Abstract
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.
The problem is then examined within the framework of Delattre's transformation system theory which affords a new reading of there lationships between growth and autocatalysis (without requiring reference to a particular reactional chemical analogue). The resulting new model constitutes an extension of Verhulst's logistics which is quite different from the well-known Richards-Nelder function. In addition to its theoretical background, one feature of the new model is the generation of varied growth kinetics, particularly a non-monotonous variation of the specific growth rate r = (1/y)(dy/dt). This property, which is often neglected, is the more valuable as a number of biological growths are characterized by a rate r which is not continuously decreasing. This specific characteristic is not predicted by the usual growth functions.
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Buis, R. 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. Acta Biotheor 45, 251–266 (1997). https://doi.org/10.1023/A:1000632008695
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DOI: https://doi.org/10.1023/A:1000632008695