Abstract
We cannot count the fish in the sea, but it is possible to evaluate their number by looking at the yields of fishing. Today, we have good mathematical models that can be used for a quantitative estimate of the fish stocks. The origin of these models is the well-known “prey-predator” model developed by Alfred Lotka and Vito Volterra in the 1920s. In this chapter, the authors explain how this model works, the important information we can get from it and how it might be used to avoid fisheries collapse. A brief excursus on Vito Volterra life is given, a fascinating figure that has been the first source of inspiration for completing the book.
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References
Volterra V. Fluctuations in the abundance of a species considered mathematically. Nature. 1926;118(2972):558–60.
Lotka AJ. Elements of physical biology. Williams and Wilkins Company: Baltimore; 1925. 435 p.
Lotka AJ. Lotka on population study, ecology, and evolution. Popul Dev Rev [Internet]. 1989 [cited 2020 Mar 21];15(3):539–50. Available from: https://www.jstor.org/stable/1972445
Hardin G. The tragedy of the commons. Science [Internet]. 1968 [cited 2013 Dec 10];162(13 December):1243–8. Available from: http://scholar.google.it/scholar?hl=en&q=garrett+hardin&btnG=&as_sdt=1,5&as_sdtp=#0
Solow R. Technical change and the aggregate production function. Q J Econ. 1956;70(1):65–94.
Ostrom E. Governing the commons: the evolution of institutions for collective action. Cambridge: Cambridge University Press; 1990.
Forrester J. The beginning of system dynamics Banquet Talk at the international meeting of the System Dynamics Society. Stuttgart, Germany. 1989.
Odum HT. Energy, ecology, and economics. Ambio [Internet]. 1973 [cited 2015 Aug 6];2(6):220–7. Available from: http://www.jstor.org/stable/4312030?seq=1#page_scan_tab_contents
Moxnes E. Not only the tragedy of the commons: misperceptions of feedback and policies for sustainable development. Syst Dyn Rev [Internet]. 2000 [cited 2016 May 8];16(4):325–48. Available from: http://onlinelibrary.wiley.com/doi/10.1002/sdr.201/abstract
Rosenblum M, Cabrajan M. In Mackerel’s plunder, hints of epic fish collapse. The New York Times [Internet]. 2012.; Available from: http://www.nytimes.com/2012/01/25/science/earth/in-mackerels-plunder-hints-of-epic-fish-collapse.html
Forrester J. World dynamics [Internet]. Cambridge, MA: Wright-Allen Press; 1971 [cited 2013 Jun 3]. Available from: http://documents.irevues.inist.fr/handle/2042/29441
Meadows DH, Meadows DL, Randers J, Bherens W III. The limits to growth. New York: Universe Books; 1972.
Bardi U. The limits to growth revisited. New York: Springer; 2011. 119 p.
Bardi U, Lavacchi A. A simple interpretation of Hubbert’s model of resource exploitation. Energies [Internet]. 2009 [cited 2012 Dec 3];2(3):646–61. Available from: http://www.mdpi.com/1996-1073/2/3/646
Perissi I, Bardi U, Bardi U, El Asmar T. Dynamic patterns of overexploitation in fisheries. Ecol Model. 2017;359
Starbuck A. History of the American whale fishery. Castle; 1989.
Watson RA, Cheung WWL, Anticamara JA, Sumaila RU, Zeller D, Pauly D. Global marine yield halved as fishing intensity redoubles. Fish Fish. 2013;14(4):493–503.
Bardi U. The seneca effect. Why growth is slow but collapse is rapid: Springer; 2017.
Bardi U. Before the collapse: a guide to the other side of growth [Internet]. Springer International Publishing; 2020 [cited 2020 Mar 8]. Available from: https://www.springer.com/gp/book/9783030290375
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Perissi, I., Bardi, U. (2021). How Many Fish in the Sea?. In: The Empty Sea . Springer, Cham. https://doi.org/10.1007/978-3-030-51898-1_5
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DOI: https://doi.org/10.1007/978-3-030-51898-1_5
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