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How useful is the ratio of fish density outside
versus inside no-take marine reserves as a metric
for fishery management control rules?
Elizabeth A. Babcock and Alec D. MacCall
Abstract: A management strategy evaluation (based on five species in the California, USA, nearshore fishery) of control
rules that reduce relative fishing effort as a function of the ratio of fish density outside versus inside no-take marine re-
serves (as a measure of depletion) showed that although the control rules allowed effort to increase at first, in the long
term, they were effective at maintaining spawning stock biomass and yield for all simulated species, including depleted
ones. Scenarios with fish movement, illegal fishing in the reserve, or post-dispersal density dependence in recruitment re-
quired higher density ratio targets, such as 60% of mature fish or 80% of all fish, to avoid stock depletion. The effort al-
lowed by multispecies density-ratio control rules depended on the relative weight given to more or less depleted species.
High variability in recruitment or in monitoring data caused the allowable effort to fluctuate. Density-ratio control rules
have the advantages that they require no historical data, they can be used at local spatial scales, and they adjust to chang-
ing environmental conditions.
Re
´
sume
´
: Nous avons e
´
value
´
la strate
´
gie de gestion applique
´
ea
`
cinq espe
`
ces dans la pe
ˆ
che commerciale pre
`
s de la co
ˆ
te
de la Californie, E
´
.-U., concernant les re
`
gles de contro
ˆ
le qui re
´
duisent l’effort relatif de pe
ˆ
che en fonction du rapport entre
la densite
´
des poissons a
`
l’exte
´
rieur et a
`
l’inte
´
rieur de re
´
serves marines a
`
pe
ˆ
che interdite (comme mesure d’e
´
puisement); il
apparaı
ˆ
t que, bien que les re
`
gles de contro
ˆ
le permettent un accroissement de l’effort de pe
ˆ
che au de
´
but, elles sont efficaces
a
`
long terme pour maintenir la biomasse du stock reproducteur et le rendement chez toutes les espe
`
ces qui ont e
´
te
´
l’objet
d’une simulation, me
ˆ
me celles qui souffrent d’e
´
puisement. Les sce
´
narios qui comprennent des de
´
placements des poissons,
de la pe
ˆ
che ille
´
gale dans la re
´
serve ou une densite
´
-de
´
pendance apre
`
s la dispersion ne
´
cessitent des cibles avec des rapports
de densite
´
plus e
´
leve
´
s, par exemple, 60 % pour les poissons matures ou 80 % pour l’ensemble des poissons, afin d’e
´
viter
l’e
´
puisement des stocks. L’effort permis d’apre
`
s les re
`
gles de contro
ˆ
le des rapports de densite
´
s applique
´
es a
`
plusieurs espe
`
-
ces de
´
pend du poids relatif donne
´
aux espe
`
ces plus ou moins e
´
puise
´
es. Une forte variabilite
´
dans le recrutement ou dans
les donne
´
es de surveillance entraı
ˆ
ne une fluctuation dans l’effort permis. Les re
`
gles de contro
ˆ
le base
´
es sur les rapports de
densite
´
s ont l’avantage de ne ne
´
cessiter aucune donne
´
e historique, de pouvoir s’appliquer aux e
´
chelles spatiales locales et
de s’ajuster aux conditions environnementales changeantes.
[Traduit par la Re
´
daction]
Introduction
Fishery management attempts to achieve a relatively large
sustainable yield while limiting the risk of severe population
declines due to inadvertent overf ishing. This is often accom-
plished through the use of control rules (e.g., Restrepo et al.
1998) that specify the level of fishing mortality (F) allowed
for a given level of biomass (B) (e.g., Fig. 1a). Target fish-
ing mortality rates and biomass levels, as well as current F
and B levels relative to the targets are generally estimated
with a stock assessment based on historical catch or catch-
at-age and biomass trend data. Such data are not often avail-
able for small-scale fisheries, recreational fisheries, and
bycatch species. For data-poor fisheries, particularly those
lacking historical catch data, decades may be required to
gather sufficient data to parameterize a stock assessment
model. In North America, Australia, New Zealand, and Eu-
rope, the fraction of major harvested fish stocks that are not
assessed ranges from 30% to >70% (Beddington et al.
2007), and the fracti on assessed is even lower in the biolog-
ically diverse multispecies fisheries of the tropics. Thus,
there is a need for methods to set appropriate fishery man-
agement policies for data-poor fisheries for which stock as-
sessment is not currently feasible (Kaufman et al. 2004;
Beddington et al. 2007).
No-take marine reserves and other forms of marine pro-
tected areas have been established in coastal waters through-
out the world as tools to accomplish conservat ion and
management objectives including protecting habitat, con-
serving biodiversity, increasing spawning stock biomass of
harvested fish populations within reserves, and, in some
cases, increasing fisheri es yields around the reserve (e.g.,
Received 21 October 2009. Accepted 2 November 2010.
Published on the NRC Research Press Web site at cjfas.nrc.ca
on 4 February 2011.
J21481
Paper handled by Associate Editor Carl Walters.
E.A. Babcock.
1
Division of Marine Biology and Fisheries,
Rosenstiel School of Marine and Atmospheric Science,
University of Miami, 4600 Rickenbacker Causeway, Miami,
FL 33149, USA.
A.D. MacCall. National Marine Fisheries Service, Southwest
Fisheries Science Center, 110 Shaffer Road, Santa Cruz,
CA 95060, USA.
1
Corresponding author (e-mail: ebabcock@rsmas.miami.edu).
343
Can. J. Fish. Aquat. Sci. 68: 343–359 (2011) doi:10.1139/F10-146 Published by NRC Research Press
Lubchenco et al. 2003). Reserves are also sometimes in-
tended as ‘‘reference sites’’ to allow scientists to compare
fished and unfished conditions (Bohnsack 1999).
For fish species that are harvested in areas around no-take
marine reserves, ratios of fish density outside versus inside
the reserves may be a useful indicator of the impact of fish-
ing. Specifically, the ratio of fish density outside to fish den-
sity inside reserves could be used as a proxy for biomass
depletion (B/B
target
) in control rules, thus eliminating the
need for a stock assessment to estimate depletion. In the ab-
sence of an assessment to estimate F/F
limit
, the y axis of the
control rule could specify an allowable level of nominal
fishing effort (an absolute response) or a level of nominal
effort relative to effort in the previous year (a relativ e re-
sponse). For example, a reserve-based control rule might
specify that if the density ratio is above the target reference
point of 60%, the fishery may continue with no additional
restrictions, even if effort has a tendency to increase; below
a limit density ratio of 20%, the fishery would be closed. In
between, effort would be reduced progressively, for example
by reducing the length of the fishing season (Fig . 1b). Den-
sity ratios could be calculated based on monitoring data, ei-
ther from visual transects, or from cooperative surveys using
recreational or commercial fishing gear fished both outside
and inside the reserve, releasing all fish caught in the re-
serve. By using typical fishing gears, the species selectivities
in the surveys are well-aligned with the corresponding selec-
tivities and species impacts in the managed fisheries.
Management using density-ratio control rules around ma-
rine reserves would requi re much less data than would man-
agement based on stock assessment. Historical catch, effort,
or abundance trend data are not needed, nor is it necessary
to document current catches (although it still may be desir-
able). Also, because the method is based on spatially ex-
plicit monitoring data, the density ratios can be calculated
at a more local spatial scale than typical stock assessments,
so that the density ratio approach may be more consistent
with the spatial scale of the fisheries and the fish popula-
tions (Palumbi 2004). However, the method may not be ef-
fective for fisheries management if some of its assumptions
are violated. For a density-ratio control rule to be effective,
the density inside the reserve must tend toward unfished
conditions, and the estimated densities outside the reserve
must be representative of the fished portion of the stock.
Movement of adult fish across the edge of the reserves
could lead to an edge effect that might introduce bias in the
data used to calculate density ratios, which in turn could al-
low too much fishing effort to develop. The redistribution of
fishing effort around the reserves to take advantage of spill-
over would have implications for fisheries yields and for the
design of monitoring programs to be used to calculate den-
sity ratios. Of course, these problems with reserve bounda-
ries also pose difficulties for conventional assessments
(Field et al. 2006).
This paper presents a management strategy evaluation
(MSE; e.g., Punt et al. 2008) of control rules based on den-
sity ratios. We simulate fisheries for a group of five hypo-
thetical species with differing life history and fishery
characteristics, based on the assessed species in the Califor-
nia nearshore fishery, and also vary the simulated movement
rates, the spatial scale and timing of density dependence in
recruitment and other aspects of their biology. We apply
several kinds of density-ratio control rules to determine
which rule would cause a simulated fish population to re-
main above a target biomass while allowing high levels of
fishery yield, for a plausible range of fish life histories. We
also evaluate the implications of using the method for a
multispecies fishery, for imperfect control of fishing effort
and for increased stochasticity in recruitment and in the
monitoring program.
Materials and methods
The MSE simulation framework (Fig. 2) included a bio-
logical model, a sampling model, a management model, and
Fig. 1. Control rules where (a) allowable fishing mortality rate (F) is a function of biomass (B) or (b) allowable fishing effort relative to
effort in the previous year is a function of the ratio of fish densities outside versus inside a no-take marine reserve.
Fig. 2. Management strategy evaluation framework.
344 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
a fisheries model. The biological model specified the popu-
lation dynamics of the fish in each spatial area, using an
age-structured model based roughly on the stock assess-
ments for five assessed species of nearshore groundfish
from central California. In each year, the sampling model si-
mulated the collection of monitoring data inside and outside
the marine reserves, roughly equivalent to a scuba monitor-
ing program. The simulated data were then used to calculate
the ratio of fish densities outside reserves to inside reserves.
The management model was a control rule that specified the
amount of fishing effort allowed in each year based on the
density ratio calculated from the previous year’s monitoring
data. The simulated fishery then occurred, including imper-
fect control of fishing effort in some scenarios, and the num-
ber of fish removed by the fishery fed back into the
biological model.
Biological model
The spatial structure of the model consisted of five se-
quential areas along a coast, of which the center, containing
20% of the coastline, was eventually designated as a pro-
tected area. Movement and larval drift occurr ed between ad-
jacent areas only, so that the two areas adjacent to the
reserve were most likely to benefit from spillover from the
reserve, compared to the two areas farthest from the reserve.
At the beginning of each year, the following equations
were used to describe the population dynamics of the target
species:
ð1Þ N
a
R
;s;t
¼ R
s;t
at the age of recruitment a
R
N
a;s;t
¼ N
a$1;s;t$1
exp½$ðF
a$1;s;t$1
þ MÞ' at intermediate ages
N
a
max
;s;t
¼ N
a
max
$1;s;t$1
exp½$ðF
a
max
$1;s;t$1
þ MÞ' þ N
a
max
;s;t$1
exp½$ðF
a
max
;s;t$1
þ MÞ' at the plus group age ða
max
Þ
where N
a,s,t
is the number of fish and F
a,s,t
is the fishing
mortality rate at age a in area s in year t, and M is the nat-
ural mortality rate. The maximum nominal age a
max
is a
‘‘plus group’’ accumulator subject to annual natural and
fishing mortality rates. For scenarios in which fish were al-
lowed to migrate between adjacent areas, movement was in-
stantaneous at the beginning of the year, immediately after
the numbers at the beginning of the year were calculated:
ð2Þ N
a;1;t
¼ð1 $ pÞN
a;1;t
þ pN
a;2;t
in the first area ðs ¼ 1Þ
N
a;s;t
¼ð1 $ 2pÞN
a;s;t
þ pN
a;s$1;t
þ pN
a;sþ1;t
in intermediate areas
N
a;s
m
;t
¼ð1 $ pÞN
a;s
m
;t
þ pN
a;s
m
$1;t
in the last areaðs
m
Þ
where p is the probability of a fish migrating from one area
to the adjacent one.
Recruitment follows the Beverton–Holt form (Dorn 2002),
for example when recruitment occurs within one spatial area
(s):
ð3Þ R
s;t
¼
0:8R
0
hB
s;t$a
R
0:2B
0
ð1 $ hÞþðh $ 0:2ÞB
s;t$a
R
expð3
t
$ s
2
R
=2Þ
where R
s,t
is number of recruits in area s in year t; B
s,t
is
spawning stock biomass calculated as the sum across all
ages of the product of numbers, weight, and fraction mature
at age; h is the steepness parameter; R
0
is unfished recruit-
ment; B
0
is unfished spawning stock biomass; s
R
is the stan-
dard deviation in recruitment; and 3
t
is an error term, which
may include autocorrelation:
ð4Þ 3
t
¼ r
R
3
t$1
þ h
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ r
2
R
q
where h is the is a normally distributed random variable
with mean 0 and standard deviation s
R
, and r
R
is the auto-
correlation in recruitment (Punt et al. 2008). The spatial dis-
tribution of recruitment can follow any of five models
(Ralston and O’Farrell 2008; Table 1), which allowed den-
sity dependence to occur either regionally or in the local
areas, either before or after larval dispersal.
Fishing mortality rates for each area, species and time
were calculated as follows:
ð5Þ F
sp;a;s;t
¼ q
sp
S
sp;a;s
E
s;t;
where q
sp
is the catchability for each species (sp), calculated
as
ð6Þ q
sp
¼
AF
sp;b
X
s
E
s
and A is the number of areas, F
sp,b
is the fully selected fish-
ing mortality rate on the whole population before the reserve
was implemented, and E
s
is the nominal effort in each area,
before the reserve was implemented (assumed to be the
same in all areas). The selectivity for each species (sp) at
age a is the sum of the selectivity at age for each fleet
(S
sp,a,f
) ( the fraction of fisheries catches in each fleet (c
f
):
ð7Þ S
sp;a
¼
X
f
c
f
S
sp;a;f
The selectivity in each fleet was either a logistic function
of length at age (L
a
):
ð8Þ S
sp;a;f
¼
1
1 þ exp½$aðL
a
$ L
50
Þ'
or double logistic in which case the left (ascending) side of
the curve followed eq. 8, while the right side declined from
1 to F
fin
following a logistic curve:
Babcock and MacCall 345
Published by NRC Research Press
ð9Þ S
sp;a;f
¼ 1 $
ð1 $ F
fin
Þ
1 þ exp½$bðL
a
$ L
50
Þ'
Length at age followed the von Bertalanffy growth func-
tion defined in terms of two reference ages (a
1
and a
2
; Me-
thot 2000):
ð10Þ L ¼ L
1
þðL
1
$ L
1
Þexp ½$Kða $ a
1
Þ'
L
1
¼ L
1
þ
ðL
2
$ L
1
Þ
1 $ exp ½$Kða
2
$ a
1
Þ'
Weight at length was calculated as
ð11Þ w ¼ aL
b
Maturity at age was a logistic function.
Sampling model
For model runs assuming perfect information, the density
ratio was calculated as the average number of fish per area
in the fished areas outside the marine reserve, divided by the
average number of fish per area inside the reserve. For runs
with uncertainty and variability, the density ratio was calcu-
lated from a sampling program designed to mimic the Part-
nership for Interdisciplinary Studies of Coastal Oceans
(PISCO) visual transect surveys (PISCO 2008). A fixed
number of transects were sampled in each spatial area in
each year, and the number of fish seen in each transect fol-
lowed a delta lognormal distribution. For each transect,
whether each species was seen at least once was determined
with a random Bernoulli draw, with probability
ð12Þ p
sp;t;s
¼ d
sp
N
sp;t;s
where N
sp,t,a
is the number of fish above the age of recruit-
ment (or the age at maturity if using control rule 5) in area s
at time t and the constant of proportionality d
sp
was calcu-
lated as
ð13Þ d
sp
¼
r
sp
B
2003
=B
o
where r
sp
is the observed proportion of positive transects in
the PISCO data in 2000–2006 and B
2003
/B
o
is the observed
depletion in 2003, according to the assessments.
For transects in which a species was observed, the count
of that species was drawn from a lognormal distribution:
ð14Þ C
sp;t;s
¼ g
sp
N
sp;t;s
expðh
c
Þ
where h
c
is a normal variable with mean zero and standard
deviation derived from PISCO transects as
ð15Þ s
sp
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ln
"
1 þðs
p
=
!
xÞ
2
r
where
!
x and s
p
are the mean and standard deviation of each
species in PISCO transects for which the species was seen,
and g
sp
is calculated as
ð16Þ g
sp
¼
!
x
B
2003
=B
o
The density ratio D
sp
for each species was calculated as
the average number of individual fish seen per transect out-
side the reserve divided by the average number seen per
transect inside the reserve, counting zero observat ions:
ð17Þ D
sp
¼
X
C
sp;out
=n
out
X
C
sp;in
=n
in
where C is the number of fish seen and n is the number of
transects either in fished areas or in the marine reserve. In
practice, density ratios should be normalized so that the ratio
is 1.0 before the implementation of the reserve. In this mod-
eling exercise, the spatial areas were identical before reserve
implementation, so it was not necessary to divide by the pre-
reserve density ratio.
Multispecies density ratios were calculated with either (1)
the arithmetic mean of the values for each species, (2) the
geometric mean, (3) the harmonic mean, or (4) the mini-
mum value across the species.
Management and fisheries models
In each simulation, we ran the model for 50 years with a
constant level of fishing effort to generate a fished popula-
tion with the level of depletion required for each species
(see next section for specifics). The marine reserve was
Table 1. Recruitment models considered.
Description Formula
I Density dependence occurs independently in each spatial area
R
s;t
¼
0:8R
s
0
hB
s;t$a
R
0:2B
s
0
ð1$hÞþðh$0:2ÞB
s;t$a
R
II Density dependence occurs at the regional level and recruits are distributed
evenly across areas, or larvae are distributed evenly followed by local
density dependence based on the local number of larvae
R
s;t
¼
1
A
#$
0:8R
o
h
P
B
s;t$a
R
0:2B
o
ð1$hÞþðh$0:2Þ
P
B
s;t$a
R
!
III Density dependence occurs within spatial areas, but recruits are spread evenly
across areas
R
s;t
¼
1
A
#$
X
s
0:8R
s
0
hB
s;t$a
R
0:2B
s
0
ð1 $ hÞþðh $ 0:2ÞB
s;t$a
R
%&
IV The pooled larvae from all areas are distributed evenly to each area, and then
density dependence occurs based on the number of spawners in each area
R
s;t
¼
0:8R
s
0
h
0:2B
s
0
ð1$hÞþðh$0:2ÞB
s;t$a
R
%&
1
A
#$
X
s
B
s;t$a
R
V Recruitment is independent in each area, but a fraction of the recruits in each
area drift to the adjacent areas before settling
R
)
s;t
¼
0:8R
s
0
hB
s;t$a
R
0:2B
s
0
ð1$hÞþðh$0:2ÞB
s;t$a
R
;
R ¼ R
)
( d
Note: A is the number of areas; d is the transition matrix for larval drift; a
R
is age at recruitment; R
s,t
is recruitment in time t in area s; and B
s,t
is
spawning stock biomass. When density dependence occurs within a spatial area (s), the corresponding unfished recruitment is
R
s
0
¼ R
0
=A and unfished
biomass is
B
s
0
¼ B
0
=A.
346 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
Table 2. Control rules used in the simulations.
Control rule
Control rule
type
Target density
ratio
Effort increase
allowed
Years
sampled
Fished areas
sampled Fish sampled
1 Effort NA 0.1 NA NA NA
2 DR 0.6 0.1 3 All All
3 DR 0.6 0.1 1 All All
4 DR 0.6 0.1 1 Far from reserve All
5 DR 0.6 0.1 1 All Mature
6 DR 0.8 0.1 1 All All
7 Effort NA 0 NA NA NA
8 DR 0.6 0 1 All All
Note: DR indicates density-ratio control rules.
Table 3. Input parameters for the simulation model and their source.
Description Parameter Values for each species
Stock name Black RF Blue RF Gopher RF Cabezon Vermilion RF
Primary reference Ralston and Dick
(2003)
Key et al.
(2007)
Key et al.
(2005)
Cope and Punt
(2005)
MacCall
(2005)
Maximum age a
max
35 44 24 17 65
Natural mortality M 0.14 0.1 0.2 0.275 0.1
Age at recruitment a
R
21111
a
f
1.68 ( 10
–5
3.41 ( 10
–5
1.32 ( 10
–5
1.24 (10
–5
1.74 (10
–5
Weight at length parameters
(male and female)
b
f
3 2.874 3.077 3.113 2.995
a
m
1.68 ( 10
–5
2.93 ( 10
–5
1.32 ( 10
–5
1.99 ( 10
–5
1.74 (10
–5
b
m
3 2.889 3.077 2.997 2.995
Growth parameters
(male and female)
a
1,f
52554
L
1,f
32.21 17.9 22.2 41.3 28.68
a
2,f
15 25 15 30 30
L
2,f
47.95 37.5 31.2 61.9 53.738
K
f
0.2022 0.147 0.186 0.18 0.1932
a
1,m
52554
L
1,m
31.88 15.7 22.2 38.6 28.68
a
2,m
15 25 15 30 30
L
2,m
45.39 31.2 31.2 46.8 53.738
K
m
0.1979 0.295 0.186 0.28 0.1932
Length at 50% maturity L
50
39.53 26 17.7 25.702 38
Slope of maturity curve k
mat
0.4103 0.7 4.3 0.743 0.5
Larval drift proportion* d 0.1 0.1 0.1 0.1 0.1
Unfished recruitment* R
o
100 000 100 000 100 000 100 000 100 000
Steepness h 0.65 0.58 0.65 0.7 0.65
Unfished recruits per spawner 4 1.1 0.91 0.23 0.71 2.9
Recruitment standard deviation s
R
0.5 0.5 0.5 1 0.7
Recruitment autocorrelation r
R
00000
Adult movement proportion* p 0.1 0.1 0.1 0.1 0.1
Depletion B
2003
/B
0
0.488 0.238 1 0.4 0.59
Fishing mortality to cause observed
depletion*
F
b
0.2 0.3 0.02 1.1 0.025
Number of fisheries 3 4 3 6 4
Proportion of positive transects in the
monitoring data (PISCO)
r 0.77 0.48 0.29 0.27 0.70
Mean number of fish seen in positive
transects (PISCO)
!
x 15.42 12.46 1.51 3.27 166.02
Standard deviation of positive
transects(PISCO)
s
p
16.97 25.49 0.75 3.32 238.72
Note: Parameter values were taken from the stock assessment documents specified in the table except where noted as from PISCO data, or set arbitrarily
(indicated with an asterisk, *).
Babcock and MacCall 347
Published by NRC Research Press
then implemented and the model was run for 50 more years.
The density-ratio control rules were implemented, beginning
from the same year that the reserve was established. After
reserve implementation, the effort displaced from the re-
serves (=20% of the total) was allocated either equally to
each open area, or was redistributed according to the ideal-
free distribution (e.g., Gillis et al. 1993). In the ideal-free
case, effort was allocated proportionally to the fraction of
the total fishable biomass in each area. In the multispecies
case, effort was allocated proportional to the total biomass
in each area.
The total allowed fishing effort, after the marine reserve
was implemented, depended on the eight control rules that
were considered (Table 2), numbered from the least to the
most precautionary. In addition to density-ratio control rules,
a scenario with constant effort (control rule 7), and one with
increasing effort (control rule 1) were included. In the case
of the density-ratio contro l rules, allowable effort each year,
as a fraction of the effort in the previous year, was calcu-
lated based on the density in the previous year (Fig. 1b). Be-
ginning the first year of the marine reserve, total allowable
effort decreased linearly from the starting effort if the meas-
ured density ratio fell below the target density ratio, and was
reduced to zero if the density ratio fell below the limit (20%
in all control rules). In the case that effort was reduced to
zero, the ‘‘previous year’s effort’’ for the purpose of calcu-
lating the allowable effort in the following year was set
equal to 10% of the effort on the year the reserve was im-
plemented; this allowed effort to increase again after it had
gone to zero, despite the fact that the control rule defines al-
lowable effort with respect to the previous year’s effort. In
some control rules the effort was allowed to increase by
10% every year that the density ratio remained above the
target density ratio, to mimic a fishery that was expanding
with no controls other than the use of a density-ratio control
rule, which only controlled effort if the density ratio
dropped below the target density ratio. The target density ra-
tio was either 60% of all fish, 80% of all fish, or 60% of
mature fish, and the density ratio was calculated either using
data from the previous year or from the three previous years,
and from either all fishing areas, or just the areas farthest
from the reserve (Table 2).
Data-rich assessed species on the US West Coast are gen-
erally managed using a fishing mortality rate target of F
40%
,
which is the fishing mortality rate that would result in a
spawning potential ratio of 40% of the unfished level (Clark
2002). As a point of comparison, we ran simulations for all
five species for 150 years with constant fishing mortality
rates between 0 and 1.0 and no marine reserves, to calculate
F
40%
and the associated spawning stock biomass and yield.
We also calculated the biomass and yield associated with
F
35%
and F
50%
, as well as with a constant F policy that
would result in an equilibrium spawning stock biomass of
40% of the unfished level (a B
40
strategy).
Fig. 3. Selectivities for (a) black rockfish, (b) blue rockfish, (c) gopher rockfish, (d) cabezon, and (e ) vermilion rockfish, inferred from
figures in Ralston and Dick (2003), Key et al. (2007), Key et al. (2005), Cope and Punt (2005), and MacCall (2005). Unbroken lines are
commercial fisheries, dashed lines are recreational fisheries, and dotted lines are commercial passenger fishing vessels.
348 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
Input data for the five speci es
The input parameters (Table 3) were loosely based on the
biology and fisheries for black rockfish ( Sebastes melanops,
Ralston and Dick 2003), blue rockfish (Sebastes mystinus,
Key et al. 2007), gopher rockfish (Sebastes carnatus, Key
et al. 2005), vermilion rockfish (Sebastes miniatus, MacCall
2005), and cabezon (Scorpaenichthys marmoratus, Cope and
Punt 2005). These species were chosen because assessmen ts
were available, and they show an interesting range of life
histories, fisheries, and levels of depletion. Most of the input
parameters were taken directly from the assessments, except
that the selectivities (Fig. 3) were estimated from figures in
most cases. For the stock recruitment relationship, we used
the steepness (h) value from the assessments, but set R
0
to
the same number for all five species. This was done because
the spatial extent of the assessments was different, so that it
was difficult to determine appropriate levels of relative
abundance. We defined the stock–recruit relationship in
terms of female spawning stock biomass, not total spawning
stock biomass (SSB) or egg production, for consistency
across species. The fraction of fish that would migrate from
one area to the next was set arbitrarily at either 0 or 10%
per year across each reserve boundary. For model runs that
included a monitoring program, the number of transects in
each area in each year was set arbitrarily to 50 in the reserve
and 25 in each outside area.
Scenarios for management strategy evaluation
Perfect information
To screen a number of factors that could influence the
performance of a density-ratio control rule, we first ran the
model for each individual species with no stochasticity in
the biological processes, with perfect information about den-
sity ratios, and with perfect control of fishing effort (i.e., no
implementation error). The factors that varied between
model runs were (1) control rule (one of the 8 control rules
defined in Table 2); (2) effort distribution (even or ideal-
free); (3) adult movement (none, or 10% diffusion); and (4)
recruitment model (5 options defined in Table 1).
There were 160 combinations of these factors fo r each
species for the single-species runs.
For the multispecies cases, we used control rules 3 and 6,
for all combinations of fleet distribution, recruitment model,
and movement model. Effort was allocated according to the
multispecies density ratio, which was calculated by geomet-
ric mean, arithmetic mean, harmonic mean, or the minimum
value, for a total of 160 multispecies runs.
The ratio of spawning stock biomass at the end of each
decade after reserve establishment to spawning stock bio-
mass when reserves were established, and the average yield
across each decade after the reserve was established were
calculated as performance indicators.
Fig. 4. Effect of type of density-ratio control rule (numbered by increasing precaution) on spawning stock biomass at the end of each decade
post reserve (bars, grouped by control rule and ordered by decade within groups), and average fishery yield across each decade (points), for
(a) black rockfish, (b) blue rockfish, (c) cabezon, and (d) vermilion rockfish. The unbroken horizontal line indicates the spawning stock
biomass at 40% of the unfished level, and the broken horizontal line is the yield associated with an F
40%
policy. Relative biomass (right side
of each plot) and yield (left side of each plot) are also shown for F
35%
, B
40%
, and F
50%
strategies. Biomass and yield are plotted relative to
the values in the year the reserve was established, and model results are averaged across all 20 life history and fleet dynamics models.
Babcock and MacCall 349
Published by NRC Research Press
Implementation error and stochasticity
Four implementation error scenarios were modeled: (A)
no implementation erro r, (B) effort inflation, (C) illegal fish-
ing in the reserve, and (D) both effort inflation and illegal
fishing. In scenarios B and D, the amount of effort in the
fished areas was always 5% more than the control rule al-
lowed, and managers were not aware of this. Thus, the al-
lowable effort specified by the control rule was always
based on the ‘‘legal’’ effort in the previous year, not the in-
flated true effort. In scenar ios C and D, the amount of illegal
fishing in the reserve increased with decreasing density ratio
up to 10% of total effort when the density ratio (D) was
very low.
ð18Þ E
reserve
¼ 0:1ð1 $ DÞ
These scenarios were run for all individual species control
rules with perfect information and no stochasticity, for six
runs per species with and without movement, using control
rules 3, 5, and 6. Recruitment was local (model I) and legal
effort was evenly distributed.
To evaluate the influence of both natural variability and
uncertainty in the calculation of density ratios we also ran
the model with variability for each individual species. For
these scenarios, we specified no implementation error, re-
cruitment model I, uniform effort distribution and move-
ment. The following factors varied: (1) monitoring program
sample size, either as specified above or multiplied by 5; (2)
log standard deviation of recruitment either 0.2 or 0.5; (3)
serial correlation of recruitment either none or 0.5; and (4)
control rule 3 or 6.
For each set of input parameters, we ran 100 simulations,
and calculated the probability that spawning stock biomass
was above 40% of the unfished spawning stock biomass
20 years after the reserve was established, as well as the
probability that the yield in the 20th year was higher than
the yield the year before the reserve was established.
Results
Description of species
Of the five species of nearshore fishes used in this simu-
lation exercise, blue rockfish was the most depleted when
the marine reserve was implemented, with a simulated
spawning stock biomass at 23.8% of unfished levels
(Table 3). Gopher rockfish, on the other hand, was at the
unfished level when the reserve was implemented; we as-
sumed that there had been a low level of fishing mortality
for gopher rockfish before implementation of the reserve.
Because of this assumption, gopher rockfish biomass never
declined significantly with any of the control rules. We
present no results for gopher rockfish, but we kept it in the
simulations because it was interesting to have one lightly
fished species in the multispecies simulations. The other
species were at intermediate levels of depletion (Table 3).
The species varied in productivity, growth, and longevity,
and in the selectivity patterns for their fisheries (Fig. 3).
Fig. 5. Black rockfish dynamics with a target density ratio of 60% (a and b, control rule 3) versus 80% (c and d, control rule 6), including
spawning stock biomass in the reserve (bold unbroken lines, left panels) and fished areas (narrow unbroken lines, left panels), total yield
(broken line, left panels), total effort (broken lines, right panels), and density ratio (bold unbroken lines, right panels), all relative to the
levels when the reserve was established, for model runs with no movement, even distribution of fishing effort, and recruitment model II.
350 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
Perfect information scenarios
For the scenarios with perfect information and no varia-
bility, the eight control rules demonstrated the expected
tradeoff between high short term yield and the maintenance
of biomass that would allow continuing yield in the long
term (Fig. 4). Control rules 2, 3, and 4 (target density ratio
of 60% and density ratio based on all post recruit fish) al-
lowed effort to increase in the first 20 years, causing bio-
mass to decline and yields to be lower in the last decade.
These control rules perfo rmed only slightly better than an
unregulated fishery with increasing effort (rule 1), and al-
lowed populations to decline to below 40% of the unfished
spawning stock biomass for all four species. Control rules 5
(target density 80%) and 6 (density ratio computed on ma-
ture fish) were better able to maintain biomass and long
term yield, and control rule 5 successfully rebuilt blue rock-
fish to 40% of unfished spawning stock biomass (Fig. 4b).
The control rule based on absolute effort (rule 8) had the
same effect as fixing effort at the current level (rule 7) for
all species except blue rockfish (Fig. 4b), for which the den-
sity ratio control rule (8) increased spawning stock biomass
because the density ratio control rule reduced effort below
the current level.
Comparing the yields and spawning stock biomass levels
in the last year of the simulation with those that would be
expected under a constant F
40%
policy (horizontal lines in
Fig. 4), control rule 3 resulted in a biomass of 41%–61% of
that under F
40%
, and a yield of 68%–79% of the yield under
F
40%
. In contrast, control rule 5 achieved a spawning stock
biomass of 103%–114% of that under F
40%
, and a yield of
80%–89% of the F
40%
yield.
Control rules 5 and 6 performed better than control rules
2, 3, and 4, but all of these rules allowed an increase in ef-
fort in the first few years after the reserve was established,
before densities could build up in the marine reserve. They
also caused effort, and consequently, biomass, to oscillate
(e.g., Fig. 5) throughout the simulation as effort increased
until the density ratio fell below the target level, which then
reduced effort until the biomass had recovered. The fluctua-
tion in effort was less extreme and appeared to damp out
over time for the control rule with a higher target density ra-
tio (rule 6, Figs. 5c and 5d), and the one based on densities
of mature fish (rule 5). Basing the allowable effort on a den-
sity ratio calculated from the previous three years, rather
than just the previous year did not reduce the fluctuati on in
effort (rule 2).
The most important biological factor influencing the ef-
fectiveness of the density-ratio control rules was whether
post-recruit fish could move between spatial areas (Fig. 6).
For the overfished blue rockfish, the population increased
without movement for all control rules; with movement, the
population was stable under control rules 5 and 6 but de-
clined under control rules 2, 3, and 4 (Fig. 6b). Specifically,
for blue rockfish under control rule 3 without movement
Fig. 6. Effect of whether or not fish move between areas (with control rules 2–4, or control rules 5 and 6) on the average across life history,
fleet dynamics and density-ratio control rules, of spawning stock biomass at the end of each decade post reserve (bars, grouped by scenario
and ordered by decade within groups), and average fishery yield across each decade (points) for (a) black rockfish, (b) blue rockfish, (c)
cabezon, and (d) vermilion rockfish. The unbroken horizontal line is spawning stock biomass at 40% of the unfished level, and the broken
horizontal line is the yield associated with an F
40%
policy.
Babcock and MacCall 351
Published by NRC Research Press
(Figs. 7a and 7b), the density ratio dropped off as effort in-
creased and then started to oscillate, but the spawning stock
biomass trend was positive even in the fished areas. With
movement (Figs. 7c and 7d), biomass did not build up as
much inside the reserve. Therefore, the density ratio fell off
only gradually, even as the total population was declining,
and the control rule did not initiate reductions in effort until
20 years after the reserve was established. For black rock-
fish, cabezon, and vermilion rockfish, which were not overf-
ished, the movement scenarios cause the population to
decline, especially using the less precautionary control rules,
while the population was stable without movement
(Figs. 6a,6c, and 6d). The yields were higher with move-
ment for the first few decades, but declined later as the bio-
mass declined, owing to overfishing.
The spatial distribution of recruitment had ver y little in-
fluence on the performance indicators in the first decade,
but became important over time as spawning stock biomass
accumulated in the marine reserve (Fig. 8). Strictly local re-
cruitment (model I) allowed the greatest increase in bio-
mass, particularly for the overfished blue rockfish; this
recruitment scenario also showed the lowest yields in the
first few decades but higher yields in the long term. The re-
cruitment model with post-dispersal density dependence
(model IV) had the highest yields at first, but both biomass
and yield decreased with time. Many control rules per-
formed badly with post-dispersal density dependence (model
IV) because, when biomass built up in the marine reserves,
this caused recruitment, paradoxically, to be lower in re-
serves. The control rule based on the density ratio of mature
fish only (rule 6, Figs. 8c and 8d) controlled effort very
well, even with post-dispersal density dependence.
Whether the fishing fleet was assumed to be evenly dis-
tributed, or able to move to areas with higher catch-per-
unit-effort (CPUE) did not influence the results substan-
tially. Model runs with spillover of adults from the reserve
and ideal-free effort distribution resulted in slightly more ef-
fort in the areas nearer the reserve, but the difference in bio-
mass and yield between the ideal-free and evenly distributed
scenarios was very small (fractions of a percent, not shown).
For the multispecies runs, the results depended on
whether the density ratios were combined by arithmetic,
geometric, or harmonic mean, or the minimum value across
the five species (Fig. 9a for black rockfish and Fig. 9b for
blue rockfish). For every species except blue rockfish
(Fig. 9b), using the minimum density ratio caused the bio-
mass at the end of the simulation to be higher than it would
have been under single-species management focused on that
species (e.g., Fig. 9a). For a typical multispecies model run
(Fig. 9c), the density ratio for gopher rockfish stayed near
1.0, while the density ratio for blue rockfish dropped off
sharply. The arithmetic mean remained higher than the geo-
metric mean, which was higher than the harmonic mean.
The contro l rule based on blue rockfish (or the minimum
value) began to reduce effort after 20 years in this scenario
(Fig. 9d), followed by the control rule for black rockfish and
Fig. 7. Blue rockfish dynamics without movement (a and b) and with movement (c and d), including spawning stock biomass in the reserve
(bold unbroken lines, left panels) and fished areas (narrow unbroken lines, left panels), total yield (broken line, left panels), total effort
(broken lines, right panels) and density ratio (bold unbroken lines, right panels), all relative to the levels when the reserve was established,
for model runs with control rule 3, even distribution of fishing effort, and recruitment model I.
352 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
cabezon, then the harmonic mean and geometric mean, then
the arithmetic mean, then finally vermilion rockfish. The go-
pher rockfish control rule had no effect in 50 years.
Implementation error and stochasticity
For the simulations with imperfect control of effort, effort
being 5% higher than the control rule specified each year
did not change the results (Fig. 10, scenario A compared
with B, and C compared with D). For both black rockfish
(Fig. 10a) and blue rockfish (Fig. 10b), the runs with effort
inflation were identical to those without. The density ratios
control rules were all able to compensate for the increase in
effort in every year, because they continued to reduce allow-
able effort until the density ratio recovered above the target
level. On the other hand, illegal fishing in the reserve re-
duced the biomass achieved by the control rules (Fig. 10,
compare scenarios A and B with scenarios C and D). In a
typical model run for black rockfish, with no movement
and control rule 3, illegal fishing in the reserve caused bio-
mass in the reserve to fluctuate (Figs. 10c and 10d), which
was not the case for the same scenario without implementa-
tion error (Figs. 5a and 5b). This caused yield to fluctuate
much more than it did without illegal fishing and reduced
the final spawning stock biomass.
For the simulations with variability in the recruitment and
the density ratio estimates, (Fig. 11) lower sample sizes in
the monitoring program increased the probability that the bi-
omass would be above the target value of 40% of unfished
SSB in 20 years (Fig. 11a) for both the more risky and the
more precautionary control rule. The effect on yield was
more variable (Fig. 11b). Increasing the variance in recruit-
ment similarly increased spawning stock biomass (Fig. 11c).
Autocorrelation in recruitment had little effect on the results
(Figs. 11e and 11f). The increasing biomass associated with
higher variability appeared to be caused by the fact that
higher variation in the density ratio (Fig. 12) meant that
each simulated density ratio trajectory occasionally fell be-
low the density ratio target, thus requiring a reduction in ef-
fort.
A control rule based on density ratio pooled across the
previous three years (control rule 2) reduced the variability
in the density ratio so that the effort, yield and biomass tra-
jectories were more similar to what would be seen with a
higher sample size in the monitoring program.
Discussion
Selection of control rules
The biomass and yield achieved with each density-ratio
control rule varied, but control rule 5 (target density ratio is
60% of mature fish) and control rule 6 (target density ratio
is 80% of all fish) both caused the spawning stock biomass
to equilibrate around 40% of the unfished level, eventually,
for most life history scenarios, achieving yields around
75%–90% of the yield that would be achieved under an
Fig. 8. Effect of recruitment model, with a density ratio target of 80% of all fish (rule 6), for (a) black rockfish and (b) blue rockfish, or a
target density ratio of 60% of mature fish (rule 5), for (c) black rockfish, and (d) blue rockfish, on spawning stock biomass at the end of
each decade post reserve (bars, grouped by recruitment model and ordered by decade within groups), and average fishery yield across each
decade (points). The unbroken horizontal line is spawning stock biomass at 40% of the unfished level, and the broken horizontal line is the
yield associated with an F
40%
policy.
Babcock and MacCall 353
Published by NRC Research Press
F
40%
policy. A related modeling study that compared cumu-
lative catches over time between optimal density-ratio con-
trol rules and optimal constant F harvest strategies, found
that the density-ratio control rules consistently achieved
around 70% of the cumulative catch achieved by the optimal
constant F strategies (McGilliard et al. 2010). In practice, it
is difficult to estimate optimal fishing mortality rates, even
for assessed species (Clark 2002), and the density-ratio con-
trol rule has the advantage that it does not require estimates
of either reference points or stock status.
Interestingly , the status of the population when the reserve
was established did not greatly influence the biomass that
was achieved at the end of the simulation under the density-
ratio control ru les. For the species that were not overfished,
the control rules allowed a greater increase in effort during
the first few decades than that allowed for the overfished
species, but the final SSB, relative to unfished levels, was
similar for all four species (not counting gopher rockfish,
which was never fished down in our simulations). There
was more variation between life history scenarios than be-
tween species with different levels of initial depletion. In
other words, if one of the more precautionary density-ratio
control rules was used, the population would eventually end
up near or above 40% of unfished SSB, irrespective of its
initial level of depletion. If this result holds for a wider vari-
ety of the fish life history types, movement patterns, and
fisheries, then the density-ratio control rule could be very
useful for low-data fisheries management.
On the other hand, the initial status of the population was
relevant when multispecies control rules were used. Because
blue rockfish started out depleted, it could develop low den-
sity ratios quickly as the population rebuilt in the reserve
and (for some scenarios) declined outside the reserve. For
vermilion rockfish, which started out at 60% of unfished
levels, the density ratio did not drop off until much later, be-
cause there was less scope for increase in the reserve. Thus,
when a multispecies density-ratio control rule was used, the
year that effort restrictions started to be imposed depended
on the relative weight given to species at differing levels of
starting depletion. This is a general problem when fish com-
plexes are managed based on an average indicator of status,
and density ratios do not perform better or worse in this re-
spect than assessment-based indicators.
Density-ratio control rules 2 through 6 had the unfortu-
nate effect that they allowed effort to increase immediately
after the reserve and the control rule were implemented,
and did not require effort reduction until the reserve had
been in place long enough for differences in fish density to
build up between fished and unfished areas (see also McGil-
liard et al. 2010). Some initial increase in effort was appro-
priate for the populations that were not overfished, but not
for the overfished blue rockfish. Additional restrictions in
Fig. 9. Multispecies density ratios compared with single-species density-ratio control rules: (a) Difference between multispecies and single-
species values for the increase in spawning stock biomass (SSB) after 50 years for black rockfish; (b) the same for blue rockfish; (c) density
ratios for a multispecies model run with perfect information, movement between areas, local recruitment and control rule 3, multispecies
density ratio calculated as the geometric mean of the values for the five species, with the other density ratio means shown for comparison;
and (d) density ratios for the five species in the same model run.
354 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
effort may be advisable for the first few years of the exis-
tence of a marine reserve, unt il there has been time for den-
sity to build up in the reserve. The more precautionary
density ratio targets (rules 5 and 6) became effective sooner
than the less precautionary ones, and also reduced the fluc-
tuation in allowable effort in the first few decades of man-
agement under the density-ratio control rule.
Fish biology
Of the variations in life history that we examined, the
amount of fish movement, not surprisingly, had the most im-
pact on the effectiveness of the density-ratio control rules.
With movement, biomass in the reserve never built up to
high levels and the density ratio remained high. Fish that
are good candidates for density-ratio control rules would be
those that tend not to migrate or move across distances com-
parable with the scale of the marine reserves in the area.
The species we used to parameterize the model tend not to
move long distances after recruitment. Black, blue, and ver-
milion rockfish, and cabezon were all recaptured very close
(<1 km) to their tagging location by Lea et al. (1999), while
gopher rockfish were recaptured up to 3 km from their tag-
ging location. Jorgensen et al. (2006) found that blue rock-
fish home ranges averaged just over 8000 m
2
, and
individuals seldom ventured more than 100 m from their
core areas, so that the authors concluded that there would
be little spillover of blue rockfish across reserve boundaries,
if the reserves were more than a kilometre across. The exist-
ing reserves in the Channel Islands range from 10 to
100 km
2
in area (Channel Islands National Marine Sanctuary
2007), while the Central Coast reserves average about
17 km
2
(Marine Life Protection Act Initiative 2007). Our
scenario of 10% of the population moving across each re-
serve boundary every year probably overestimates the im-
pact of movement for blue rockfish in this region, but other
species may move this much or more.
A more detailed understanding of fish movement and mi-
gratory behavior would allow for better prediction of the
likely effectiveness of a density-ratio control rule. For exam-
ple, the number of fish that leave the reserve to be exposed
to the fishery would depend on whether fish movement is or
is not density dependent, whether fish move to form spawn-
ing aggregations, whether there is ontogenetic movement
from one habitat or depth range to another, and whether pre-
ferred habitat types straddle the reserve boundary (Botsford
et al. 2009). These questions should be explored, although,
for the purposes of a density-ratio control rule, the only re-
quirement is that the rate of movement across the reserve
boundary must be low enough to allow biomass to accumu-
late in the reserve.
We also found that the timing and spatial scale of density
dependence in recruitment could influence the effectiveness
of density-ratio control rules. For the case of post settlement
density dependence, the high biomass in the reserve caused
Fig. 10. Effect of imperfect control of effort on spawning stock biomass at the end of each decade post reserve [bars, grouped by scenario
(A, perfect effort control; B, effort inflation; C, illegal fishing in the reserve; D, illegal fishing and effort inflation) and ordered by decade
within groups], and average fishery yield across each decade (points) averaged across 6 runs with control rules 3,5 and 6 with and without
movement, for (a) black rockfish, and (b) blue rockfish The unbroken horizontal line is the spawning stock biomass at 40% of unfished
levels, and the broken horizontal line is the yield associated with an F
40%
policy. Details are shown for a black rockfish model run under
scenario C without movement and with control rule 3 (c and d, compare with Figs. 5a and 5b).
Babcock and MacCall 355
Published by NRC Research Press
lower recruitment, a phenomenon that could occur for spe-
cies with strict habitat requirements in which the presence
of large numbers of conspecifics negatively impacts settlers
(Ralston and O’Farrell 2008). Using a control rule based on
the density ratio of mature fish performed well with post-
dispersal density dependence, and in fact that control rule
(rule 5) performed well for all scenarios. A density-ratio
control rule based on densities of mature fish is also more
analogous to the reference points based on spawning stock
biomass that are used for management of California near-
shore species (Kaufman et al. 2004).
Our model did not include spatial patterns in benthic hab-
itat or current flow. Differences in habitat quality inside ver-
sus outside the reserve can be removed by normalizing the
density ratio to the value that was measured the year before
the reserve was implemented (assuming monitoring was
available before the reserve), but temporal changes in habi-
tat quality, or interactions between habitat and abundance
could bias the density ratio. The density ratio could also be
biased by source–sink dynamics, for example, if many of the
larval fish settling in the reserve were produced by spawners
in the fished area. Future modeling efforts using three-
dimensional, spatially explicit models may identify issues
that were not apparent in our simple one-dimensional model.
Density-ratio control rules could also be problematic in
the presence of density dependence in growth, size and age
at maturity, or size and age of sex change for hermaphro-
dites (e.g., Ga
˚
rdmark et al. 2006). Diseases and parasites
can also be more prevalent in higher density conditions,
which could cause abundance of some species to decline in
reserves (Behrens and Lafferty 2004). Such effects could
bias the density ratio or the assumed equivalence of popula-
tion dynamics inside and outside the protected areas.
One key gap in our modeling exercise is trophic structure.
As biomass of large fish builds up in reserves, increased pre-
dation can cause a decrease in density of prey species (e.g.,
Behrens and Lafferty 2004). Large, mobile, apex predators,
such as sharks, will not be protected by a small reserve
(Chapman et al. 2005) and so may not reach their unfished
level. This can allow the large fish one trophic level below
sharks in the food web to be even more numerous and to eat
more small fish than they would in unfished conditions. Den-
sity ratio management would probably be most effective for
large meso-predators that tend to benefit from reserves, and
not necessarily for lower trophic level fish. This is would be
an interesting avenue for further research.
Fishery characteristics
The model assumed that selectivities, relative contribu-
tions of each fishing gear, and (for the multispecies runs)
relative catch ability of each species are constant over time.
In a real fishery, there would be changes over time in the
Fig. 11. Change in the probability of achieving two management objectives (left panels, spawning stock biomass greater than 40% of unf-
ished in year 20; right panels, yield higher in year 20 than in year 1), when additional variability is added to the simulations by reducing the
sample size in the monitoring data (a and b), increasing the standard deviation in recruitment (c and d) or adding autocorrelation to recruit-
ment (e and f). Each panel includes 16 single model runs (monitoring sample size is inflated by or not, s
R
= 0.2 or 0.5, r
R
= 0 or 01) for
each species (black rockfish, blue rockfish, cabezon, and vermillion rockfish). Open boxes indicate control rule 3 (target density ratio 60%),
filled boxes indicate control rule 6 (target density ratio 80%).
356 Can. J. Fish. Aquat. Sci. Vol. 68, 2011
Published by NRC Research Press
relative importance of different gear types. Also, both rec-
reational and commercial fisheries can change their target
species, and thus change their catch composition without
changing fishing effort. If a multispecies control rule was
used, changes in targeting could cause overfishing of more
depleted species. The single-species control rules, because
they are based on a direct estimate of fish abundance, will
respond automatically to such changes in targeting and gear
use. Under a multispecies control rule, additional regulations
including prohibited species, or time/area closures and gear
regulations to shift fishing pressure from depleted species to
nondepleted species might be necessary (Shepherd 2003).
The control rules we simulated controlled relative or ab-
solute effort. For some fisheries it may be possible to use
density-ratio control rules to set catch quotas. The catch lim-
its could be set at current catch levels for the first year, and
then subsequent catch limits could be set with a density-
ratio control rule that specifies catch relative to the previous
year’s catch as a function of the density ratio. A catch con-
trol rule would require complete and accurate catch data, so
fisheries where a large portion of the fishing mortality is
recreational, small scale fishing or discards could be prob-
lematic. Illegal fishing in the reserve can bias the density ra-
tio, so it is necessary that the reference reserves be well
enforced. A density-ratio control rule could provide an addi-
tional incentive for illegal fishing, not just because of the
presence of large and abundant fish, but also in an attempt
to reduce the density ratio so that the fishery will not be
subject to additional effort restrictions.
One advantage of density ratio management would be that
it could be done at a more local spatial scale than stock as-
sessment-based management, which tends to be applied
coast-wide. Density ratios can be calculated at spatial scales
considered appropriate to the biology of the fish (Palumbi
2004). Provided that monitoring data are available, those
coastal species with very short dispersal distances and very
localized recruitment dynamics could be managed with den-
sity ratios calculated for reserves within a spatial area on the
scale of a few kilometres, while species with longer disper-
sal distances could be managed from density ratios calcu-
lated from whole networks of marine reserves at scales
similar to that used for stock assessment.
Implications of variability
With high levels of variability in recruitment and rela-
tively low sample sizes in the monitoring program, the den-
sity ratio could vary dramatically from one year to the next,
even with a relatively stable spawning stock biomass. While
this variability had the unintended consequence of making
any control rule more precautionary (because effort was re-
duced every time the density ratio happened to fall below
the target), in practice it would not be desirable to impose
effort controls on the fishery in response to random fluctua-
tions in the density ratio. The multiple year density ratio
(rule 2) provided for more stable management with an
equivalent level of monitoring effort.
Fig. 12. Blue rockfish dynamics with high (a and b) versus low (c and d) sample size in the monitoring program, showing expected values
of spawning stock biomass in the reserve (bold line in left panels) and fished areas (narrow lines in left panels), and total yield (broken line
in left panels), and 10 simulated density ratio time series (narrow lines in right panels), for control rule 3 with migration, even effort dis-
tribution, recruitment model I, low variability in recruitment, and no autocorrelation.
Babcock and MacCall 357
Published by NRC Research Press
We did not include environmentally driven changes in re-
cruitment beyond autocorrelation in recruitment. If poor en-
vironmental conditions caused recruitment to decline
throughout the region, the density ratio would respond im-
mediately. Fishing would be allowed to continue at current
levels despite the declining population. This is a fundamen-
tal difference from typical fishery management based on
stock assessment, in which the status of the population is
calculated relative to some constant biomass target, and
fluctuations in the stock are assumed to be caused by fishing
pressure, even if they are actually due to low frequency en-
vironmental fluctuations. In stock assessment-based manage-
ment, a series of low recruitment years would usually lead
to reduced catch quotas as managers try to stop the decline
and rebuild the population to the fixed target. A density-
ratio control rule, on the other hand, would adjust to chang-
ing environmental conditions, because the management
target is relative to curren t conditions in the reserve, not to
historical conditions. Thus, the same target density ratio
would result in a higher or lower spawning stock biomass
relative to historical unfished condit ions, depending on
whether the stock is experiencing a period of high produc-
tivity or a period of low productivity. Whether biomass
reference points should be calculated relative to a static his-
torical standard (‘‘biomass before fishing began’’) or a dy-
namic standard (‘‘the biomass that would currently be
present if the fishery had never existed’’) is a management
decision, not a scientific one, and equally extends to fishery
management under a conventional data-rich stock assess-
ment approaches (Sibert et al. 2006; Field et al. 2010). The
density ratio is most useful for managing for a dynamic bio-
mass standard.
There is a risk of depleting the stock relative to the dy-
namic biomass standard if, for any reason other than envi-
ronmental variability, the fish biomass declines in the
reserve. Fish movement across the reserve boundary, illegal
fishing in the reserve, a density-mediated disease outbreak,
or unanticipated trophic interactions could all cause the
density-ratio control rule to fail because densities in the re-
serve remain below the level that would have been seen if
there was no fishing in the region. Therefore, a precaution-
ary management system based on density ratios should also
examine the trend in density of fish in the reserve to identify
whether one of these risky scenarios is occurring. If the
monitoring program included length data (which it should),
indicators such as the average length of fish inside and out-
side the reserve, and fraction of fish above the age at matur-
ity inside and outside the reserve, could also be used to
determine whether densities inside the reserve are increasing
as expected. For example, one could develop a decision tree
management system (e.g., Prince et al. 2008; Wilson et al.
2010) in which, if density is stable or increasing in the re-
serve, a density-ratio control rule is used, but if density is
decreasing in the reserve more stringent management meas-
ures are specified.
Based on our simulations, a target density ratio of 60% of
mature fish or 80% of all fish would perform well for a
wide range of fish life history characteristics. Density ratios
calculated across multiple years are useful for dampening
out the variability in the density ratio for a given level of
monitoring effort. For multispecies fisheries, if a few species
are thought to be at risk relative to the others, then it may be
necessary to impose independent management measures for
the at-risk stocks, and apply density-ratio control rules for
the more productive species that are the primary basis of
the fishery. Once a density-ratio control rule is established,
it is important to monitor indicators, such as a sudden de-
crease in density inside the reserve, or dramatic change in
the relative densities of the species in the fishery, which
might be an early warning that a density-ratio control rule
is not adequate.
Acknowledgements
Thanks to Carey McGilliard, John Field, Rod Fujita, Mei-
sha Key, Jono Wilson, Burr Heneman, and the rest of the
density ratio working group and the monitoring data applica-
tions project for input on the methodology. Thanks to Jenn
Caselle and PISCO for providing the PISCO subtidal moni-
toring data. Thanks to the Commonweal Ocean Policy Pro-
gram for funding E. Babcock’s work on this project, and
the Marine Protected Area Science Integration project for
funding the working group meetings.
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