the role of mathematics and computer science in ecological theory



The issues of climate change and biodiversity loss are definitely the major concerns for 21st-century science. Ecology is one of the most involved sciences in this challenge. Undoubtedly, mathematics and computer simulations have played an important role in the development of theoretical ecology for almost one century. They are often designated as "modeling". But what are "modeling" and "theory" in ecology and what are the places occupied respectively by mathematics and computer science are still controversial issues.

The structure considered for the semester is a succession of one-week workshops gathering a dozen of invited scientists. Several workshops will include Bernoulli lectures for a wider audience. Additionally, a small number of scientists will be in residence at the CIB for several months. One of the goals of the program is to introduce mathematicians and computer scientists to problems of theoretical ecology that are often not familiar to them. Graduate students and other scientists wishing to attend are welcome to apply. Application forms are available on this page.


Non-adaptive selection: explaining macroscopic laws in ecology and evolution

Workshop organizers: Lev Ginzburg, Roger Arditi, and Louis-Félix Bersier (U. Fribourg, CH)
Dates: July 07–11, 2014

Much of biological thinking starts with the view that, given enough time, anything can evolve. We think that it is more fruitful to delineate first the forbidden states of ecology and evolution—“forbidden” not because they cannot occur, but because they cannot last. Our hypothesis is that much of the structure and stability of biodiversity seen at the macro level is the result of an ongoing process of selective elimination of unstable configurations. Selective elimination processes are powerful non-adaptive evolutionary forces, and they are not specific to biological systems. The evolution of the planetary system or, for example, of the rings of Saturn has been driven by the elimination of many physical bodies. The elimination processes in biology are different only in that the forces of evolution continually generate biological systems that approach or transgress eliminative boundaries, and thus elimination is a never-ending process. Various observed macroscopic ecological laws can be explained by the mathematical conditions of stability in systems of interacting species. This is a fruitful approach that was initiated by Robert May in the 1970s and has been attracting more attention in the last decade.

Speakers and/or invited participants: Stefano Allesina, Priyanga Amarasekare, Roger Arditi, Louis-Félix Bersier, Jonathan Borrelli, Ivan Chase, John Damuth, Lev Ginzburg, Robert Holt, Claude Lobry, Dmitrii Logofet, Carlos Melian, Mark Novak, Rudolf Rohr, Axel Rossberg, Matthew Spencer, Khai Tran

Application form: click here

Dispersal and competition of populations and communities in spatially inhomogeneous environments

Workshop organizer: Donald DeAngelis (U. Miami, FL, USA)
Dates: August 4–8, 2014

Nature is highly heterogeneous and ecologists are trying to understand the effects of spatial heterogeneity on population dynamics and community biodiversity. Two different approaches, one by theoretical ecologists using discrete-space models and dispersal kernels and another by mathematicians using partial differential equations, have been independently reaching consistent conclusions. One is that a population feeding on heterogeneously distributed resources and diffusing can attain higher total biomass than a population feeding on the same mean resource density distributed homogeneously. Despite the similar subject matter and similar results of the two different mathematical approaches, as far as we know there have not been joint meetings that involve the key mathematicians and theoretical ecologists. The objective of the workshop is to review and synthesize progress in these approaches to population dynamics on heterogeneous landscapes, and to relate this to real populations and communities in a way to inform PhD students of this subject area.

Speakers and/or invited participants: Roger Arditi, Peter Chesson, Chris Cosner, Don DeAngelis, Vlastimil Krivan, Adrian Lam, Claude Lobry, Yuan Lou, Patrizio Mariani, David Murrell, Wei-Ming Ni, Robin Snyder, Bo Zhang

Application form: click here

Validation of uncertain ecological models with imprecise data

Workshop organizer: Scott Ferson (Applied Biomathematics, Setauket, NY, USA)
Dates: September 15–19, 2014

The predictive capability of ecological models, which determines what we can reliably infer from them, is assessed by whether and how closely the model can be shown to yield predictions conforming with available empirical observations beyond those data used in the model calibration process. Realistic ecological models usually incorporate stochasticity to mimic the variability in the natural world, which means that their predictions are often expressed as probability distributions or similarly uncertain numbers.  Validation of these models must also contend with data that are usually sparse and often imprecise. But this stochasticity and imprecision complicate the validation process considerably.  There are various ways of measuring dissimilarity when predictions and data are scalar point values or low-dimensional vectors, but when either or both are distributions or interval ranges, the notion of dissimilarity is more subtle, because they can overlap, and they can be in close agreement over some possible values but in stark disagreement over other values.  A match between the model and data can sometimes be easier to establish when the predictions are uncertain because of ambiguities about the model structure or when empirical measurements are imprecise, but the resulting predictive capability is degraded by both phenomena.  One might hope to define a scalar metric that assesses in some overall sense the dissimilarity between predictions and observations.  But there may be cases in which it would be more informative and useful to distinguish predictions and observations in two senses, say, one concerned with epistemic uncertainty and one concerned with aleatory uncertainty.  This workshop will investigate the appropriate accounting that is needed for conducting proper validations and estimating predictive capabilities of ecological models.

Speakers and/or invited participants: Nadia Ben Abdallah, Jean Chesson, Jeffrey Dambacher, Scott Ferson, Andy Hart, Claude Lobry, Sebastian Schreiber

Application form: click here

Discrete, explicit simulations versus continuous, aggregated models

Workshop organizers: Fabien Campillo (INRIA, Sophia-Antipolis, FR), Claude Lobry, Roger Arditi, and Yuri Tyutyunov (Southern Federal University and Russian Academy of Sciences, Rostov-on-Don, RU)
Dates: October 13–17, 2014

Continuous models (i.e., differential and partial differential equations) are appropriate to analyze the qualitative behavior of population dynamics but are only suitable to represent very large populations. Otherwise, they can lead to absurd quantities like an "atto-fox". For small populations, discontinuous representations (branching processes, IBMs) must be used but are less tractable. In particular, due to excessive computing time, they are not suitable for very large populations. Unfortunately, interactions between populations having a very large number of individuals and populations having a little number of individuals are common and their modeling is a source of new and interesting problems. On the other hand, complex models, often formulated as simulation models (e.g., IBMs) in order to mimic closely the biological interactions only acquire general, theoretical interest if simple rules can be inferred from them.

The two questions of reliable simulations and emergence of simple rules will be explored on such ecological problems as:
– emergence of predator interference in predator-prey systems,
– self-organization of population spatial patterns,
– use of process algebra in deriving population-level models,
– modeling collective behavior of animals,
– invasion success factors.

Speakers and/or invited participants: Roger Arditi, Michel Benaïm, Nicolas Champagnat, Guillaume Deffuant, Jérôme Harmand, Claude Lobry, Alexander Medvinsky, Tewfik Sari, Inna Senina, Feodor Surkov, Lyudmila Titova, Yuri Tyutyunov

Application form: click here

Multi-scale models, slow-fast differential equations, averaging in ecology

Workshop organizers: Mathieu Desroches (INRIA, Rocquencourt, FR), Olivier Faugeras (INRIA, Sophia-Antipolis, FR), Claude Lobry, and Tewfik Sari (IRSTEA, Montpellier, FR)
Dates: November 17–21, 2014

During the last few decades, considerable developments have occurred in the domain of slow-fast differential equations with applications to various domains of science like mechanics, automatic control, neurophysiology, etc. Some applications exist in the domain of theoretical ecology. The aim of this workshop is to gather mathematicians specialists of slow-fast systems and singular perturbations in order to review recent advances in the mathematical field and in population dynamics, and to investigate the potential applications.

Speakers and/or invited participants: Roger Arditi, Manon Baudel, Peter beim Graben, Eric Benoît, Nils Berglund, Morten Brøns, Bertrand Cloez, Bo Deng, Fabio Dercole, Mathieu Desroches, Francine Diener, Marc Diener, Bob Kooi, Martin Krupa, Claude Lobry, Nadir Sari, Tewfik Sari, Imme van den Berg, Martin Wechselberger, Antonios Zagaris

Application form: click here

Microbial ecology and mathematical modelling

Workshop organizers: Jérôme Harmand and Jean-Jacques Godon (INRA, Narbonne, FR), Claude Lobry, and Roger Arditi
Dates: December 15–19, 2014

The optimization of bioprocesses has benefited very little from the enormous progress made over the past 20 years in the observation of the dynamics of microbial ecosystems. It could have been expected that the accumulated knowledge about "who is there" in a microbial ecosystem would have led to optimize the process operations, which is actually not the case. It becomes clear that research combining microbiology and ecological concepts is needed to explore the "who does what" question before being able to address, in the future, the challenge of manipulating the ecosystem in order to manage microbial communities.

The objective of the workshop is to study how ecological concepts applied to microbial ecology can be formalized using mathematical models and to identify key questions that must be necessarily investigated by a cross-view between microbiologists and mathematicians. Questions to be investigated include: What drives ecosystems diversity? What is the role of interactions on diversity? With which magnitude is diversity driven by viruses?

Speakers and/or invited participants: Roger Arditi, Boumediène Benyahia, Stéphane Blain, Théodore Bouchez, Stéphane Chaillou, Bertrand Cloez, Jean-Jacques Godon, Jérôme Harmand, Claude Lobry, Boumediène Moussa Boudjemaa, Ingrid Obernosterer, Alain Rapaport, Tewfik Sari, Matthew Wade

Application form: click here

Follow-up workshop
Persistence of population models in temporally fluctuating environments

Workshop organizers: Michel Benaïm (U. Neuchâtel, CH), Claude Lobry, and Roger Arditi
Dates: February 9–12, 2015

In population dynamics, environmental fluctuations (such as light, precipitation, temperature, nutrient availability, etc.)  are usually described as  deterministic (typically, periodic) or stochastic variations of the parameters characterizing the model. Understanding under what conditions these external forces can be beneficial or detrimental to the existence of populations is a question of theoretical and practical importance in ecology.

In automatic control theory, a completely different scientific area, one is interested by the equilibrium stability of some object (say, an airplane) under permanent disturbances that can be deterministic or stochastic.

The aim of the workshop is to gather people active in the areas of either "population dynamics" or "automatic control", for exchange of experience and possible cross-fertilization.

Speakers and/or invited participants: Roger Arditi, Vincent Bansaye, Michel Benaïm, Yacine Chitour, Bertrand Cloez, Fritz Colonius, Lorens Imhof, Claude Lobry, Florent Malrieu, Guilherme Mazanti, Christian Mazza, Alain Rapaport, Gregory Roth, Gauthier Sallet, Nadir Sari, Tewfik Sari, Mario Sigalotti, Pierre-André Zitt

Application form: click here


  • Roger Arditi (University of Fribourg, Switzerland)
  • Donald L. DeAngelis (University of Miami, FL, USA)
  • Lev R. Ginzburg (Stony Brook University, NY, USA)
  • Claude Lobry (Université de Nice-Sophia-Antipolis and INRIA-Sophia-Antipolis, France)


July – December 2014
and follow-up activity in February 2015



Station 7
CH-1015 Lausanne
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Bernoulli Lectures

Thu, July 10, 17:15–18:15: Stefano Allesina (U. Chicago)
Thu, Aug. 7, 16:15–17:15: Peter Chesson (U. Arizona)
Thu, Oct. 16, 16:15–17:15: Michel Benaïm (U. Neuchâtel)
Tue, Nov. 18, 16:15–17:15: Francine Diener, Marc Diener, and Martin Krupa

Special Journal Issue

Contacts will be taken with a journal in order to publish a special issue entitled:

The role of mathematics and computer science in ecological theory

Submissions from participants to the special semester at CIB are invited. All papers will be peer-reviewed.

Graduate course in mathematical and theoretical ecology

Dates: October to December 2014

This weekly course will be open to graduate students belonging to several doctoral schools of Western Switzerland and neighboring France. The course will be given in French unless there is demand for the use of English.

Application form: click here

Schedule: Every Wednesday 11:00–12:30 and 14:00–15:30 starting Oct. 1, except during workshop weeks (see left). Bernoulli lectures (see above) are also open to students.

Équations différentielles et modélisation de la

dynamique des populations

Les prérequis mathématiques sont réduits au minimum. Des séances de mise à niveau pourront être mises en place si des auditeurs le désirent.

Chap 1. De Lotka-Volterra à la ratio-dépendance

Enseignants principaux : C. Lobry et R. Arditi
Nous décrivons l’évolution des modèles de la relation de “proie-prédateur” (ou encore “ressource-consommateur”) à partir du modèle historique de Lotka-Volterra.
– Le modèle de Lotka-Volterra
– Premières améliorations : Gause, Kolmogorov, Rosenzweig-MacArthur...
– Le modèle ratio-dépendant
– Le théorème d’exclusion compétitive (cas ressource-dépendant)
– Le théorème de non-exclusion compétitive (cas ratio-dépendant)

Chap 2. Le problème "atto-fox" et la persistance dans les systèmes lents-rapides

Enseignant principal : C. Lobry
Les modèles de relation ressource-consommateur ont généralement deux échelles de temps, rapide pour la ressource, lente pour le consommateur. Ce fait a des conséquences importantes sur la question de la persistance.
– Définitions de la persistance et le problème "atto-fox"
– Théorème de Tychonov
– La théorie des bifurcations dynamiques : le retard à la bifurcation
– Les systèmes lents-rapides et leurs "canards"
– Applications au modèle de Rosenzweig-MacArthur

Chap 3. Les parades à atto-fox

Enseignants : C. Lobry, Michel Benaïm (U. de Neuchâtel), Christian Mazza (U. de Fribourg)

Les deux chapitres précédents ont montré :
– Chap. 1 : Par leur simplicité conceptuelle et mathématique, les modèles en équations différentielles sont un outil précieux de l’écologie théorique.
– Chap. 2 : Par leur incapacité à représenter une extinction en temps fini, ces modèles sont susceptibles de graves artefacts.
Ce chapitre proposera des parades qui préservent la simplicité en renforçant la sécurité. Il sera beaucoup plus ouvert que le précédent et son programme sera précisé plus tard. Quelques thèmes à titre indicatif :
– processus de naissance et de mort,
– la persistance dans les modèles stochastiques,
– le modèle de Rosenzweig-MacArthur revisité en stochastique,
– couplages entre modèles de Rosenzweig-MacArthur, spatialisation.
Ce n’est pas un chapitre proprement dit mais un "souci" tout au long du cours. Les simulations seront utilisées non seulement pour illustrer les modèles mais aussi pour aider à comprendre certains problèmes.

Un plan plus détaillé se trouve ici (pdf).