CHARACTERIZATION OF THE STRUCTURE OF A GR OWTH-PROCESS - APPLICATION TO THE GROWTH OF THE PLEURIDIOPHORAL CELLS OF THE ALGA ANTITHAMNION PLUMULA

The analysis of a growth kinetics y(t) is carried out using the genera lized logistic model of Richards - Nelder. Two types of processes, ter med mono- and multi-logistic, on be distinguished. In a mono-logistic process, the phenomenon is adequately described by only one logistic f unction. The growth kinetics is then characterized by the properties o f each of phases G(1) to G(4), with boundaries defined by the singular points Gamma(max), V-max and Gamma(min) (Buis, 1991, 1993). The growt h structure (temporal or diachronic structure) is defined by the relat ive contribution of the various phases to the expression of the total growth (duration, growth amount, in relative values per phase, indepen dently of y(max)). This temporal distribution of the growth activity i s a discretized representation of the trajectory y(0) --> y(max). A mu lti-logistic process corresponds to any growth kinetics which is the s um of 2 or several generalized logistics. The number of singular point s (local extrema of V and Gamma), and therefore the number of phases G , are then higher than in the mono-logistic case. The growth structure defines precisely the kinetics of the phenomenon as well as the relat ive importance of the various logistic components in the course of tim e. The application presented concerns the growth of the pleuridiophora l cells of the alga Antithamnion plumula (Rhodophyceae, Ceramiales). C ells elongation is of the bi-logistic type. The elongation growth stru cture characteristics afford a clear discrimination between the sporop hyte and the male and female gametophytes. Whereas component 1 (which is the more important at the beginning of growth) hardly changes, comp onent 2 varies dramatically with the thallus ploidy. In contrast, ther e are few differences between the two gametophytes. The growth structu re concept is thus liable to lead to original results. Beyond the exam ple selected, the approach considered is put forward as a simple but p recise characterization method for any growth kinetics based on tempor al variations of the growth activity [(V, Gamma) couple].