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A four-parameter generalization of the logistic curve is proposed for the description of population growth and decline. Limiting cases of this new model include logistic and exponential growth and decline. Unlike an earlier generalization, which is monotonic, the present asymptotic curve declines after reaching a single maximum. In studies of natural populations, where many factors are interacting and where population growth may initially have beneficial effects, the present model may be more widely applicable than more complicated and restrictive theoretical models. The fitting of the present curve and of the corresponding log-normal variation belts through multiplicative iteratively-reweighted least squares is illustrated on data about an experimental population of Paramecium caudatum and about the seasonal change in the numbers of captures of male Meromyza variegata. This model could be applied also to populations of molecules or cells within individual organisms.

Information treatment, especially in a natural medium, may be done by a random system: given an input, possible solutions are randomly selected and successively tested until the right one is found and then emitted. This paper is a mathematical study of this type of system and its use as a model of some natural (biological) systems. The theoretical development is illustrated by several examples of possible applications to biological cases. We study, under different assumptions, the distribution of the number of trials needed to treat the input, the distribution of the time for this treatment, and the distribution of the average amount of information treated in a trial or in a unit of time. We consider the case of error, and study some optimal conditions of operation and the occurrence of memory influencing the treatment of an input according to previously processed inputs.

Chez les individus d'une mEme espece, un caractere hereditaire est suppose associe a une “cible” constituee de plusieurs particules, independantes entre elles, et susceptibles de se presenter sous diverses formes. Le phenotype depend de la repartition de ces differentes formes dans la cible. A la division cellulaire correspond un certain mode de division de la cible, permettant la transmission des particules d'une generation a l'autre, et induisant des regles d'apparition des divers phenotypes. Le probleme de la determination du nombre des particules constituant la cible est examine ici, et une solution est exposee. Cette solution tient compte a la fois des aspects mathematiques (etude theorique du processus), experimentaux (observation de l'evolution genetique d'une mutation provoquee par un agent mutagene) et numeriques (une technique d'ajustements numeriques complete avantageusement l'etude theorique).

A new seven-parameter asymptotic growth curve has been applied to longitudinal data on the height of 13 boys and 14 girls from 1 month to 19 years of age. The residual sums of squares with this new curve were 7.5 times lower on the average than with the currently-used five-parameter curve No. 1 of Preece and Baines (1978, Annals of Human Biology 5, 1-24) and 2.4 times lower than with the recent six-parameter curve of Shohoji and Sasaki (1987, Growth 51, 432-450). The new curve is expressed with respect to total age, passes through the origin, and fits infants as satisfactorily as older children.