Eco-evolutionary Software



Figure 1
Deployment of polymorphism in a population subjected to asymmetric competition
(ZEN simulation, model from Kisdi & Geritz 2001).
The distribution of phenotypes is shown along evolutionary time in ordinates.


Ecological models with an evolutionary component allow to study several biological phenomena: host-pathogens interactions, coevolution of plants and pollinisators, mimicry, development of the immune system, evolution of cooperation, evolution of life history traits, and more generally biodiversity and speciation.

What is simulated by ZEN ? The evolution of populations under the mutation-selection process 

ZEN uses an individual-based (in fact ‘phenotype-based’) approach with 3 components:

During the ZEN simulation, mutant phenotypes created by the triggering of mutations interact with resident phenotypes. They persist or go extinct, possibly leading to evolutionary branching and polymorphism (Figs. 1, 2).


How does ZEN work ?

Models are described in a text file using a reduced declaration language, and studied by means of a simple interface with convenient graphics. The ZEN kernel is a symbolic evaluator handling ‘polymorphic’ variables.



Figure 2
Close up of an evolutionary branching showing the jumps in adaptive trait
(evolutionary time in abscissas, model from Ravigné 2000).


Theoretical Context

The first evolutionary models in biology are verbal arguments, like Fisher’s proof that the primary sex ratio is 1/2. Theoretical evolutionary models started to develop in the 80’s with quantitative genetics and game theory. In this context originated the important notion of Evolutionary Stable Strategy (ESS), which had premises in the work of Hamilton on kin selection.

The recent theory of adaptive dynamics (Metz et al. 1996, Dieckmann & Law 1996) is based on population dynamics, and incorporates implicitly an hereditary mechanism operating on continuous adaptive traits. The evolutionary outcome is determined from the persistence of rare mutants in a resident population by computing their fitness gradient in the ecological setup.

A great achievement of the theory is the classification of the possible evolutionary outcomes, making a synthesis of previous results. A fascinating eventuality is that of evolutionary branching, which stems from the biological nature of the models, and does not appear in physical systems. In this situation, ecological constraints lead to disruptive selection, and possibly to sympatric speciation.



ZEN is distributed free of charge. Users are under their own responsibility.

Computer / System



PC Windows

Self-extracting file


Double-click on autozen.exe

It will expand in directory c:/zen


PC Linux

Compressed file zen.tar.gz

Linux version is identical to Windows version

Expand distribution file zen.tar.gz using command tar -xzf zen.tar.gz

For installation, consult file ZenLinuxInstall.txt



Compressed file


Console version, no graphics

Program file: zenc

The ZEN package is provided with example model files and a complete user’s manual.

After installation, the ZEN directory should contain:



Drag and drop any model file *.zen on the ZEN program icon. The program is run with the file as input. Click compile to process the file, and run to run the model. Consult the reference manual zenref.pdf for more information.




Stéphane Legendre

Web site of Stéphane Legendre

Mail to Stéphane Legendre


The ZEN computer project was funded by an Action Incitative Bioinformatique from the CNRS.




Laboratoire d’écologie
Ecole Normale Supérieure
Jean Clobert
Régis Ferrière
Minus van Baalen


Institut des sciences de l’évolution
Université Montpellier 2
Isabelle Olivieri
Ophélie Ronce
Virginie Ravigné



Nicolas Champagnat, Guillaume Chapron, Mathias Gauduchon.