title: [Biological mutualism, concepts and models].
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.
authors.affiliation: E.M.A. S2HEP, Sciences, Société, Historicité, Education, Pratiques, Université de Lyon, Université Lyon 1, 38, bd Niels Bohr, 69622 Villeurbanne Cedex, France.
authors.forename: Olivier
authors.initials: O
authors.lastname: Perru
mesh_terms: D000818:Animals; D001686:Biological Phenomena; D020387:Food Chain; D049672:History, 19th Century; D049673:History, 20th Century; D049674:History, 21st Century; D006801:Humans; D007558:Italy; D008954:Models, Biological; D011157:Population Dynamics / Q000266:history*; D013559:Symbiosis; D014481:United States