Maximal yields from multispecies fisheries systems: Rules for systems with multiple trophic levels Hiroyuki Matsuda (Yokohama Nat’l Univ.) Peter A. Abrams (Univ. Toronto) 1 Kyoto Declaration and Plan of Action on the Sustainable Contribution of Fisheries to Food Security in 1992 (FAO) • Article 14 “When and where appropriate, consider harvesting multiple trophic levels in a manner consistent with sustainable development of these resources”. http://www.fao.org/fi/agreem/kyoto/kyoe.asp 2 Prey-predator model for “sardine” x and “tuna” y • dx/dt = (r - a x - b y - f) x • dy/dt = (-d + e b x - g) y • Maximize total yield fx+pgy at the equilibrium 3 • Optimal solution is either • to catch sardine after tuna goes extinct; or • to catch tuna only. Fishing effort on predator fy Paradox of Kyoto Declaration Fishing effort on prey 4fx Examples of biological community at MSY (Matsuda & Abrams in review) 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 5 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 6 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 7 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 8 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 9 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 10 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 11 Examples of biological community at MSY (Matsuda & Abrams in review) Solution maximizing total yield from community MSY solution often reduces species and links; 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 12 Examples of biological community at MSY (Matsuda & Abrams in review) 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 13 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 14 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 15 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 16 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 17 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 18 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence exploit more species, more trophic levels. 5 5 4 1 5 4 5 6 4 4 3 2 6 5 4 3 (e) 6 6 6 (d) (c) (b) (a) 3 3 1 2 1 3 2 1 2 1 2 19 Examples of biological community at MSY (Matsuda & Abrams in review) Constrained MSY that guarantee coexistence exploit more species, more trophic levels. (d) (c) (b) (a) 6 6 6 5 5 4 1 100% 5 4 5 6 4 4 3 2 6 5 4 3 (e) 3 3 1 92% 2 3 1 2 61% 1 2 12% 1 2 6% 20 Conclusion of story 2 • MSY theory does not guarantee species coexistence • Fisheries must take care of biodiversity conservation explicitly = Foodweb constraint to reconciling fisheries with conservation 21 Requiem to Maximum Sustainable Yield Theory surplus production • Ecosystems are uncertain, nonequilibrium and complex. • MSY theory ignores all the three. • Does MSY theory guarantee species persistence? - No!! 22 Stock abundance Feedback control in fishing effort is powerful... dE U N N * dt A straw man says; • Even though the MSY level is unknown, the feedback control stabilizes a broad range of target stock level. f(N) dN f ( N ) qEN dt Stock size N 23 Feedback control in fishing effort is powerful... dE U N N * dt dN f ( N ) qEN dt N* f(N) A straw man says; • Even though the MSY level is unknown, the feedback control stabilizes a broad range of target stock level. Stock size N 24 Feedback control in fishing effort is powerful... dE U N N * dt dN f ( N ) qEN dt N* f(N) A straw man says; • Even though the MSY level is unknown, the feedback control stabilizes a broad range of target stock level. Stock size N 25 Feedback control in fishing effort is powerful... dE U N N * dt dN f ( N ) qEN dt N* f(N) A straw man says; • Even though the MSY level is unknown, the feedback control stabilizes a broad range of target stock level. Stock size N 26 Feedback control with community interactions also result in undesired outcomes. (M & A in preparation) dNi ri a ji N j qei Ni dt j 9 10 8 r = (0.454,1.059,1.186,0.247,-0.006,-0.028,-0.059,-0.704,-0.308,-0.238) A = (aji) = 1. 0.74 0.19 0.31 0. 0. 0. 0. 0.7 0.46 0.74 1. 0.87 0.08 0.46 0.66 0.48 0.73 0.84 0. 0.19 0.87 1. 0.96 0.08 0.14 0.83 0. 0. 0.68 7 0.31 0.08 0.96 1. 0. 0. 0. 0.28 0. 0.88 0. 0.46 0.08 0. 0.1 0. 0. 0.92 0.15 0.84 0. 0.66 0.14 0. 0. 0.1 0.01 0. 0.5 0.69 0. 0.48 0.83 0. 0. 0.01 0.1 0.56 0. 0. e9 = 0.1, ei = 0 0. 0.73 0. 0.28 0.92 0. 0.56 0.1 0.28 0. 0.7 0.84 0. 0. 0.15 0.5 0. 0.28 0.1 0. 0.46 0. 0.68 0.88 0.84 0.69 0. 0. 0. 0.1 5 6 1 4 2 3 27 Feedback control may result in extinction of other species (sp. 6). ratio de9/dt = u(N9-N9*) 28 Conclusion of story 3 • Single stock monitoring is dangerous • Target stock level is much more sensitive than we have considered in single stock models. • We must monitor not only stock level of target species, but also the “entire” ecosystem. 29
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