Mathematical Models and Methods in Applied Sciences Vol. 18, No. 11 (2008) 1927–1944 c  World Scientific Publishing Company A CONTINUOUS SIZE-STRUCTURED RED CORAL GROWTH MODEL P.-E. JABIN UMR 6621, J-A. Dieudonn´ e Department, University of Nice Sophia-Antipolis, Parc Valrose, Nice Cedex 2, 06108, France jabin@unice.fr V. LEMESLE UMR 6540, COM, Mediterranean University, Campus de Luminy Case 901, Marseille Cedex 9, 13288, France valerie.lemesle@univmed.fr D. AURELLE UMR 6540, COM, Mediterranean University, Rue de la Batterie des Lions, Marseille, 13007, France didier.aurelle@univmed.fr Received 20 August 2007 Revised 14 February 2008 Communicated by N. Bellomo The aim of this paper is to derive and analyze the mathematical properties of a new continuous size-structured model for red coral (Corallium rubrum, L.) growth. Since historical Leslie models 4 are often used to deal with some ecological problems, a new approach is here proposed and give some promising results. The main advantage of using continuous model is that we hope to describe precisely the mass mortality events, observed in Mediterranean sea, and its consequences on red coral dynamics. Simula- tions’ studies allow us to qualitatively discuss some questions about red coral popula- tions dynamics. The development of this method should be useful for the study of the conservation of red coral populations. Keywords : Population dynamics; size-structured continuous model; asymptotic analysis; conservation biology. 1. Introduction The analysis of the consequences of environmental changes on the dynamics of natu- ral populations takes advantage of modelling studies. For example the development of specific models may allow to evaluate the extinction risks of populations under 1927