Two models for the control of sea lice infections using chemical treatments and biological control on farmed salmon populations
George Gettinby (1), Maya Groner (2), Ruth Cox (2), Chris Robbins (3) and Crawford Revie (2)
(1) University of Strathclyde, Glasgow, Scotland, (2) University of Prince Edward Island, Canada, (3) Grallator Ltd, UK
Objectives: To formulate models to inform how best to manage the control of sea lice populations which are a major threat to aquaculture and salmon production worldwide.
Methods: Two types of models are used to investigate the interaction between sea lice and salmon populations. In the first model changes in lice population stages are represented using four differential-delay equations. Time dependent solutions are obtained using algorithms embedded in the Sea Lice Difference Equation Simulator software. This enables treatment regimens under different geographical and environmental conditions to be investigated. The second model adopts a different approach to facilitate the introduction of a further fish population i.e. wrasse. Wrasse along with several other fish species are increasingly being used as "cleaner" fish because they feed on lice which are attached to salmon [1][2]. Using an individual-based modelling approach and simulations implemented using proprietary modelling software the density relationship between wrasse and salmon populations was investigated.
Results: Early work using the population modelling approach provided a parsimonious mathematical representation of the growth of the sea lice population [3] [4]. Using numerical methods it was possible to obtain solutions to the differential equations which reflected day-to-day changes in sea lice counts per salmon. The model identified when to apply treatments that would be less costly and more effective. The model lacked flexibility, stochasticity and did not take cognisance of sea water temperature and its effect on development and survival time of the lice stages. Experiences of adapting the model in Scotland and Norway [5] showed that it was not always stable and small changes in parameters could produce very different outcomes. The introduction of biological control and the use of cleaner fish led to investigating an individual-based modelling (IBM) approach [6][7][8]. A simple IBM which takes account of biological development rates associated with water temperature [9] showed that the use of wrasse fish to graze on sea lice in salmon production units can provide an effective way forward for salmon aquaculture.
Conclusion: Sea lice are a major threat worldwide to the sustainability of farmed and wild salmons stocks. They are affected by a large number of factors on salmon farms. Mathematical modelling offers a way of assessing the simultaneous impact of these factors.
References:
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[2] Treasurer JW. Wrasse (Labridae) as cleaner-fish of sea lice on farmed Atlantic salmon in west Scotland. In: Wrasse: Biology and Use in Aquaculture (ed by MDJ Sayer, JW Treasurer & MJ Costello), (1996) pp. 185-195. Fishing News Book, Oxford.
[3] Revie CW, Robbins C, Gettinby G, Kelly L, Treasurer JW. A mathematical model of the growth of sea lice, Lepeophtheirus salmonis, populations on farmed Atlantic salmon, Salmo salar L., in Scotland and its use in the assessment of treatment strategies. J. Fish Dis. (2005) 28: 603-613.
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[5] Gettinby G, Robbins C, Lees F, Heuch PA, Finstad B, Malkenes R and Revie CW. Use of a mathematical model to describe the epidemiology of Lepeophtherius salmonis on farmed Atlantic salmon Salmo salar in the Hardangerfjord, Norway. Aquaculture (2011) 320: 164-170.
[6] Cox R, Groner M, Gettinby G, Revie CW. Modelling the efficacy of cleaner fish for the biological control of sea lice in farmed salmon. Proceedings of the 13th ISVEE Conference, Aug 20-24, 2012, Maastricht, Netherlands.
[7] Groner M, Cox R, Gettinby G, Revie CW. Individual-based models: A new approach to understanding the biological control of sea lice. Proceedings of the 9th International Sea Lice conference, May 21-23, 2012, Bergen, Norway.
[8] Groner ML, Cox R, Gettinby G and Revie CW. Use of agent-based modelling to predict benefits of cleaner fish in controlling sea lice, Lepeophtheirus salmonis, infestations on farmed Atlantic salmon, Salmo salar L. Journal of Fish Diseases (2012) doi:10.1111/jfd.12017.
[9] Stien A, Bjørn PA, Heuch PA, Elston D. Population dynamics of salmon lice Lepeophtheirus salmonis on Atlantic salmon and sea trout. Mar. Ecol. Prog. Ser. (2005) 290:263-275.
