I will present some recent results regarding a variation of the well-known voter model, called the noisy voter model, on finite graphs. The noisy voter model is a spin system which works exactly like the voter model but spins can change spontaneously. The random changes of spins are parameterised in p ∈ [0, 1] in such a way that for p = 0 we return to the original voter model, whereas 3 for p = 1 only random changes of spin occur, ignoring the voting steps. I will show that for many sequences of growing graphs, there is a critical parameter pc such that the behaviour of the noisy voter model is quite dierent, in particular, for p << pc, the system behaves like the standard voter model, whereas for p>> pc the system becomes disordered. Our results are obtained by analysing the time-reversed dual process associated with the noisy voter model, which features a system of coalescing random walks of dependent length that may be of independent interest.

Speaker: Lionel Truquet (ENSAI, Rennes, France)
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Abstract: Absence/presence data corresponding to multiple species are widely encountered in Ecology.However, a good understanding of the interactions between species across the time require parsimonious and easily interpretable multivariate time series models for binary data. In this work, we develop some time series versions of probit/logistic regression models with a exible probabilistic framework that allows to incorporate various types of information in the dynamic such as endogenous/exogenous and fixed/time-varying covariates. Inference methods can be based on composite and pseudo-likelihood estimators. We will present some theoretical guarantees from a single path or a longitudinal analysis.

Speaker: Cristóbal Quiñinao (Universidad de O'Higgins)
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Abstract: In this talk, we consider a (control) optimization problem, which involves a stochastic dynamic. The model proposes selecting the best control function that keeps bounded a stochastic process over an interval of time with a high probability level. Here, the stochastic process is governed by a stochastic dierential equation aspected by a stochastic process. This setting becomes a chanceconstrained control optimization problem, where the constraint is given by the probability level of infinitely many random inequalities. Since such a model is challenging, we discretize the dynamic and restrict the space of control functions to piecewise mappings. On the one hand, it transforms the infinite-dimensional optimization problem into a finite-dimensional one. On the other hand, it allows us to provide the well-posedness of the problem and approximation. Finally, the results are illustrated with numerical results, where classical models for the growth of a population are considered.

Speaker: M. Isidora Ávila-Thieme (Advanced Conservation Strategies, USA; .Instituto Milenio en Socio-Ecología Costera, Chile; Universidad Católica de la Santísima Concepción, Chile)
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Abstract: One of the critical problems for sustainable fisheries management stems from the inevitable propagation of the eects on the target species to the entire ecosystem via interactions with many other species, which may or may not be themselves fished by humans. Thus, even when a single species is `well-managed', there is large uncertainty on the impacts of such exploitation on the rest of the ecosystem. In this talk, you will see how a multiple species model, specifically the Allometric Trophic Network (ATN) model, in combination with empirical information, helps us to examine some of the community-wide consequences of harvesting on two heavily exploited coastal marine food webs, the intertidal rocky-shore and shallow-subtidal food-webs of central Chile.

Speaker: Denis Villemonais (Inria Nancy - Grand Est; Université de Lorraine, Nancy, France)
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Abstract: After the presentation of some basic facts about quasi-stationary distributions, the talk will focus on the application of the concept for the limiting distribution of measure valued Polya urns and for the analysis of distributed systems.

Speaker: Nicolas Champagnat (Inria Nancy - Grand Est; Université de Lorraine, Nancy, France)
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Abstract: Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transfered with frequency dependent rate. Our goal is to analyze the trade-o between natural evolution to higher birth rates and transfer, which drives the population towards lower birth rates. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. This is joint work with Sylvie Méléard and Chi Tran Viet.

Speaker: Pablo Marquet (Departamento de Ecología, PUC; Instituto de Ecología y Biodiversidad; Santa Fe Institute)
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Abstract: One of the main conceptual reference frames in biology is the concept of levels of organization, whereby life is organized according to increasing levels of morphological and functional complexity; from cells to tissues, organs, individuals, populations, communities and ecosystems. This ordered, and perfectly nested hierarchy it is becoming increasingly perceived as a straight-jacket to use it in thinking about nature. For example, individuals are at the same time complete ecosystems, so-called “holobionts” that form a co-evolved, metabolic interdependent entity, whereby microbes and hosts provide each other with essential metabolic substrates and products. This begs the question of How can we conceptualize the so called “levels of organization” so as to make progress in understanding life? In this proposal will attempt to tackle this question. A co-evolutionary network that exchanges matter, energy, and information, that is a metabolic network, is, we claim, the kernel of life’s organization across scales. We propose that this network grows recursively, following simple algorithmic rules, and exploring all possible configurations (innovations), some of which become stabilized, spread and persist to become part of larger networks of interactions and so on, recursively. In this talk I will discuss this notion and present evidence for the existence of recurring processes from genes to species communities.

Speaker: Sergio Navarrete (Estación Costera de Investigaciones Marinas, Las Cruces Departamento de Ecología Pontificia Universidad Católica de Chile)
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Abstract: The wonderful complexity of species interactions has both fascinated and baffled ecologists and evolutionary biologists for decades. Darwin’s depiction of the “entangled bank” probably best convey the concept that species are constantly being shaped by a complex suite of selective pressures and tradeoffs imposed by direct and indirect species interactions. To study these complex systems, ecologists have used both, a simplifying reductionist approach, mostly in the form of experimental manipulations, as well as a holistic approach that embraces this complexity, initially in the form of a feeble food web theory, and recently as a more robust network theory that was drawn from other fields and applied to ecological systems. The inclusion a decade ago of non-trophic interactions in ecological networks that portrayed only consumption food webs, represented a major conceptual and practical advance. Indeed, critical non-trophic interactions deeply shape the entangled bank. Significant strides have also been taken in modeling food webs and ecological networks. Yet, conceptual, theoretical and empirical breakthroughs are still needed if this holistic approach is to become a useful tool to model real ecological systems