IIFET 2006 Portsmouth Proceedings ON THE JOINT MANAGEMENT OF CATCH AND BYCATCH AND THE USE OF MARINE RESERVES Siv Reithe, Norwegian College of Fishery Science, University of Tromsø, Norway. e-mail: [email protected] ABSTRACT This paper explores the possibility of using marine reserves to protect stocks subject to bycatch problems. The importance of migration rates and growth rates of both target and bycatch species and costs are analyzed. Pure open access equilibrium harvest of target species and stock level of bycatch species are compared to those generated by a reserve and open access in the harvest zone. Win-win situations, situations where both harvest of target species and stock size of bycatch species increase, are searched for. It is shown that using a reserve to protect a slow moving bycatch species is more likely to be a success than in the case of a fast moving bycatch species. Furthermore, a fast moving species is worse off after the introduction of a reserve if it has an intrinsic growth rate that is lower than the target species, and in some cases a reserve may actually drive the bycatch stock to extinction. No win-win situations are found in the case of a fast moving species. In the case of a slow moving bycatch species a reserve increases stock size and in cases with low unit cost of effort win-win situations are identified. INTRODUCTION Bycatch is a common problem in fisheries. [1] estimated the world’s total discards to be about 25% of the total commercial catch (by weight). In the fishery south east of Australia more than 100 species are caught, but only 15 of them account for 80% of the value [2]. In the Northeastern US only half of the total catch (by weight) taken by ground fish trawl, sink gillnet and scallop dredge vessels at Georges Bank during the 1990s consisted of the targeted species [3]. In the same region, protected species like harbor porpoise, right whale, leatherback and green sea turtles are taken as bycatch in different fisheries [4]. Other examples of fisheries with bycatch problems are dolphins caught in tuna fisheries and juvenile cod, haddock, redfish and greenland halibut taken as bycatch in the Barents Sea shrimp fishery. In many fisheries where there are bycatch problems the problem is sought dealt with with technical constraints on gear such as sorting grids in trawl bags, mesh size and shape restrictions. Also economic instruments such as taxes or tradable permits may be used to protect species that are taken as bycatch. This paper analyzes the possibilities of using marine reserves as a tool in the management of bycatch. The possibilities of win-win situations, defined as cases where both biomass of bycatch stock and harvest of targeted species occur, are also sought for. Some studies on the use of temporarily closed areas as a method of reducing bycatch or protect bycatch species have been conducted. [5] compare the use of temporarily closed areas and individual transferable quotas (ITQs) on bycatch of harbour porpoise in the New England multispecies gillnet fisheries and find that for a given level of bycatch ITQs are more profitable. [6] evaluate a suggested model for bycatch management using temporarily closed areas in the Barents Sea. Here, an area is closed whenever a maximum number of juvenile fish of different species are caught in the shrimp trawl nets. The decision to close is based on bioeconomic 1 IIFET 2006 Portsmouth Proceedings criteria balancing the value of lost shrimp catches resulting from a closure, and the value of future loss of catches of fish which will be taken as bycatch if the area is not closed. The maximum number of juveniles allowed in the shrimp catches will in certain cases be so high that, in practice, closure will not occur. [7] examines how the creation of a reserve of a given size affects harvest of targeted species and stock level of bycatch species under different assumptions regarding the ecological interactions between the two species. It is found that if there are no interactions between targeted and bycatch species or if bycatch species prey on bycatch species, a reserve increase the biomass of the bycatch stock, but if the two species compete, the biomass of the bycatch stock decreases a result of the reserve. In many analyses of marine reserves it is assumed that the biomass in the area covered by a reserve will increase as the result of the reserve. [8] reviews a number of empirical studies on the effects on marine reserves and finds that this is not the case for all species. [9] finds that for three out of ten species covered by a reserve outside South Africa no increase in abundance within the reserve could be detected. Their migratory nature was described as the probable cause for these findings. Others have found that the concentration of fish of certain species is greater in the harvest zone than within the reserve [10, 11]. In these cases other explanations have been forwarded; decreased competition with target species in the fishing zone and predator- prey interactions. In this paper we consider two cases for the bycatch stock; i) the abundance of fish is higher within the reserve then in the harvest zone, ii) the distribution of does not alter as a result of the reserve and the reason is speed of migration. In the first case we set the migration coefficient low, hence, the analysis may bee seen as a comparison of two extremes, the outcome of a reserve for one fast moving and one slow moving bycatch species. This paper extends previous works in that speed of migration, growth rate and the success of a reserve are analyzed in the setting of a bycatch species, and in that these factors are analyzed in relation to the properties of the targeted species. It is shown that the speed of motion of the bycatch species clearly matter when measuring the effect of a reserve, but also that how fast it grows relative to targeted specie and the unit cost of effort plays an important role. The outline of the paper is as follows; first the model is described, then a comparison of the effects of a reserve on the two bycatch stocks is made. In the third section the possibilities of win-win situations are identified. Some concluding remarks finalize the paper. THE MODEL Pre-reserve dynamics The model for the targeted species and bycatch species with migration is from [12]. This model is chosen because it has the property that pre- and post-reserve harvest is equal. The pre-reserve dynamics with harvest are given by ( 1 ) S& = r[]S(1− S) − ES Where S is the normalized stock level, r the intrinsic growth rate and E is normalized effort so that the catchability coefficient equals r. The rent function is defined as 2 IIFET 2006 Portsmouth Proceedings ( 2 ) π = prES − aE where p is a constant price per unit catch of targeted species and a is the cost per unit effort. Under open access the equilibrium rent is zero, resulting in an equilibrium stock level of the a targeted species S = = c . pr The equilibrium stock level, found by equating (1) to zero and solving for S, is ( 3 ) S(E) =1− E The dynamics of the bycatch stock are described by the following: ( 4 ) Z& = gZ(1− Z) − qEZ Where Z is the normalized stock level, g is the intrinsic growth rate and q is the catchability coefficient of the bycatch function. The equilibrium stock level of bycatch stock is q ( 5 ) Z(E) =1− E g Post-reserve dynamics When implementing a reserve of size 0 < m < 1, S = S1 + S2, where S1 is the stock in the reserve and S2 the stock in the fishable area and S1/m and S2/(1-m) are the densities. Growth after reserve formation is assumed to equal growth prior to reserve formation. The dynamics after reserve formation then become: ⎡ ⎛ S1 S2 ⎞⎤ ( 6 ) S&1 = r⎢S1 (1− S1 − S 2 ) − γ ⎜ − ⎟⎥ ⎣ ⎝ m 1− m ⎠⎦ ⎡ ⎛ S1 S 2 ⎞ S 2 ⎤ ( 7 ) S&2 = r⎢S 2 (1− S1 − S 2 ) + γ ⎜ − ⎟ − E ⎥ ⎣ ⎝ m 1− m ⎠ 1− m⎦ Where γ is the ratio of the migration coefficient over the intrinsic growth rate. Adding (6) and (7) we get ⎡ S2 ⎤ ( 8 ) S& = r⎢S(1− S) − E ⎥ ⎣ 1− m⎦ Hence, equilibrium yield from the targeted stock is H = rS(1-S) as prior to reserve formation. With open access in area 2 equilibrium stock densities as functions of effort becomes 3 IIFET 2006 Portsmouth Proceedings ( 9 ) S2 = c(1− m) m(1− c(1+ m)) −γ − (γ + (c(1+ m) −1)m)2 + 4cm2γ ( 10 ) S = 1 2m For the bycatch stock in question we shall consider two cases. In the first case, following Reithe (2006), we assume that reserve formation does not affect the distribution of the stock, that is, post-reserve density is uniform throughout its entire distribution area. The growth is therefore only affected by reserve formation through changes in effort and post-reserve dynamics are described by ( 11 ) Z& = gZ(1− Z) − qE(m)Z(1− m) Equilibrium stock with a reserve and open access is given by q ( 12 ) Z(E,m) =1− E(m)(1− m) g This approach may be a good approximation either when the species is very fast moving, or when the catchability coefficient is low. In the second case migration is explicitly modeled; ⎡ ⎛ Z1 Z 2 ⎞⎤ ( 13 ) Z&1 = g⎢Z1 (1− Z1 − Z 2 ) − λ⎜ − ⎟⎥ ⎣ ⎝ m 1− m ⎠⎦ ⎡ ⎛ Z1 Z 2 ⎞⎤ Z 2 ( 14 ) Z& 2 = g⎢Z 2 (1− Z1 − Z 2 ) + λ⎜ − ⎟⎥ − qE ⎣ ⎝ m 1− m ⎠⎦ 1− m Where λ is the ratio of the migration coefficient over the intrinsic growth rate for the bycatch species.