WORKING PAPER SERIES

ISSN 1503-299X WORKING PAPER SERIES No. 12/2005 ON THE ECONOMICS O BIOLOGICAL INVASION: AN APPLICATION TO RECREATIONAL ISHING Jon Olaf Olaussen Deparmen of Economics N-7491 Trondheim, Norway www.sv.nnu.no/iso/wp/wp.hm

On he Economics of Biological Invasion: An applicaion o recreaional fishing by Jon Olaf Olaussen Deparmen of Economics, Norwegian Universiy of Science and Technology 7491 Trondheim, Norway e-mail: jonola@sv.nnu.no ABSTRACT: The paper demonsraes four general mechanisms ha may affec economically valuable species when exposed o biological invasion. We disinguish beween an ecological level effec and an ecological growh effec. In addiion we presen an economic quaniy effec working hrough demand. inally we sugges ha here is an economic qualiy effec ha reflecs he possibiliy ha invasions affec he harvesing agens direcly hrough new demand-side forces. or example, his may occur because he sae of he original species or he ecosysem is alered. We depar from he exising lieraure by revealing ecological and economic forces ha explain why differen agens may lack incenives o conrol invasions. The heoreical model is illusraed by he case where escaped farmed salmon influence wild Alanic salmon fisheries. Keywords: Biological invasion, escaped farmed Salmon, recreaional fishing, bioeconomic model. I would like o hank Anders Skonhof for valuable suggesions and commens on earlier versions of his paper. 1

1. Inroducion During he las few decades, here has been increasing concern abou invasive species in various ecosysems. Holmes (1998) argued ha invasive alien species are he second mos imporan cause of biodiversiy loss worldwide, beaen only by habia aleraion. In some insances, invasive species are inroduced o a new environmen in order o obain some recreaional or commercial gain. Perhaps he mos famous case is he release of 24 wild rabbis by Thomas Ausin for spor huning on his propery in Ausralia in 1859, which had far-reaching consequences (All-science-fair-projecs 2004). In oher insances, human aciviy indirecly has allowed inruders o esablish hemselves in a new environmen by disurbing he naural balance in he environmen, e.g. via polluion. In addiion, humans have accidenally brough invasive species o new places as sowaways in cargos. One well-known example is he Zebra mussels from he Caspian Sea ha were inroduced o he Grea Lakes in he USA via ballas waer from a ransoceanic vessel in he 1980s (Grea Lakes Science Cenre 2000). Alhough he economic consequences of non-indigenous species are recognized as imporan, here have been few aemps o quanify hem. This is due o a lack of good daa, as well as uncerainies and measuremen problems when facing he many componens ha are difficul o quanify accuraely (Perrings e al. 2000). One excepion is Pimenel e al. (1999), who esimaed oal economic damages and associaed conrol coss due o invasive species in he USA o be $138 million per year. Several auhors in Perrings e al. (2000) deal wih he economics of biological invasions. A general model se-up was given in Barbier (2001). As in Knowler and Barbier (2000), he focus was on separaing he ex-pos and ex-ane economic consequences of biological invasions. Knowler and Barbier sudied he inroducion of comb jelly (Mnemiopsis leidyi) in he Black Sea and is impac on he commercial Black Sea anchovy fishery. Knowler e al. 2

(2001) examined he exen o which polluion conrol could have prevened he ecological regime shif imposed by he comb jelly. Higgins e al. (1997) invesigaed alernaive responses o he invasion of a woody species ha has displaced a naive plan species, in a siuaion where boh species are valuable. Sele and Shogren (2002) developed a general model o sudy he inroducion ino Yellowsone Lake of exoic lake rou, which pose a risk o he naive cuhroa rou. In heir model, park managers, operaing as social planners, divided heir budge beween conrolling he lake rou and an alernaive service, he improvemen of a non-species good. By conras, humans divided heir ime ino eiher species consumpion or spending leisure ime on a non-species composie good. Eiswerh and van Kooen (2002), Horan e al. (2000), Olson and Roy (2002), and Shogren (2000) sudied uncerainy wih respec o species invasion. Several auhors, including Buhle e al. (2004) and Hill and Greahead (2000), sudied cos effecive conrol. In a join TC-CV sudy, Nunes and van den Bergh (2004) explored he exen o which people value proecion agains exoic species. In his paper, we analyze ye anoher poenial concern, namely he influence escaped farmed species may have on he naural habians. More specifically, we sudy he effecs ha escaped farmed salmon may have on wild Alanic salmon. Norway has been he world leader in farmed salmon since his echnique was pioneered in he early 1960s. Producion has risen rapidly from abou 600 onnes in 1974 o abou 500 000 onnes oday (Bjørndal 1990, Saisics Norway 2004). Salmon farming is one of he mos imporan indusries in rural Norway, wih a yearly firs-hand value (landed value) of abou 10 billion Norwegian kroner (NOK) (1.3 billion EUR). However, since he very beginning of he salmon farming indusry, salmon have uninenionally been allowed o escape from ne pens ha are damaged by sorms, seals, and oers, or by daily wear and ear. The number of accidenal escapes 3

decreased in he mid-1990s because of safey invesmens in he sea ranches. Neverheless, approximaely 400 000 salmon sill escape yearly from fish farms in Norway (Table 1), a number exceeding he average oal wild spawning sock (NOU 1999). The wild Alanic salmon sock is radiionally harvesed in wo differen fisheries in Norway during is spawning run. irs, he marine commercial fishery caches abou 40% of he spawning biomass in fishnes in he fjords and inles. The escapemen from his fishery eners he rivers and is harvesed by a recreaional fishery. When he fishing season in he river closes, he escapemen from hese sequenial fisheries akes par in he reproducion process in he river in he lae auumn. Spawning escaped farmed salmon (ES) may have a number of negaive effecs on he naural growh and economic value of wild salmon. The mos imporan effecs are he spread of diseases and he mixing of genes hrough inerbreeding, which affec he reproducion rae as well as he inrinsic value of he wild salmon. armed salmon digs in he naives spawning gravel, ge more aggressive and risk willing offspring (NOU 1999:9), and increases he sea lice densiy (Grimnes e al. 1996). However, escaped farmed salmon may also have posiive effecs. armed salmon can poenially increase he salmon sock available for boh marine and recreaional harvess, ceeris paribus, and hus improve he profiabiliy of hese fisheries. As repored in able 1, escaped farmed salmon consiue a subsanial par of caches. This is no o say ha invasion is no problem for he sociey as a whole, bu i may reveal economic forces inducing lack of incenives for differen agens o conrol he invasion. These mechanisms are ignored in he previous lieraure. TABLE 1 ABOUT HERE 4

The analysis in his paper differs from he previous sudies in various ways. irs, he model formulaion is more general as i encompasses boh ex ane and ex pos effecs of invasions wihin he same model framework. Knowler and Barbier (2000) sressed he imporance of comparing he ex ane wih he ex-pos invasion case. We disinguish beween changing ecological and economic forces, which have poenially differen effecs depending on he iniial sae. This focus allows us o depar from he sylized ex ane versus ex pos framework as he biological and economic consequences may change wih differen levels of invasion. The consan ecological srucural shif proposed by Knowler and Barbier (2000) is replaced by a shif ha depends on he magniude of he invasive influx. Second, he general problem of invasion as a resul of escapemen from fish farms raises some specific new problems ha have no ye been considered. We address one of hese problems by explicily aking ino accoun he poenially ambiguous effec of biological invasion hrough demand-side effecs. In many respecs, i may be impossible for he differen harvesers o separae he wild and escaped species ha hey cach. Hence, if invasion increases he oal sock, demand may increases due o wha will be called he economic quaniy effec 1. However, i is relaively easy o discover wheher here are geneic differences or variaions beween he wild and he reared species hrough geneic invesigaion. Hence, knowledge abou he composiion of he cach, as well as he composiion of he breeding sock, is ofen available. Thus, harvesers know he likelihood of geing a farmed insead of a wild salmon. urhermore, harvesers may be concerned abou he healh of he wild sock due o crossbreeding when he share of invasive salmon in he breeding sock is high. This could be relaed direcly o he exisence value of he geneically 1 More generally, his effec reflecs all siuaions in which he invasive species is conneced o a harves value. 5

wild species or o he loss of biodiversiy due o gene flow from he reared o he wild species. Anoher inerpreaion is ha harvesers simply prefer o harves "clean" or "pure" wild Alanic salmon. This will be called he economic qualiy effec. The wo economic effecs boh affec he economic equilibrium condiion. Nex, on he ecological side here are wo effecs, which work in opposie direcions: he ecological growh effec, which is negaive, and he ecological level effec, which is posiive. In he specific case of ES, he former effec reflecs a general decrease in he growh rae of he wild salmon due o crossbreeding, whereas he laer reflecs he yearly influx of escaped salmon ha add o he oal salmon sock (see below). 2 Analogous o he economic effecs, hese ecological effecs boh affecs he ecological equilibrium condiion. We also analyse he consequences of invasions when here is a sequenial harves of boh he invasive and he wild sock. When he composiion of he cach, in erms of he share of he invasive species, differs beween he various harvesers, we gain an addiional managemen ool. By alering he share of he oal harves beween he differen harvesers, we can change he composiion of he escapemen from hese sequenial fisheries (Appendix B). The res of he paper is organized as follows. Secion wo formulaes an ecological model for he Alanic salmon species, and secion hree defines he ecological equilibrium. In secion four, he economics of he river fishery are examined and he economic equilibrium condiion is defined. Nex, in secion five, he resuls are combined o esablish he bioeconomic 2 Noe ha in he case where geneic differences beween naive and alien species are high, as e.g. in Knowler and Barbier (2000), crossbreeding is no an opion, and hence only he ecological growh effec applies. However, in such cases, here is clearly an analogue o his level effec if he invasive species is exposed o harvesing. 6

equilibrium. In secion six, he model is illusraed by uilizing ecological and economic daa from he Norwegian river Orkla. Secion seven concludes he paper. 2. The Ecological Model irs, we consider a wild fish sock in he absence of escaped farmed salmon. The size of he wild populaion in biomass (or number of fish) a he beginning of he fishing season in year is X. Boh a marine and a river fishery ac on he salmon during he spawning run from is offshore environmen o he coas, where reproducion akes place in is paren or home` river. The marine fishery impacs on he sock firs because his harves akes place in he fjords and inles before he salmon reaches heir spawning river (see figure 1). or a marine harves rae 0 h 1, he number of wild fish removed from he populaion is hx. Accordingly, he escapemen o he home river is (1 h ) X = S1,. The river fishery explois his spawning populaion along he upsream migraion. When he harvesing fracion here is 0 y 1, he river escapemen is (1 y)(1 h) X = (1 y) S1, = S2,. This spawning sock hence yields a subsequen recruimen R ( S 2, ) o he sock in year + τ, where τ is he ime lag from spawning o mauraion age (see e.g. Walers, 1986). 3 Throughou he analysis, i is assumed ha he sock-recruimen relaionship (.) R is of he Sheperd ype, wih R (). 0, R (). 0 and R ( 0) = 0 (more deails below) (Sheperd 1982). The fracion of he recruis ha survive up o maure age + τ is 0< z < 1. urher, we assume ha none of he spawners survive and we wrie he populaion dynamics when here is no invasion as X + τ = zr( S2, ) 4. 3 See Clark (1976) for an analysis of he dynamics of a delay-difference recruimen model. 4 Hvidsen e al. (2004) find ha only 0.3%-3.8% of he spawners survive jusifying his simplifying assumpion. 7

The influx of escaped farmed salmon (ES) ino he ecosysem is a yearly even. We assume ha all ES ake par in he upsream migraion. As he escapemen is due o uninenional releases from he fish farms, X, is exogenous and no subjec o an equaion of moion. As already indicaed, he invasive ES have wo imporan ecological effecs, he ecological growh effec and he ecological level effec. irs, as in Knowler and Barbier (2000), he ecological growh effec reflecs he fac ha he populaion dynamics of he residen species is srucurally alered by he esablishmen of he invader species (farmed salmon) X. This effec hence indicaes he exen o which he growh funcion is negaively affeced by crossbreeding (gene flow), desrucion of breeding ness, and compeiion for food due o he invasion (see Hindar e al. 1991, Lura 1990, Lura and Sægrow 1991, McGinniy e al. (2003) and leming e al. (2000)). In general we allow he negaive ecological growh effec o be increasing, decreasing or consan wih he number of ES (see below). The ecological level effec, on he oher hand, reflecs he fac ha he ES add o he wild sock hrough a yearly influx. Knowler and Barbier (2000) analysed a siuaion where he invader preys upon he residen species, and hence heir model have negaive effec on recruimen. In our case, a kind of predaory behaviour occurs when he ES dig up wild fish spawning ness, bu he ES also spawn hemselves. We define wild fish as all salmon ha originae from river spawning. Hence, by assumpion, offspring is defined as wild fish, even if recruimen may conain hybrids (crossbreedings of wild and reared salmon) and he offspring of wo farmed parens. 5 5 In doing so, we neglec one aspec of biological invasion because he negaive effec on he gene flow due o inbreeding will coninue in he nex generaion (leming e al. 2000). However, his influence on he wild fish populaion is parly aken ino accoun by he srucural shif (growh funcion shifing down). 8

The spawning fracion of he salmon sock is harvesed ogeher wih he escaped farmed salmon, X (again, see figure 1). However, only a proporion of he escaped fish is available o harves because he reared salmon ypically sars is spawning migraion laer han he wild sock (Lura and Sægrov 1993, NOU 1999). Hence, only he fracion ax is available in he marine fishery, where 0 a 1. Accordingly, wih he marine fishery harvesing fracion h, he escapemen of reared fish from he marine harves is (1 h ) ax available in he marine fishery is (1 ax ). The fracion no. Hence, he oal sock afer he marine fishery season ends is (1 ah) X = S1,. Moreover, as mos of he escaped farmed salmon ener he river afer he fishing season finishes, only he fracion 0 b 1 is available for spor fishing (iske e al. 2000). We denoe he sock ha is available in he river fishery as b(1 ah ) X = bs. Hence, wih he harvesing fracion y, he fracion ybs is harvesed in he 1, river. Accordingly, (1 y ) bs survives o be par of he spawning sock. In addiion, he spawning sock includes he par of he sock ha eners he river afer he fishing season closes, (1 bs ). The par of he sock ha eners he spawning sock in he river in a given year is herefore (1 by) S1, = S2,. Consequenly, he recruimen funcion wih ES is wrien as: (1) X = zr S2, + S2,, S2, +τ. The firs erm in he brackes represens he posiive ecological level effec of he yearly influx of ES, conribuing o recruimen in he same manner as he wild sock. The negaive ecological growh effec in he recruimen funcion is indicaed by he las erm in he brackes. Noice ha his differs from Knowler and Barbier (2000), who considered a consan srucural shif, whereas we consider a marginal effec from he ES. Generally, he negaive 9

ecological growh effec may be increasing, decreasing or consan wih he level of ES as discussed below. IGURE 1 ABOUT HERE 3. The Ecological Equilibrium In he remainder of he paper, we focus on an equilibrium model, raher han he dynamic forces, because our main goal is o esablish he driving forces ha follow an invasion. 6 Alhough we do no claim ha he dynamic forces are negligible, we argue ha he gain in analyical racabiliy from neglecing he dynamic forces offses he loss of deails in regard o he shor-erm dynamics. 7 ollowing he approach aken by Anderson (1983, 1993), McConnel and Suinen (1989), and Lee (1996), we measure recreaional fishing effor in erms of he number of daily fishing permis sold. 8 In real life, fishing permis may be for one day, one week, or a whole season. However, as in Skonhof and Logsein (2003), we collapse hese possibiliies ino one-day permis because hese are he mos common ype. Thus, he fishing effor is direcly expressed in erms of he number of day permis, D. (Again, he effec of X is ambiguous, as will be discussed below.) We assume he offake in he river follows he Schaefer-ype harves funcion. Hence, he oal river yield is wrien as: (2) Y = qd S1 + bs 1, 6 or he same reason, he marine harves rae h is kep in he background, enering he model exogenously. 7 See e.g. Olaussen and Skonhof (2005) for a dynamic analysis of recreaional fishing. 8 Ohers have used a differen approach for insance, Bishop and Samples (1980), Cook and McGaw (1996) and Laukkanen (2001) use he acual cach. 10

where Y is he oal offake, q is he cachabiliy coefficien, and D is effor measured in number of fishing days. The conen in he bracke on he righ-hand side of equaion (2) is he oal biomass ha is available in he recreaional fishery. Moreover we have ha he oal offake in he river per definiion wries (3) Y = y S1+ bs 1. Hence, from equaion (2) and (3) i follows ha he fishing moraliy fracion y given marine harves rae h, he equilibrium version of equaion (1) is wrien = qd. or a (4) ( 2 2, 2 ) ((1 ) 1 (1 ) 1, (1 ) 1 ) X = zr S + S S = zr qd S + bqd S bqd S ((1 )(1 ) (1 )(1 ), (1 )(1 ) ) = zr qd h X + bqd ah X bqd ah X. The oal differenial of he equilibrium condiion (4) wih respec o he sock and fishing effor yields (..)( 2 + 2 ) D + (..) 1 (..)( + ) dx zr S S zr S = dd zr S S 2 2 X D. Boh erms in he numeraor are negaive as increasing he effor decreases he sock as long as R (..) > 0. The denominaor is posiive as long as zr ( ) S2 S2.. ( + ) < 1. Hence, we find ha he ecological equilibrium condiion is decreasing in he X-D plane as long as zr ( ) S2 S2 X 0 <.. ( + ) < 1 hold. Noe ha a high oal spawning sock yields a low growh rae and vice versa which indicae ha he X 11

condiion o some exen are self-fulfilling. See also he numerical secion below 9 and Appendix C for more deails. As discussed above, shifs in X yield wo separae ecological effecs, he ecological growh effec and he ecological level effec. Based on our assumpions, he growh funcion shifs down whenever ES are presen, and he marginal effec of ES is consan. This means ha he ecological equilibrium condiion becomes seeper in he X-D plane due o he reduced growh rae of he species (see igure 2). As we have a yearly influx of ES, he ecological level effec operaes in he opposie direcion because, ceeris paribus, more ES increase spawning. The inuiion behind he ecological level effec is clear, because a given fishing effor is compaible wih more fish when here is a yearly influx added o he sock. IGURE 2 ABOUT HERE Hence, based on he wo conflicing ecological mechanisms, he oal sock effec depends on he iniial sock size, as indicaed by he shif from curve 1 o curve 1` in igure 2. The ecological level effec of he direc invasion shifs he ecological equilibrium condiion ou in he X-D plane. A he same ime, he slope becomes seeper because of he srucural change (reduced growh). Increasing he marine harves rae always makes he ecological equilibrium condiion seeper. Accordingly, less fishing effor in he river is compaible wih he same sock size when he marine harves increases. The same conclusion holds for he cachabiliy parameer, in he sense ha when each angler is more effecive, for example because of more effecive fishing equipmen, hen less fishing effor in he river is compaible wih he same sock size. 9 In he res of he paper, we only focus on he case where R (..) > 0 holds because sock sizes where R < 0 are unlikely o occur in real life for Alanic salmon (see e.g. Hansen e al. 1996 and Hvidsen e al. 2004). 12

4. The Economic Equilibrium We now urn o he economic par of he model. Saring wih demand, his is a quesion abou wha recreaional anglers look for in he fishing experience. The price of he fishing license and he number of fishing days are expeced o be imporan. However, as Anderson (1983), among ohers, emphasized, he average size of he fish caugh, he oal amoun of fishing effor by all individuals, he anglers income, he marke price of fish, companions, and he naure of he surroundings may also play a role. However, empirical evidence shows ha wo of he mos imporan deerminans of fishing rip saisfacion in he Norwegian Alanic salmon fishery are he price of permis and he size of he cach, measured as average cach per day (iske and Aas 2001). 10 As we focus on he issue of invasive species, we have added he above menioned economic effecs (quaniy and qualiy) in he demand funcion. The inverse demand funcion is hence a funcion of he number of fishing permis, in addiion o he size of he wild and he ES sock: (5) + + / P= P( D, X, X ). The signs above he argumens indicae he sign of he parial derivaive wih respec o he number of fishing permis, D, and he signs of he shif in he inverse demand funcion when he wild sock and he number of ES change, respecively. The inverse demand schedule is downward sloping in he number of fishing days as he willingness o pay for he fishing experience ceeris paribus decreases. On he oher hand, i shifs upwards in he P-D plane 10 In a survey of Norwegian rivers, 92% of spor fishermen repored ha he qualiy of he river in erms of average cach per day was imporan. In addiion, 72% repored ha he price of fishing permis was imporan (iske and Aas 2001) 13

when he wild sock, X, increases due o he economic qualiy effec. or a higher sock (quaniy), he average cach per day increases. 11 inally, we have he ambiguous demand effec of ES. The posiive economic quaniy effec is counerbalanced by he negaive economic qualiy effec. The economic quaniy effec means ha, ceeris paribus, he angler always regards caching one more fish as posiive, even if he fish is an ES. This assumpion is realisic because spor fishermen are rarely able o idenify a salmon as an ES, especially if i is no recenly escaped (NOU 1999) 12. The economic qualiy effec is always negaive as i capures fishermen s concerns abou he share of ES in he spawning sock. 13 One of he required aribues of a fishing experience may be ha he fish are wild. When he repored share of ES in he breeding sock is high, he likelihood of any cach being a farmed salmon is higher. Given ha he anglers prefer he geneically "clean" wild fish, a greaer ES-share may reduce heir willingness o pay for he fishing experience. This effec may originae from a concern abou he sae of a specific river s salmon sock, or simply from he fishermen s self-ineresed regard o heir own cach, or boh. However, he cause is of minor imporance here, as he main poin is o esablish ha he economic qualiy effec is negaive. or a given ES level, his negaive effec decreases as he wild sock increases because he share of ES in he oal sock decreases (again, see he specificaion below). Moreover, he economic qualiy effec is assumed o be sronger when he share of ES in he spawning sock is higher. 11 See also Olaussen and Skonhof (2005) for more deails on his shif in demand. 12 Recenly escaped (adul) farmed fish is ofen characerized by poorly developed and damaged fins, especially he caudal (ail) fin, small gills, skin bruises and general deformaions. However, hese signs are rarely observed when he fish escapes a an early life sage. 13 These numbers are repored from yearly biological invesigaions of he spawning sock. This means ha informaion abou he average share of ES in he spawning populaion is available and, in many cases, par of he common knowledge of anglers. 14

On he supply side, he landowners ake ino accoun he cos of selling fishing permis, CD. ( ) This cos is generally relaed o he aciviies underaken by he landowners in order o provide he permi, such as adverising, adminisraion, and supervision, as well as he consrucion and mainenance of parking los, racks, fishing hus, and so forh. Generally, here are fixed as well as variable coss. We assume myopic, monopolisic managemen of he river. The radiional view is ha even a very small spawning sock is able o fully replenish he river, so here is lile reason for he landowners o consider he nex generaion sock. Therefore, hey ac as de faco myopic resource managers (reaing he salmon sock as exogenous). Anoher possible explanaion for his shor-sighed behaviour is ha, due o he ime lag in recruimen, he landowners know ha recruimen does no reurn for a leas five years (τ=5). As he landowners canno conrol he marine fishery, he harves in he fjords induces an exra source of uncerainy abou fuure sock. urhermore, he argumen for myopic resource managemen seems o be even sronger in he case of ES, as ES add o he complexiy observed by he river manager wih respec o he salmon sock. The monopolisic assumpion means ha he river landowners, who offer fishing permis o he recreaional anglers, are able o ake advanage of he downward slope of he demand curve. The assumpion of monopolisic behaviour fis wih he behaviour of Norwegian landowners in a ypical large salmon river, where salmon ourism forms a noeworhy par of he landowner s income. By conras, price-aking behaviour exiss in many small rivers, as indicaed by Olaussen and Skonhof (2005). The river fishery profi wries π= PDX (,, X ) D CD ( ), and accordingly, he firs-order condiion is: (6) PD + P C = 0. D 15

The firs-order condiion gives he number of fishing permis as a funcion of he fish sock. Noe ha he sock size affecs his firs order-condiion only hrough demand because he myopic landowners do no ake he sock size effec ino accoun in he profi funcion as menioned above. Differeniaion of he firs-order condiion yields [ ] P + P D C dd= P dx. Assuming ha he second-order condiion for he maximum 2 D D X holds, he conen in he bracke on he lef-hand side is negaive. Hence, he economic equilibrium condiion is posiively sloped in he X-D plane. The inerpreaion is clear-cu as more fish are compaible wih more fishing permis because demand increases. The permi sale is posiive only if he willingness o pay for fishing permis exceeds he cos of providing hem. Hence, he minimum level of he sock mus yield P(0, X, X ) C(0) o ensure posiive supply. X influences he economic equilibrium hrough he economic quaniy effec and he economic qualiy effec. Depending on which effec is dominan, he economic equilibrium condiion shifs ouwards or inwards in he X-D plane when he amoun of ES increases (see igure 2). The economic quaniy effec shifs he equilibrium condiion inwards. This means ha he fishing effor compaible wih a given sock size increases because he yearly influx creaes increasing demand. In addiion, i indicaes ha he minimum sock level compaible wih posiive demand decreases. On he oher hand, he economic qualiy effec always shifs he equilibrium condiion ou because his negaive effec reduces demand for a given wild sock. Which effec ha dominaes is an empirical quesion and is likely o vary from case o case, and, perhaps more imporan, i will depend on he iniial invasion level. However, some general poins can be made. One realisic assumpion seems o be ha he economic qualiy effec will diminish wih 16

an increasing wild sock. In oher words, he higher is he proporion of wild salmon in he oal sock, he smaller will be he share of he ES in he spawning populaion. Accordingly, he negaive economic qualiy effec will be less. The basic idea is ha he iniial siuaion affecs how a change in he number of ES operaes. In he P-D plane, his means ha for a given iniial sock, increasing levels of X shifs he inverse demand schedule up if he economic quaniy effec dominaes he economic qualiy effec and he vice versa. Moreover, for a given effor level, he inverse demand schedule is more concave in he P-X plane when X > 0 (see also numerical secion below). This assumpions leads o he economic equilibrium condiion depiced in igure 2, where he economic qualiy effec dominaes he economic quaniy effec only for small iniial wild sock sizes. The same line of arguing indicaes ha if he economic qualiy effec is low, hen here is a greaer likelihood ha D will increase as he number of ES increases. Moreover, if here is no economic qualiy effec, he curve simply shifs unambiguously inwards in he X-D plane due o he posiive economic quaniy effec. In addiion, noice ha he economic qualiy effec means ha if he wild sock changes, demand respond more in he pos- han in he pre-invasion case. This is because, pos-invasion, here is an addiional demand effec induced by he changing composiion of he spawning sock. 5. The Bioeconomic Equilibrium As illusraed in igure 2, he bioeconomic equilibrium, in which boh he ecological and economic equilibrium condiions are saisfied, is represened by he inercepion beween he curves. Comparing he pre- and pos-invasion saes, ha is, comparing X = 0 (curves 1 and 2) wih X >0 (curves 1` and 2`), we find ha he effecs on sock ( X ) and effor ( D ) are boh ambiguous. This follows direcly since boh equilibrium condiions shif simulaneously. The 17

fac ha he bioeconomic resul of an invasion direcly depends on he iniial sae highlighs he imporance of separaing beween differen iniial levels of invasion. If we concenrae on he difference beween he pre-and he pos-invasion siuaions, we are required o ake all four effecs ino accoun. Moreover, if we are already in a pos-invasion environmen, all effecs will sill apply. As discussed above, and shown in igure 2, i is no possible o make general saemens abou he sock and he number of fishing days when we have changes in he number of ES. As noed, he iniial siuaion is an imporan deerminan of he consequences for sock and effor flowing from an increased invasion. or a given level of invasion, we find ha when he level of he wild sock is low, he share of reared salmon in he spawning sock is relaively high. This means ha he economic qualiy effec will be imporan, placing us on he seeper par of he economic equilibrium condiion depiced in igure 2. rom his equilibrium, we know ha he schedule shifs down and rises more seeply in he X-D plane a he same ime. rom he ecological equilibrium schedule, we find ha he slope is flaer when he sock is low (he convex ecological equilibrium schedule), increasing he likelihood ha X will increase as he number of ES increases (see igure 2). Thus, boh he ecological and he economic forces operae in he same direcion when he iniial sock level is low. If we urn o a siuaion where he level of he wild sock is high, hen he share of invasive fish in he spawning sock is small, making he economic qualiy effec negligible o he spor anglers. As noed above, ceeris paribus his increases he likelihood ha fishing effor will increase wih an increase in he number of ES. However, due o he seep fall in he ecological condiion when he sock is high, he bioeconomic resul is more likely o reduce sock and effor, as indicaed in igure 3. To come o more definie conclusions abou he 18

magniude of he differen effecs, we illusrae he model wih an example based on he Norwegian Salmon River Orkla. IGURE 3 ABOUT HERE 6. A Numerical Illusraion 6.1 Daa and specific funcional forms The biological daa are in accordance wih a ypical large Alanic salmon river in Norway, as represened by he river Orkla, which is siuaed some 500 km norh of Oslo. A biological invesigaion conduced by Hvidsen e al. (2004) provides he only daa available worldwide ha esimaes he recruimen funcion in a large Alanic salmon river. Moreover, he Orkla River is one of he "cleanes" large salmon rivers in Norway wih respec o biological invasion. I has low levels of escaped farmed salmon in boh cach saisics and he spawning populaion according o iske e al. (2000), hese levels average 1% and 18%, respecively. In he marine fisheries, iske e al. (2000) showed ha, on average, 32% of he marine offake is made up of ES (see Appendix A for a calibraion of he biological model). Biological research sugges ha he recruimen funcion R (..) is close o he Beveron Hol ype, bu ha neiher he Cushing nor he Ricker ype recruiemen can be ruled ou. I is herefore convenien o wrie i as he Sheperd (1982) recruimen funcion 14 : (7) η r(1 ε ( S2 ) ) S2 + S 2 R(..) =, γ S2 + S 2 1+ K 14 The Sheperd funcion produces he Cushing recruimen funcion when γ<1, he Beveron Hol recruimen funcion when γ=1, and he Ricker recruimen funcion when γ>1. 19

where r is he maximum recruis per spawning salmon, and K is he sock level where densiy dependen moraliy facors sar o dominae sock independen facors. 15 inally, he compensaion parameer γ is he degree o which densiy-independen effecs compensae for changes in sock size. The baseline parameer values are given in Appendix A. The pre- invasion recruimen is found by seing X = 0. Noe ha he marginal negaive ecological growh effec of ES is consan when η = 1, decreasing for η < 1, and increasing when η> 1. In he numerical simulaions we assume 1 η = and ha he resricion ( X ) 1 ε < holds 16. Turning o he economic funcions, we sar ou by defining he inverse demand funcion when here are no ES (pre invasion): (8) PDX (,, X ) =αqs1 β D. The choke price α gives he maximum willingness o pay when he qualiy-ranslaed cach is one fish per day, whereas β reflecs he price response in a sandard manner. In he case of invasion, he inverse demand funcion is specified as follows ( ) θ S 2 (9) PDX (,, X ) =α q S1 bs1 D w + β. S 2 15 Noe ha he numbers repored in Hvidsen e al. (2004) are measured as recruis per egg per square mere. However, we have ranslaed hem ino he corresponding number of recruis per spawning salmon in he river (available on reques). 16 leming e al (2000) show in a conrolled experimen ha he produciviy of he naives are depressed by 30% when he share of farmed o naives in he spawning populaion were 57%. However, if here is an increasing or decreasing marginal negaive impac is no analysed as i is a one-sho experimen. 20

Noe ha equaion (9) reduces o (8) when here are no ES presen. The ambiguous demand effecs following ES are easiliy recognised in equaion (9). The demand increases via he cach per day-channel inducing he economic quaniy effec in he erm α qs1. On he oher hand, he proporion of farmed fish in he oal sock increases, leading o he economic qualiy effec ha operaes via he las erm on he righ-hand side. The specificaion of he economic qualiy effec means ha when X >0, he inverse demand increases a a decreasing rae wih X in he P-X plane, as explained in secion 4. This means ha he smaller he level of he wild sock is, he more he increased invasion reduces demand hrough he economic qualiy effec (more on his below). All parameers are defined and he baseline values are given in Appendix A. inally, he cos funcion is specified as CD ( ) = c0 + cd, where c 0 and c are he fixed and he marginal coss of providing fishing permis, respecively. Wih hese specificaions, in he pos-invasion case, we express he number of fishing permis from he dπ firs-order condiion, = 0, as: dd (10) S 2 α q( S1+ S1 ) c w S 2 D = 2β θ. The pre-invasion demand is found simply by inroducing X = 0 (and hus S 1 = S 2 = 0 ). Noe ha alhough he share of ES in he spawning sock influences demand direcly, equaion (10) reflecs he fac ha landowners do no see heir own fishing permi sales as an insrumen o influence his share. One possible reason for his is ha a very small proporion of he river cach consiss of ES. On he oher hand, his would be an argumen for he landowners o decrease heir harves in order o increase he share of wild salmon in he 21

spawning sock. However, consisen wih our assumpion ha hey are myopic, he landowners ignore he spawning sock, including he composiion of wild and farmed spawners. Noe ha wih no economic qualiy effec in demand, w = 0, he equilibrium condiion shifs up in he X-D plane when X > 0, and ha he slope of he equilibrium condiion changes when w > 0 and X > 0 (see also discussion above and Appendix C for deails). Recall also ha D is more likely o increase in X, he higher X is, as he negaive economic qualiy effec diminishes. In addiion, we find ha when demand is generally higher for a given sock size, as indicaed by an increase in α, hen D is more likely o increase wih X. By conras and for obvious reasons, when anglers are more concerned abou negaive ES effecs ( w ) his works in he oher direcion. 6.2 Resuls Table 2 repors he resuls in he pre- and pos-invasion siuaions wih he baseline parameer values. Noe ha he escapemen only modesly affecs he sock because he ES have wo conradicory effecs on he wild sock (see above). Consequenly, in he pos-invasion case, he marginal sock change is larges when he escapemen rae is low. or example, his could be a siuaion where safey invesmens in he sea farming indusry have reduced he escapemen rae, or where aquaculure is abandoned in some fjords in order o esablish naional farming free zones. 17 In addiion, noice ha he fishing effor increases when he number of ES shifs from he pre-invasion case, where ES=0, o he pos-invasion case, where ES=2000, and i is almos he same as pre-invasion when ES=4000. However, increasing he number of ES furher decreases he fishing effor because of he increasing economic qualiy effec, even if he sock increases. In addiion, noice ha he wild sock is no sricly increasing wih an increased level of ES, meaning ha, for he baseline parameer 17 The Norwegian governmen imposed his regulaion on some fjords in 2003. The fjord where he river Orkla runs ou (Trondheimsfjorden) was esablished as one of he farming free zones. 22

values, he negaive ecological growh effec dominaes when he proporion of ES reaches a cerain level. TABLE 2 ABOUT HERE urher, in he pos-invasion siuaion, we find ha he profi may rise because of an increase in he invasive sock (he direc economic quaniy effec). Comparing ES=0 and ES=2 shows ha he sock increase causes an increase in he number of fishing days, wihou affecing he permi price. This highlighs an imporan fac, which is ha, given an invasion, he equilibrium profi may rise wih an increasing yearly influx. In oher words, he yearly influx may hide he reduced biomass producion rae. However, as long as he share of ES in he spawning sock maers o he anglers, hen a higher invasion level will mean he economic qualiy effec increases in imporance. Hence, he fishing effor and profis may fall dramaically. Noe ha he angler surplus, and hus he oal surplus in he river, follows he exac same paern as he monopolisic profi. The decreasing price follows direcly from he negaive economic qualiy effec on demand. or he baseline invasion level, ES=6000, he ES levels in he marine harves and he river harves are 25% and 8% respecively, whereas 48% of he spawning sock consiss of ES. Now, we urn o a siuaion where he anglers consider "a fish as a fish", boh in heir harves and in he spawning sock. 18 This means ha he las erm in he inverse demand funcion is negleced, w=0. The only way ha he ES ranslae direcly ino demand is hrough he effec on he overall sock. The sock increases modesly as he number of ES increases. In addiion, boh he fishing effor and permi prices increase due o he economic quaniy effec. 18 i.e. anglers are no concerned wheher salmon is farmed or wild 23

The resuls repored in able 3 hence reflec his siuaion, where he ecological level effec on he wild sock dominaes he ecological growh effec. Thus, one problemaic aspec of invasion is hidden when here is no economic qualiy effec. When he economic qualiy effec applies, he ex-pos wild sock is always higher han in he absence of his effec. This is because he fishing effor is higher when anglers are no concerned abou he number of reared fish in he populaion. The profi, he angler surplus, and hence, he oal surplus, are sricly increasing as he number of ES increases. In he baseline case when ES=6000, 26% of he marine harves, 9% of he river spor harves, and 71% of he spawning sock consis of farmed salmon. This means ha when here is an economic qualiy effec, he proporion of farmed o wild salmon in he spawning sock is reduced. However, he manner in which he concern abou invasive species reduces his share hrough he economic qualiy effec is no sraighforward. When demand is reduced because of he economic qualiy effec, he share of wild salmon in he spawning sock increases relaive o he reared salmon share because he anglers mainly cach wild fish. Therefore, he mechanism is no he resul of any deliberae acion by he anglers o decrease he share of reared fish in he spawning sock, bu raher, i is a forunae consequence of reduced demand. TABLE 3 ABOUT HERE 7. Concluding Remarks The paper demonsraes four differen mechanisms ha may be imporan when escaped reared species mix wih heir wild congeners, and hereby, we reveal some imporan policy implicaions. Our resuls indicae ha, even if he growh rae of he wild species is reduced, 24

he oal sock may increase when here is an ecological invasion. Hence, measures o reduce an invasion may very well reduce he overall surplus because less biomass will be available for harves. On ineresing resul is ha, if here is no economic qualiy effec, he harvesing effor will be higher due o he economic quaniy effec and, hence, he sock will be less han before he invasion. In his case, he profi and he angler surplus will always be higher ex pos he invasion, and boh will increase wih invasion of he farmed species. Thus, one consequence ha follows direcly from he analyses is ha reporing he share of invasive species in an ecosysem may reduce he demand for harvesing he wild species. This will in urn increase he wild sock and depending on he composiion of he cach, he share of residen species in he ecosysem may increase. inally, he effec on overall surplus of shuing down one sequenial harves aciviy in he case of an invasion is generally ambiguous because he share of he invasive species in he spawning populaion (or ecosysem) may increase (see Appendix B). The mechanisms discussed in he paper may be ransferable o oher siuaions where escaped farmed animals mix wih heir wild congeners, or where an ecosysem faces a yearly influx of invasive species for any reason. We have demonsraed ha, even aking invasive damage ino accoun, in many insances, he overall surplus may rise following an invasion. Of course, his may have implicaions for incenives o reduce he escapemen of farmed species. As shown, paricipans in he harves may wan invasions o persis. Perhaps more imporanly, hese economic forces, or lack of incenives, may explain why policymakers mus inervene if hey wan o reduce invasions. On he oher hand, one ineresing exension of he model developed here is o incorporae a social planner managing boh he marine and he recreaional fishery, as he oucome of such planning wih respec o profi, angler surplus and share of invasive in he spawning sock seems far from clear cu. Making he model more realisic by including 25

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