| Article | Olivier Perru, Le mutualisme biologique, concepts et modèles |
Abstract | Mutualism is a biological association for a mutual benefit between two
different species. In this paper, firstly, we examine the history and signification of mutualism
in relation to symbiosis. Then, we consider the link between concepts and models of
mutualism. Models of mutualism depend on different concepts we use: If mutualism is
situated at populations’ level, it will be expressed by Lotka-Volterra models, concerning
exclusively populations’ size. If mutualism is considered as a resources’ exchange or
a biological market increasing the fitness of these organisms, it will be described at an
individual level by a cost-benefit model. Our analysis will be limited to the history and
epistemology of Lotka-Volterra models and we hypothesize that these models are adapted at
first to translate dynamic evolutions of mutualism. They render stability or variations of size
and assume that there are clear distinctions and a state of equilibrium between populations
of different species. Italian mathematician Vito Volterra demonstrated that biological
associations consist in a constant relation between some species. In 1931 and 1935, Volterra
described the general form of antagonistic or mutualistic biological associations by the same
differential equations. We recognize that these equations have been more used to model
competition or prey-predator interactions, but a simple sign change allows describing
mutualism.
The epistemological problem is the following: Volterra’s equations help us to
conceptualize a global phenomenon. However, mutualistic interactions may have stronger
effects away from equilibrium and these effects may be better understood at individual
level. We conclude that, between 1985 and 2000, some researchers carried on working and
converting Lotka-Volterra models but this description appeared as insufficient. So, other
researchers adopted an economical viewpoint, considering mutualism as a biological market. |
Keywords | Mutualism, Lotka-Volterra models, biological associations, mutualistic
populations |
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