Jean-François Arnoldi

Centre for Biodiversity Theory and Modelling
Station d’Ecologie Théorique et Expérimentale du CNRS
09200 Moulis, France


Research interests

My work at the CBTM focuses on the various concepts and definitions of stability used in biodiversity modeling and empirical studies. Resilience, reactivity, and temporal variability are complementary and rather intuitive notions to describe the ability of ecosystems to absorb perturbations. However, the relationship between these concepts, and their link with empirical measures, are not obvious. We recently explained how to compare resilience, reactivity and variability, paving the way towards a more coherent perspective on stability, both theoretical and empirical.

My current goal is to provide a simple framework to answer questions raised by empirical founding, such as the correlations and de-correlations of stability measurements; or the more fundamental issue of addressing the stability of large ecosystems, that always exhibit a substantial turnover of rare species, preventing classic mathematical frameworks to apply. Overall, applying, and possibly developing, elegant mathematical approaches to modestly help understanding the complex dynamics of nature, truly fascinates me.


During my PHD, I investigated the transient states (called resonant states) controlling the convergence towards statistical equilibrium in deterministic, chaotic, dynamical systems. A nice introduction to those topics can be found on Frédéric Faure's home page (my Phd supervisor) at: .

Summary CV

I am a postdoctoral researcher at the CBTM working on theoretical aspects of biodiversity modeling, focusing on stability properties of ecosystems. I graduated in 2012 from Grenoble University (France) after completing a PHD in pure Mathematics at the Fourier Institute. I received my MS in theoretical physics from Ecole Normale Supérieure de Lyon in 2008.

During my gap year between my PhD defense and the start of my current position, I traveled to the US and around Europe. During that time, I became a certified climbing guide and coach. Some of my climbing realizations led to published articles in specialized magazines and websites.


  • Zelnik Y., Arnoldi J.-F. and Loreau M. (2019)— The three regimes of spatial recovery. Ecology, 100(2), e02586. Download
  • Zelnik Y.R., Arnoldi J.-F. and Loreau M. (2018) — The impact of spatial and temporal dimensions of disturbances on ecosystem stability. Frontiers in Ecology and Evolution, Volume 6 - Article 224. Download
  • Barbier M., Arnoldi J.-F., Bunin G. and Loreau M. (2018) — Generic assembly patterns in complex ecological communities. PNAS. Download
  • Arnoldi J.-F., Bideault A., Loreau M. and Haegeman B. (2017) — How ecosystems recover from pulse perturbations: A theory of short- to long-term responses. Journal of Theoretical Biology 436 (2018) 79–92. Download
  • Wang S., Loreau M., Arnoldi J.-F., Fang J., Abd Rahman A., Tao S. and de Mazancourt C. (2017) — An invariability-area relationship sheds new light on the spatial scaling of ecological stability. Nature Communications. Download
  • Haegeman B., Arnoldi J.-F., Wang S., de Mazancourt C., Montoya J.M. and Loreau M. (2016) — Resilience, Invariability, and Ecological Stability across Levels of Organization. bioRxiv. Download
  • Arnoldi J.-F. and Haegeman B. (2016) — Unifying dynamical and structural stability of equilibria. Proceedings of the Royal Society A. Download
  • Arnoldi J.-F., Haegeman B., Revilla T. and Loreau M. (2016) — Particularity of "Universal resilience patterns in complex networks”. bioRxiv. Download

  • Arnoldi J.-F., Loreau M., Haegeman B. (2015) - Resilience, reactivity and variability: A mathematical comparison of ecological stability measures. Journal of Theoretical Biology. Download

  • Arnoldi J.-F., Faure F. and Weich T. (2015) - Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. Ergodic Theory and Dynamical Systems. arXiv

  • Arnoldi J.-F. (2012) - Résonances de Ruelle à la limite semiclassique/ Ruelle resonances in the semiclassical limit. PhD under the supervision of Frédéric Faure.

  • Arnoldi J.-F. (2012) - Fractal Weyl Law for skew extensions of expanding maps. Non-linearity, 25: 1671-1693.