Aquaculture Technology and the Sustainability of Fisheries

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1 the Sustainability Esther Regnier & Katheline Paris School of Economics and University Paris 1 Panthon-Sorbonne IIFET 2012

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3 50% of world marine fish stocks are fully exploited, 32% are overexploited (FAO 2010). The maximum capture fishery potential from world s oceans has been reached. : is it really an option? Annual average growth rate of aquaculture from 1970 to 2008: 8.3% (FAO 2010). In 2010, capture fisheries managed to provide 9 kg of food fish per capita, per year, versus 8.6 kg for aquaculture (FAO 2010). But the production methods of aquaculture present limitations in terms of environmental sustainability.

4 depends on natural populations for the feeding of 48% of its production (FAO & IFFO data). In 2009 it consumed 63% of fishmeal and 81% of fish oil world production (IFFO). FIFO: number of tons of wild fish necessary to produce 1 ton of farmed fish. Tacon and Metian (2008), Naylor et al. (2009): for carnivorous species (salmon) FIFO reaches 4.9. The more carnivorous the farmed fish species is, the better for s (at least in western countries) but the more inefficient the production technique.

5 Literature review Market interactions: Anderson (1985, MRE); Ye and Beddington (1996, MRE) Biological interactions: Hanesson (2003, Marine Policy)

6 Motivation Investigate the impact of aquaculture production on wild fish stocks, taking into account two key components: (1) its dependence on reduction fisheries; (2) s. We answer this question focusing on the food fish demand arising from wealthy countries. Stylized model including the demand side and three productive sectors: a edible fish fishery, a reduction fishery and the aquaculture sector. Wild and farmed fish are strong (but not perfect) substitutes. Study the long term outcomes and the short term adjustments of fish stocks, supply and prices.

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8 The demand side Utility function of the representative : U(Y 1t, Y 2t ) = [(1 α(k))y 1 1 σ 1t + α(k)y 1 1 σ 2t ] 1/(1 1 σ ), σ > 1 Y 1 : wild species Y 2 : farmed fish σ: elasticity of substitution between wild and farmed fish k ]0, k max ]: efficiency of aquaculture in converting feed fish into farmed fish the lower k the less efficient aquaculture is, and the higher the FIFO ratio the lower k the more carnivorous the farmed fish is, and the more s like it. α(k) [α min ; 0.5[: weights s for each type of fish; α (k) < 0

9 s budget constraint: P 1t Y 1t + P 2t Y 2t = I Partial equilibrium: s spending on fish exogenous Demand functions for the two types of fish: Y d 1t = Y d 2t = I t P 1t [1 + a(k) ( P1t P 2t ) σ 1 ] I t ( ) ] σ 1 P 2t [1 + 1 P2t a(k) P 1t with a(k) = ( α(k) ) σ 1 α(k)

10 The supply side The fisheries Dynamics of the edible fish (species 1) and feed fish (species 3) fisheries described by the Schaefer model (1954): { Ẋit = F i (X it ) Y it Ė it = βπ it = β(p it Y it ce it ), β > 0 with ( F i (X it ) = r i X it 1 X ) it K i Y it = q i E it X it where i = 1, 3, X i :stock level; E i : effort level; K i : carrying capacity; q i : catchability coefficient; r i : intrinsic growth rate of the population;

11 The supply side The aquaculture sector In the aquaculture sector farmers are in competition on the farmed fish (species 2) market. At each date farmers demand the input quantity of feed fish such as to maximize their profit: Production function: π 2t = P 2t Y 2t P 3t Y 3t Y 2t = k(y 3t ) γ, γ ]0, 1[ k: efficiency of the aquaculture sector From the production function, we have: γ = P 3tY 3t P 2t Y 2t

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13 The demand function reduces to: Y d 1t = I t P 1t The price elasticity of demand is unitary. We add to the previous dynamic system the equilibrium of the wild fish market at each date Y 1t = Y d 1 (P 1t). Eliminating P 1 and Y 1 yields: { Ẋ1t = F 1 (X 1t ) q 1 E 1t X 1t Ė 1t = β (I ce 1t )

14 The unique stationary stock and effort are: { ( ) X1 K = 1 1 q 1I r 1 c iff q 1I r 1 c < 1 0 otherwise { I E1 = c iff q 1I r 1 c < 1 0 otherwise 1 wild fish is doomed to extinction in the long run. if q 1I r 1 c The steady state is a stable node. The permanent fitting of price to equalize supply and demand results in smooth trajectories compared to the Textbooks case of infinite elasticity of demand (Clark, 1990 for instance).

15 Dynamics of the capture P1 constant P1 endogenous

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17 The coupling We equalize supplies and demands to reach equilibrium on all 3 fish markets: The final dynamic system is: with Ẋ 1t = F 1 [(X 1t ) q 1 E 1t ] X 1t Ė 1t = β I 1+A t ce 1t Ẋ 3t = F 3 [(X 3t ) q 3 E 3t X ] 3t Ė 3t = β γ A ti 1+A t ce 3t A t = a(k) 1 σ A t = a(k) ( k(q3 E 3t X 3t ) γ q 1 E 1t X 1t ( ) σ 1 P1t P 2t ) σ 1 σ The nature of the steady state, derived from this 4 dimensions matrix, is a stable node.

18 Steady state outcomes X 1 = K 1 (1 q 1I r 1 c Ê 1 = I c 1 1+ X 3 = K 3 (1 γ q 3I r 3 c Ê 3 = γ I c  = a(k) 1 σ  1+ ) 1 1+ )  1+ ( k(q 3 Ê 3 X 3) γ q 1 Ê 1 X 1 ) σ 1 σ Capture : ( ) X1 = K 1 1 q 1I r 1 c E 1 = I c

19 Proposition 1 X 1 > X1 and Ê 1 < E1 : alleviates pressure on the wild edible fish stock in the long run. Moreover, as P 1 = c q 1 X 1, the wild edible fish price is always lower in the long run in presence of aquaculture. Thus, we have Finally, Y 1 < Ŷ 1. X 1 Ŷ 2 > 0 P 1 Ŷ 2 < 0 always satisfied when X1 < X 1 < K 1 /2, never satisfied in the opposite case: K 1 /2 < X1 < X 1. may also be satisfied when the stock is overexploited in the reference situation and becomes larger that K 1 /2 in the presence of aquaculture. In any event, it seems obvious that Y 1 < Ŷ 1 + Ŷ 2, else aquaculture would have no reasons to be.

20 Proposition 2 Condition of coexistence of aquaculture and the edible fish fishery: I < r 1c + 1 r 3 c q 1 γ q 3 r 1c q 1 is the maximum admissible incomes for the existence in the long run of the capture 1 r 3 c γ q 3 idem for aquaculture alone. in presence of aquaculture, the capture fishery can bear a higher income level. Under this condition, the interior steady state is unique.

21 Proposition 3 Eliminating  yields: Ê 1 + Ê3 γ = I c Total effective long run level of harvesting effort: Ê 1 + Ê 3. Virtual total level of effort: I /c, constant (Remember that absent aquaculture the optimal level of effort in the capture fishery is E 1 = I /c). It must be splitted into: an effective effort Ê 1 devoted to catch the edible wild species, a virtual effort Ê 3 /γ > Ê 3 devoted not only to catch the feed species but also to transform it into edible farmed fish.

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23 The choice of the farmed species Influence of the choice of the farmed species, k, on the steady state variables d X 1 and [ 1 σ 1 1 σ 1 + Â dâ > 0, dê 1 dâ < 0, d X 3 dâ < 0, dê 3 dâ > 0 ( ( γ 2 K ) ( 3 + Â 2 K ))] 1 dâ X 3 X 1 Â = 1 ( ka ) (k) + (σ 1) σ a(k) If X 1 < K 1 2 and X 3 < K 3 2, the left-hand side member of this equation is unambiguously positive. If a (k) = 0: the right-hand side member is also positive dâ dk > 0. If a (k) = 0 the process can be reverses: there exists a threshold value of the parameter k above which dâ under which dâ dk > 0 (depending on α(k)). dk < 0 and

24 Numerical Simulations Simulation of the evolution of the steady state outcomes according to the parameters k We test the following specifications of the preference function: k α(k) = α max (α max α min ), 0 < α k min < α max ; max α(k) = C; with α min the minimum and α max the maximum weight affected to Y 2. Table: Calibration of the model. K 1 r 1 q 1 I c β σ K 3 r 3 q 3 γ k α min α max k max C K 1, K 3 : 10 4 tons; r 1, r 3 : years 1 ; k: kg; c, I : $

25 X 1 (k) Ŷ 1 (k) P 1 (k) X 3 (k) Ŷ 2 (k) P 2 (k) Figure: Steady state outcomes as a function of k for two specification of α(k)

26 Figure: s utility as a function of k, for two specification of α(k).

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28 Many hopes are placed in aquaculture. For substitutable wild and farmed products: provides social benefits by decreasing food fish prices and increasing global supply. reduces harvesting edible fish stocks. The fact that fed aquaculture relies on a limited input narrows its stainability, production potential and economic accessibility. The different causes that can be pursued are hardly compatible: maxu, maxπ, maxx 1, maxx 3, maxy tot... What are the potential options in order to improve aquaculture s sustainability? Improving FIFO ratios trough technological progress, by genetically modifying farmed species, finding a relevant substitute to feed fish; Modifying? Offering the appropriate farmed substitute product?

29 What remains to be done? Account for biological interaction between edible and feed fish (ecosystemic approach). Seek for the optimal management strategy Further investigations are needed to shade light on s behavior towards farmed products: What is the true shape of α? It may depend on species considered, countries consumption habits, etc.