Contributed paper

207

The Impacts of Waiting Cooperative Management of
a Transboundary Fish Stock Vulnerable to Climate Variability:
the Case of Pacific Sardine
Gakushi ISHIMURA1*, Sam HERRICK2 and Ussif Rashid SUMAILA3
1

Center for Sustainability Science, Hokkaido University
N 9 W 8, Kita-Ku, Sapporo, Hokkaido, 060-0809, Japan
2
NOAA Fisheries Services, Southwest Fisheries Science Center
3333 North Torrey Pines Court, La Jolla, CA, 92037-1022, USA
3
Fisheries Centre, University of British Columbia,
AERL, 2202 Main Mall, Vancouver, B.C., Canada, V6T 1Z4*e-mail: gakugaku@census.hokudai.ac.jp

Abstract
Challenges in the management of a transboundary fish stock, with time variant and asymmetric
distribution of biomass caused by ocean climate variability, lie in waiting the implementation of cooperative
management and the incurring of impact due to such waits. This is particularly true for Pacific sardine(Sardinops sagax), which has exhibited extreme decadal variability corresponding to warm and cold regime
shifts of the California Current Ecosystem (CCE). Pacific sardine is exclusively fished by Canada, the U.S.
and Mexico without any cooperative agreements in place. Our study applied a three-agent bioeconomic
framework that incorporated environmental effects on sardine abundance and biomass distribution to estimate
the impact of waiting cooperative management of this fishery. Our results showed that the impact of waiting
cooperative management is significant for a country having a dominant share, while countries that have minor
shares gain economic benefits from waiting cooperative management.
Key words: climate change, cooperative management, economic, fishery, impact,transboundary management

1. Introduction
Ocean climate variability, on both inter-annual anddecadal scales, alters the marine environment over time
(Brander, 2007). Impacts that can result through suchchanges in the marine environment include food availability and the habitats for marine organisms. Fish stocks
often respond to these changes by 1) increasing or
reducing their abundance; and 2) migrating to habitats
conducive for growth and reproduction. These two
responses are not mutually exclusive, and jointly result inchanges in the local fish availability, thus inevitably
threatening the spatial stability of available fish stocks
for fisheries exploitation.
This issue of spatial instability is a critical challenge
particularly with a transboundary fish stock which is
exclusively shared by more than one country. Without
cooperative agreements, competing fishing activities,
upon which the impacts of ocean climate variability
could have compounding effects, threaten transboundary
fish stocks. Two critical elements to fisheries manageGlobal Environmental Research
18/2014: 207-216
printed in Japan

ment need to be agreed on for there to be cooperation in
the use of a transboundary fish stock (Munro et al, 2004).
First, the size of the fish stock left unfished, called theescapement biomass, must be agreed upon to ensure theresource’s sustainability. The escapement biomass thus
defines the total allowable catch (TAC) permitted to participating fishing countries. Second, the allocated shareof the total catch permitted to each country needs to beaddressed. Fixed shares of catch have often been allottedby considering the catch history of the countries involved,
fixed physical distribution of stocks, or the migration
patterns of a transboundary fish stock. With spatial instability of a fish stock caused by ocean climate variability, fixed allocations may no longer be effective, andtherefore, it is anticipated that challenges to establishingcooperative transboundary management will arise.
Potential uncertainties in fisheries production andspatial distribution arising from ocean climate variability
have received increasing attention in transboundary fishery management over the years. A body of scientificstudies on the impacts of ocean climate variability on a©2014 AIRIES208

G. ISHIMURA et al.

fishery has quickly developed, but it is mostly limited togeographical considerations or methodological approaches rather than by anticipating effects on a fishstock or fisheries (Brander, 2010). In terms of practicalcase studies on transboundary fish stocks under climate
variability, Laukkanen (2003) devised a multinational
fishing game for Northern Baltic salmon with environmental variability in recruitment, and concluded that
there were significant effects from environmental variability on maintaining cooperative management. Miller
and Munro (2004) undertook a case study of Canada - US
Pacific salmon fishery management in which abundanceand distribution changes related to ocean climate
variability are taken into account, and concluded thatpredictions of the impacts of environmental variability on
a fish stock are a key to successful cooperative managements. Despite these three studies successfully demonstrating the need for cooperative management oftransboundary fish stocks under ocean climate variability,
studies that estimate the risk of overexploitation and theloss of potential economic benefits, from a transboundary
fish stock under ocean climate variability and noncooperative management are largely absent from theacademic literature.
A large challenge in the management of a transboundary fish stock, where its availability is affected byocean climate variability, lies in waiting implementationof cooperative management and consequently incurring
the impact of such waits. First, it takes a long time torecognize and confirm changes in a fish stock caused byocean climate variability, to which must be added thetime needed to predict anticipated changes. Second,
negotiations to establish cooperative management takeadditional time because of likely conflicts in economic
interests compounded by political obstructions. Suchnegotiations also include agreements on anticipatedchanges to a fish stock and decisions on sharing future
benefits among the participating stakeholders on both thedomestic and international levels. These difficulties all
serve to wait the adoption of cooperative management ofa transboundary fish stock.
As in Miller (2007), one key to the stability ofcooperative management of a transboundary fish stock is
to maintain the participating countries’ incentives tocontinue to cooperate, despite changes in fish abundanceand distribution. Therefore, revealing the impact of
waiting such cooperative management, which includes
both the potential loss of economic benefits and the riskof stock depletion, would help give countries sufficientincentives to engage in cooperative exploitation to avoid
potential negative outcomes. Although the number ofglobal studies on the impact of adapting to climatechanges is rapidly increasing (e.g., World Bank, 2009),
studies on the impacts of waiting cooperative management on a transboundary fish stock under ocean climate
variability have been largely absent until now.
Transboundary fishery management of Pacificsardine (Sardinops sagax) in the California Current Ecosystem (CCE) is now faced with the aforementioned
challenges, under ocean climate variability. Inter-annualand decadal scale climate variability, with drivers such as
the El Niño/Southern Oscillation (ENSO) and the Pacific
Decadal Oscillation (PDO), has shaped the ocean climateof the CCE, which extends up to southern Vancouver
Island from Baja California (Field and Frandis, 2002).
Since the early twentieth century, three ocean climate
regime shifts have been recognized; a warm regime from
1925 to 1947, a cold regime between the 1940s and late1970s, and a warm regime from 1977 to the present(Figure 1) (McFarlane et al., 2000).
To this end, this study aims to reveal the impact of
waiting cooperative exploitation of the Pacific sardine
fish stock under ocean climate variability. Ishimura et al.
(2013) developed a three-country transboundary fisherybioeconomic model for Pacific sardine incorporating
distribution and abundance uncertainties under CCE
ocean climate variability. They showed the potential
effects on economic and biological outcomes fromcooperative and non-cooperative management of the
Pacific sardine stock by the three countries rather thanFig. 1 Biomass changes of Pacific sardine over time (biomass data from Hill et al.
2009) and the climate regime in the California current ecosystem.

The impacts of waiting cooperative management with climate variability

precise estimations of biomass and economic outcomes.
This study further extends their model to estimate theimpact and the risk of depletion to a fish stock, in thiscase Pacific sardine, from waits in cooperative exploitations. This study differ from Ishimura et al. (2013) byfocusing on the impact of the waiting of cooperative
management among three countries. In the study, we
conduct 35-year simulations, and define the ‘impact of
waiting’ as the difference in net economic benefits
between a) cooperative management by the three countries for all 35 years, and b) cooperative management
after i years of non-cooperative management. We summarize and discuss the results from the simulations.

2. Material and Methods
2.1 Pacific sardine in the California Current
Ecosystem
The abundance and distribution of the northern stock1)of Pacific sardine, which is the largest substock in the
CCE that is exclusively fished by Canada, the U.S. andMexico, has exhibited extreme variations as result of
three regime shifts in the CCE (Herrick et al., 2007). In
this study, hereafter, the term Pacific sardine implies thisnorthern stock. Until the early 1940s under a warm
regime, the biomass of Pacific sardine varied between
1.2 million and 2.8 million tonnes, and sardine fisheries
were widespread in Canada, the U.S. and Mexico.
Between the late 1940s and 1970s a cold regime shift in
the CCE, combined with overfishing, resulted in thecollapse of the Pacific sardine stock, with biomass failingbelow 5,000 tonnes. As abundance decreased, the spatial
availability for commercial fisheries shifted from a wide
range to the limited southern region of southern
California and Mexico. Finally, directed fisheries for
Pacific sardine in the U.S. were closed in 1974. In the
1980s, a warm regime shift occurred in the California
Current, and coupled with conservation efforts, theabundance of Pacific sardine rebounded to 1940s levels,and reappeared in the waters of the Northwest U.S.
(Oregon and Washington) and Canada. In 1986, directedfisheries for Pacific sardine officially reopened in the U.S.
Canada removed Pacific sardine from its endangered
species list and reopened its sardine fisheries in 2003. In
2006, the estimated biomass of Pacific sardine reached
1.2 million tonnes. In 2008, the estimated biomass
decreased to 0.58 million tonnes. Latest improvements tothe stock assessment model have resulted in a retrospective reduction in biomass estimates for recent years(Hill et al., 2009). In summary, warm regimes enhance
the abundance of Pacific sardine and expand its distribution. Cold regimes lessen abundance and restrict
distribution.
2.2 Model overview
Our integrated model mimics ocean climate variability in the CCE and the abundance and distribution ofPacific sardine stocks corresponding to ocean climate
variability. Previous studies have demonstrated signifi-

209

cant correlations between the annual average sea surface
temperature (SST) at the Scripps Institute of Oceanography pier, abundance, and distribution of Pacific sardine2)(e.g. Jacobson et al., 2005; Herrick et al., 2007). This
study therefore assumes that SST is a major driver ofbiomass abundance and the geographical distribution ofPacific sardine, and adapts the model developed by
Ishimura et al. (2013). Our alternative stochastic model
consists of four components: a) a population dynamics
model driven by SST; b) a biomass distribution model
spread over three countries; c) an SST development
model; and d) an information model of fish stock
distribution. We integrate these four components tomodel the expected population dynamics and distributionof Pacific sardine.
2.3 Population dynamics model driven by SST
We adapt a surplus production model with environmentally dependent components developed by Jacobson
et al. (2005), and assume that the fish stock migrates
from a spawning area to each country’s fishing grounds
and then returns to their spawning ground for reproduction. Fishing is assumed to occur after reproduction, andoccurs simultaneously in each country’s fishery. From
the Gompertz-Fox model (Fox, 1970), Jacobson et al.
(2005) calculated environmentally dependent surplus
production as:⎛ Sy ⎞
By +1 = S y − eη S y ln ⎜ γ⎜ I ⎟⎟⎝ y⎠

S y = B y − h yCanada − hUy . S . − h yMexico

where By and Sy are the biomass and escapement biomass
at year y, respectively. The constant e is Euler’s number(2.718), Iy is SST at year y, which affects the stock’s
carrying capacity. η and γ are constants. For the GompertzFox model, the second term express the surplus (orgrowth) of escapement, η is the ratio of the maximum
productivity over the carrying capacity (Quinn & Deriso,1999). The constant γ is a scaling factor for SST to thecarrying capacity. Ishimura et al. (2013) estimated η(0.04) and γ (2.55) by using updated stock assessment
data from Hill et al. (2009). This study incorporates theseestimations.
2.4 Objective function under cooperative
management
Here, we assume that the three countries fish cooperatively thereby acting as the sole owner of the fish stockand seek to maximize joint benefits by adjusting the*
optimal escapement biomass, S y . The objective functionthat maximizes the present value of the economic benefit
at year y (fsolo,y) is assumed to be:max⎛ S * ⎞ ⎪⎫⎪⎧d ⋅ p ⋅ ⎨−eη S *y ln ⎜ γ y ⎟ ⎬⎜ Iy ⎟⎝⎠ ⎭⎪⎩⎪f solo , y ( S *y ) = p ⋅ ( By − S *y ) +1− dG. ISHIMURA et al.

210
where d = 1
1+ r

where d is the discount factor and r is the discount rate.
We assume a constant net economic price per unit catch(p= 0.03 USD per pound). The first term expresses the
economic benefits from the current catch and the second
term expresses the future economic benefit (Hannesson,2007). In this study uses a discount rate, 5% to project
economic and biological outcomes. With rates of 3%,
10% and 15% applied to assess the sensitivity of themodel to different discounting rates. For the maximization of the objective function under sole ownership(cooperative management), the optimal escapement bio*
mass ( S y ) is calculated using the first order condition of afollowing equation:*
S solo,y =Iyγ⎛ 1− d ⎞
−⎜1+
⎟
deη ⎠

e⎝

2.5 Objective function under non-cooperative
management
Hannesson (2007) studied a transboundary fish stockthat migrates between two countries with time-variant
distribution changes under climate change. Two complementary assumptions related to the maximization problem are assumed in his study. First, the minor country,with less than a half share (distribution) of a fish stock,has an incentive to fish the biomass level down to zero
( S Minor * = 0 ). Second, the major country with more thanhalf the share (distribution) of a fish stock has an incentive to leave the stock in the ocean until it reaches thelevel that maximizes net present value of the benefits.
This paper adopts this variant major/minor frameworkand develops an optimal escapement biomass for
non-cooperative management based on the updated
Jacobson’s population dynamics model by Ishimura et al.,(2013). The escapement biomass that maximize the present value for invariant shares of a fish stock are:⎛ 1− d⎞⎧−⎜+1⎟⎪⎪ S Majar* = I y e ⎝⎜ deη Dˆ w , y ⎠⎟ if Dˆ > 0.5w, y⎨ w, yγ⎪
Minor *
S w, y = 0 Otherwise
⎪⎩

where
is the expected distribution of a fish stock.
Hanneson’s analysis was for a two-agent model, where afish stock’s distribution clearly defined which country ismajor and minor except when the two countries’ distributions were the same ( ) and the two countries jointly
acted as the sole owner. In our three-agent model with
Canada, the U.S. and Mexico, however, it is possible forthe biomass distributions of all countries to be less than0.5, in which case all countries act as minor players. This
could lead to the drastic depletion of Pacific sardine.
2.6 Sea surface temperature development model
The nature of the climate regime of the CCE is basedon decadal scale interchanges of warm and cold regime

shifts (two or three regime shifts during the twentiethcentury). This study adopts a 35-year time trajectory
where one regime shift from warm to cold and vice versa,
would be appropriate. We use an increasing and a decreasing trend of SST (τ), calculated as:τ y +1 = τ y + μ + σΔz y
Δz y ~ N (0,1)

where y is year. This equation generates a stochastic SST
trend as the sum of two components: 1) a static driven
part, μ; and 2) a stochastic error term, Δz y . In this study,
the value for μ andσare 0.044 and 0.602, respectively,
obtained from the average annual SIO SST from 1970 to
2002, which is considered a warm regime period in the
CCE (from Ishimura et al., 2013). The situation in the2010 CCE might be the initial stage of a cold regime shift,
but this is yet to be confirmed since it takes several years
to confirm warm and cold climate regimes. Therefore,
the period from 1970 to 2002, which has been confirmed
as a warm climate regime is the period which we use as abasis to estimate ocean climate variability. This study
evaluates two scenarios for SST trends, 1) an increasing(time-increment) SST trend (μ=0.044); and 2) a decreasing (time-decrement) SST trend (μ= – 0.044).
2.7 Biomass distribution model driven by SST
The biomass distribution model of Pacific sardine is adiscrete three-box model (from Ishimura et al., 2013).
With changes in SST, the sardine biomass is redistributed
between Mexico (MX), the U.S. (US) and Canada (CA) ina discrete manner. The general pattern of the distributionof Pacific sardine within country w (Dw) relative to theothers is assumed to be linear when the SST (τ) drops
below the low threshold level (τlow), and then approaches
zero (Dw=0) as the high threshold level of SST (τhigh) isreached.
⎧DMX , y = min ⎡⎣1, (τ highMX − τ y ) / (τ highMX − τ lowMX ) ⎤⎦⎪⎪⎨ DUS , y = (1 − DMX , y ) ⋅ min ⎡⎣1, (τ highUS − τ y ) / (τ highUS − τ lowUS ) ⎤⎦⎪DCA, y = 1 − DMX , y − DUS , y⎪⎩s.t. 0 ≤ Dw, y ≤ 1
DMX , y + DUS , y + DCA , y = 1

This study models biomass distribution by estimatinga direct relationship between SST and discrete biomass
distributions over the Exclusive Economic Zones (EEZs)of Mexico, the U.S. and Canada based on three descriptive facts. First, the current U.S. harvest policy for Pacificsardine assumes a fixed distribution with 87 % of thenorthern stock in U.S. waters (California, Oregon andWashington) and 13 % in Mexican waters, and does notinclude a percentage for Canada. Second, Canadian management assumes a fixed biomass distribution where 10% ofThe impacts of waiting cooperative management with climate variability
the northern stock is assumed to enter Canadian waters(DFO, 2004). This assumption is based on an analysis ofhistorical catch and trawl survey data. Third, around 1990,
Pacific sardine reappeared in Canadian waters. Based on theabove observations and analyses, this study makes two
assumptions about the relationship between SST and thebiomass distribution of Pacific sardine. First, at an SST of
17.9oC, which was the five-year average SIO SST in 1999,
the proportions of the biomass of Pacific sardine in Mexico,
the U.S. and Canada are set at 13%, 78% and 9%, respectively. Second, at a SST of 17.5oC, which was the five-year
average in 1992, the proportions of the biomass of Pacificsardine in Mexico, the U.S. and Canada are 20%, 77% and3%, respectively. We set different high and low thresholdlevels for Mexico (τhigh,MX =18.3 and τlow,MX =15) and the U.S.
(τhigh,US =21.5 and τlow,US =17.5), with Canada having theresiduals.
Since our intention in this study is not the precise
estimation of biomass or economic outcomes, but rather
to examine the effects of waiting cooperative management, we use five-year averages from 1997 and 2001, aconfirmed warm regime of the CCE, as the initial SST,
17.9oC, and initial biomass, 1.2 million tones, in thesimulations. The initial biomass distributions for Mexico,
the U.S. and Canada are set at 13%, 78%, and 9%,
respectively. As SST reaches 19.4oC, more than half thebiomass is distributed in Canadian waters3). More thanhalf the biomass is distributed in Mexican waters when
the SST drops below 16.7oC (Fig. 2).

2.8 Information model for biomass distribution
We incorporate an auto-correlation function into theestimation of expected fish share for each country basedon the assumption that changes in the biomass distribution of Pacific sardine is based on existing and past timeseries of biomass distributions. Therefore, a time dependent auto-correlated error function is appropriate.
This is expressed as:

211

Dˆ w, y = ρ ⋅ Dw, y + (1 − ρ ) Dˆ w, y −1

s.t. 0 ≤ Dˆ w , y ≤ 1
Dˆ w,0 = Dw,0

where
is an expected distribution of Pacific sardine
at time y in country w, and ρis the auto-correlation
weighting factor. The value of the weighting factor (ρ)
captures the information wait regarding a fish stock’s
distribution. The magnitude of the weighting factor affects the amount of the stock, expects to have availability
to update their fishing strategy. In the simulations, we
assume symmetric information for the three countries
and arbitrarily set the weighting factor at ρ = 0.5.
Sensitivity analysis was carried out in Ishimura et al.
(2013).
2.9 Catch
Due to the time-variant fish stock distribution and information waits, the target catch might be more than theamount of fish available in each country’s waters. Also
this study assumes homogeneous fisheries among three
countries in terms of fishing capitals (e.g., gears, vessels,
technologies). The catch in a given year for each country
is expressed as:^

where the target catch h is induced by the expecteddistribution ( ), biomass (B) and the optimal escapement
biomass (S) at year y.
2.10 Impact of waiting cooperative management
The present value (PV) of the net economic benefits
from fishing by the three countries over the 35-year time
horizon of the 10,000 simulations is taken as the measure

Fig. 2 Development of the modeled biomass distribution and carrying capacity in accordance with the SST.

G. ISHIMURA et al.

212

of economic performance. The average of the present
value of benefits received by each country is calculatedas:PV w =

k
1 10,000∑ PVw
10, 000 k =1

kwhere PVw is the net present value for country, w, in thekth simulation:
35

PV = ∑ d
k
w

y =1

y −1

⋅π

2.11 Biological indicators - the conservation risk
We assume that the conservation risk, or the probability that the biomass falls below 10 % of the initialbiomass (1.2 million tonnes), happens at least once overthe 35-year time horizon. Ten percent was chosenbecause of the biological resilience of Pacific sardine ishigh as shown by its history (less than 5,000 tonnes of a
Pacific sardine during 1970s).
P( Byk < 0.1B0 ) =kw, y

We define the ith year wait of cooperative management in the 35-year projection as:
1) From the first to ith year, all countries engage in
non-cooperative management,
2) From i th +1 year to 35th year, all countries engage incooperative management.
The impact of waiting cooperative management for acountry, w, (Cw,i) is assumed to be the difference between
the present value of benefits under cooperative management over the entire 35-year period and the ith-year waitin non-cooperative management.
C w ,i = PV w ,35 − PV w ,iThe 35-year time horizon is assumed as the management time horizon in this study. The total impact to thethree countries is defined as the sum of the individual
impact to the three countries:

CTotal ,i =CCanada ,i + CU .S .,i + CMexico,iThis is a generalization of many earlier results ofgame theoretic models of fishing, where the difference innet benefits under cooperative and non-cooperative
management (i.e., the loss due to non-cooperation
throughout the time horizon of the analysis) are expected
to motivate cooperation.

1 10,000∑ I (Byk < 0.1B0 )10,000 k=1

where I (Byk < ϕ B0 ) is an indicator that equals 1 if the biomass during year y in simulation k is less than ϕ (0.1) of
the initial biomass.

3. Results
The results of impacts of waiting cooperative
management with a discount rate of 0.05 are presented inTables 1 and 2, respectively. Since a zero-year wait incooperative management implies cooperative exploitation for all years, the impact for the zero-year wait is zero.
The 35th-year wait implies that all countries are engaged
in non-cooperative management through all years. The
maximum total impact of 88.1 million USD occurred atthe 25th-year of wait (Table 1) for the time-increment SST
scenario, and 80.6 million USD for the time-decrement
SST scenario (Table 2); the impacts of waiting cooperative management then decreased beyond the 25th-year of
wait. The total impact for the time-increment and decrement SST scenario showed a ‘concave’ trend. This implies that cooperative management should not be attempted if the expected wait in implementing cooperative
management were to exceed 25 years. This is because thetotal impact of wait is the sum of all the three countries’
impacts, the significantly high impact for the U.S. offsets
the economic benefits of engaging in non-cooperative
behavior for Canada and Mexico. With more wait incooperative management, 1) there is less benefit from

Table 1 The impact (million USD) of waiting cooperative management to each country separately andcollectively in the time-increment SST scenario with discount rates, r=0.05. Note that the total
payoffs slightly may differ from the sum of the three countries’ impacts due to rounding.
Impact of i th -year wait of cooperative management in the 35-year projection (million USD)
1
5
10
15
20
25
30
35
Total
2.0
18.8
45.5
66.0
81.2
88.1
84.8
81.8
CAN
–5.1
–22.9
–17.6
–9.6
–0.8
3.7
2.8
2.7
US
17.1
69.3
94.6
104.5
109.2
110.5
108.2
106.0
MX
–10.0
–27.6
–31.4
–29.0
–27.3
–26.2
–26.2
–26.9
Table 2 The impact (million USD) of waiting cooperative management for total and each country inthe time-decrement SST scenario with discount rates, r=0.05. Note that the average total
payoffs slightly may differ from the sum of the three countries’ impacts due to rounding.
Impact of i th -year wait of cooperative management in the 35-year projection (million USD)
1
5
10
15
20
25
30
35
Total
2.1
18.0
42.1
60.9
74.3
80.6
78.5
74.5
CAN
–5.3
–25.2
–28.4
–26.4
–24.8
–21.7
–22.9
–23.6
US
17.3
67.8
91.4
101.6
106.4
107.1
85.9
103.3
MX
–10.0
–24.6
–20.9
–14.3
–7.3
–4.7
–3.9
–5.2

The impacts of waiting cooperative management with climate variability

fewer years of cooperative management; and 2) the impact to rebuild to the optimal escapement biomass from adepleted stock level would result in high conservation
risks in later years (see Tables 3 and 4). With combinations of these elements, a ‘concave’ type trend appeared.
It is, however, certain that the wait in cooperative
exploitation increases the conservation risk proportional
to the years of wait, for all discount rates and both ocean
climate scenarios (Tables 3 and 4).
In both ocean climate scenarios, the most distinguishing feature is the significant impacts for the U.S(Tables 1 and 2). As the major country, under noncooperative management, the U.S. has an incentive tomaintain the optimal escapement biomass for future
benefits by setting low or even zero catch, while the othertwo countries benefit from such U.S. conservation efforts.
After any wait, once the three countries are engaged incooperative management, the U.S. engages in rebuilding
the biomass up to the optimal escapement biomass, forfuture benefits. As it turns out then impacts to the U.S. torebuild or maintain the optimal escapement biomass are
incurred regardless of how many years of wait there arein cooperative management. On top of the impact of
rebuilding the biomass for all years, there is also economic loss due to an inability to achieve optimal escapement biomass, an added impact for the U.S.
While the impact to the U.S. is significant, the impacts to Canada and Mexico appear to be negative except
for Canada, for more than a 20th -year of wait in thetime-increment SST scenario (Table 1). The negative
impact implies that Canada and Mexico benefit by waiting cooperative management. For SSTs up to 19.5oC in
the time-increment SST scenario and down to 16.7oC in
the time-decrement SST scenario, Canada and Mexico
are always minor countries, i.e., they always have lessthan half of the biomass distribution within their waters(Fig. 2). As minor countries, Canada and Mexico benefit
from engaging in non-cooperative rather than co-operative behavior. Under non-cooperative management,
the conservation efforts by the U.S. to maintain the
optimal escapement biomass bring benefits to Canada
and Mexico.
In the time-increment scenario with r = 0.03 and 0.05
(Fig. 3), the wait of cooperation beyond the 10th and 20thyears respectively left Canada with the impact of rebuilding up to the optimal escapement biomass. This isbecause the stochastic time-increment SST scenario
shifted biomass towards Canada and made Canada the
major country, hence the impact of rebuilding a biomass
to the optimal escapement biomass appears as impacts
for Canada (e.g., 3.7 million USD for a 25th-year of waitin Table 1). The results of the time-decrement scenario
with r = 0.03 showed a similar result for Mexico because
the stochastic time-decrement SST scenario shifted thebiomass distribution into Mexican waters (Fig. 4).
For the sensitivity analysis, this study applies four different discount rates arbitrarily, r = 0.03, 0.05, 0.1 and 0.15.
These showed identical trends for the time-increment andtime-decrement scenarios except for the impacts to
Canada when r=0.03 and r=0.05 in the time increment
SST scenario, and Mexico when r=0.03 in the time decrement SST scenarios (Figs. 3 and 4). Due to the discounting of the future net benefits, one would expect lessnet benefit and less impact for waiting cooperation forhigher discount rates (e.g., r = 0.15). This is explicitly
confirmed in the modeled total impacts and the impacts
for the U.S. for both time-increment and time-decrement
SST scenarios. Both ocean climate scenarios showed thesame trends for the total impact, the impacts to the U.S
and Mexico as well as for the conservation risk (Tables 3
and 4). At the end of the 35-year simulations, under boththe time-increment and time-decrement scenarios SSTs
are expected to be 19.5oC and 16.4oC, respectively,
without stochastic disturbance. In this case, the U.S.
emerges as the major country with more than half of thebiomass distribution (Fig. 2).

Table 3 The conservation risk (%) for the time-increment SST scenario - probability that thebiomass falls below 10 % of the initial biomass (1.2 million tonnes) at least once overthe 35-year simulation.

Discount rate
0.03
0.05
0.1
0.15

Conservation index of waiting ith –year in cooperative management (%)
1
5
10
15
20
25
30
35
0.0
1.6
5.1
13.8
23.7
32.3
39.2
44.0
0.0
1.6
5.3
13.4
24.3
33.0
38.7
43.8
0.0
2.2
8.1
18.2
27.9
36.8
43.0
48.3
0.0
4.3
16.3
30.7
41.3
48.5
53.9
58.3

Table 4 The conservation risk (%) for the time-decrement SST scenario - probability that thebiomass falls below 10 % of the initial biomass (1.2 million tonnes) at least once overthe 35-year simulation.

Discount rate
0.03
0.05
0.1
0.15

213

Conservation index of waiting ith –year in cooperative management (%)
1
5
10
15
20
25
30
35
0.0
1.4
5.2
13.9
22.5
31.1
37.5
41.6
0.0
1.6
5.6
14.2
23.4
31.6
38.2
42.4
0.0
2.2
8.0
18.7
27.9
36.6
41.7
46.6
0.0
4.2
16.4
31.0
41.4
47.4
54.6
56.7

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G. ISHIMURA et al.

In both climate scenarios, the impact of waiting cooperation with r = 0.15 yielded less negative results thanwhen r = 0.1 for Canada and Mexico (Figs. 3 and 4). In
addition to the net economic benefits of a higher discountrate, higher discounting drives the optimal escapement
biomass level lower. The lower escapement biomass set
by the U.S. leads to less spillover benefits for Canada and
Mexico, which then results in less negative impacts for
Canada and Mexico. The conservation risks shown in
Tables 3 and 4 confirmed a lower biomass under r = 0.15
relative to other discount rates in both ocean climate
scenarios.

4. Discussion
The purpose of this study was to compute the impact
of waiting cooperative management of Pacific sardine in
the CCE under the influence of ocean climate variability.
Two significant impacts of waiting cooperative management are, 1) loss of the economic benefit that can begained by maintaining the optimal biomass for future
benefits; and 2) the impacts incurred to rebuild stocks to
the optimal escapement biomass once they are depletedby an extended period of non-cooperative management.
As the years of waiting cooperative management in-Years of delaying cooperative management

Years of delaying cooperative management

Years of delaying cooperative management

Years of delaying cooperative management

Fig. 3 Sensitivities of the impact of waiting cooperative management in the time-increment SST scenario with four discount rates(r = 0.03, 0.05, 0.1 and 0.15).

The impacts of waiting cooperative management with climate variability

215

Fig. 4 Sensitivities of the impact of waiting cooperative management in the time-decrement SST scenario with four discount rates(r = 0.03, 0.05, 0.1 and 0.15).

creased, more drastic conservation efforts were required
to replenish the fish stock to the optimal escapement
biomass. The U.S. bears the impact of restoration because of its status as the major resource holder under bothocean climate scenarios.
Ishimura et al. (2013) emphasized the potential failure of unilateral efforts to maximize conservation andmanagement benefits from Pacific sardine. The results ofthis study support this. In addition, this study suggeststhat the leading roles of U.S. toward cooperative management.
As Miller and Munro (2004) noted, the predictions of

the impacts on a fish stock and the economic benefits toparticipants in shared fish stock fisheries are keys forcooperative behavior. Our results demonstrated thepotential impact incurred from waiting cooperative management given ocean climate variability. Although it is
not the precisely defined impact, our estimated impact of
waiting cooperative management and the conservation
risk would be useful information toward engaging thethree countries in cooperative management. The significant impacts incurred by the major country for resourceshare (the U.S.) provides a strong incentive for cooperative management; conversely, the negative impacts for

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G. ISHIMURA et al.

minor countries for resource share (Canada and Mexico)
explicitly suggest that there is less incentive for them tocooperate. Our results suggested that a key for achieving
cooperative management of a transboundary fish stock
under ocean climate variability, establishing the meansby which a major country for resource share can motivate
minor countries for resource share to engage in cooperative fishing behavior.

5. Conclusion
In this study, simulations of a three-country transboundary fishery for Pacific sardine, which incorporate
ocean climate variability in the CCE, revealed thepotential impact of waiting cooperative management by
participants in the fishery.
The study clearly suggested that Canada and Mexico
have less incentive to engage in cooperative managementon the grounds that these countries actually benefits from
non-cooperation. On the other hand, this study demonstrated that the U.S. has significant incentive to engage incooperative management immediately. Moreover the
results of this study can be reference for the initial allocations of quota.
Our study revealed that most of the impact of waiting
cooperative management is incurred by the country thathas the dominant share of a transboundary fish stock – inthis study, it is the U.S.. Hence, that is the country has thedominant share of that a transboundary fish stock shouldtake the initiative to bring about cooperative management
to reduce the impact of waiting cooperative management.
The limitations of this study lay on the set assumptions of constant parameters. For example, the constantprice of the Pacific sardine would not be suitable if thedemand on Pacific sardine change or under high discountrate which implies incentives for immediate utilizations.
The model in this study, however, has flexibility andshould be modified according to specific circumstances.
It is noted that the far-reaching process of building cooperative fishery management among multiple countries
will be extremely challenging due to political considerations and diverse economic motivations. It is suggested
that future studies of cooperative exploitation need tofurther address the impacts and the risks that result fromocean climate variability.
Notes:
1)

2)

3)

Three substocks of Pacific sardine in the CCE are widely
recognized. These are the 1) northern substock, which is foundfrom northern Baja California to south-eastern Alaska;
2) southern substock whose distribution ranges from Baja
California to southern California; and 3) Gulf of California
substock ,which spends its life within the Gulf of California.
SST at the Scripps Institute of Oceanography pier, in La Jolla,
California (SIO SST), is often used as an indicator of thedecadal cold-warm shifts in the CCE.
The historical maximum and minimum SIO between 1918 and2002 was 19.1oC in 1997 and 15.5 in 1975, respectively.

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