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MARINE ECOLOGY PROGRESS SERIES
Mar Ecol Prog Ser
Vol. 530: 223–232, 2015
doi: 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$ 35
billion fishing household income and US$ 8 billion
profits a year (Arnason et al. 2009). It provides em -
ployment in fishing, processing, and ancillary serv-
ices, as well as through subsistence-based activities
at 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$ 220
to 235 billion in 2003 (Dyck & Sumaila 2010). Nearly
1 billion people worldwide, or about 20% of the
global population, rely on fish as a primary source of
animal protein (FAO 2011). In many cases, fishing is
undertaken for economic and/or social benefits such
as revenues and livelihoods. But there is increasing
focus 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 to
shift to ecosystem-based fisheries management
(Pitcher & Lam 2010). This means that fisheries man-
agement needs to achieve a more balanced portfolio
of 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 economic
benefits and conservation of vulnerable marine species can be assessed using the ratio between
the discount rate of fishers and the intrinsic rate of growth of the exploited populations. In this
paper, we use this theory to identify areas of the global ocean where higher vulnerability of fishes
to overfishing would be expected in the absence of management. We derive an index to evaluate
the 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 estimating
the 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 fishing
country. 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 and
southeastern coast of Africa, and in the Antarctic region. It should be noted that this index does
not account for the management regime currently in place in different areas, and thus mainly
reflects the vulnerability resulting from the intrinsic life history characteristics of the fish species
being targeted and the discount rates of the fishers exploiting them. Despite the uncertainties of
this global-scale analysis, our study highlights the potential applications of large-scale spatial
bioeconomics in identifying areas where fish stocks are more likely to be over-exploited when
there 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 or
stocks to local or near global extinction. For example,
the Chinese bahaba Bahaba taipengensis in the
South and East China Seas is inherently highly vul-
nerable to fishing because of its large body size and
its tendency to form spawning aggregations. The spe-
cies is considered to be Critically Endangered under
the IUCN Red List of Endangered Species (www.
redlist.org) primarily because it is highly targeted for
its extremely valuable swimbladder as a traditional
Chinese medicine (Sadovy & Cheung 2003). Another
example is the sea otter Enhydra lutris, which was
hunted to near extinction along the North American
coast for the fur trade (Doroff et al. 2003).
Life history and population dynamic theories predict
that fish populations with a low reproductive rate are
intrinsically more vulnerable to over-exploitation
(Reynolds et al. 2005). This applies particularly to
fishes that are large, slow-growing and late-maturing
(Cheung et al. 2005). When subjected to similar fish -
ing mortality rates, abundance of species with higher
intrinsic vulnerability decrease faster than species
with lower vulnerability, all else being equal (Cheung
& Pitcher 2008). This systematic difference in sensitiv-
ity to fishing between fish species is partly the reason
behind the increasing dominance of less vulnerable
fish species in global fish catches (Cheung et al. 2007).
However, such intrinsic vulnerability does not account
for 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 fishing
strategy is a function of the productivity of the ex-
ploited population (represented by the intrinsic rate of
population increase), cost of fishing, price of the catch
and the discount rate (Clark 1973). A common driver
of 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 discount
rate determines how much the flow of future costs and
benefits 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 (or
lose) in the future (Sumaila 2004). Given this situation,
it would be economically reasonable to increase the
current exploitation of the resource, particularly if we
will only incur the costs associated with such an action
in the distant future (Sumaila & Walters 2005). In fish-
eries, fishers are considered to have their own private
discount 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 been
estimated in a few cases (e.g. Fehr & Leibbrandt 2008,
Teh et al. 2009). According to Clark (1973), when the
discount 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 the
stocks. When the discount rate is much higher than
the fishes’ population growth rate, the theory predicts
that it is economically rational to drive fish stocks to
extinction (Clark 1973). Thus, we can expect that fish
stocks in regions where discount rates are high while
population growth rate is low would have a relatively
higher vulnerability to overfishing.
A range of fisheries management strategies and
tactics have been proposed to ensure the sustainabil-
ity of fisheries (Walters & Martell 2004). Some are
‘command-and-control’ type management measures
that manage fisheries through limiting fishing or
other activities, e.g. marine protected areas, while
others are ‘incentive’-based measures that use eco-
nomic or other incentives to encourage sustainable
fishing 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 identifying
suitable strategies and tactics to effectively manage
the fisheries.
In the present study, we aimed to identify, on a
global scale, the bioeconomic vulnerability of fishes
to overfishing. We derived an index to evaluate the
vulnerability resulting from both the intrinsic biolog-
ical characteristics and the economic factors that may
lead to overfishing. We collected published discount
rates of countries that are reported to fish in the
ocean. We estimated the intrinsic population growth
rate for major exploited fish species in the world.
Finally, using these estimates, we calculated the
bioeconomic vulnerability index on a 0.5° latitude ×
0.5° longitude grid for each taxon and fishing country
from the ‘Sea Around Us’ project and identified areas
where the potential for overfishing is most severe.
We discuss the potential application of such an index
to 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 private
fishing unit (δ) is equal to or higher than the intrinsic
224
Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing
population growth rate (r) of a given fish species, the
economically optimal fishing strategy would be to
overexploit the targeted stock. The biological compo-
nent of this model is based on a simple Schaefer
model, in which
(1)
where Xis the biomass and Nis the carrying capac-
ity. Marginal change in population growth can be
obtained by differentiating Eq. (1) with respect to X:
(2)
Thus,
limX0F’(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 pis the unit price of a catch, c(X) is the unit
fishing cost, and Y(t) is the catch in period t. Solving
for Eq. (4) results in a biomass level, X*, that gives the
optimal 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 & Munro
1975). 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 the
ocean over a period of time. Specifically, the first
term is an expression of the instantaneous marginal
return on the fish, while the second term denotes the
impact of investment in Xon the cost of fishing, c(X),
which is called the Marginal Stock Effect (MSE)
(Clark & Munro 1975). On the right-hand side, δ
denotes the rate of return if a fish is caught and sold
and the return is deposited in a bank account or
invested elsewhere. Eq. (5) therefore states that the
economically optimal stock level of a species is ob -
tained when the ‘own rate of interest’ of the fish is
exactly equal to the discount rate.
Now, as Xapproaches 0, c(X) increases towards in -
finity as it becomes more and more difficult to find
and catch fish when using the same technology,
which implies
lim(X*)0F’(X*) = δ(6)
Combining Eqs. (1) and (5) and under the condition
that the price per unit of fish > c(0) (means that it
would be worthwhile economically to catch every
fish in the ocean), Clark’s (1973) model shows that
the necessary and sufficient conditions for overfish-
ing and extinction as the economically rational fish-
ing strategy under private resource ownership are
δ>rand δ> 2 · r, respectively. Moreover, the model
implies 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 growth
rate of the population.
Based on these conditions, we derived an index (θ)
to indicate the risk of over-exploitation according to
the discount rate of the fisheries and the intrinsic
population growth rate of the exploited fishes. This
index is based on the assumption that δ> r is the suf-
ficient and necessary condition to engage in overfish-
ing, in which both δand rare expressed as annual
rates. Thus, we defined this index simply as
(7)
The index has a negative value when the discount
rate of the fisheries is higher than the intrinsic popu-
lation growth rate of the exploited population, and
vice versa. Based on Clark (1973), a negative or low
index value indicates strong incentive for over-
exploitation. When δ≥2 · r, and therefore θ≤−1, the
incentive for over-exploitation is so high that it may
drive the species or stock to extinction.
Global fisheries catch data
We calculated the bioeconomic vulnerability index
for all major exploited fish species in the world.
These include 852 taxa of marine fishes that are
reported at the species, genera and family levels by
the United Nations Food and Agriculture Organiza-
tion (FAO). In 2005, these taxa made up 84% of the
global reported fish catch and were exploited by 178
countries. We extracted spatially-explicit catch data
on a 0.5° latitude × 0.5° longitude grid for each taxon
and each fishing country from the global catch data-
base of the Sea Around Us project (see www.sea
aroundus.org and Watson et al. [2004] for the
detailed description of the database development).
The Sea Around Us catch data (www.seaaroundus.
org) originates from a range of sources including the
FAO fisheries database supplemented by regional
datasets, e.g. from the International Council for the
Exploration of the Sea (ICES) for Europe. Details of
the spatial allocation of catches are documented in
Watson 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–FX r X X
N
()
=⋅’( ) 1– 2
FX r X
N
⋅=δ’( *) – ’( *) ( *)
–(*)
FX cX FX
pcX
()
θ=δ
1– r
225
Mar Ecol Prog Ser 530: 223–232, 2015
tion, the operation of fleets in the Exclusive Economic
Zone of maritime countries (e.g. through docu-
mented access agreements) and the known habitat-
driven distribution of the reported marine taxa. As a
result, the location (0.5° × 0.5° cell) of each fishing
nation’s catch and the quantity caught were obtained
for each year and for each reported taxon from this
dataset.
Discount rate by fishing countries
The most readily available discount rate data is the
official country-level discount rate. We collated such
data for all fishing countries. For countries where
officially published discount rates were not available,
we assumed that the average Central Bank lending
rates are proxy of their discount rates, obtained from
statistics published by the International Monetary
Fund. For countries that did not pub lish such data,
we used the discount rates as sumed by the World
Bank, which were 7 and 10% for developed and
developing countries, respective ly (see Table S1 in
the 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 World
Bank’s discount rates have been used in economic
analysis of other global-scale fisheries, such as ‘the
Sunken Billions’ by Arnason et al. (2009).
Because country-level discount rates may not re -
flect the discount rate of the private sector and may
largely underestimate the discount rate of the fishing
sector (Teh 2011, Teh et al. 2014), we attempted to
estimate the private discount rate of the fishing sector.
However, the availability of empirically estimated
private discount rates is very limited. Available esti-
mates for fisheries in Ghana (Akpalu 2008), Sabah
(Malaysia) and Fiji (Teh 2011) range from 130 to
200% (Teh et al. 2014). We used these figures to
determine the potential private discount rate for the
fisheries in each country. Since the published dis-
count rates are mainly for fishers in developing coun-
tries, we divided fishing countries into low, medium
and high development according to their published
Human Development Index. Based on our collated
data, the average country-level discount rates of less
developed countries were assumed to be 1.5 and 2
times higher than the discount rates of moderately
and highly developed countries, respectively. Thus,
we assumed that fishers in the moderately developed
countries have a discount rate of 165% (median of
the available private discount rate estimates for the
fishing sector), while the highly and less developed
countries were assigned discount rates of 110 and
220%, 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,
ris approximated from the following equation:
∑A
a= 0 e–r· a· la· ma= 1 (8)
where aand Aare the age-class and longevity of the
population, respectively; lais the expected survivor-
ship of females from age 0 to age a; and mais the
expected 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 riteratively, using a
numerical minimization function (Solver in Microsoft
Excel). We assumed a Beverton-Holt recruitment
function and expressed it as a function of the steep-
ness parameter h, defined as the recruitment when
spawning biomass is 20% of the unfished level (Man-
gel et al. 2010). In general, hscales between 0.2 to 1
(Mangel et al. 2010).
Thus,
(9)
and
(10)
where B0is spawning biomass and and R0is recruit-
ment of the unfished population, and thus, B0/R0is
the unfished equilibrium spawning biomass per re -
cruit. αand βare paramaters determining the shape
of the Beverton-Holt stock recruitment function. B0/R0
is calculated from
(11)
where ρais the proportion of sexually matured
females at age a. We assumed a knife-edge maturity
schedule in which all females become mature after
the age of maturity; Wais the weight-at-age that is
estimated from the von Bertalanffy growth function:
Wa= W∞· [1 – e–k(a–t0)]3(12)
where W∞is the asymptotic weight, kis the growth
parameter and t0is the theoretical age-at-birth.
Recruit (fecundity) per spawning biomass (ma) was
calculated using the following:
(13)
⋅=α+β
0.2
0.2
00
0
hR B
B
B
R
h
h
α=1–
4
0
0
∑
=⋅⋅ρ
=
0
0
0
B
RWl
a
Aaaa
=⋅ρ
mB
a
a
aa
226
Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing
Biological parameters were obtained from online
databases. Life history parameters, including the von
Bertalanffy growth parameters, age-at-maturity,
longevity and natural mortality rates for all the 852
species were obtained from the FishBase database
(www.fishbase.org). For higher taxonomic level taxa
(genus and family levels), the average values of the
species belonging to the same genus and family were
used.
Since estimates for the steepness
parameter hare not available for most
of the species, we used a range of val-
ues of hreported in published studies
(see Myers et al. 1999). A meta-analy-
sis of over 700 stock−recruitment
relationships al lo w ed for the estima-
tion of average steepness hpara -
meters for 57 fish species (Myers et al.
1999). These estimated hparameters
have a median of 0.62 and an upper
(75%) and lower (25%) quartile of
0.82 and 0.48, respectively. We calcu-
lated the mid-, upper- and lower-
range estimates of rby applying the
median upper and lower quartile val-
ues of the hparameter 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 as
annual rate) and discount rate δ, we
calculated the vulnerability index for
each taxon− fishing country combina-
tion. We then calculated an average vulnerability
index for all taxon− fishing country combinations
weighted by their catch (Fig. 1). This was repeated
for all the spatial cells using estimates of runder the
mid-, upper- and lower-range values.
RESULTS
Our results show that bioeconomic vulnerability
was high in many regions. Regions with high vulner-
ability to overfishing are indicated by cells with a
high negative bioeconomic vulnerability index value.
Considering all the 852 fish taxa included in this
study and assuming that fisheries operated with the
official country-level discount rate, vulnerability to
overfishing was predicted to be high in the following
regions: northeastern coast of Canada, the Pacific
coast of Mexico, Peruvian coast, South Pacific (off-
shore of New Zealand in particular), southern and
southeastern coast of Africa, and the Antarctic region
(Fig. 2A). Regions with the highest vulnerability
include the central East Pacific, Southern Ocean and
Antarctic region.
Vulnerability calculated based on estimates from
country-level discount rates probably largely
underestimated the potential vulnerability because
227
Fig. 1. Schematic summarizing the algorithm developed to
calculate the bioeconomic vulnerability index in each 0.5°
latitude × 0.5° longitude cell of the world ocean. Thickness
of 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 discount
rates were used instead of country-
level discount rates, most of the
world ocean became highly vulner-
able to overfishing (bioeconomic
vulnerability 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 Australia
and the central Pacific.
When demersal and pelagic fishes
were analyzed separately, different
patterns of vulnerability to overfish-
ing emerged (Fig. 3). Because of the
high catch of pelagic fishes, the vul-
nerability index for all fishes weigh -
ted towards the pelagic groups
(Fig. 3A,B). Thus, the general pattern
of vulnerability of pelagic fishes is
similar to that of all fishes, except in
some areas in the Arctic and around
the Antarctic where pelagic fishes
were not reported. For demersal
fishes, high vulnerability areas are
concentrated in the continental shelf
region (Fig. 3C,D). Vulnerability is
particularly high offshore of the cen-
tral eastern Pacific, southwest At -
lantic, around Iceland, south of the
Indian coast and the Indo-Pacific
region.
The high vulnerability to overfish-
ing in many regions is largely driven
by high discount rates, while in
some regions low intrinsic growth
rates also contribute to it (Fig. 4). In
most areas, the average intrinsic
growth rate weighted by the catch
of each taxon ranges from 0.1 to 0.5.
The Arctic (along the north coast of
North America) and the Antarctic
show high average intrinsic rates as
a result of the low diversity of
exploited fish with mostly slow-
growing life histories. Country-level
discount rates are highest in the
southwest Atlantic, part of the central Atlantic and
Pacific 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 western
Indian Ocean, and around New Zealand. In these
regions, private discount rates were estimated to be
over 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 from
fishing is relatively higher. Some ar-
eas identified as vulnerable coincide
with regions that are identified as
over-ex ploited or rebuilding from
overfishing (Worm et al. 2009), in clu -
ding the northeastern coast of Cana da
and the Pacific coast of Mexico. How-
ever, the index does not consider the
effectiveness of existing fisheries
management measures. Thus, fisher -
ies in areas with high bioeconomic
vulnerability, such as the waters
around New Zealand, may not be
over- exploited because of effective
management. On the other hand, ar-
eas with poor fishe ries management
effectiveness, such as in fisheries of
some developing countries, could be
more vulnerable to over-exploitation
than areas in New Zea land waters.
Moreover, the vulnerability of devel-
oping countries’ regions may be un-
der-estimated be cause of the lack of
good-quality fisheries data.
Our results highlight the potentially
tough trade-off in fisheries manage-
ment in many parts of the world
ocean. Such a trade-off is expected to
be most intense in areas where vul-
nerability to overfishing is high;
meaning that the economic incentive
to over-exploit is strong for the fishing
industry and the society, while pro-
ductivity of fishes is low. In these
areas, effective fisheries management is more ur -
gently needed, if not already implemented, to help
protect the vulnerable ecosystem. For example, if the
main driver for the high discount rate at the country
and private levels is poverty, alleviating poverty in
these regions should be a priority (Brashares et al.
2014). In cases where a large part of the distribution
range of low-productivity species falls within these
regions, fishing may greatly increase the risk of over-
exploitation. Creating marine reserves, to protect
such species, may become a necessary strategy to
safeguard their continued existence.
A ‘win-win’ solution between conservation and
economic gains is most likely in areas where bio -
economic vulnerability at both country and private
levels is low, while the average intrinsic population
growth rates of the exploited species are high. An
example is the Gulf of Alaska. Since there is reason-
able economic incentive for conservation, a range of
fisheries management options is likely to be effec-
tive. It has been suggested that the effectiveness of
different governance systems (e.g. command-and-
control, privatization, exclusive fishing rights, allo-
cated quotas, self-governance and co-management)
in achieving sustainable fisheries management is
dependent 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 vulnerability
index: (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 and
the regulator is likely to be high, management poli-
cies that involve self-governance or co-management
could be effective.
Various uncertainties exist that may affect the
interpretation of the bioeconomic vulnerability in -
dex at the global scale. Because our study is at a
global scale, it does not represent detailed regional
and local differences in the ecology and socio-eco-
nomics of fisheries. For example, intrinsic popula-
tion growth rate and discount rate can vary between
different stocks (for a species), regions and time. In
the future, regional applications of the index could
better reflect complexity at finer spatial scales. On
the other hand, fisheries and socio-economic data
are largely limited in many regions, particularly in
economically developing areas. The broad global-
scale approach em ployed in this study allowed us to
evaluate general patterns and highlight priority
areas for further ana lysis. Empirically estimated dis-
count rates for fishing countries and fishers are
rarely available. Thus, we had to make assumptions
in estimating the discount rates, which may not
accurately reflect the true values. Specifically, we
used the limited available estimates of private dis-
count rate for fisheries, which are largely from de -
veloping countries and small-scale fisheries, and
extrapolated 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 much
higher than other fisheries in developed countries,
and that the validity of the extrapolation of discount
rates assumed in our study is uncertain. Thus, vulner-
ability of some of the fisheries may be over-estimated
when the extrapolated private discount rates were
used. Similarly, estimated intrinsic rates of popula-
tion increase are considered an ap proximation, with
one of the main uncertainties being the estimation of
the steepness parameter h. Our analyses suggest that
alternative estimates of discount rate and intrinsic
rate of population increase affect the absolute values
of the vulnerability index. However, the relative dif-
ferences in vulnerability between regions are gener-
ally robust to alternative values of δand r. The
advantage of our approach is that the range of dis-
count rates and intrinsic growth rates used in the
analysis can easily be varied and the model re-run.
Calculated vulnerability may vary depending on
the structure of the algorithm used in calculating the
vulnerability index. For example, the vulnerability
index does not incorporate the marginal stock effect
(Clark & Munro 1975, Clark et al. 1979) or the effects
of detrimental subsidies to fishing (Sumaila et al.
2010), which would affect the incentive to overfish.
Moreover, populations may interact ecologically
through trophic linkages or technically through, e.g.
bycatch, and this may affect their vulnerability.
These secondary effects of fishing are not captured in
the index. On the other hand, there are trade-offs be -
tween having a simple index with known structural
uncertainty and a complex index that increases data
uncertainty. For example, the Ocean Health Index
(Halpern et al. 2012) is a comprehensive index to
evaluate ocean sustainability. However, it is data
intensive, and so the uncertainty associated with the
large number of input data may complicate its
interpretation. We opt for the earlier option as the
primary objective of this study is to broadly identify
areas of the world ocean with high potential vulner -
ability to overfishing. The global focus of the analysis
and 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 not
explored 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 overfishing
relative to fishes, this study may over-estimate the
vulnerability of regions where invertebrates are an
important part of the fishery. Further studies can
apply the vulnerability index described here to the
invertebrate fisheries. These would include the in -
corporation of the marginal stock effect and subsidies
into the assessment of vulnerability and effectiveness
of 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 is
a need to carry out more studies on public and pri-
vate (fishing sector) discount rates to improve our
understanding of the economic drivers of over-
exploitation.
CONCLUSIONS
Using the bioeconomic vulnerability index devel-
oped in this paper, we show that some areas of the
world ocean are likely to face difficult trade-offs
between conservation and exploitation. Exploited
fish populations in these regions have relatively low
230
Cheung & Sumaila: Bioeconomic index of vulnerability to overfishing
intrinsic biological vulnerability to fishing (low intrin-
sic rate of population increase) while the economic
incentive to over-exploit, driven by high discount
rates, is strong. In contrast, areas with low vulnerabil-
ity suggest that conservation and fishing exploitation
could coexist without much conflict of interest.
Future incorporation of the marginal stock effects,
subsidies, im proved biological and economic data
could refine the general picture depicted in this
study. Studies that incorporate an analysis of how
existing management arrangements are likely to
affect the patterns identified in the current contribu-
tion would be very interesting.
Acknowledgements. This project is funded by the Pew
Charitable Trust through U.R.S.’s Pew Marine Conservation
fellowship. W.W.L.C. acknowledges funding support from
the National Geographic Society, Natural Sciences and
Engineering Research Council of Canada, and Nippon
Foundation. We thank M. L. D. Palomares for provision of
data 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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