Sur l'interprétation de la loi logistique de croissance: Une re-lecture de la relation entre autocatalyse et croissance on the interpretation of the logistic law of growth: A new reading of the relationships between autocatalysis and growth
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Acta Biotheoretica 45 (3-4) (1997)
The logistic function now constitutes the most widely used model for there presentation of growth kinetics of the continuous monotonous type in biological systems (populations, organisms, organs, ...). This ubiquity led to consider logistics from a phenomenological rather than mechanistic viewpoint. Whence the question : can logistics be given an interpretation, a signification which confers the rank of an "explicative" model to it? This Note presents some critical comments on the relationships between logistics and three types of biological systems : population demography, environmental resources, autocatalyzed reactions. The so-called functional (in the mathematical meaning) interpretation, which is then discussed, is based upon a variational principle : the occurrence of a minimum of a function associated with the logistic law. Its present limitation to the only simple logistics of Verhulst and the difficulties of its expression in biological terms are then pointed out.
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