Optimization of shellﬁsh production carrying capacity at a farm scale D. Brigolin a, * , A. Davydov b,c , R. Pastres a , I. Petrenko c a University of Venice, Venice, Italy b International Institute for Applied System Analysis, Laxenburg, Austria c Vladimir State University, Vladimir, Russia article info Keywords: Optimization State constraints Ecological carrying capacity abstract In this paper, we investigate the relationship between the production and ecological carry- ing capacity of shellﬁsh cultured species (mussels, oysters, clams, etc.) and the spatial dis- tribution of shellﬁsh density within a licensed area. In order to achieve this goal, we used an analytical model for simulating the impact of a shellﬁsh farm on the concentration of suspended particles or dissolved substances, namely dissolved oxygen in steady-state con- ditions. The results show that the impact depends on the spatial distribution of the rearing density within the licensed area. In particular, we found a family of non-homogeneous dis- tribution of rearing density which allow one to increase the biomass yield in respect to the homogeneous one, while complying with constraints on suspended particles or dissolved substances. These results may be relevant for enhancing both the production and ecolog- ical carrying capacity of shellﬁsh farms. Ó 2008 Elsevier Inc. All rights reserved. 1. Introduction Shellﬁsh aquaculture is a rapidly growing resource sector around the world (see [5]). Bivalve shellﬁsh culture (mussels, oysters, clams, etc.) is a particularly attractive form of aquaculture as this type of farming does not require the addition of artiﬁcial food supplements. However, the fact that bivalve culture relies on natural sources of food is a signiﬁcant constraint on the production potential of growing regions. Hence, bivalve farmers have a strong interest in assessing the biomass den- sity can be supported by the surrounding environment. On the other hand, most shellﬁsh farming activities occur in estuaries, inshore coastal waters, and, more recently, in open off-shore coastal areas which often host a diverse range of human activities. As a consequence, opposition to the expansion of shellﬁsh farming by other users of coastal waters has increased, especially in developed countries [9]. Objections to expansion have generally centered on loss of amenities and recreational areas, and degradation of the envi- ronment. As a result, shellﬁsh aquaculture, widely promoted as a ‘‘green” industry, is now on the environmentalists’ radar screen. According to [3] environmental hazards of shellﬁsh farming activities include: (i) organic enrichment of the sediment around shellﬁsh farms [10], (ii) reduction in food supplies for other ﬁlter feeding organisms and (iii) habitat disturbance and degradation. These issues led to identify four categories of carrying capacity [11]: (a) Physical carrying capacity: the total area of marine farms that can be accommodated in the available physical space. (b) Production carrying capacity: the stoking density of bivalves at which harvests are maximized. 0096-3003/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2008.05.118 * Corresponding author. E-mail addresses: brigo@unive.it (D. Brigolin), davydov@vpti.vladimir.ru, davydov@iiasa.ac.at (A. Davydov), pastres@unive.it (R. Pastres), petrenko_irina @bk.ru (I. Petrenko). Applied Mathematics and Computation 204 (2008) 532–540 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc