A factorial model to predict phosphorus waste output of rainbow trout (Oncorhynchus mykiss) Katheline Hua 1 , Cornelis F M de Lange 1 , Arthur J Niimi 2 , Gordon Cole 3 , Richard D Moccia 1 , Ming Z Fan 1 & Dominique P Bureau 1 1 Department of Animal and Poultry Science, University of Guelph, Guelph, ON, Canada 2 Great Lakes Laboratory for Fisheries and Aquatic Sciences, Department of Fisheries and Oceans, Burlington, ON, Canada 3 Aqua-Cage Fisheries, Parry Sound, ON, Canada Correspondence: K Hua, Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario, Canada N1G 2W1. E-mail: khua@uoguelph.ca Abstract Minimizing phosphorus (P) wastes is considered to be a key factor for environmental sustainability of freshwater aquaculture operations in many parts of the world. A factorial P model, consisting of digest- ibility, whole-body P deposition, P waste output and limnological transformation sub-models, was con- structed to simulate the e¡ects of di¡erent dietary P sources and levels on P utilization in salmonids. This factorial P model was developed based on informa- tion from the literature for rainbow trout ( Oncor- hynchus mykiss ). This factorial model runs on the platform of a ¢sh bioenergetics model that provides dynamic estimates of feed intake of salmonids based on diet composition and growth rate. Simulations suggest that this model can potentially be a useful tool for waste output management of salmonid cul- ture operations. Keywords: phosphorus, waste, model, rainbow trout, aquaculture Introduction Phosphorus (P) is the ¢rst limiting factor for algal growth in freshwater and excess P can stimulate eu- trophication of water bodies (Gibson 1997; Wetzel 2001). Minimizing P wastes is considered to be a key factor for the environmental sustainability of fresh- water aquaculture operations. Total P waste outputs were estimated to be in the range of 1.4^25 g kg  1 biomass of rainbow trout produced (Wiesmann, Scheid & Pfe¡er 1988; Ruohonen, Vielma & Grove 1999; Green, Hardy & Brannon 2002a, b). The quan- tityand forms of P waste output are a¡ected byavari- ety of factors, including dietary P level, digestibility of dietary P, deposition of P by the ¢sh, feed composition and feed e⁄ciency (Cho & Bureau 1998). These var- ious factors contribute to the signi¢cant variation in the estimates of P waste outputs reported in the literature. Estimating waste outputs on the basis of nutrient balances has been shown to be an accurate, econom- ical and £exible approach for ¢sh culture operations (Cho, Hynes, Wood & Yoshida 1991, 1994). Using this approach, solid waste outputs are estimated based on the apparent digestibility of nutrients, whereas dissolved (soluble) waste outputs are estimated based on digestible nutrient intake and deposition. This mass balance approach is particularly useful for aquaculture operations, such as cage ¢sh culture op- erations, where direct estimates of waste outputs using chemical or limnological methods are too di⁄- cult or costly to obtain on a routine basis (Cho et al . 1991,1994; Papatryphon, Petit, van der Werf, Kaushik & Claver 2005). The dietary P that is consumed but not digested is excreted largely as solid wastes, whereas the digestible portion that is not retained is excreted as soluble waste output. Not all forms of P excreted by ¢sh have an equal potential to contribute to eutrophication. Bioavailable P is the sum of imme- diatelyavailable P (orthophosphates) and those forms that can yield available P under the conditions of phy- sical, chemical and biological processes (Bostr˛m, Persson & Broberg 1988). Soluble P waste excreted through the non-faecal excretion route is readily available to algae and can, consequently, have a Aquaculture Research, 2008, 39, 1059^1068 doi: 10.1111/j.1365-2109.2008.01966.x r 2008 The Authors Journal Compilation r 2008 Blackwell Publishing Ltd 1059