Community dynamics and sensitivity to model structure: toward a 1 probabilistic view of process-based model predictions 2

International audienc

Appendices to: Community dynamics and sensitivity to model structure: toward a probabilistic view of process-based model predictions. Aldebert & Stouffer, J. R. Soc. Interface, 2018 from Community dynamics and sensitivity to model structure: towards a probabilistic view of process-based model predictions

Statistical inference and mechanistic, process-based modelling represent two philosophically different streams of research whose primary goal is to make predictions. Here, we merge elements from both approaches to keep the theoretical power of process-based models while also considering their predictive uncertainty using Bayesian statistics. In environmental and biological sciences, the predictive uncertainty of process-based models is usually reduced to parametric uncertainty. Here, we propose a practical approach to tackle the added issue of structural sensitivity, the sensitivity of predictions to the choice between quantitatively close and biologically plausible models. In contrast to earlier studies that presented alternative predictions based on alternative models, we propose a probabilistic view of these predictions that include the uncertainty in model construction and the parametric uncertainty of each model. As a proof of concept, we apply this approach to a predator-prey system described by the classical Rosenzweig–MacArthur model, and we observe that parametric sensitivity is regularly overcome by structural sensitivity. In addition to tackling theoretical questions about model sensitivity, the proposed approach can also be extended to make probabilistic predictions based on more complex models in an operational context. Both perspectives represent important steps towards providing better model predictions in biology, and beyond

Structural sensitivity and resilience in a predator-prey model with density-dependent mortality

International audienceNumerous formulations with the same mathematical properties can be relevant to model a biological process. Different formulations can predict different model dynamics like equilibrium vs. oscillations even if they are quantitatively close (structural sensitivity). The question we address in this paper is: does the choice of a formulation affect predictions on the number of stable states? We focus on a predator–prey model with predator competition that exhibits multiple stable states. A bifurcation analysis is realized with respect to prey carrying capacity and species body mass ratio within range of values found in food web models. Bifurcation diagrams built for two type-II functional responses are different in two ways. First, the kind of stable state (equilibrium vs. oscillations) is different for 26.0– 49.4% of the parameter values, depending on the parameter space investigated. Using generalized modelling, we highlight the role of functional response slope in this difference. Secondly, the number of stable states is higher with Ivlev’s functional response for 0.1–14.3% of the parameter values. These two changes interact to create differentmodel predictions if a parameter value or a state variable is altered. In these two examples of disturbance, Holling’s disc equation predicts a higher system resilience. Indeed, Ivlev’s functional response predicts that disturbance may trap the system into an alternative stable state that can be escaped from only by a larger alteration (hysteresis phenomena). Two questions arise from this work: (i) how much complex ecological models can be affected by this sensitivity to model formulation? and (ii) how to deal with these uncertainties in model predictions

Does structural sensitivity alter complexity–stability relationships?

International audienceStructural sensitivity, namely the sensitivity of a model dynamics to slight changes in its mathematical formulation, has already been studied in some models with a small number of state variables. The aim of this study is to investigate the impact of structural sensitivity in a food web model. Especially, the importance of structural sensitivity is compared to that of trophic complexity (number of species, connectance), which is known to strongly influence food web dynamics. Food web structures are built using the niche model. Then food web dynamics are modeled using several type II functional responses parameterized to fit the same predation fluxes. Food web persistence was found to be mostly determined by trophic complexity. At the opposite, even if food web connectance promotes equilibrium dynamics, their occurrence is mainly driven by the choice of the functional response. These conclusions are robust to changes in some parameter values, the fitting method and some model assumptions. In a one-prey/one-predator system, it was shown that the possibility that multiple stable states coexist can be highly structural sensitive. Quantifying this type of uncertainty at the scale of ecosystem models will be both a natural extension to this work and a challenging issue

Analysis of a predator–prey model with specific time scales: a geometrical approach proving the occurrence of canard solutions

International audienceWe study a predator-prey model with different characteristic time scales for the prey and predator populations, assuming that the predator dynamics is much slower than the prey one. Geometrical Singular Perturbation theory provides the mathematical framework for analyzing the dynamical properties of the model. This model exhibits a Hopf bifurcation and we prove that when this bifurcation occurs, a canard phenomenon arises. We provide an analytic expression to get an approximation of the bifurcation parameter value for which a maximal canard solution occurs. The model is the well-known Rosenzweig-MacArthur predator-prey differential system. An invariant manifold with a stable and an unstable branches occurs and a geometrical approach is used to explicitly determine a solution at the intersection of these branches. The method used to perform this analysis is based on Blow-up techniques. The analysis of the vector field on the blown-up object at an equilibrium point where a Hopf bifurcation occurs with zero perturbation parameter representing the time scales ratio, allows to prove the result. Numerical simulations illustrate the result and allow to see the canard explosion phenomenon

Identifying lateral boundary conditions for the M2 tide in a coastal model using a stochastic gradient descent algorithm

International audienc

A Fast and Generic Method to Identify Parameters in Complex and Embedded Geophysical Models: The Example of Turbulent Mixing in the Ocean

International audienceGeophysical systems are generally described by nonlinear mathematical models. These models often involve partial differential equations like the Navier-Stokes equations, and embed sub-models describing various processes, such as sub-grid turbulent mixing or biological processes (e.g., growth and interactions of living organisms). The resulting models are costly to develop and to run, bringing together scientists from different disciplines. Moreover, the resulting model predictions remain sensitive to various forms of uncertainty

Three-Dimensional Bifurcation Analysis of a Predator-Prey Model with Uncertain Formulation

International audienc