Prediction of biomass in Norwegian fish farms

Abstract

We have constructed a statistical model to forecast, with uncertainty, the stock of Norwegian farmed Atlantic salmon (Salmo salar). The model provided good predictions of future biomass of Norwegian farmed salmon and can also be used to perform "what-if" analysis exploring the impact of varying scenarios for stocking and slaughtering. The model is based on the number of fish in each mass class (0-1, 1-2, …, 10+ kg) and their average mass. The model, which is related to standard size-structured models, computes the number of fish growing into the next mass class the next month and the number of fish remaining in the same mass class. In addition, the number of new fish stocked, fish lost, slaughtered, and wasted, as well as the sea temperature related to the growth, were modelled. All the model parameters were estimated based on monthly data from 2002 to 2007, and the model was validated statistically. Any animal production involving cycles may benefit from this forecasting tool.Résumé : Nous avons construit un modèle statistique pour prédire, avec l'incertitude, le stock des saumons atlantiques (Salmo salar) norvégiens d'élevage. Le modèle fournit de bonnes prédictions de la biomasse future des saumons norvégiens d'élevage et peut aussi servir à faire une analyse de simulation (« qu'arrive-t-il si? ») qui explore l'impact de divers scéna-rios d'empoissonnement et de récolte. Le modèle est basé sur le nombre de poissons dans chaque classe de masse (0-1, 1-2, ..., 10+ kg) et leur masse moyenne. Le modèle, qui est apparenté aux modèles standard structurés en fonction de la taille, calcule le nombre de poissons qui passent par croissance dans la classe de masse supérieure le mois suivant et le nombre de poissons qui demeurent dans la même classe de masse. De plus, il y a modélisation du nombre de nouveaux poissons empoissonnés, des poissons perdus, tués et gaspillés, de même que de la température de la mer en relation avec la croissance. Tous les paramètres du modèle ont été estimés à partir de données mensuelles de 2002 à 2007 et le modèle a été validé statistiquement. Cet outil de prédiction peut être utile pour toute production animale comportant des cycles.[Traduit par la Rédaction]

Growth and survival model of Pacific bluefin tuna ( Thunnus orientalis ) for capture‐based aquaculture in Mexico

“…Even though the suggested equation in this study described growth satisfactorily, further efforts should be performed to increase the accuracy of predictions and parametrize an equation that includes the effect of environmental variables. Although growth rates depend on many factors, such as feed, light conditions, oxygen and SST (Løland, Aldrin, Steinbakk, Huseby, & Grøttum, ), evidently temperature has been the most relevant factor to explain PBFT growth rates (Jusup, Klanjscek, Matsuda, & Kooijman, ). Moreover, despite food availability affects the maximum individual size, the size of the ration is affected by SST (Jusup et al., ; Katavić, Tičina, & Franičević, ).…”

The Importance of Temperature in Farmed Salmon Growth: Regional Growth Functions for Norwegian Farmed Salmon

“…The data contain two types of errors; i) farmers fail to report data, and ii) farmers report incorrect numbers (measurement error). The first error is impossible to observe in the dataset but is documented by Løland et al (2011), who have access to the individual farmers' data, while the second error can be observed to some extent. At the beginning and end of the data series for each county when few fish are present in the pens, some strange observations are reported.…”

“…To my knowledge, only two other studies have examined the development of biomass on an aggregate level. Asheim et al (2011) study how biomass development affects short run supply using aggregated time series data, while Løland et al (2011) have established a model to predict biomass in Norwegian fish farms using data from individual farmers that they have aggregated to regional data. The latter study computes the number of fish growing into the next weight class (0-1 kg, 1-2 kg, …, 10 kg).…”

Mathematical models for optimizing production chain planning in salmon farming

“…In the literature, we found that Løland et al. () model the distribution of the weight of a specific weight class as a beta distribution and estimate the parameters based on real data from a Norwegian fishery. The choice of the beta distribution seems to be arbitrary and only motivated by the tractability that this distribution provides.…”

“…We discussed this assumption with the freshwater planning team and they agreed that this was a reasonable modeling assumption; however, we were not able to validate this empirically. In the literature, we found that Løland et al (2011) model the distribution of the weight of a specific weight class as a beta distribution and estimate the parameters based on real data from a Norwegian fishery. The choice of the beta distribution seems to be arbitrary and only motivated by the tractability that this distribution provides.…”