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Optimal Fishing Policies That Maximize Sustainable Ecosystem Services

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Optimal Fishing Policies That Maximize Sustainable Ecosystem Services K. Tsukamoto, T. Kawamura, T. Takeuchi, T. D. Beard, Jr. and M. J. Kaiser, eds. Fisheries for Global Welfare and Environment, 5th World Fisheries Congress 2008, pp. 359–369. © by TERRAPUB 2008. Optimal Fishing Policies That Maximize Sustainable Ecosystem Services Hiroyuki Matsuda,1* Mitsutaku Makino2 and Koji Kotani3 1Faculty of Environment and Information Sciences Yokohama National University 79-7, Tokiwadai, Yokohama 240-8501, Japan 2National Research Institute of Fisheries Sciences Fisheries Research Agency 2-12-4, Fukuura, Yokohama 236-8648, Japan 3Graduate School of International Relations International University of Japan 777 Kokusai-cho, Niigata 949-7277, Japan *E-mail: [email protected] The classic theory of fisheries management seeks a maximum sustainable yield from a target species. There are several variations that include uncertainty, fluctuation, and species interactions. The knowledge that sustainable fisheries do not always guarantee conservation of a diversity of species is well known. Ecosystems provide several categories of ecosystem services to human well- being: supporting, provisioning, regulating, and cultural services. Fishery yields belong to provisioning services. The existence of living marine resources may maintain these services, and certainly a much larger contribution from regu- lating services than that from fishery yields. Therefore, we define an optimal fishing strategy that maximizes the total ecosystem service instead of a sus- tainable fishery yield. We call this the fishing policy for “maximum sustainable ecosystem service” (MSES). The regulating service likely depends on the stand- ing biomass, while the provisioning service from fisheries depends on the catch amount. We obtain fishing policies for MSES in a single species model with and without uncertainties and in multiple species models. In any case, fishing efforts are usually much smaller than those for a maximum sustainable yield (MSY). We also discuss the role of fisheries in sustaining ecosystem serv- ices, and the nature of ecosystem comanagement. KEYWORDS maximum sustainable ecosystem service; MSES; uncertainty; ecosystem comanagement; maximum sustainable yield 360 H. MATSUDA et al. able yield under which all species coexist. 1. Introduction However, Matsuda and Abrams (2006) did not incorporate ecosystem service into the The theory of maximum sustainable yield optimal fisheries policy. (MSY) takes into account the long-term yield In this paper, we consider an optimal from living marine resources. This theory policy that maximizes the total ecosystem implicitly assumes that a fishing ban does service under some mathematically simple not produce any benefit from marine eco- assumptions. We call this the maximum sus- systems, although this theory explicitly as- tainable ecosystem service, or MSES. We sumes a negative relationship between yield assume that an ecosystem service other than and standing stock abundance. However, fishery yields depends on the standing ecosystems give us a variety of benefits biomass, while the fishery yield depends on (World Resource Institute 2005). Harvests the catch amount. Regulation of fishing ef- from agriculture, forestry and fisheries are forts usually enhances the standing biomass, just a small part of the ecosystem service while it usually decreases the fishery yield. (Costanza et al. 1997; Satake and Rudel We compare the MSY and MSES policies in 2007). Ecosystem services include support- (1) a single deterministic stock dynamic ing services such as soil formation, photo- model, (2) a stochastic model for a single synthesis, and nutrient cycling, provisioning species with measurement errors and proc- services such as food, water, timber, and ess uncertainty and (3) food web models fiber; regulating services that affect climate, consisting of six species. We also discuss the floods, disease, waste, and water quality; and role of comanagement in the ecosystem ap- cultural services that provide recreational, proach. aesthetic, and spiritual benefits (World Re- source Institute 2005). Fishery yields belong 2. Optimal Fishing Policy That to provisioning services. The existence of liv- Maximizes Ecosystem Service ing marine resources may maintain these services and certainly make a larger contri- To take account these ecosystem services, we bution to the total ecosystem service than assume that the total ecosystem service from fishery yields (Costanza et al. 1997). a target fish resource, denoted by V(N, C) is There are some criticisms of the theory given by of MSY (Matsuda and Abrams 2008). The MSY fishing policy does not reflect uncer- V(N, C) = Y(C) – cE + S(N) (1) tainty in stock estimates (measurement er- rors) and in the relationship between the where Y(C) is the yield from fisheries with spawning stock and recruitment (process catch amount C, cE is the cost of fisheries uncertainties). The MSY policy also ignores with fishing effort E, and S(N) is the ecosys- the complexity in ecosystem processes be- tem service other than fishery yields with cause the theory uses single stock dynamic stock abundance N. Hereafter, we simply call models (Matsuda and Katsukawa 2002). S(N) the utility of standing biomass. Matsuda and Abrams (2006) analyzed the We assume the following fish stock dy- maximum sustainable yield from entire food namics : webs with an independent fishing effort for each species. They concluded that MSY dN/dt = f (N)N – C, policy does not guarantee the coexistence of f (N) = r – aN, species and proposed the concept of “con- C = qEN, strained MSY” that maximizes the sustain- Y(C) = pqEN (2) Optimal fishing policies 361 where t is an arbitrary time unit, f(N) is the per capita reproduction rate, r is the intrin- sic rate of population increase, a is the mag- nitude of density effect, q is catchability, and p is the price of fish. Although we have as- sumed linear functions for cost (cE) and yield (pqEN), the nonlinear relationship for either cost or catch may produce a more complex result. The carrying capacity, denoted by K, is given by r/a. The utility of standing biomass, S(N), is Fig. 1. The relationship between stock abun- likely to be a convex or sigmoid curve be- dance and its utility given by Eq. (3). Bold and cause the utility usually saturates when the thin curves represent the cases where B is 50 stock is sufficiently abundant. We assume the and 10% of K, respectively. following specific function: S(N) = S∞N2/(B2 + N2) (3) where S∞ is the limit of S(N) when N is the positive infinity, B is the stock abundance where S(N) is the half of S∞. We assumed a sigmoid function of N as shown in Fig. 1. In the first step we obtain the optimal fishing effort that maximizes the total eco- system service V(N, C) given by Eq. (1) at equilibrium stock abundance of Eq. (2). The equilibrium stock abundance, denoted by N*, is given by Fig. 2. The relationship between the fishing effort and the total ecosystem service for three N* = (r – qE)/a (4) cases of parameters. Bold, thin and dotted curves represent the cases where (S∞, B) = (100, 10), The total ecosystem service at the equilib- (100, 50), (0, —), respectively. Other parameters are chosen as = 0.01, r = 1, q = 1, p = 1, c = 0.1. * a rium, denoted by V , is The optimal effort for each case is indicated by closed circles. V* = pqEN* – cE + S(N*) (5) If the utility of the standing biomass is negligible (S(N) = 0) as is usually assumed If S(N) is an increasing function of N, in classical fisheries theory, V* is a uni-mo- the optimal effort is always smaller than Eopt dal function of E and the optimal fishing ef- without the utility of standing biomass. How- ever, the distance between E with positive fort, denoted by Eopt, is well known by opt S(N) and Eopt without S(N) depends on the 2 magnitude and curvature of S(N). We nu- Eopt = (pqr – ac)/2pq (6) merically obtained the optimal effort for vari- ∞ If cost c is negligible, Eopt becomes the ef- ous parameters of S and B as shown in fort at the maximum sustainable yield Fig. 2. Despite the fact that the maximum * * * ∞ (MSY). The quantity V when E = Eopt is Vopt(N , C ), when (S , B) = (100, 50) is larger * * ∞ known as the maximum economic yield. than Vopt(N , C ) when (S , B) = (100, 10), 362 H. MATSUDA et al. the latter optimal effort is smaller than the ment error ζ(t). In this case, the fishing ef- former. fort Et likely depends on time because the The derivative of V* with E is stock fluctuates with process errors. In the decision making, fishers just use the estimate * * * ˜ ˜ dV /dE = pqN – c – [pqE + s′(N )]q/a (7) N t, therefore Et is a function F of N t. We here assume one of the simplest ways because dN*/dE = –q/a. that is similar to Reed (1979): The optimal effort is smaller when the derivative of utility of the standing resource f (Nt, ξt) = exp(r + ξt – aNt) (9) with respect to the stock is of a larger mag- nitude (|dS/dN| is larger). If S∞ > (Ba2 + We also incorporate measurement uncer- r2)2(rpq – ac)/2Bqra3, dV*/dE at E = 0 is nega- tainty: tive and the fishing ban is optimal. For pa- rameter values given in Fig. 2, the fishing G(Nt, ζt) = Nt exp(ζt) (10) ban is optimal when S∞ > 47595 if B = 10 or when S∞ > 9995 if B = 50. The optimal harvesting policy is ob- tained by the dynamic programming theory 3. Optimal Fishing Policy with (Mangel and Clark 1988) although the solu- Process Uncertainty and tion is still analytically unknown if a meas- Measurement Errors urement error exists (Kotani et al. 2008). Here we simply assume that the allowable Equation (1), that includes the value of effort rule in actual fisheries management in ecosystem service, is simple because any the USA, Japan, and other countries as types of uncertainties, intrinsic instability, shown in Fig.
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