MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 530: 223–232, 2015doi: 10.3354/meps11135

Published June 18

INTRODUCTION

Fishing is an important economic, social and cul-tural activity for many communities in the world.Global marine fisheries currently directly and indi-rectly support 35 million jobs, generating a US$ 35billion fishing household income and US$ 8 billionprofits a year (Arnason et al. 2009). It provides em -ployment in fishing, processing, and ancillary serv-ices, as well as through subsistence-based activitiesat the community level (Roy et al. 2009, Teh 2011,Teh et al. 2011). The economic impact of marine fish-eries to the world economy was estimated at US$ 220to 235 billion in 2003 (Dyck & Sumaila 2010). Nearly

1 billion people worldwide, or about 20% of theglobal population, rely on fish as a primary source ofanimal protein (FAO 2011). In many cases, fishing isundertaken for economic and/or social benefits suchas revenues and livelihoods. But there is increasingfocus on the impacts of over-exploitation on the con-servation of marine species (Dulvy et al. 2003,Sadovy de Mitcheson et al. 2013), and the need toshift to ecosystem-based fisheries management(Pitcher & Lam 2010). This means that fisheries man-agement needs to achieve a more balanced portfolioof objectives.

The trade-offs between economic, social and con-servation objectives become severe when the vulner-

© Inter-Research 2015 · www.int-res.com*Corresponding author: w.cheung@fisheries.ubc.ca

Economic incentives and overfishing:a bioeconomic vulnerability index

William W. L. Cheung1,*, U. Rashid Sumaila2

1Changing Oceans Research Unit and 2Fisheries Economics Research Unit, University of British Columbia, 2202 Main Mall,Vancouver, BC V6T 1Z4, Canada

ABSTRACT: Bioeconomic theory predicts that the trade-offs between maximization of economicbenefits and conservation of vulnerable marine species can be assessed using the ratio betweenthe discount rate of fishers and the intrinsic rate of growth of the exploited populations. In thispaper, we use this theory to identify areas of the global ocean where higher vulnerability of fishesto overfishing would be expected in the absence of management. We derive an index to evaluatethe level of vulnerability by comparing discount rates and fishes’ intrinsic population growth rates.Using published discount rates of countries that are reported to fish in the ocean and estimatingthe intrinsic population growth rate for major exploited fishes in the world, we calculate the vulnerability index for each 0.5° latitude × 0.5° longitude grid for each taxon and each fishingcountry. Our study shows that vulnerability is inherently high on the northeastern coast of Canada, the Pacific coast of Mexico, the Peruvian coast, in the South Pacific, on the southern andsoutheastern coast of Africa, and in the Antarctic region. It should be noted that this index doesnot account for the management regime currently in place in different areas, and thus mainlyreflects the vulnerability resulting from the intrinsic life history characteristics of the fish speciesbeing targeted and the discount rates of the fishers exploiting them. Despite the uncertainties ofthis global-scale analysis, our study highlights the potential applications of large-scale spatialbioeconomics in identifying areas where fish stocks are more likely to be over-exploited whenthere is no effective fisheries management; this applies to many fisheries around the world today.

KEY WORDS: Vulnerability · Discount rate · Overfishing · Fisheries · Spatial bioeconomics

Resale or republication not permitted without written consent of the publisher

Contribution to the Theme Section ‘Economics of marine ecosystem conservation’ FREEREE ACCESSCCESS

Mar Ecol Prog Ser 530: 223–232, 2015

ability of exploited species to fishing and the in cen -tive for overfishing are both high (Norse et al. 2012).In some extreme cases, fishing can drive species orstocks to local or near global extinction. For example,the Chinese bahaba Bahaba taipengensis in theSouth and East China Seas is inherently highly vul-nerable to fishing because of its large body size andits tendency to form spawning aggregations. The spe-cies is considered to be Critically Endangered underthe IUCN Red List of Endangered Species (www.redlist.org) primarily because it is highly targeted forits extremely valuable swimbladder as a traditionalChinese medicine (Sadovy & Cheung 2003). Anotherexample is the sea otter Enhydra lutris, which washunted to near extinction along the North Americancoast for the fur trade (Doroff et al. 2003).

Life history and population dynamic theories predictthat fish populations with a low reproductive rate areintrinsically more vulnerable to over-exploitation(Reynolds et al. 2005). This applies particularly tofishes that are large, slow-growing and late-maturing(Cheung et al. 2005). When subjected to similar fish -ing mortality rates, abundance of species with higherintrinsic vulnerability decrease faster than specieswith lower vulnerability, all else being equal (Cheung& Pitcher 2008). This systematic difference in sensitiv-ity to fishing between fish species is partly the reasonbehind the increasing dominance of less vulnerablefish species in global fish catches (Cheung et al. 2007).However, such intrinsic vulnerability does not accountfor non-biological factors, such as intensity of fishing,which ultimately determine the level of fishing mor-tality and exploitation status of the populations.

Bioeconomic theory predicts that optimal fishingstrategy is a function of the productivity of the ex-ploited population (represented by the intrinsic rate ofpopulation increase), cost of fishing, price of the catchand the discount rate (Clark 1973). A common driverof overfishing is the open access nature of fisheries re-sources, under which each fishing unit seeks to maxi-mize its own benefits from fishing, leading to over-ex-ploitation of the resources. Moreover, the discountrate determines how much the flow of future costs andbenefits is discounted to obtain the net present value.Thus, a high discount rate means that we value cur-rent benefits much more than those we can get (orlose) in the future (Sumaila 2004). Given this situation,it would be economically reasonable to increase thecurrent exploitation of the resource, particularly if wewill only incur the costs associated with such an actionin the distant future (Sumaila & Walters 2005). In fish-eries, fishers are considered to have their own privatediscount rate that is based on the intuitive discounting

they apply in their decision-making processes. How-ever, the private discount rate of fishers has only beenestimated in a few cases (e.g. Fehr & Leibbrandt 2008,Teh et al. 2009). According to Clark (1973), when thediscount rate is higher than the intrinsic rate of popu-lation increase, and all else being equal, the economi-cally optimal fishing strategy would be to overfish thestocks. When the discount rate is much higher thanthe fishes’ population growth rate, the theory predictsthat it is economically rational to drive fish stocks toextinction (Clark 1973). Thus, we can expect that fishstocks in regions where discount rates are high whilepopulation growth rate is low would have a relativelyhigher vulnerability to overfishing.

A range of fisheries management strategies andtactics have been proposed to ensure the sustainabil-ity of fisheries (Walters & Martell 2004). Some are‘command-and-control’ type management measuresthat manage fisheries through limiting fishing orother activities, e.g. marine protected areas, whileothers are ‘incentive’-based measures that use eco-nomic or other incentives to encourage sustainablefishing practices, e.g. transferrable quotas. However,these measures have their pros and cons. Under-standing the key drivers and vulnerability to over-fishing provides useful information for identifyingsuitable strategies and tactics to effectively managethe fisheries.

In the present study, we aimed to identify, on aglobal scale, the bioeconomic vulnerability of fishesto overfishing. We derived an index to evaluate thevulnerability resulting from both the intrinsic biolog-ical characteristics and the economic factors that maylead to overfishing. We collected published discountrates of countries that are reported to fish in theocean. We estimated the intrinsic population growthrate for major exploited fish species in the world.Finally, using these estimates, we calculated thebioeconomic vulnerability index on a 0.5° latitude ×0.5° longitude grid for each taxon and fishing countryfrom the ‘Sea Around Us’ project and identified areaswhere the potential for overfishing is most severe.We discuss the potential application of such an indexto the evaluation of fisheries management options.

METHODS

Deriving a bioeconomic vulnerability index

Clark’s theory (Clark 1973) shows that under cer-tain conditions, when the discount rate of a privatefishing unit (δ) is equal to or higher than the intrinsic

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Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing

population growth rate (r) of a given fish species, theeconomically optimal fishing strategy would be tooverexploit the targeted stock. The biological compo-nent of this model is based on a simple Schaefermodel, in which

(1)

where X is the biomass and N is the carrying capac-ity. Marginal change in population growth can beobtained by differentiating Eq. (1) with respect to X:

(2)

Thus,limX0 F’(X) = r (3)

Assuming the fisheries manager’s goal is to maxi-mize the present value (PV) of profits from the fish-ery, maximum PV can be determined as follows:

maxPV = ∫0∞ e–δ(p – c(X))Y(t)dt (4)

where p is the unit price of a catch, c(X) is the unitfishing cost, and Y(t) is the catch in period t. Solvingfor Eq. (4) results in a biomass level, X*, that gives theoptimal discounted profit (Clark & Munro 1975):

(5)

Eq. (5) is a re-expression of the golden rule of cap-ital theory for a renewable resource (Clark & Munro1975). The left-hand side of the equation is an ex -pression of the ‘own interest rate’, which is essen-tially the instantaneous return on fish left in theocean over a period of time. Specifically, the firstterm is an expression of the instantaneous marginalreturn on the fish, while the second term denotes theimpact of investment in X on the cost of fishing, c(X),which is called the Marginal Stock Effect (MSE)(Clark & Munro 1975). On the right-hand side, δdenotes the rate of return if a fish is caught and soldand the return is deposited in a bank account orinvested elsewhere. Eq. (5) therefore states that theeconomically optimal stock level of a species is ob -tained when the ‘own rate of interest’ of the fish isexactly equal to the discount rate.

Now, as X approaches 0, c(X) increases towards in -finity as it becomes more and more difficult to findand catch fish when using the same technology,which implies

lim(X*)0 F’(X*) = δ (6)

Combining Eqs. (1) and (5) and under the conditionthat the price per unit of fish > c(0) (means that itwould be worthwhile economically to catch every

fish in the ocean), Clark’s (1973) model shows thatthe necessary and sufficient conditions for overfish-ing and extinction as the economically rational fish-ing strategy under private resource ownership areδ > r and δ > 2 · r, respectively. Moreover, the modelimplies that a private owner of the fishery is indiffer-ent between ‘fish in the bank’ and ‘fish in the ocean’when the discount rate equals the intrinsic growthrate of the population.

Based on these conditions, we derived an index (θ)to indicate the risk of over-exploitation according tothe discount rate of the fisheries and the intrinsicpopulation growth rate of the exploited fishes. Thisindex is based on the assumption that δ > r is the suf-ficient and necessary condition to engage in overfish-ing, in which both δ and r are expressed as annualrates. Thus, we defined this index simply as

(7)

The index has a negative value when the discountrate of the fisheries is higher than the intrinsic popu-lation growth rate of the exploited population, andvice versa. Based on Clark (1973), a negative or lowindex value indicates strong incentive for over-exploitation. When δ ≥ 2 · r, and therefore θ ≤ −1, theincentive for over-exploitation is so high that it maydrive the species or stock to extinction.

Global fisheries catch data

We calculated the bioeconomic vulnerability indexfor all major exploited fish species in the world.These include 852 taxa of marine fishes that arereported at the species, genera and family levels bythe United Nations Food and Agriculture Organiza-tion (FAO). In 2005, these taxa made up 84% of theglobal reported fish catch and were exploited by 178countries. We extracted spatially-explicit catch dataon a 0.5° latitude × 0.5° longitude grid for each taxonand each fishing country from the global catch data-base of the Sea Around Us project (see www.seaaroundus.org and Watson et al. [2004] for thedetailed description of the database development).

The Sea Around Us catch data (www.seaaroundus.org) originates from a range of sources including theFAO fisheries database supplemented by regionaldatasets, e.g. from the International Council for theExploration of the Sea (ICES) for Europe. Details ofthe spatial allocation of catches are documented inWatson et al. (2004). It is quality-checked and map -ped to a grid of (0.5° × 0.5°) spatial cells using a rule-based approach based on original spatial informa-

( )= ⋅ ⋅( ) 1–F X r XXN

( )= ⋅’( ) 1–2

F X rX

N

⋅ = δ’( *) –’( *) ( *)

– ( *)F X

c X F Xp c X

( )θ = δ1–

r

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Mar Ecol Prog Ser 530: 223–232, 2015

tion, the operation of fleets in the Exclusive EconomicZone of maritime countries (e.g. through docu-mented access agreements) and the known habitat-driven distribution of the reported marine taxa. As aresult, the location (0.5° × 0.5° cell) of each fishingnation’s catch and the quantity caught were obtainedfor each year and for each reported taxon from thisdataset.

Discount rate by fishing countries

The most readily available discount rate data is theofficial country-level discount rate. We collated suchdata for all fishing countries. For countries whereofficially published discount rates were not available,we assumed that the average Central Bank lendingrates are proxy of their discount rates, obtained fromstatistics published by the International MonetaryFund. For countries that did not pub lish such data,we used the discount rates as sumed by the WorldBank, which were 7 and 10% for developed anddeveloping countries, respective ly (see Table S1 inthe Supplement at www.int-res. com/articles/suppl/m530p223_supp.pdf for the list of country-level dis-count rate used). It is worth noting that the WorldBank’s discount rates have been used in economicanalysis of other global-scale fisheries, such as ‘theSunken Billions’ by Arnason et al. (2009).

Because country-level discount rates may not re -flect the discount rate of the private sector and maylargely underestimate the discount rate of the fishingsector (Teh 2011, Teh et al. 2014), we attempted toestimate the private discount rate of the fishing sector.However, the availability of empirically estimatedprivate discount rates is very limited. Available esti-mates for fisheries in Ghana (Akpalu 2008), Sabah(Malaysia) and Fiji (Teh 2011) range from 130 to200% (Teh et al. 2014). We used these figures todetermine the potential private discount rate for thefisheries in each country. Since the published dis-count rates are mainly for fishers in developing coun-tries, we divided fishing countries into low, mediumand high development according to their publishedHuman Development Index. Based on our collateddata, the average country-level discount rates of lessdeveloped countries were assumed to be 1.5 and 2times higher than the discount rates of moderatelyand highly developed countries, respectively. Thus,we assumed that fishers in the moderately developedcountries have a discount rate of 165% (median ofthe available private discount rate estimates for thefishing sector), while the highly and less developed

countries were assigned discount rates of 110 and220%, respectively.

Estimating intrinsic population growth rate (r)

We estimated the intrinsic population growth rate(Table S2 in the Supplement) based on the Euler-Lotka method (McAllister et al. 2001). In this method,r is approximated from the following equation:

∑Aa = 0 e–r · a · la · ma = 1 (8)

where a and A are the age-class and longevity of thepopulation, respectively; la is the expected survivor-ship of females from age 0 to age a; and ma is theexpected number of age-0 female offspring per indi-vidual female or fecundity at age a.

We estimated the parameters in Eq. (8) using Eqs.(9−13) and then solved for r iteratively, using anumerical minimization function (Solver in MicrosoftExcel). We assumed a Beverton-Holt recruitmentfunction and expressed it as a function of the steep-ness parameter h, defined as the recruitment whenspawning biomass is 20% of the unfished level (Man-gel et al. 2010). In general, h scales between 0.2 to 1(Mangel et al. 2010).

Thus,(9)

and

(10)

where B0 is spawning biomass and and R0 is recruit-ment of the unfished population, and thus, B0/R0 isthe unfished equilibrium spawning biomass per re -cruit. α and β are paramaters determining the shapeof the Beverton-Holt stock recruitment function. B0/R0

is calculated from

(11)

where ρa is the proportion of sexually maturedfemales at age a. We assumed a knife-edge maturityschedule in which all females become mature afterthe age of maturity; Wa is the weight-at-age that isestimated from the von Bertalanffy growth function:

Wa = W∞ · [1 – e–k(a–t0)]3 (12)

where W∞ is the asymptotic weight, k is the growthparameter and t0 is the theoretical age-at-birth.

Recruit (fecundity) per spawning biomass (ma) wascalculated using the following:

(13)

⋅ =α + β

0.20.2

00

0h R

BB

BR

hh

α = 1 –4

0

0

∑= ⋅ ⋅ρ=0

00

BR

W laA

a a a

= ⋅ ρm

Ba

aa a

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Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing

Biological parameters were obtained from onlinedatabases. Life history parameters, including the vonBertalanffy growth parameters, age-at-maturity,longevity and natural mortality rates for all the 852species were obtained from the FishBase database(www.fishbase.org). For higher taxonomic level taxa(genus and family levels), the average values of thespecies belonging to the same genus and family wereused.

Since estimates for the steepnessparameter h are not available for mostof the species, we used a range of val-ues of h reported in published studies(see Myers et al. 1999). A meta-analy-sis of over 700 stock−recruitmentrelationships al lo w ed for the estima-tion of average steepness h para -meters for 57 fish species (Myers et al.1999). These estimated h parametershave a median of 0.62 and an upper(75%) and lower (25%) quartile of0.82 and 0.48, respectively. We calcu-lated the mid-, upper- and lower-range estimates of r by applying themedian upper and lower quartile val-ues of the h parameter to Eq. (13).This also provided the mid-, upper-and lower-range estimates of the vul-nerability index (Eq. 7).

Using the estimated intrinsic popu-lation growth rate r (expressed asannual rate) and discount rate δ, wecalculated the vulnerability index foreach taxon− fishing country combina-

tion. We then calculated an average vulnerabilityindex for all taxon− fishing country combinationsweighted by their catch (Fig. 1). This was repeatedfor all the spatial cells using estimates of r under themid-, upper- and lower-range values.

RESULTS

Our results show that bioeconomic vulnerabilitywas high in many regions. Regions with high vulner-ability to overfishing are indicated by cells with ahigh negative bioeconomic vulnerability index value.Considering all the 852 fish taxa included in thisstudy and assuming that fisheries operated with theofficial country-level discount rate, vulnerability tooverfishing was predicted to be high in the followingregions: northeastern coast of Canada, the Pacificcoast of Mexico, Peruvian coast, South Pacific (off-shore of New Zealand in particular), southern andsoutheastern coast of Africa, and the Antarctic region(Fig. 2A). Regions with the highest vulnerabilityinclude the central East Pacific, Southern Ocean andAntarctic region.

Vulnerability calculated based on estimates fromcountry-level discount rates probably largelyunderestimated the potential vulnerability because

227

Fig. 1. Schematic summarizing the algorithm developed tocalculate the bioeconomic vulnerability index in each 0.5°latitude × 0.5° longitude cell of the world ocean. Thicknessof arrows represents the weight of a fish taxon (1, 2, 3, etc.)caught by a country (A, B, C etc.) with the respective dis-count rate δ (δA, δB, δC, etc.) while r (r1, r2, r3, etc.) is the esti-mated intrinsic rate of population increase of a fish pop-

ulation

Fig. 2. Bioeconomic vulnerability index (BVI) of all exploited fishes calculated based on (A) country-level and (B) private discount rates

Mar Ecol Prog Ser 530: 223–232, 2015

of the difference between country-level and private-discount rates.When estima ted private discountrates were used instead of country-level discount rates, most of theworld ocean became highly vulner-able to overfishing (bioeconomicvulnerability in dex < 0) (Fig. 2B).Particularly, regions with high vul-nerability expanded into the Medi-terranean Sea, mid-Atlantic, Arctic,west and south coast of Australiaand the central Pacific.

When demersal and pelagic fisheswere analyzed separately, differentpatterns of vulnerability to overfish-ing emerged (Fig. 3). Because of thehigh catch of pelagic fishes, the vul-nerability index for all fishes weigh -ted towards the pelagic groups(Fig. 3A,B). Thus, the general patternof vulnerability of pelagic fishes issimilar to that of all fishes, except insome areas in the Arctic and aroundthe Antarctic where pelagic fisheswere not reported. For demersalfishes, high vulnerability areas areconcentrated in the continental shelfregion (Fig. 3C,D). Vulnerability isparticularly high offshore of the cen-tral eastern Pacific, southwest At -lantic, around Iceland, south of theIndian coast and the Indo-Pacificregion.

The high vulnerability to overfish-ing in many regions is largely drivenby high discount rates, while insome regions low intrinsic growthrates also contribute to it (Fig. 4). Inmost areas, the average intrinsicgrowth rate weighted by the catchof each taxon ranges from 0.1 to 0.5.The Arctic (along the north coast ofNorth America) and the Antarcticshow high average intrinsic rates asa result of the low diversity ofexploited fish with mostly slow-growing life histories. Country-leveldiscount rates are highest in thesouthwest Atlantic, part of the central Atlantic andPacific and the Indo-Pacific regions. Private dis-count rates are high in most of the world oceans,particularly the Canadian Arctic, the central and

southeast Pacific, West African coast, the westernIndian Ocean, and around New Zealand. In theseregions, private discount rates were estimated to beover 180%.

228

Fig. 3. Bioeconomic vulnerability index (BVI) for pelagic (A,B) and demersal(C,D) fishes calculated based on (A,C) country-level and (B,D) private discount

rates

Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing

DISCUSSION

The bioeconomic vulnerability in -dex highlighted areas where the in -trinsic risk of over-exploitation fromfishing is relatively higher. Some ar-eas identified as vulnerable coincidewith regions that are identified asover-ex ploited or rebuilding fromoverfishing (Worm et al. 2009), in clu -ding the northeastern coast of Cana daand the Pacific coast of Mexico. How-ever, the index does not consider theeffectiveness of existing fisheriesmanagement measures. Thus, fisher -ies in areas with high bioeconomicvulnerability, such as the watersaround New Zealand, may not beover- exploited because of effectivemanagement. On the other hand, ar-eas with poor fishe ries managementeffectiveness, such as in fisheries ofsome developing countries, could bemore vulnerable to over-exploitationthan areas in New Zea land waters.Moreover, the vulnerability of devel-oping countries’ regions may be un-der-estimated be cause of the lack ofgood-quality fisheries data.

Our results highlight the potentiallytough trade-off in fisheries manage-ment in many parts of the worldocean. Such a trade-off is expected tobe most intense in areas where vul-nerability to overfishing is high;meaning that the economic incentiveto over-exploit is strong for the fishingindustry and the society, while pro-ductivity of fishes is low. In theseareas, effective fisheries management is more ur -gently needed, if not already implemented, to helpprotect the vulnerable ecosystem. For example, if themain driver for the high discount rate at the countryand private levels is poverty, alleviating poverty inthese regions should be a priority (Brashares et al.2014). In cases where a large part of the distributionrange of low-productivity species falls within theseregions, fishing may greatly increase the risk of over-exploitation. Creating marine reserves, to protectsuch species, may become a necessary strategy tosafeguard their continued existence.

A ‘win-win’ solution between conservation andeconomic gains is most likely in areas where bio -

economic vulnerability at both country and privatelevels is low, while the average intrinsic populationgrowth rates of the exploited species are high. Anexample is the Gulf of Alaska. Since there is reason-able economic incentive for conservation, a range offisheries management options is likely to be effec-tive. It has been suggested that the effectiveness ofdifferent governance systems (e.g. command-and-control, privatization, exclusive fishing rights, allo-cated quotas, self-governance and co-management)in achieving sustainable fisheries management isdependent on the difference in discount rates be -tween regulators (e.g. the state) and fishers (Sumaila& Domínguez-Torreiro 2010). In this case, since the

229

Fig. 4. Parameters that were used to calculate the bioeconomic vulnerabilityindex: (A) average intrinsic growth rate of the exploited fishes, (B) country-level discount rate, and (C) private discount rates of the fishing countries in

each 0.5° × 0.5° cell

Mar Ecol Prog Ser 530: 223–232, 2015

motivation to conserve by both the fishing sector andthe regulator is likely to be high, management poli-cies that involve self-governance or co-managementcould be effective.

Various uncertainties exist that may affect theinterpretation of the bioeconomic vulnerability in -dex at the global scale. Because our study is at aglobal scale, it does not represent detailed regionaland local differences in the ecology and socio-eco-nomics of fisheries. For example, intrinsic popula-tion growth rate and discount rate can vary betweendifferent stocks (for a species), regions and time. Inthe future, regional applications of the index couldbetter reflect complexity at finer spatial scales. Onthe other hand, fisheries and socio-economic dataare largely limited in many regions, particularly ineconomically developing areas. The broad global-scale approach em ployed in this study allowed us toevaluate general patterns and highlight priorityareas for further ana lysis. Empirically estimated dis-count rates for fishing countries and fishers arerarely available. Thus, we had to make assumptionsin estimating the discount rates, which may notaccurately reflect the true values. Specifically, weused the limited available estimates of private dis-count rate for fisheries, which are largely from de -veloping countries and small-scale fisheries, andextrapolated these to developed regions and large-scale fisheries albeit after using the Human Devel-opment Index to differentiate countries.

It is worth noting that the discount rates of develop-ing countries and small-scale fisheries may be muchhigher than other fisheries in developed countries,and that the validity of the extrapolation of discountrates assumed in our study is uncertain. Thus, vulner-ability of some of the fisheries may be over-estimatedwhen the extrapolated private discount rates wereused. Similarly, estimated intrinsic rates of popula-tion increase are considered an ap proximation, withone of the main uncertainties being the estimation ofthe steepness parameter h. Our analyses suggest thatalternative estimates of discount rate and intrinsicrate of population increase affect the absolute valuesof the vulnerability index. However, the relative dif-ferences in vulnerability between regions are gener-ally robust to alternative values of δ and r. Theadvantage of our approach is that the range of dis-count rates and intrinsic growth rates used in theanalysis can easily be varied and the model re-run.

Calculated vulnerability may vary depending onthe structure of the algorithm used in calculating thevulnerability index. For example, the vulnerabilityindex does not incorporate the marginal stock effect

(Clark & Munro 1975, Clark et al. 1979) or the effectsof detrimental subsidies to fishing (Sumaila et al.2010), which would affect the incentive to overfish.Moreover, populations may interact ecologicallythrough trophic linkages or technically through, e.g.bycatch, and this may affect their vulnerability.These secondary effects of fishing are not captured inthe index. On the other hand, there are trade-offs be -tween having a simple index with known structuraluncertainty and a complex index that increases datauncertainty. For example, the Ocean Health Index(Halpern et al. 2012) is a comprehensive index toevaluate ocean sustainability. However, it is dataintensive, and so the uncertainty associated with thelarge number of input data may complicate its interpretation. We opt for the earlier option as theprimary objective of this study is to broadly identifyareas of the world ocean with high potential vulner -ability to overfishing. The global focus of the analysisand the inclusion of a large number of exploited species favour the use of a simple index that is of pol-icy relevance.

Future studies should examine other factors notexplored in this analysis that may affect the vulner -ability of the exploited populations. We did not in -clude invertebrate fisheries in this study. Since inver-tebrates are generally more resilient to overfishingrelative to fishes, this study may over-estimate thevulnerability of regions where invertebrates are animportant part of the fishery. Further studies canapply the vulnerability index described here to theinvertebrate fisheries. These would include the in -corporation of the marginal stock effect and subsidiesinto the assessment of vulnerability and effectivenessof existing fishing management measures. Particu-larly, the established global databases on fish prices(Sumaila et al. 2007, Swartz et al. 2013), fishing cost(Lam et al. 2011), fishing effort (Anticamara et al.2011) and subsidies (Sumaila et al. 2010) would facil-itate such an analysis. Also, we propose that there isa need to carry out more studies on public and pri-vate (fishing sector) discount rates to improve ourunderstanding of the economic drivers of over-exploitation.

CONCLUSIONS

Using the bioeconomic vulnerability index devel-oped in this paper, we show that some areas of theworld ocean are likely to face difficult trade-offsbetween conservation and exploitation. Exploitedfish populations in these regions have relatively low

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Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing

intrinsic biological vulnerability to fishing (low intrin-sic rate of population increase) while the economicincentive to over-exploit, driven by high discountrates, is strong. In contrast, areas with low vulnerabil-ity suggest that conservation and fishing exploitationcould coexist without much conflict of interest.Future incorporation of the marginal stock effects,subsidies, im proved biological and economic datacould refine the general picture depicted in thisstudy. Studies that incorporate an analysis of howexisting management arrangements are likely toaffect the patterns identified in the current contribu-tion would be very interesting.

Acknowledgements. This project is funded by the PewCharitable Trust through U.R.S.’s Pew Marine Conservationfellowship. W.W.L.C. acknowledges funding support fromthe National Geographic Society, Natural Sciences andEngineering Research Council of Canada, and NipponFoundation. We thank M. L. D. Palomares for provision ofdata from FishBase.

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Submitted: March 17, 2014; Accepted: November 24, 2014 Proofs received from author(s): March 8, 2015

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