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You’re two minutes away from understanding viability theory!

Viability theory is a mathematical framework developed in France in the early 1990s that has been applied to various fields: fisheries, robotics, finance, anthropology, etc. In recent years, it has been used by researchers at INRA (National Institute for Agricultural Research) in the area of agroecology to study complex and unpredictable systems. The principle behind it? Using algorithms to determine the conditions required for a system to preserve certain properties over time. For example, how do we preserve productivity and maintain biodiversity in a pasture-based livestock system?

At INRA, in cooperation with colleagues from CNRS and IRSTEA, viability theory has been put to work in many research efforts on sustainable development and renewable resource management: livestock, fisheries, forestry, water and environmental policy.

La théorie de viabilité
By Aurélie Coen
Updated on 02/20/2018
Published on 08/29/2017

A tried and tested theory…

With regard to agriculture, this mathematical framework was first used to study livestock systems that involved several species in the context of climate uncertainties. This work showed how combining various species within a single herd makes it easier to withstand environmental variations. Next, our research centred on studying agricultural practices to balance the productive and ecological dimensions of grazing in an area facing major environmental challenges: the Marais Poitevin wetlands area. This work showed how adjusting grazing periods and intensity helps balance agricultural production goals with ecological goals.

…used in a broad range of situations.

At present, viability theory is being used to evaluate the ability of livestock systems to confront uncertainty in savanna systems in southern Africa, dairy systems in Wisconsin, and pastoral systems in Mongolia. In addition to livestock systems, this theory is also being used in crop systems, applied to wheat fertilisation and to vegetable-producing and agroforestry systems in tropical or temperate environments.

The concepts behind viability theory

Viability theory is a mathematical framework developed in France by the mathematician Jean-Pierre Aubin (Aubin 1991; http://vimades.com/aubin/). Starting in the 1990s, other mathematicians built on his work by applying it to renewable resource management (De Lara and Doyen 2008; http://gretha.u-bordeaux.fr/fr/members/doyen-luc)and to complex system resilience analysis at the LISC lab at IRSTEA (http://motive.cemagref.fr/lisc/viability_publications#defining_resilience_within_viability_theory). Viability theory has also been used in economics to formalize the concept of sustainable development. It offers a way to tackle intergenerational equity in multiple issues problems (https://sites.google.com/site/martinetvincent/home).
This theory applies to the analysis of controlled dynamic systems. Using it involves defining a system characterised by states and controls, formalising their dynamics, and determining how the system can preserve a set of properties found to be important, expressed as constraints in the state space. The algorithms associated with viability theory then identify all of the conditions (combinations of states and controls) that enable the system to fulfil the constraints over time, and therefore keep itself in good health.


Muriel Tichit : muriel.tichit@agroparistech.fr

Rodolphe Sabatier : rodolphe.sabatier@inra.fr

Francesco Accatino : francesco.accatino@inra.fr