Ecological Applications, 16(6), 2006, pp. 2276–2292
? 2006 by the Ecological Society of America
CONTINUED DECLINE OF AN ATLANTIC COD POPULATION:
HOW IMPORTANT IS GRAY SEAL PREDATION?
M. KURTIS TRZCINSKI,1ROBERT MOHN, AND W. DON BOWEN
Population Ecology Division, Bedford Institute of Oceanography, Department of Fisheries and Oceans, P.O. Box 1006,
Dartmouth, Nova Scotia, B2Y 4A2 Canada
experienced drastic changes. Once common top predators are a small fraction of their
historical abundance, and much of the current community structure is now dominated by
pelagic fishes and invertebrates. Embedded within this food web, Atlantic cod and gray seal
populations have recently exhibited nearly opposite trends. Since 1984, cod populations have
decreased exponentially at a rate averaging 17% per year, whereas gray seals have continued to
increase exponentially at a rate of 12%. We reexamined the impact of gray seals on Atlantic
cod dynamics using more than 30 years of data on the population trends of cod and gray seals
while incorporating new information on seal diet and seasonal distribution. The closure of the
cod fishery over 10 years ago allowed for a better estimation of natural mortality rates. We
quantified the impact of seals on ESS cod by (1) estimating trends in seal and cod abundance,
(2) estimating the total energy needed for seal growth and maintenance from an energetics
model, (3) using estimates of the percentage of cod in the total diet derived from quantitative
fatty acid signature analysis (QFASA) and of the size-specific selectivity of cod consumed
(derived from otoliths collected from fecal samples), and (4) assuming a gray seal functional
response. Uncertainties of the model estimates were calculated using the Hessian
approximation of the variance–covariance matrix. Between 1993 and 2000, cod comprised,
on average, ,5% of a gray seal’s diet. Our model shows that, since the closure of the fishery,
gray seals have imposed a significant level of instantaneous mortality (0.21), and along with
other unknown sources of natural mortality (0.62), are contributing to the failure of this cod
stock to recover.
The continental shelf ecosystem on the Eastern Scotian Shelf (ESS) has
grypus; population dynamics model; population recovery.
Atlantic cod; energetics model; Gadus morhua; generalist predator; gray seal; Halichoerus
Changes that are unprecedented during the past
several centuries have occurred recently in the world’s
oceans, including marked declines in top predators.
Sharks (Baum et al. 2003, Baum and Myers 2004), tuna
and billfish (Cox et al. 2002, Myers and Worm 2003,
Ward and Myers 2005), and some whales (Clapham et
al. 1999) are currently a small fraction of their historical
abundance. These decreases, along with the concurrent
increases in pelagic fishes (Fogarty and Murawski 1998)
and invertebrates (Worm and Myers 2003), may indicate
that vast regions of the ocean have entered a new
dynamical regime (Zwanenburg et al. 2002, Choi et al.
2004, Frank et al. 2005, Mangel and Levin 2005, Myers
and Worm 2005).
Atlantic cod (Gadus morhua) populations have also
been decimated throughout their range, primarily due to
overfishing (Hutchings and Myers 1994, Myers et al.
1996, 1997a). Many fisheries managers and scientists
expected cod to recover quickly after fishing moratoria
were imposed on stocks off eastern Canada in 1992 and
1993. This view was based on the assumption that cod
were resilient to large decreases in abundance because of
their high fecundity. Furthermore, several cod popula-
tions, including that on the Eastern Scotian Shelf (ESS),
rapidly recovered when fishing pressure was reduced in
1977 with the introduction of the 200-mile limit, which
extended Canada’s fishing jurisdiction and had the effect
of reducing fishing pressure from foreign fleets. Howev-
er, Canada’s fishing fleet rapidly filled this gap. Few
ventured to predict recovery times after the moratoria;
however, Myers et al. (1997b) used a Ricker model to
predict an 18% population increase under the best of
conditions, or a doubling time of four years, with a
fishable population in a little over 10 years. Neverthe-
less, cod and many other depleted fish stocks have not
recovered (Hutchings 2000, Hutchings and Reynolds
2004). Dangerously low levels of cod abundance have
prompted the Committee on the Status of Endangered
Wildlife in Canada (COSEWIC) to recommend that the
Canadian government list the cod populations of
Newfoundland and Labrador as endangered, the pop-
ulation of the northern Gulf of St. Lawrence as
Manuscript received 20 October 2005; revised 28 April 2006;
accepted 3 May 2006. Corresponding Editor: P. K. Dayton.
1Present address: M. Kurtis Trzcinski, Parks Canada,
Atlantic Service Centre, 1869 Upper Water Street, Halifax,
Nova Scotia, B3J 1S9, Canada.
threatened, and the Maritime population as of special
concern (COSEWIC 2003). The failure of those stocks
to recover may be due, in part, to low reproductive rates
at low population size (Myers et al. 1999), but a lack of a
broader understanding of how population growth rate is
affected by the environment (Brander and Mohn 2004),
fish behavior (Brawn 1961, Rowe and Hutchings 2003),
and food-web interactions (Yodzis 1998, 2000) may also
The potential negative effects of upper-trophic-level
predators, such as pinnipeds, on the dynamics of fish
populations of commercial importance has been hy-
pothesized for decades (e.g., Malouf 1986) and is a
continuing source of debate among fishermen, resource
managers, and ecologists (FRCC 2001, Lavigne 2003).
However, concern about the effect of pinniped predation
on prey populations is simply an example of the broader
issue of the role of top-down effects on prey dynamics
and the structure and functioning of marine ecosystems
worldwide (e.g., Estes et al. 1998, Myers and Worm
The ESS cod stock, located off the coast of Nova
Scotia, Canada (Fig. 1, Northwest Atlantic Fisheries
Organization [NAFO] subdivisions 4Vs and 4W), has
been fished for several centuries (Rosenberg et al. 2003).
From 1958–1974, commercial landings of this stock
ranged between 40000 and 80000 t (1 t ¼ 1 Mg) before
declining to 10000 t in 1977 (Fanning et al. 2003). The
stock increased after the establishment of the 200-mile
limit in 1977, and landings peaked at 50000 t in 1985.
Since 1984, cod abundance has declined exponentially at
a rate of 17% per year, and in 1993, a fishing
moratorium was imposed and remains in effect. The
mass of age-8 cod peaked in the late 1970s then
decreased monotonically from 5.5 kg to 2.0 kg; during
this same period, age at maturity decreased from age
four to three (Fanning et al. 2003). ESS cod used to
spawn in both the spring and fall, but now only the fall
spawning component remains (Frank et al. 1994).
In contrast to the widespread declines of many marine
predators, gray seal (Halichoerus grypus) populations
have increased in eastern Canada. Most gray seals are
born at colonies located in the southern Gulf of St.
Lawrence and on Sable Island located on the Eastern
Scotian Shelf, but newer and smaller colonies are located
along the eastern shore of Nova Scotia and at several
sites in the northeastern United States (Mansfield and
Beck 1977, Hammill et al. 1998, Waring et al. 2002).
Gray seals are large (adults weigh between 100 and 350
kg), wide-ranging predators that exhibit marked sea-
sonal changes in distribution and foraging effort (Beck
et al. 2003b, Austin et al. 2004; G. Breed et al.,
unpublished manuscript). They are generalists, feeding
on a wide range of pelagic and demersal fishes, including
Atlantic cod (Bowen et al. 1993, Bowen and Harrison
1994). The population breeding on Sable Island is a
striking example of the exponential increase of a long-
living marine mammal, having increased at a rate of
12.8% annually for more than 25 years (Bowen et al.
2003). An earlier study found that gray seals had little
St. Lawrence (NAFO subarea 4T), Canada.
Eastern Scotian Shelf (NAFO [Northwest Atlantic Fisheries Organization] subareas 4W and 4Vs) and southern Gulf of
December 2006 2277HOW IMPORTANT IS GRAY SEAL PREDATION?
effect on the collapse of cod on the ESS (Mohn and
Bowen 1996); however, a more recent study suggested
that gray seal predation was impeding population
recovery (Fu et al. 2001).
Understanding the factors, including predation, that
limit the recovery of depressed populations is clearly
important to design effective recovery strategies (Sinclair
et al. 1998). Even if the limiting factors are beyond our
control (e.g., ocean temperature), a better understanding
of the limiting factors provides a firmer basis for
establishing expectations about both the timeframe
and extent of recovery. The closure of the cod fishery
in 1993, more than 30 years of data on the population
trends of cod and gray seals, new information on gray
seal diet, derived from quantitative fatty acid signature
analysis (QFASA), and seasonal distribution data of
gray seals derived from satellite tags, provide a basis for
reexamining the impact of gray seals on the dynamics of
a severely depressed stock of Atlantic cod. We used a
statistical catch-at-age population model of ESS cod and
compared estimated gray seal predation mortality to
other sources of mortality.
We quantified the impact of gray seals (Halichoerus
grypus) on Eastern Scotian Shelf (ESS) Atlantic cod
(Gadus morhua) by (1) estimating trends in seal and cod
abundance, (2) estimating the total energy needed for
seal growth and maintenance using an energetic model,
(3) using estimates of the percentage of cod in the total
diet and the size-specific selectivity of cod consumed,
and (4) modeling a gray seal functional response. The
model was constructed using AD Model Builder (Four-
nier 1996). Maunder (2004) provides a succinct review of
the structure and capabilities of AD Model Builder. The
model first fit to seal and cod abundances, then
estimated the number of cod consumed based on seal
diet information and the energy needed to maintain
estimated gray seal population trends.
Uncertainties in terms of variances for model param-
eters and state variables were estimated from the
Hessian approximation of the variance–covariance
matrix at the optimized solution. A Bayesian model
with informative priors and resultant posteriors was not
performed because the data would not support the
estimation of the variances in the likelihood function.
Instead, these variances were assumed or inferred from
the literature. Thus, for most parameters, means and
variances were used as penalty functions (Appendix) in a
role similar to Bayesian priors. Some parameters were fit
in log space to avoid negative values (like numbers at-
age) and because the log data had better behaved error
Estimating gray seal abundance
As in Mohn and Bowen (1996), we separately
estimated population trends on Sable Island and other
Canadian colonies, including the Gulf of St. Lawrence.
The pup production of gray seals on Sable Island was
estimated in most years from 1962 to 1990 based on
tagging all weaned pups (Mansfield and Beck 1977,
Stobo and Zwanenburg 1990). High population abun-
dance in recent years required that pup production be
estimated from aerial photography (Bowen et al. 2003),
with the most recent estimate being in the spring of 2004
(Bowen et al., in press). Both year–class tagging and
aerial surveys were conducted on Sable Island in 1989
and 1990 and indicated that the two methods gave
comparable results (Bowen et al. 2003). Pup production
in the Gulf of St. Lawrence was estimated from mark–
recapture studies (Hammill et al. 1992, 1998, Myers et
al. 1997a) and aerial surveys (Hammill and Gosselin
2005). Estimates of pup production in the Gulf of St.
Lawrence are more variable than at Sable Island because
pups are born on drifting ice, suffer higher mortality,
and are more difficult to census (Myers et al. 1997a,
Hammill et al. 1998). Production at small islands in the
Gulf of St. Lawrence and along the eastern shore of
Nova Scotia was determined by visual counts or year–
Previously, a simple exponential population model
was fit to the data on pup production (Mohn and Bowen
1996, Bowen et al. 2003), however, the Sable Island
population has begun to show evidence of density
dependence. Females were about 16 times less likely to
be primiparous at-age 4 yr from 1998 to 2000 compared
to cohorts in the mid to late 1980s, and the upper 95%
confidence interval for pup production in 2004 falls
below confidence intervals predicted from the exponen-
tial model (Bowen et al., in press). Consequently, we
parameterized a theta-logistic model using several
assumptions about the strength and timing of density
dependence and the level of carrying capacity.
We denoted the total number of seals as Nt,a,s, where
the subscript t indexes the year; a, age; and s, sex. In our
model, age-0 refers to pups in their first year of life (from
birth to January 1st the following year). Males ages 1–9
yr and females ages 1–5 yr were considered as juveniles,
even though some females can give birth as early as age
4. Males older than 9 yr and females older than 5 yr were
referred to as adults. We distinguished between mortal-
ity at different life stages using superscripts (e.g., MPup
), and use subscripts to denote rates for
different sex or age classes.
Reviews of population dynamics in large mammals
indicate that one of the first signs of density dependence
is a decrease in juvenile survival (Fowler 1987). It is at
this stage that we model density dependence in the Sable
Island population with the theta-logistic function. We
assumed that all other natural mortality rates were
instantaneous, density independent, and constant over
our study period. Given the observed exponential rate of
increase of pup production in the Sable Island popula-
tion over the period from 1976 to 1997, these
assumptions seem warranted (Bowen et al. 2003) but
will need to be modified as the population approaches
M. KURTIS TRZCINSKI ET AL.2278
Vol. 16, No. 6
carrying capacity. Data on pup production suggest that
mortality rates in the Gulf of St. Lawrence population
are not constant, but this assumption is necessary to
approximate population dynamics with the exponential
model. For both the Sable Island and Gulf of St.
Lawrence populations, we used separate mortality rates
for pups, juveniles, and adults. The age-specific birth
rates ba, were based on pregnancy rates reported in
Mansfield and Beck (1977) and Hammill and Gosselin
(1995). We used a 1:1 sex ratio at birth (Bowen,
The number of pups produced in the next year, Ptþ1,s,
is the sum of the number of females, Nt,a,f, multiplied by
the age-specific pregnancy rate ba:
The number of pups surviving to the next year in the
Sable Island population is given by
where N is total population size, K is carrying capacity,
and h is the degree of density dependence. The degree of
density dependence in gray seals is unknown, but
Harting (2002:101) argued that h for marine mammals
should be around 2.4, which he found support for in
monk (Monachus schauinslandi) and fur seals (Taylor
and DeMaster 1993). We use this value, 2.4, in our
analysis. The number of juveniles (juvenile males ages 1–
9, females ages 1–5 yr) in the Sable Island population is
Since carrying capacity can not be estimated without
more data, we varied K until the 2004 model estimate of
pup production fell within the confidence interval of the
2004 aerial survey estimate. MPupwas estimated from
the pup count data, whereas MJuvwas fixed (Table 1).
Our model did not allow adults to survive beyond age
39. Adult numbers (males aged .9, females aged .5)
are given by
Total population size is given by
The model for the Gulf population assumed density-
independent survival for all stages and accounted for
hunting removals (Zwanenburg and Bowen 1990, Ham-
mill et al. 1998). Mohn and Bowen (1996) argued that
mortality rates should be different for males and females
based on their differences in longevity; however, there
are few data that can be used to evaluate this
assumption. Consequently, we fixed the mortality rates
of juveniles, adult males, and adult females at the values
guided by Mohn and Bowen (1996), Schwarz and Stobo
(2000), Hall et al. (2002), and Manske et al. (2002).
(Although instantaneous rates of mortality or predation
are formally defined in units of reciprocal time (years),
for readability they have been dropped.) Schwarz and
Stobo (2000) noted that their estimates of adult female
survival (0.92) was probably biased low, while Manske
et al. (2002) indicated that their estimate of adult male
survival (0.97) was probably biased high. We split the
difference and assumed that adult survival for male and
females was 0.95, which corresponds to an instanta-
neous mortality of 0.05. We modeled the uncertainty in
these parameters with a lognormal distribution where r
¼0.1. Juveniles were assumed to have the same mortality
as adults (Table 1). The rates concur with observations
that males and females often live to their mid 30s, while
a few survive into their early 40s. Estimates of pup
mortality were obtained by minimizing an objective
function that is the sum of the negative-log likelihoods
for the pup count data from both populations (Quinn
and Deriso 1999). We used lognormal error structures
for all likelihoods.
We incremented our predator–prey model on a
quarterly basis. For pups, the annual mortality was
partitioned such that 75% occurred between January
and July, whereas survival was assumed to be constant
over the season for juveniles and adults.
Juvenile and adult gray seals move long distances
during foraging, and mark–recapture data indicate there
is some movement between the Sable Island and Gulf of
St. Lawrence breeding populations (Mansfield and Beck
1977, Stobo et al. 1990, Lavigueur and Hammill 1993).
We updated assumptions about seasonal movement in
Mohn and Bowen (1996) with data on at-sea distribution
of gray seals derived from Argos based satellite tags.
Tags were fitted to juvenile and adult gray seals in the
southern Gulf of St. Lawrence in the summers of 1993–
for Sable Island and Gulf of St. Lawrence gray seal
Instantaneous rates of natural mortality (mean 6 SE)
Instantaneous rate of natural mortality
Sable IslandGulf of St. Lawrence
0.103 6 0.044
0.0507 6 0.005
0.0507 6 0.005
0.0506 6 0.005
1.46 6 0.089
0.0507 6 0.005
0.0507 6 0.005
0.0503 6 0.005
Notes: Initial population size and pup mortality (in 1962)
were estimated by fitting to pup count data. Initial population
(N1962) was 392 6 25 seals for Sable Island and 3704 6 372 for
Gulf of St. Lawrence (mean 6 SE). Mortalities for juveniles and
for adult males and females were set at 0.05, and the uncertainty
was modeled by a lognormal distribution with r ¼ 0.1 (see
Methods: Estimating gray seal abundance).
December 20062279HOW IMPORTANT IS GRAY SEAL PREDATION?
2004 (M. Hammill, unpublished data) and at Sable Island
from 1995 through 2004 (Bowen et al. 2006; G. Breed
and W. D. Bowen, unpublished data). The satellite
tagging data indicated that the fraction of the Gulf of
St. Lawrence and Sable Island components of the
population inhabiting the ESS area varied seasonally
(Table 2). Too few seals have been tagged to examine
Cod abundance and biomass
As with standard fishery models, our cod population
was reconstructed from catch-at-age and abundance
data. Data were collected from the commercial fishery
including bycatch and from four research surveys. The
summer (July) survey started in 1970 and has run
continuously to the present. A fall (September) survey
was started in 1978 and a spring (March) survey, in 1979.
Both of these surveys ended in 1984. The stratification of
the spring survey was redesigned and was run from 1986
to 2002, but not in 1998. Cod length and mass were
recorded for all fish, a subsample of fish were aged, and
length–age keys were used to estimate mean number
caught-at-age per tow. Mean numbers per tow were
scaled by area swept to arrive at estimates of total
abundance-at-age for the entire Eastern Scotian Shelf.
The fishery on the ESS cod stock was closed in 1993,
thus the total mortality from the model is essentially
natural mortality for this latter period. The model is a
statistical catch-at-age model (e.g., Quinn and Deriso
1999, Savereide and Quinn 2004), structurally similar to
that described in Fu et al. (2001) and is written in the same
enviroment, AD Model Builder. However, there are a
number of important differences between our model and
of cod are treated. In Fu et al., the removals, as had been
estimated by one of two models in Mohn and Bowen
(1996), are treated as data. In this study, the cod
population model and the seal population model are
coupled via predation, and the models are iterated until
convergence to estimate seal predation mortality.
Several studies have concluded that the natural
mortality of Atlantic cod has increased in recent years
(Fu et al. 2001, Sinclair 2001, Fanning et al. 2003). Cod
natural mortality in Fu et al. (2001) was partitioned into
immature (ages 1–4) and mature (?5) categories and
then modeled as a random walk. In this study, we
modeled temporal increases in M with a four-parameter
logistic function of time. Natural mortality was assumed
to be 0.2 in 1970: the logistic slope parameter was fixed
at three years, and the model estimated the inflection
year and the asymptotic mortality. In addition to the
data used by Fu et al., we used six more years of survey
data since the closure of the fishery, providing greater
insight into recent levels of natural mortality.
A total of 100 parameters were estimated by the cod
population model. Cod numbers at-age in 1970 were
estimated to initialize the model (12 parameters), and
recruitment (age-1) from 1971 to 2003 were estimated
(33 parameters). Fishing mortality was assumed to be
separable and thus described by two components:
selectivity (14 parameters) and annual mortality (34
parameters) (Quinn and Deriso 1999). Gear selectivity
was estimated separately for the commercial fishery and
the research survey over periods of gear change. The
survey gear changed in the early 1980s, and the
extension of jurisdiction in 1977 affected the commercial
selectivity. The coefficents scaling the catch in the
research survey to total population size were estimated
for each period (five parameters), along with two
prarameters for changes in natural mortality. We
present the estimates of the fit to the research survey
data and the estimates of spawning stock biomass,
fishing mortality rates, and natural mortality after the
iterations of the seal and cod models have converged.
Seal energetics model
The daily gross energy intake (GEI; in watts) of an
individual gray seal was estimated as
where d, a, and s index day, age (0–39 for males and
females), and sex; BM is body mass (kg); ME is
metabolizable energy (i.e., the proportion of the GEI
available to the animal); TBE is total body energy
(watts); and 3.4 3 BM0:75
d;a;sis the Kleiber equation
(Kleiber 1975). We multiplied the Kleiber equation by
1.7, the estimated increase in metabolism during diving,
and therefore a proxy for field metabolic rate (Sparling
and Fedak 2004). The Kleiber multiplier was increased
to 2.5 to account for the increased metabolism of pups
(Worthy 1987) and decreased to 1.07 to account for the
lower energy metabolism of females during the summer
(Boily and Lavigne 1995, Beck et al. 2003b). ME was
assumed to be 83%, based on experimental work on
seals by Ronald et al. (1984).
Lifetime changes in body mass of males and females
were estimated by fitting the Gompertz growth model to
data collected in the Gulf of St. Lawrence between 1988
and 1992 (Hammill, unpublished data; Fig. 4 in Mohn
and Bowen 1996). An annual growth rate GRa,swas
Lawrence gray seal populations inhabiting the Eastern
Scotian Shelf (ESS).
The percentage of the Sable Island and Gulf of St.
Seal population at ESS (%),
Notes: The Sable Island estimates are separated into three
categories: young of the year (YOY) and males and females .1
year old (n¼24, 49, and 51 individuals, respectively). The Gulf
population estimates are for combined ages (n¼54 individuals).
Estimates were derived from Argos-based satellite tags.
M. KURTIS TRZCINSKI ET AL.2280
Vol. 16, No. 6
calculated from the Gompertz curves and converted to a
daily rate. These estimates were combined with estimates
of seasonal changes in body mass from Beck et al.
(2003a) to produce daily estimates of lifetime changes in
body mass (kg):
BMd;a;s¼ BMa;sþ gs;id þ GRa;sd þ c
where d is the day of the year, gs,iis the daily rate of gain
or loss in body mass over the season (i ¼ 1...3 for pups
and juveniles, i¼1...4 for adult males, and i¼1...5 for
adult females), and c is a constant that centers the
seasonal pattern on the body mass reported in Beck et
al. (2003a). Modeled changes in body mass throughout
the life span of males and females are shown in Fig. 2.
During the first year of life, pup body mass declines
from an average of 54.0 kg at weaning (Boness et al.
1995) to 37.3 kg at approximately five months of age and
remains roughly constant through nine months of age
(Cooper 2004). We added the daily amount of energy
(watts) needed to account for seasonal changes in total
body energy (TBE) to the Kleiber equation. Changes in
adult TBE were modeled using estimates from Beck et
al. (2003a). Seasonal changes in juvenile TBE were
calculated as the energy density needed for growth
(11.39 6 0.98 kJ/d) multiplied by the daily growth rate
(Bowen et al. 1999). Seals’ consumption was set to 0
during times of terrestrial fasting (i.e., breeding, molt),
providing more realistic estimates of seasonal food
consumption by seals.
Fraction of cod in the diet
method that provides estimates of diet consumed by
individual seals over periods of weeks to months by
estimating the proportion of prey species eaten that
minimizes the statistical distance between the fatty acid
composition of the predator and that of a mixture of prey
(Iverson et al. 2004). Previous estimates of percentage of
cod in the diet were derived from the identification of
otoliths recovered from feces and stomach contents
(Bowen et al. 1993, Bowen and Harrison 1994, Mohn
and Bowen 1996). These estimates are known to suffer
the diet that consists of large, robust otoliths, such as cod
(Jobling and Breiby 1986). Diet estimates from fecal
area, in our case, the immediate area surrounding Sable
Island. Initial estimates wereas highas 15.2%(Mohn and
the addition of subsequent data. Estimates from QFASA
year gray seals. For adults, values ranged from 0% to
4.5%, while young-of-the-year values averaged 8.6% of
the diet (Appendix). However, samples from young-of-
the-year come only from the spring and may be biased
upward because young seals sampled on Sable Island at
this time of the year may have been foraging mainly in
other parts of the continental shelf.
Although QFASA provides estimates of the percent-
age of cod in the diet, it does not provide much
resolution of the size of cod consumed. Thus, we have
assumed that otoliths collected from scat and stomachs
represent the size distribution of cod eaten. These data
indicate that smaller fish (,30 cm), rather than larger,
are consumed more often by seals (Bowen et al. 1993,
Bowen and Harrison 1994, 2006). We calculated the age-
frequency distribution of cod consumed by seals (pa)
from otoliths collected from fecal samples from 1991 to
1997. This required that fish length be calculated from
otolith length using the regression reported by Bowen
and Harrison (1994), which was then assigned to an age
class based on the length-at-age frequencies calculated
from a sample of the entire cod population (Fig. 3). We
then used the length–mass relationship to calculate the
mean annual mass of a cod consumed (StomW). We
assumed that the cod lengths sought by seals were
constant over time, but since we know that the cod
length–mass relationship changed during the study
period, we calculated the mean mass of a cod consumed
by seals for each year.
The functional response of gray seals to changes in
cod density is unknown. Therefore, we analyzed our
lifetime of (a) males and (b) females.
Changes in gray seal body mass modeled across the
December 20062281HOW IMPORTANT IS GRAY SEAL PREDATION?
model under two assumptions about feeding rates. Our
data on the proportion of cod in the diet, from the
QFASA model, exhibited interannual variability but
little evidence of an annual trend. Thus in one case, we
assumed that a constant proportion of cod was eaten
regardless of cod abundance (constant-ration model).
Although this might be ecologically reasonable over a
limited range of cod abundance, the large observed
changes in cod abundance over the duration of our
study make this assumption unlikely. Thus, we exam-
ined a second scenario whereby consumption rates
decreased hyperbolically with cod abundance (Type 2
functional response) in view of the evidence from other
predators (e.g., Assenburg et al. 2006).
The amount of biomass needed to maintain seal
growth (SG) was calculated quarterly by summing the
daily gross energy intake (GEI) into quarters, then
dividing by the average energy (AE in kJ/g) of prey
within a quarter and converting to metric tons:
Recent estimates calculated from 28 prey species
known to be consumed by gray seals indicate that AE
varies seasonally: 5.28, 5.26, and 5.46 kJ/g for winter,
summer, and fall (C. A. Beck et al., unpublished
manuscript; Appendix). The total biomass (TB) of prey
eaten bytheseal populationper quarter wascalculated as
where N is the number of seals, and mq is the
proportion of seals remaining on the ESS during each
quarter (Table 2). Since we did not have data on pup
movement for the Gulf of St. Lawrence population,
we assumed that pups born in the Gulf move on the
ESS at the same rate as adults.
In the constant-ration model, the biomass of cod
eaten (E) per quarter is a constant fraction of the total
where f1þis the fraction of cod in the diet of seals age-1
and older, and f0is the fraction of cod in the diet of
young-of-the-year (mean values in Table 3). The number
of cod eaten (NE) annually is then
where StomW is the mean mass of cod consumed from
1970 to 2003, and pais the proportion of cod consumed
at-age. From the otolith data for the period 1991–1997,
we calculated pa¼ (0.341, 0.344, 0.217, 0.076, 0.018,
0.003) (Fig. 3).
We formulated the functional-response model by
calculating an interaction coefficient (qa) between the
number of seals and the number of cod across age
classes. Since there was no evidence of an annual trend
in the proportion of cod in the diet for years with
QFASA diet information (1993–2000), we calculated
our interaction coefficient at the start of the QFASA
data series. First we calculated the number of cod
consumed at-age in 1993 as
where E is the mean biomass of cod eaten from the
constant-ration model for 1993. The interaction between
cod and seals was then calculated as follows:
where Cais the mean number of cod-at-age, and N is the
mean number of seals on the ESS in 1993. It is often
The frequency of cod lengths consumed by gray seals determined from otolith length (n¼309). Dotted lines indicate age
M. KURTIS TRZCINSKI ET AL.2282
Vol. 16, No. 6
observed that predator consumption rates increase with
prey density up to a maximum level. We parameterized a
hyperbolic functional response by assuming that the
proportion of cod calculated from scat from 1991–1997
represented the maximum proportion of cod in a seal’s
diet. This assumption seems reasonable because gray
seal scats represent short-term diet from foraging trips
close to Sable Island, which is an area where cod are
commonly found (Fanning et al. 2003). We calculated
the asymptotic attack rate (qa,max) by setting f1þ¼ 0.22
and recalculating q as
We assumed that each qa derived from QFASA
provides an accurate estimate of attack rates at low cod
abundance. If we then assume a hyperbolic functional
response, the number of cod eaten is given by
where StomW is the mean mass of cod consumed over
1971–2003. Fig. 4 shows the functional response of seals
to age-1 and age-2 cod.
Estimating parameter uncertainty
The model incorporates parameter uncertainty in two
ways. The means and variances of several parameters in
the seal population dynamics model were estimated
directly from the pup count data (Table 1), by
minimizing an objective function that is the negative-
log likelihood for observed vs. predicted pup numbers.
However, the majority of parameters were taken from
other studies (Appendix). For these parameters, a
probability density function was calculated and con-
verted into a negative-log likelihood. These likelihoods
were added to the objective function and acted as
penalty functions (Breen et al. 2003). In both cases,
(a) age-1 and (b) age-2 cod. The linear functional response
(dotted line) was not used but was added for comparison.
The functional response (solid line) of gray seals to
Age- and sex-specific abundance, daily energy intake, daily food intake, and annual food intake of gray seals on the ESS
No. seals in 2003
per individual (W)
per individual (kg)
consumption (metric tons)
MaleFemale Male FemaleMale Female MaleFemale
? Average over all ages.
? Mean field approximations were used to calculate annual population consumption. The estimates of total consumption in
Table 4 are more accurate.
December 20062283HOW IMPORTANT IS GRAY SEAL PREDATION?
variances from the Hessian matrix are carried through
the model and are reflected as uncertainty in the final
estimates of consumption. Consequently, a large
amount of variability has been incorporated into the
model from a wide variety of sources. This variability
can be broadly categorized into uncertainty in gray seal
(1) population dynamics, (2) energetics, and (3) cod
consumption. Several sources of error were not includ-
ed, as each model component contains a few fixed values
(Table 1, Appendix). Variability in the cod model was
incorporated by running the seal model at 61 SE of cod
numbers at-age. We present the range in mortality
estimates due to seal predation and other sources.
Gray seal (Halichoerus grypus) populations have
continued to increase on Sable Island, but the 2004
estimate suggests that the rate of increase in pup
production has slowed (Fig. 5). In the Gulf of St.
Lawrence, pup production also increased over time, with
the 2004 estimate the highest in the series (Hammill and
Gosselin 2005; Fig. 6). The carrying capacity of the
Sable Island population was estimated at 430000 gray
seals, with the density-dependent parameter, h, held
constant at 2.4 (Trzcinski et al. 2005). Combining
estimates of total population size with estimates of
seasonal movement patterns, the model predicted a
steady rise in the number of gray seals using the study
area from fewer than 8494 seals (6691 SE) in 1970 to
158750 seals (67186 SE) in 2003 (Fig. 7). However, there
was also a strong seasonal signal, such that numbers in
2003 varied from about 128000 in summer to 182000 in
winter (Fig. 7).
Fig. 8a shows the fit to the cod abundance estimates
from four-survey series. The Atlantic cod (Gadus
morhua) numbers show continued decline since the early
1980s. Spawning stock biomass is shown in Fig. 8b.
Current estimates for either number or biomass are the
lowest in the entire 34-year time series, despite the
closure of the fishery in 1993 and low fishing mortality
rates thereafter (Fig. 8c). We estimated a spawning
biomass of 6524 t (1 SE: 2180–20547 t) in 2003, and our
overall trends are in broad agreement with those
reported in pervious assessments (Fu et al. 2001,
Fanning et al. 2003). Since 1984, the spawning biomass
has fallen more rapidly than the number of cod,
indicating a change in the age and size structure of the
cod population, and resulting in a larger proportion of
the dwindling stock becoming available to seal predation
The energetics model estimated that, on average,
males consumed 1.61 tons and females 1.35 tons of food
per year (Table 3). Young-of-the-year comprised ;22%
of the gray seal population. Yet, despite their smaller
size, they consumed ;17.7% of the total prey biomass.
Total consumption varied seasonally, but the three age–
sex classes showed contrasting patterns (Table 4).
Consumption by young-of-the-year, as a proportion of
the total, was highest in the first quarter and lowest in
the third and fourth quarters. Consumption by adult
males was fairly consistent across the first three quarters,
then increased in the last quarter, whereas consumption
by adult females was high in the first quarter (i.e., post-
reproduction), low in second and third quarters, and
highest in the fourth quarter. The increase in consump-
tion by adult males and females in the fourth quarter
was caused by the rapid increase in body energy storage
leading up to the breeding season (Beck et al. 2003a).
Under the assumption of a constant ration of cod, the
model estimated that 29.3 (69.0 SE) million cod were
consumed by seals in 2003 (Fig. 9b), corresponding to a
mass of 5369 (69519 SE) metric tons. By comparison, the
functional-response model estimated that 16.7 (627.7
SE) million cod were consumed in 2003 (Fig. 9),
corresponding to 2899 (4888 SE) tons. In 2003, the
functional-response model estimated that each seal
consumed 97 cod (i.e., 50.4, 36.5, 5.3, 4.4, and 0.7 cod
at ages 1–5, respectively).
Prior to 1995, the instantaneous mortality rate of cod
(ages 1–5) due to seal predation was low, averaging less
than 0.01. Seal predation mortality rates increased as the
seal population grew and the cod population further
declined. The functional-response model estimated seal
predation mortality to average 0.21 since the closure of
to the pup production of the Sable Island gray seal population.
In early years, only partial censuses (plus symbols) were
completed. These data were added to the plot for reference
but were not fit to by the model. The model of exponential
increases (dotted line) was not used but was added for
comparison. (b) Model estimates of total population size.
Vertical lines indicate the 95% CI.
(a) Census counts (circles) and model fit (solid line)
M. KURTIS TRZCINSKI ET AL. 2284
Vol. 16, No. 6
the fishery (across ages 1–5) and 0.31 in 2003 (Fig. 10).
Although fecal data indicated that gray seals consume
cod ages one to eight, the highest mortality rates
occurred on cod aged two, three, and four (i.e., 0.35,
0.28, and 0.19 since 1993). We estimated that instanta-
neous natural mortality due to factors other than gray
seal predation was 0.78 in 2003 and has averaged 0.62
since 1993. Therefore, the functional-response model
estimates mortality due to gray seals on two, three, and
four year old cod was 57%, 46%, and 30% of the natural
mortality attributed to other causes (or 36%, 31%, and
23% of all mortality including bycatch mortality).
Seasonal consumption of cod by seals varied with seal
age and sex. Current data indicate that adult males did
not consume measurable amounts of cod in the second
quarter and consumed the most cod in the fourth
quarter. In contrast, females consumed the greatest
proportion of cod in the second and third quarters
leading up to the breeding season (Table 5). Overall,
young-of-the-year consumed the most cod, adult males
the least, and adult females consumed approximately
three times more than males (Table 5).
The Gulf of St. Lawrence population had a relatively
minor predation impact on the ESS, consuming only
8.8% of the total biomass and 7.5% of the cod. Although
comparatively low, their impact peaked in the fourth
Symbols represent four data sets collected using different methods; estimates were calculated from pups recaptured at Anticosti
Island (circles), Sable Island (from Hammill et al. 1998; squares), from Myers et al. (1997a; triangles), and aerial survey methods
(Hammill and Gosselin 2005; 3 symbols). Vertical lines indicate 6SE. (b) Model estimates of total population size. Vertical lines
indicate the 95% CI.
(a) Census counts and model fit (solid line) to the pup production of the Gulf of St. Lawrence gray seal population.
(Eastern Scotian Shelf) accounting for population trends and
immigration and emigration.
Estimated total number of gray seals on the ESS
December 20062285 HOW IMPORTANT IS GRAY SEAL PREDATION?
quarter with the migration onto the ESS, presumably in
response to the formation of ice in the Gulf of St.
Lawrence (Table 2; G. Breed and W. D. Bowen,
Our uncertainty in the amount of cod consumed by
gray seals is large. For example, the functional-response
model estimated that 16.7 million cod were consumed by
seals in 2003 (Fig. 9b), but 1 SE is 6 27.7, making the
95% confidence limits on that estimate approximately
655.4 million cod. Despite our uncertainty about seal
predation mortality (i.e., our estimate includes 0 because
of the high uncertainty in the consumption term [neither
cod nor seals include 0]), the model indicates that gray
seals accounted for a small but perhaps significant
fraction of the natural mortality from other sources
(Fig. 10). The contribution of the uncertainty in gray
seal population dynamics and the number of seals
foraging on the ESS to our uncertainty in cod
consumption was small (Fig. 11a) compared with our
uncertainty in gray seal energetics (Fig. 11b) and diet
(Fig. 11c). By far the greatest uncertainty in our estimate
of cod consumption is due to our uncertainty in cod
population dynamics (Figs. 8 and 12). Variation in cod
numbers at-age affects both the strength of the
interaction coefficient calculated in 1993 and our
estimate of the impact of gray seal predation on cod
Predators in both terrestrial and marine systems have
been blamed for the declines of many species of
commercial or recreational value (Punt and Butterworth
1995, Yodzis 1998, Treves and Karanth 2003, Wood-
roffe et al. 2005). Proposals to reduce predator
populations come from the notion that they are the
principal source of natural mortality. While this may be
true in some cases (Sinclair et al. 1998, Courchamp et al.
2003, Wittmer et al. 2005), in others it is not (Punt and
Butterworth 1995, Valkama 2005). Our model indicates
that during the 11-yr period of the fishing moratorium
(i.e., through 2003) there is little evidence that gray seals
(Halichoerus grypus) were the principal source of natural
mortality on the ESS Atlantic cod (Gadus morhua) stock.
Although any mortality on a depleted population
undergoing further decline is detrimental to population
recovery, even the complete removal of gray seal
predation would not assure the recovery of the cod
population, given the high levels of other sources of
natural mortality. We estimate that current instanta-
neous natural mortality rates of young fish (ages 1–5),
after accounting for seal predation, is 0.78, which is
similar to our estimates of fishing mortality on older fish
(.5) during the heyday of the fishery.
Although we are still uncertain about both elements
of model structure and some parameters of the model,
several improvements have been made to the predation
model of Mohn and Bowen (1996). In the earlier model,
the seasonal fraction of the Sable Island and Gulf of St.
Lawrence components of the population that foraged on
the ESS was largely unknown. Satellite telemetry studies
(points) and predicted by a statistical catch-at-age model
(lines). (b) The estimated trends in cod spawning stock biomass
(SSB; solid line) and the biomass of cod selected by seals
(dashed line) (1 metric ton ¼ 1 Mg). (c) The instantaneous
fishing mortality for fully selected ages. Dotted lines in (b) and
(c) are 6SE.
(a) Abundance index in four research surveys
gray seal population on the ESS for 2003.
Estimated annual consumption of biomass by the
Proportion of biomass consumed,
First Second ThirdFourth
Notes: Annual consumption was partitioned into three
population categories and the proportion consumed by quarter.
M. KURTIS TRZCINSKI ET AL.2286
Vol. 16, No. 6
have provided empirical estimates of the seasonal
distribution, and it is now evident that many gray seals
make long foraging trips far beyond the ESS (Austin et
al. 2004; Table 2) and that the seasonal use of the ESS
varies by sex and age group. The bioenergetic model
now includes good estimates of the metabolic cost of
diving (Sparling and Fedak 2004), a growth premium
calculated from the Gompertz curve, and seasonal
variation in body mass and total body energy (Beck et
al. 2003a), all of which result in better estimates of the
seasonal energy requirements of the population.
Another important improvement in our model is the
new estimates of proportion of cod in the diet of gray
seals derived from QFASA (Iverson et al. 2004; C. A.
Beck et al., unpublished manuscript; Appendix). QFASA
presumably provides a more accurate population level
estimate of proportion of cod in the diet because it
integrates consumption over a broader spatial domain
and a time frame from weeks to months (Iverson et al.
2004). By contrast, scat and stomach contents estimates,
used in the earlier model (i.e., Mohn and Bowen 1996),
provide information mainly on the last meal eaten
within 100 km of the collection site (Bowen and
Harrison 1994). This means that gray seal diet in a
large fraction of the ESS cannot be investigated using
scats or stomach contents. Nevertheless, otoliths col-
lected from scats and stomach contents provided critical
information on the length of prey eaten (Bowen and
Harrison 1994, 2006; Fig. 3). Thus, given the difficulty in
estimating the diet of pinnipeds, the use of multiple
methods is valuable.
QFASA is a new method for estimating the diet of
predators. As with any method, it has strengths and
weaknesses. As noted above, one of the strengths of the
method is that it provides information on the diet of
individuals over ecologically relevant spatial and tem-
poral scales. However, the method relies on having good
estimates of the fatty acid composition of potential prey
and the fact that prey species eaten have distinct fatty
acid signatures. If prey eaten by the predator is not
included in the QFASA model, it will not be identified.
Evidence to date indicates that potential gray seal prey
can be reliably distinguished (Budge et al. 2002).
Furthermore, gray seal diets were estimated using a
prey library of 28 species of fish and invertebrates from
the study area that were either known (from scats or
stomachs) or suspected (because of abundance and
depth availability) to be eaten by this species (C. A. Beck
et al., unpublished manuscript).
Lastly, we have added a hyperbolic functional
response to the predation model. Although the param-
eters of the response are guided by data, they are clearly
provisional. The hyperbolic functional response is
commonly observed in predators (Murdoch and Bence
1987, Turchin 2003), including pinnipeds (Mori and
functional-response (solid line) models for (a) the percentage of
cod in a gray seal’s diet and (b) the number of cod eaten by the
ESS gray seal population.
Results of the constant-ration (dashed line) and the
fully selected fish (F, dotted line), estimated increase in natural
mortality (Mn) for ages 1–5, and estimated trend in seal
predation mortality (Ms) of cod ages 1–5 from the functional-
response model. (b) The estimated instantaneous mortality rate
caused by gray seal predation. The dotted lines in (b) are 6SE,
estimated from the Hessian approximation of the variance–
(a) The instantaneous fishing mortality rate for
December 2006 2287 HOW IMPORTANT IS GRAY SEAL PREDATION?
Boyd 2004, Assenburg et al. 2006). The largest effect of
including a hyperbolic function response was to
constrain consumption rates when cod were abundant
in the 1980s. However, even in recent years the
functional-response model predicted only 54% of the
cod consumption estimated by the constant-ration
model (Fig. 9, Table 5). This underscores the importance
of further research on the functional responses of gray
We have included a measure of variability in most of
the parameters in the model (Table 1, Appendix). This
variability is clearly reflected in the width of the
confidence limits on our estimates of gray seal predation
mortality. Nevertheless, we have certainly not included
all sources of variability in model parameters. We also
examined model structure in relation to the form of the
functional response. However, we have assumed that
density dependence takes the form of reduced pup and
juvenile survival. Although this is a reasonable assump-
tion based on analogy to other mammals, we have no
evidence to support this assumption in the case of our
population. Other forms of density dependence, say
reductions in fecundity, could have large effects on our
estimate of gray seal population size and, in turn, on
estimates of predation mortality. However, we have no
data on changes in fecundity.
We did not reexamine the sensitivity of our model to
input parameters, but we expect the relative importance
of parameters would be similar to the earlier model by
Mohn and Bowen (1996: Table 10) because of the
structural similarity of the two models. Based on the
earlier model, estimates of cod consumption, and thus
predation mortality, are expected to be most sensitive to
changes in the size of the seal population, the
composition of seal diet, and seal metabolic rates.
It is becoming widely recognized by ecologists that
heterogeneity in predation pressure in both time and
space can have impacts on prey populations that are not
evident in simpler models (Hassell 2000, Alonzo et al.
2003, Jackson et al. 2004). Thus, an important result of
our model is the strong seasonal pattern of predation on
cod. The impact of gray seal predation on the ESS cod
population appears to be greatest just prior to and
following the breeding season (fourth and first quarters),
which corresponds to the aggregation of the population
near the breeding colony on Sable Island and the initial
foraging trips of weaned pups. Consequently, the impact
of gray seals on cod is spatially diffuse over much of the
year, but during the breeding season the impact
increases in intensity in the vicinity of Sable Island.
This temporal and spatial variation in gray seal
predation could have important effects on the recovery
of the cod population, if the region surrounding Sable
for 2003. Annual consumption was partitioned into three population categories and the
proportion consumed by quarter.
Estimated annual consumption of cod biomass by the gray seal population on the ESS
Proportion of biomass consumed,
population dynamics; (b) population dynamics and energetics;
and (c) population dynamics, energetics, and diet on the
coefficient of variation (CV) of cod consumption.
The contribution of the uncertainty in (a) gray seal
M. KURTIS TRZCINSKI ET AL. 2288
Vol. 16, No. 6
Island is a cod spawning or nursery area. At times, high
densities of eggs and larvae have been found near Sable
Island in ichthyoplankton surveys, but the data are too
sparse to determine the importance of this area to cod
reproduction (Department of Fisheries and Oceans,
Canada; Stewart et al. 2003).
Generalist predators can drive alternative prey to
extinction (Murdoch and Bence 1987, Holt and Lawton
1994, Wittmer et al. 2005; but see further discussion later
in this paper). To the extent that gray seals consume cod,
they are having a negative impact on the recovery of the
declining ESS cod stock. Of course, any removal of
individuals from a population which has exponentially
declined at a rate of 17% per year for 10 years would be
detrimental to population recovery, whether by concur-
rent fisheries, by seals, or other sources of natural
mortality. However, QFASA estimates of diet indicate
that gray seals consume relatively little cod, and that
sandlance (Ammodytes dubius) and redfish (Sebastes
spp.) account for most of their diet (Bowen et al. 2006).
There is also some evidence that gray seals do not
positively select for cod relative to their abundance
(Bowen and Harrison 2006), which has also been
observed in harp seals (Lawson et al. 1998).
Why cod stocks, including the ESS stock, showed
rapid recovery after fishing pressure was reduced in 1977
with the introduction of the 200-mile limit and not after
the closure of the fishery in 1993 remains poorly
understood. Many things have changed in the ESS
ecosystem over the study period (1970–2003), including
fishing practices, the age structure of cod, the abundance
of predators, and sea temperature (Zwanenburg et al.
2002, Choi et al. 2004, Frank et al. 2005). The current
state, where pelagic fish and seals are abundant,
presumably makes it more difficult for cod to survive
early life stages (Swain and Sinclair 2000, Walters and
Kitchell 2001). However, cod feed on many members of
the community (Link and Garrison 2002), making it
difficult to predict their response to changes in the seal
population or fishing pressure (Yodzis 1998, 2000).
Generalist predators, such as gray seals, can actually
have a positive impact on less preferred prey through
indirect interactions (Punt and Butterworth 1995,
Yodzis 1998). Much focus has been placed on recruit-
ment variability and the high mortality of young cod,
but few have explained the increased mortality in older
(5þ) cod observed by Fanning et al. (2003). Large cod
and seals have considerable dietary overlap (Link and
Garrison 2002; C. A. Beck et al., unpublished manuscript)
and could be competing for common resources.
The abundance of Atlantic cod on the ESS has
decreased exponentially at a rate averaging 17% per year
over the past several decades. In addition to this recent
decline, there is strong evidence, based on historical
catch data, that this stock has decreased substantially
over several centuries (Myers et al. 2001, Rosenberg et
al. 2003). In the several decades prior to the 1980s, seal
predation must have had little impact on the abundance
and dynamics of this cod stock, given that there were so
few seals. Presumably, the current state of this cod stock
is largely the result of the long-term effects of overfishing
(Hutchings and Myers 1994, Hutchings 2005), rather
than the relatively recent increase in gray seals.
The closure of the cod fishery and the continuation of
trawl surveys allowed us to better estimate the natural
mortality of cod (Trzcinski et al., unpublished manu-
script). However, it is still very difficult to estimate
natural mortality, particularly on young fish and while
the cod population is rare. Our estimate of impact, the
ratio of mortality due to seal predation to natural
mortality, is sensitive to our assumptions about natural
mortality. While it is clear that natural mortality has
increased, it is difficult to say by how much. This
information is important in understanding the current
state of the cod population, and its potential for
recovery, while allowing us to place the mortality caused
by gray seals in perspective.
This work would not have been possible without the
foresight and work of those studying gray seals since the
1960s to whom we are greatly indebted. We thank M. Hammill,
D. Austin, G. Breed, C. Beck, and S. Iverson for sharing data,
J. Gibson and J. Black for modeling advice, and M. Hammill,
G. Chouinard, A. Sinclair, and anonymous reviewers for
comments on the manuscript. The research was funded by the
Atlantic Seal Research Program, Department of Fisheries and
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