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Population dynamics of porbeagle in the northwest Atlantic, with an assessment of status to 2009 and projections for recovery

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A forward projecting, age-and sex-structured life history model, fit to catch-at-length and catch per unit effort data to the end of 2008, was used to evaluate porbeagle (Lamna nasus) population dynamics in the northwest Atlantic. Four variants of the population model were evaluated, all of which differ in their assumed productivity. The total population size is currently estimated to be about 22% to 27% of its size in 1961 and about 95% to 103% its size in 2001. The estimated number of mature females in 2009 is in the range of 11,000 to 14,000 individuals, or 12% to 16% of its 1961 level and 83% to 103% of its 2001 value. All population models predict recovery to SSN 20% before 2014 if the human-induced mortality rate is kept at or below 4% of the vulnerable biomass. Under the low productivity model, recovery to SSN MSY is predicted to take over 100 years at exploitation rates of 4% of the vulnerable biomass. All models except that with the lowest productivity predict that keeping the rate of human-induced mortality to less than 4% of the vulnerable biomass would be precautionary and would keep expected recovery times to SSN MSY on the order of decades.
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SCRS/2009/095 Collect. Vol. Sci. Pap. ICCAT, 65(6): 2109-2182 (2010)
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POPULATION DYNAMICS OF PORBEAGLE IN THE NORTHWEST
ATLANTIC, WITH AN ASSESSMENT OF STATUS TO 2009
AND PROJECTIONS FOR RECOVERY
Steven E. Campana, A. Jamie F. Gibson, Mark Fowler,
Anna Dorey and Warren Joyce1
SUMMARY
A forward projecting, age- and sex-structured life history model, fit to catch-at-length and
catch per unit effort data to the end of 2008, was used to evaluate porbeagle (Lamna nasus)
population dynamics in the northwest Atlantic. Four variants of the population model were
evaluated, all of which differ in their assumed productivity. The total population size is
currently estimated to be about 22% to 27% of its size in 1961 and about 95% to 103% its size
in 2001. The estimated number of mature females in 2009 is in the range of 11,000 to 14,000
individuals, or 12% to 16% of its 1961 level and 83% to 103% of its 2001 value. All population
models predict recovery to SSN20% before 2014 if the human-induced mortality rate is kept at or
below 4% of the vulnerable biomass. Under the low productivity model, recovery to SSNMSY is
predicted to take over 100 years at exploitation rates of 4% of the vulnerable biomass. All
models except that with the lowest productivity predict that keeping the rate of human-induced
mortality to less than 4% of the vulnerable biomass would be precautionary and would keep
expected recovery times to SSNMSY on the order of decades.
RÉSUMÉ
Nous avons utilisé un modèle du cycle vital, structuré par âge et par sexe, qui réalise des
projections en avant, et ajusté à des données de prise par taille et de capture par unité d'effort
jusqu’à la fin de 2008, en vue d’évaluer la dynamique de la population de requin-taupe
commun (Lamna nasus) dans l’Atlantique Nord-Ouest. Quatre variantes du modèle de
population ont été évaluées, toutes étant divergentes dans leur productivité postulée.
Actuellement, on estime que la taille totale de la population correspond à environ 22% à 27%
de sa taille de 1961 et à environ 95% à 103% de sa taille en 2001. En 2009, le nombre estimé
de femelles matures se situait dans une fourchette allant de 11.000 à 14.000 spécimens, ou
représentait 12% à 16% de son niveau de 1961 et 83% à 103% de sa valeur de 2001. Tous les
modèles de population prédisent un rétablissement à SSN20% avant 2014 si le taux de mortalité
causée par l'homme est maintenu à 4% ou en dessous de la biomasse vulnérable. Selon le
modèle de faible productivité, il est prévu que le rétablissement à SSNPME prenne plus de 100
ans à des taux d’exploitation de 4% de la biomasse vulnérable. Tous les modèles, sauf celui
doté de la plus faible productivité, prédisent que le fait de maintenir le taux de mortalité causée
par l’homme à moins de 4% de la biomasse vulnérable serait préventif et maintiendrait les
délais escomptés de rétablissement à SSNPME de l’ordre de décennies.
RESUMEN
Se ha utilizado un modelo de ciclo vital, estructurado por edad y sexo que realiza proyecciones
hacia delante y ajustado a los datos de captura por talla y de captura por unidad de esfuerzo
hasta finales de 2008 para evaluar la dinámica de la población del marrajo sardinero (Lamna
nasus) en el Atlántico noroccidental. Se evaluaron cuatro variantes del modelo de población y
todas diferían en su productividad asumida. Actualmente se estima que el tamaño total de la
población es, aproximadamente, entre el 22% y el 27% del tamaño de 1961 y
aproximadamente entre el 95% y el 103% de su tamaño en 2001. El número estimado de
hembras maduras en 2009 osciló entre 11.000 y 14.000 ejemplares, o entre el 12 y el 16% de
su nivel en 1961, y entre el 83% y el 103% de su valor de 2001. Todos los modelos de
1 Population Ecology Division, Science Branch, Department of Fisheries and Oceans, Bedford Institute of Oceanography, P.O. Box 1006,
Dartmouth, N.S. Canada, B2Y 4A2; Email: Steven.Campana@mar.dfo-mpo.gc.ca
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población predicen la recuperación hasta SSN20% antes de 2014 si la tasa de mortalidad
inducida por el hombre se mantiene en o por debajo del 4% de la biomasa vulnerable. En el
modelo de baja productividad, se predice que la recuperación hasta SSNRMS requeriría más de
100 años con tasas de explotación del 4% de la biomasa vulnerable. Todos los demás modelos
excepto el de la productividad más baja predicen que mantener la tasa de mortalidad inducida
por el hombre en menos del 4% de la biomasa vulnerable sería precautorio y mantendría los
plazos de recuperación previstos hasta alcanzar SSNRMS en el orden de décadas.
KEYWORDS
Porbeagle, stock assessment, recovery assessment, population model, catch
1. Introduction
The porbeagle shark (Lamna nasus) is a large cold-temperate pelagic shark species of the family Lamnidae that
occurs in the North Atlantic, South Atlantic and South Pacific oceans. The species range extends from
Newfoundland to New Jersey and possibly to South Carolina in the West Atlantic, and from Iceland and the
western Barents Sea to Morocco and the Mediterranean in the East Atlantic. It is the only large shark species for
which a directed commercial fishery exists in Canadian coastal waters.
Fisheries management plans for pelagic sharks in Atlantic Canada established non-restrictive catch guidelines of
1500t for porbeagle prior to 1997 (O’Boyle et al. 1996). Because of the limited scientific information that was
available at the time, abundance, mortality and yield calculations could not be made. Therefore, a provisional
TAC of 1000t was set in place for the period 1997-1999, based largely on historic catches and the observation
that recent catch rates had declined (O’Boyle et al. 1998).
In 1998, an intensive research program on all aspects of porbeagle biology and population dynamics was
initiated at the Bedford Institute of Oceanography. The research was carried out with the support and funding of
the porbeagle shark fishing industry, and in collaboration with the Apex Predators Program of the U.S. National
Marine Fisheries Service (NMFS), and greatly increased our understanding of porbeagle biology and population
dynamics (Campana et al. 2002a,b, 2003, 2008; Campana and Joyce 2004; Cassoff et al. 2007; Jensen et al.
2002; Joyce et al. 2002; Natanson et al. 2002). The research program led to two analytical stock assessments of
porbeagle (Campana et al. 1999, 2001). Based on those assessments, the Shark Management Plan for 2002-2006
reduced the TAC to 250t, a value that was thought to correspond with FMSY and was expected to allow for stock
recovery. An updated assessment in 2005 (Gibson and Campana 2005) further reduced the TAC to 185t , with
125 t allocated to the directed fishery in Scotia-Fundy, 50t for by-catch, and 10t to the Gulf of St. Lawrence.
In May 2004, the Committee on the Status of Endangered Wildlife in Canada (COSEWIC) designated the
porbeagle as an endangered species, and recommended that it be listed under Schedule 1 of Canada’s Species at
Risk Act (SARA) (COSEWIC 2004). After extensive consultations both within and outside of government, the
decision was taken not to list the species under SARA. The basis for the decision was that the porbeagle
population was lower than desirable (standing at about 190,000 sharks in 2005), but was projected to be
increasing, and that catch levels for the fishery were intentionally set at levels which would allow the population
to recover. Implicit in this decision was the recognition that if population recovery could not be demonstrated,
the desirability of the fishery would be re-evaluated.
The present document provides an up-to-the-date summary of current population status and recovery potential
for porbeagle shark. The basis for the document is a statistical analysis of available data to the end of 2008 using
a life history based, age-structured population model, which is used to evaluate current population status and
trends. The population model is then used to evaluate potential recovery trajectories given various management
options and exploitation rates, as well as time frames for recovery.
2. Population biology
2.1 Morphometry
Various measures of porbeagle size have been used in the past: Aasen (1963) used dorsal length and a non-
standard measure of total length, the Scotia-Fundy observer program uses total length, the NF observer program
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uses fork length, dockside monitors have sometimes used dressed carcass weight, and the fishing industry uses
inter-dorsal length. To convert all of these measurements into a common currency, it was necessary to develop a
series of inter-conversion factors (Campana et al. (1999, 2001). Fork length measured over the curve of the body
is the measurement used in this assessment. The most common conversions are shown below.
FL = 3.64 + 0.95*AasenTL
Flcurved = FLstraight
FL = 0.99 + 0.885*TL
TL = 1.12*FL
W = 0.00005*FL2.713
where FL is fork length measured over the curve of the body in cm, TL is total length, AasenTL is Aasen’s
(1963) non-standard measure of TL, and W is weight in kg..
2.2 Stock structure
Evidence presented in previous reports indicates that there is only one stock of porbeagle in the northwest
Atlantic, and that there is no appreciable mixing of porbeagle from the northeast Atlantic with those in the
northwest Atlantic (Campana et al. 1999, 2001). Month to month shifts in the location of the fishery suggest that
porbeagle carry out extensive annual migrations up and down the east coast of Canada, with no indication of the
presence of separate stocks. Porbeagle first appear in the Gulf of Maine, Georges Bank and southern Scotian
Shelf in Jan-Feb, move northeast along the Scotian Shelf through the spring, and then appear off the south coast
of NF and in the Gulf of St. Lawrence in the summer and fall. Catches in the late fall suggest a return movement
to the southwest. This pattern is reproduceable from year to year. A map of geographic locations and fishing
banks is shown in Figure 1.
The results of tagging studies carried out by Norway, Canada and the US also document extensive annual
migrations in the NW Atlantic. A total of 197 recaptures were reported in Campana et al. (1999). A further 12
recaptures have since been reported; all recaptures have been mapped in Figure 2. Movements between the
Grand Banks, Scotian Shelf and Gulf of Maine were common. None of the tagged porbeagle were recaptured on
the east side of the Atlantic, and none of the porbeagle tagged in the eastern Atlantic were recaptured off the
North American coast (Stevens 1990).
2.3 Age, growth, longevity and natural mortality
Porbeagle age can be accurately determined from vertebral sections. The life span of porbeagle is estimated to
be between 25 and 46 years and generation time is about 18 years (Campana et al. 2002; Natanson et al. 2002).
In both sexes, growth rate appears to decrease slightly at the onset of sexual maturity. Since females mature at an
older age than do males, females grow to a larger size. Figure 3 presents the von Bertalanffy growth parameters
by sex, as well as that of the combined sexes. Predicted lengths and weights at each age are also shown,
although observed sizes at age 0 and 1 were used to minimize distortions due to seasonality and partial
recruitment of the young fish to the fishery.
It is possible that the ages of very old porbeagle (>25 yr) are underestimated by vertebral band counts, as has
been observed in the slow-growing New Zealand population (Francis et al. 2007). If true, the growth rate of old
porbeagle is somewhat slower than that suggested by the von Bertalanffy growth parameters. The fact that the
Linf of the females is considerably larger than the largest porbeagles normally observed suggests that growth
overestimation of the oldest fish (and only the oldest fish) is a possibility. For this reason, the combined growth
curve has been used in most analyses.
Porbeagle are thought to have a low natural mortality. Instantaneous natural mortality is estimated to be 0.10 for
immature porbeagle, 0.15 for mature males, and 0.20 for mature females (Campana et al. 2008). Although these
estimates are conditional on the gear selectivity assumed in their calculation, they are presently the best available
for this population.
2.4 Porbeagle reproduction
Porbeagle sharks have low fecundity and a late age of sexual maturation. Jensen et al. (2002) reported that males
mature between 160 - 190 cm in fork length (L50 ~ 174 cm; A50 ~ Age 8) while females mature between 205 -
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230 cm (L50 ~ 217 cm; A50 ~ Age 13) (Figure 4). Porbeagles are ovoviviparous and oophagous, with an average
litter size of 3.9 pups in the NW Atlantic.
Our research indicates that mating occurs in at least two locations. The first mating ground to be identified was
on the Grand Banks, off southern New Foundland and at the entrance to the Gulf of St. Lawrence (Figure 5).
Most large females collected in these areas in the late summer or early fall were pregnant, suggesting that mating
took place during the summer (Jensen et al. 2002). A second mating ground was identified on Georges Bank in
June 2007, based on very high catch rates of mature females which did not appear to be feeding (Figure 5).
Mature males were absent at the time, suggesting that mating had not yet begun. Allowing for the delay between
mating and the production of visible embryos, mating time on Georges Bank and off New Foundland is
probably very similar. The location of the pupping ground remains unknown. Birth apparently occurs in late
winter or spring after an 8-9 month gestation period (Aasen 1963; Francis and Stevens 1999; Jensen et al. 2002).
There is no evidence of an extended latency period after birth, since virtually all sexually mature females are
pregnant in the fall. Therefore, the reproductive cycle is 1 yr.
2.5 Temperature, depth and feeding
Porbeagle appear to occupy well defined and relatively constant temperatures throughout the year (Campana and
Joyce 2004). Based on temperature at the depth of the gear, porbeagle were caught at a mean temperature of 7.4
0C, with 50% being caught between 5-10 0C. Temperature at depth was a significant predictor of catch rate;
however, sea surface temperature was a poor predictor of catch rate. There was no significant seasonal pattern in
temperature, suggesting that the porbeagle adjusted their location to occupy the preferred temperature range.
For much of the spring, porbeagle were caught most frequently in waters immediately adjacent to the frontal
edge separating cool Shelf waters from warmer offshore waters (Figure 6). Porbeagle were not associated with
fronts in the fall fishery, although the temperature occupied was similar to that observed in the spring (5-10 0C).
The porbeagle is primarily an opportunistic piscivore with a diet characterized by a wide range of species (Joyce
et al. 2002). Teleosts occurred in the majority of stomachs and constituted 91% of the diet by weight.
Cephalopods occurred in 12% and were the second most important food category consumed. Diet composition
changed seasonally following a migration from deep to shallow water. The relative contribution of groundfish
increased with shark size, while the contribution of cephalopods decreased. Other elasmobranchs were
occasionally eaten by large porbeagles, but marine mammals and birds were never found in the stomachs (Joyce
et al. 2002).
3. Porbeagle shark survey
Canada’s first fishery-independent survey of porbeagle shark abundance was carried out by Atlantic Canadian
fishermen working in conjunction with DFO scientists in June 2007. The objective of the survey was to provide
a baseline for monitoring the population health and abundance of porbeagle and other sharks found off of
Atlantic Canada. Subsequent surveys will be carried out using the same design and stations, thus allowing for
exact comparison with the 2007 survey. The second survey was carried out in June 2009, but the data have not
yet been analyzed.
The 2007 shark survey covered 50 stations in Atlantic Canada stretching from the Canada-US border up to
northern Newfoundland, an area of more than 200,000 km2 (Figure 7). Pelagic longline gear fit with #8 or #9 J
hooks and baited with squid was fished from the surface to the bottom and back, at repeating intervals. A total of
600 hooks were fished each set, with a total soak time of about 6 hr. Scientific staff were present on the survey
boats throughout the survey.
Porbeagles (n=865) were caught throughout the survey area, but were most common around the deep basins and
on the edge of the continental shelf (Figure 7). Catch rates were highest in water temperatures of 6o C (at the
depth of the fishing gear) and at depths of 100 m; catch rates were low in waters colder than 30 and warmer than
8o. Mature female porbeagles were only caught on the shelf edge. Mean porbeagle fork length was 159 cm and
48 kg in weight. However, fork length ranged between 98 cm and 223 cm.
Comparison of the survey abundance index with previous commercial catch rates was difficult, since June was
not a popular fishing month historically, especially by small vessels. However, it appears that survey catch rates
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were roughly comparable with those from 2000-2006, as predicted by Gibson and Campana’s (2005) population
model; catch rates were higher in some areas such as near the shelf edge, and lower in other areas such as the
Grand Banks. The real value of the shark survey will become apparent when comparing the 2007 survey results
to those from the 2009 survey.
4. The fishery
4.1 Landings
The commercial landings reported here are the combined reported landings (all countries) for the northwest
Atlantic (NAFO areas 3-6) from 1961 to 2008 (Table 1). All foreign data after 1978 came from the Scotia-
Fundy Observer Program (SFOP) or Newfoundland Observer Program (NFOP) and are thus considered
accurate. Canadian landings data are considered to be relatively accurate, especially after 1996.
Landings rose from about 1,900 t in 1961 to over 9,000 t in 1964 and then fell to less than 1,000 t in 1970 as a
result of collapse of the fishery (Table 1; Figure 8). Reported landings remained less than 500 t until 1989, and
then increased to a high of about 2000 t in 1992. Landings since 1998 have been restricted by quota, and have
been less than 230 t since 2002 (125 t in 2008). Most of the landings are from the directed porbeagle pelagic
longline fishery, although with recent quota reductions, the percent of landings as by-catch has increased (Table
2). Reported landings of porbeagle in fisheries outside the Scotia-Fundy region are lower and have been under
20 t since 2002 (Table 3). There is almost no recreational fishery for porbeagle sharks.
For the population model, the catch was apportioned to three areas: NF-Gulf = Gulf of St. Lawrence, area north
of Laurentian Channel, plus NAFO Division 4Vn; Basin = Basins and inshore regions of Scotian Shelf, and the
Shelf edge = area over and around the edge of the Scotian Shelf, plus the Gulf of Maine (Figure 1). The split
was accomplished based on location of the reported catch for the years 1989 to 2004, and using the 1988 to
2002 averages for years prior to 1988 (Table 4). Nearly all directed landings since 2003 were from the Basin
and Shelf edge areas (Table 4).
4.2 Location and size composition of the catch
Almost all landed porbeagle have been caught on the edge and in the deep basins of the Scotian Shelf since 2005
(Figure 9). Most of this fishing activity took place in the spring.
The Total Allowable Catch (TAC) for porbeagle in Canada was reduced from 850 t to 250 t in 2002, and further
reduced to 185 t beginning in 2006. This reduction in catch quota resulted in the disappearance of the large
offshore vessels from the directed fishery, and thus a major contraction in the area fished (Figure 10). Observed
catches by Canadian observers in the 1990s were historically distributed along the edge and in the deep basins of
the Scotian Shelf, but also in the Gulf of St Lawrence and on the Newfoundland Shelf. Most observed catches
since the year 2000 have only been along the shelf edges and in the deep basins. All life history stages have
roughly similar distributions (Figure 10). Young of the year distribution has been conspicuously absent from the
inshore Newfoundland shelf since 2000, but this is probably largely due to the closure of the Newfoundland
mating grounds to directed shark fishing in 2000.
To this point, there has been very little information available on porbeagle catches outside of the Canadian EEZ.
Mapping of U.S. 2000-2007 observed catches and tag releases/recaptures (in a roughly 1:1 ratio) (NMFS 2008)
indicates that porbeagle are found outside of Canadian waters in substantial numbers, particularly off the
northeastern U.S. and off the shelf edge east of the Grand Banks (Figure 11). YOY porbeagle were particularly
prevalent off the eastern edge of the Grand Banks, along the shelf edge in both Canadian and northeastern U.S.
waters, and inshore in northeastern U.S. waters. Juveniles were distributed similarly, but with lesser numbers off
the Grand Banks. Adults were seldom caught. Given the mixture of tagged and observed sharks used in this
database, the mapped distribution is unlikely to be representative of distributional proportions, but does give a
good idea of distribution outside of Canadian waters, but within the area fished by U.S. fishermen.
Observed U.S. catch locations of juvenile porbeagles <120 cm FL, excluding observations from the tagging
database, show that most juveniles were captured off the continental shelf east of the Grand Banks and off the
northeastern U.S. coastline (Figure 12). Given that most of these observations were obtained from the U.S.
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pelagic longline fishery, the observed distribution largely reflects that of the U.S. high seas fishery.
Nevertheless, it reinforces the perspective provided by Figure 11 that juvenile porbeagles often occur in deep
water off the continental shelf.
Catch quantities and catch locations of porbeagle by the international fleet on the high seas appear to be
incompletely recorded.
The size composition of the Canadian catch has changed since 1990 (Figure 13). When disaggregated by time
periods corresponding to an unrestricted fishery (1990-1999), a reduced TAC (2000-2004), and the recent very
reduced TAC (2005-2008), the overall size range and modal size of the catch has remained roughly constant at
80-260 cm and 120-140 cm FL, respectively. However, there were noticably more larger sharks (>140 cm FL)
caught before 2005 than after 2005, presumably reflecting a loss of larger sharks from the fishery, as well as the
closure of the Newfoundland mating grounds.
4.3 Discards
As a commercially valuable species, unlanded by-catch of porbeagle in Canadian fisheries is presumed to be
minimal. To quantify this unlanded by-catch, observer records of discarded porbeagle catch relative to target
large pelagic catch (tuna, swordfish, porbeagle) were calculated by fishery, NAFO area, season and year. The
proportion of porbeagle in each observer cell was then multiplied by the total reported landings (from ZIF until
2002, and from MARFIS and other regional statistics after 2002) of the target catch in each cell to obtain the
estimated discarded porbeagle catch in each cell. Estimated porbeagle discards were minimal (average of <5 t)
for all cells except that of the large pelagic longliners between July and December. Observer coverage for this
fleet and time period averaged 8% of total landings, but less in terms of number of trips. Total estimated
porbeagle discards by the large pelagic fleet in the latter half of the year have averaged 21 t annually since 1996,
with an average of 27 t annually since 2000 (Table 5). The size composition of these discards is unknown.
Porbeagle discards by the international high seas fishery are unknown and largely unrecorded.
5. Population model – input data
The data entered into the population model are updated from those presented in Campana et al. (2001) and
Gibson and Campana (2005).
5.1 Commercial catch rates (CPUE)
Catch-per-unit-effort (CPUE) is used as the primary index of abundance in this analysis. Calculations of
porbeagle CPUE were based on porbeagle-directed longline catches, which account for virtually all historical
catches. Initial examination of the catch rate data indicated that the major data sources could be categorized by
country (Canada, Faroes), vessel identity (CFV), season, and area fished.
Porbeagle CPUE was calculated in two ways: on the basis of catch weight per hook, and using separate
calculations of numbers of mature and immature sharks per hook. Both indices are presented to show trends in
abundance, but only the weight per hook index was used to calibrate the population model. Only vessels that
fished in a season and area in three or more years were included in the CPUE analyses.
To disaggregate CPUE into rates for immature and mature sharks; Campana et al. (2001) calculated CPUE in
terms of ln-transformed numbers per hook. A fork length equal to 200 cm is approximately midway between the
lengths corresponding to 50% maturity in males and females, and is therefore a proxy for sexually mature
porbeagles (Jensen et al. 2002). To calculate catch rate at length, the length composition was determined for
each of the 3 subareas in each of 3 seasons (Jan-Mar, Apr-June, July-Dec) based on available measurements
each year. Set by set catch rates in terms of weight were converted to numbers based on the mean weight of the
length composition of the subarea-season-year cell, then apportioned according to the length frequency.
Numbers above 200 cm FL were pooled within a set to form the index for mature sharks, while the remainder
were pooled to form the index for immature sharks.
Error plots summarizing the three CPUE data sets are shown in Figure 14. The CPUE by weight data remained
relatively high after 2002 in both the Basin and Shelf Edge areas; the NF-Gulf area has not been consistently
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fished since 2002 (Figure 14a). Much of this trend has apparently been due to catch rates of immature sharks,
which have remained relatively high in both the Basin and Shelf Edge after 2002 (Figure 14b). In contrast, the
CPUE of mature sharks has continued to decline in the Basin, and been erratic on the Shelf Edge (Figure 14b).
The marked decline in CPUE of mature sharks in the NF-Gulf area prior to 2002 has previously been noted
(Campana et al. 2001).
At least two issues exist with these CPUE data when deriving an index of abundance. First, the spatial
distribution of the fishing effort has decreased markedly in the last few years (Figure 15). Coincidental with this
change has been an increase in CPUE after 2002 in the smaller area presently being fished, indicating either
increased abundance, increased efficiency, a change in methods or a change in the distribution of porbeagle in
recent years. Second, there is little overlap in the vessels that took part in the fishery in the late 1980s and 1990s
and those presently fishing (Tables 6.1 to 6.3). This issue creates difficulties separating year effects (changes in
abundance) from vessel effects (changes in the fleet), and not all vessels fish with the same efficiency (Figure
16). Differences in catchability also exist among seasons (Figure 17).
CPUE time series are often standardized to correct for differences in the timing and gear used in the fishery
(Maunder and Punt 2004) prior to being included in the assessment model. Alternatively, the standardization
may be integrated into the assessment model, a method that has been shown to provide greater precision in
biomass estimates than when the standardization is done prior to fitting the assessment model (Maunder 2001).
The latter approach was used here, whereby the CPUE by weight standardization was integrated into the
assessment model. We fit several models, starting with a simple model with a single catchability coefficient for
all vessels in all areas in all seasons, then adding coefficients for area, CFV and season, and adding coefficients
for combinations of these variables, in a stepwise fashion (Gibson and Campana 2005). This analysis was done
with two weightings of the catch at length data (by changing the assumed sample size). Based on the Akaike
Information Criterion (AIC), a model with separate catchability coefficients each vessel, in each area and in each
season (each vessel, area and season combination is used as a separate index of abundance) was the best model
and was retained for the analyses herein. Full details are shown in Gibson and Campana (2005).
5.2 Catch at length
Campana et al. (1999, 2001) describe the porbeagle length data set and standardizations. Over 152,000 length
measurements are available for known sex porbeagle, and more are available when sharks of unknown sex are
included. To estimate the proportion of the catch by length, we assigned porbeagle to 5 cm length categories
ranging from 65 to 285 cm total length. When fitting the model, we used sex specific data for the years: 1995
and 1998 - 2008 for the Basin region; 1988, 1989 to 1996, 1998 to 2000 and 2002 for the NF-Gulf region; and
1961, 1981, and 1990 to 2008 for the Shelf-Edge region. Observed proportions at length and sample sizes are
shown in the Results section (Figures 20.1 to 20.8).
5.3 Tagging data
Descriptions of the porbeagle tagging programs are provided by Campana et al. (1999). Following Campana et
al. (2001) and Gibson and Campana (2005), we included only sharks less than 125 cm fork length at the time of
tagging and assumed these sharks were either age 0 or age 1. Between 1980 and 1999, a total of 1083 porbeagle
sharks in this size category were tagged, resulting in 121 recaptures (Table 7).
6. Population model
This model is a forward-projecting age- and sex-structured population dynamics model first presented in
Campana et al. (2001) and Harley (2002), and then modified in Gibson and Campana (2005). Within this model,
the population is projected forward from an equilibrium starting abundance and age distribution by adding
recruitment and removing catches. A key assumption in the model is that the porbeagle population was at an
unfished equilibrium at the beginning of 1961, when the directed commercial fisheries for porbeagle began.
Model parameter estimates (e.g. selectivity parameters and catchability coefficients) are obtained by fitting the
model to the available datasets using maximum likelihood.
6.1 Population dynamics in the model
Of primary interest is the number of fish in year t, of sex s and of age a, denoted Nt,s,a. The number of fish in
each age class in the next year is given by an exponential decay model. Here, the total mortality rate is the sum
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of the sex and age specific instantaneous natural mortality rate (Ms,a) and the fishery (g) specific exploitation rate
in each year, sex and age class ( gast
u,, ).
g
gast
M
astast ueNN as )1( ,,,,1,,1 ,.
Litter size is not thought to vary with age in porbeagle, so the spawner-recruit relationship is expressed in terms
of the number of females rather than biomass. Using the letter F to denote the female sex category, the number
of female spawners in year t (SSNt) is a function of Nt,F,a and the probability that a female fish of age a is mature
at that age (mF,a):
a
aatt mNSSN ,F,F,
The life cycle is closed by modeling the number of age-1 fish of each sex in the year t+1 as a function of SSNt
using a Beverton-Holt spawner-recruit (Hilborn and Walters 1992) relationship:
5.0
1
)2/(
1,,1
2
t
e
R
SSN
SSN
N
asy
t
t
st
Here,
is the slope at the origin, and in the deterministic model is the maximum rate at which female spawners
can produce age-1 recruits at low population sizes (Myers et al. 1999), and Rasy is the asymptotic recruitment
level (expressed as the number of age-1 recruits). Rasy is the limit approached by Rt as St approaches infinity
(Beverton-Holt models are often written in terms of the half saturation constant, K, which is related to Rasy
by: KRasy
). A 1:1 sex ratio at birth is assumed. Recruitment can vary around the fitted relationship though
the log of a recruitment deviate for each year ( t
), in which case a correction for transformation bias based on
the standard deviation of the log recruitment deviate (
) is applied to each deviate. As written, a lognormal
error structure for recruitment (Myers et al. 1995) is assumed. In comparison with the other commonly used 2-
parameter SR model, the Ricker model, the Beverton-Holt model has the advantage that Rasy can be rescaled and
interpreted as an estimate of carrying capacity (Gibson and Myers 2003a, Myers et al. 2001), but is not a
precautionary model selection because it typically provides estimates of
(and its related reference points) that
are higher than those from the Ricker model (Gibson and Myers 2003b, Myers et al. 1999). Reference points
provided herein are therefore not precautionary with respect to SR model selection.
6.2 Commercial fisheries
The commercial fisheries are included in the population dynamics through gast
u,, . This term consists of two
separable components: the gear (or fishery) and sex specific selectivity of the commercial fisheries sg
a
s, and the
exploitation rate of the fully exploited age class by each gear in each year, g
t
u:
g
t
sgg ast usu a
,
,,
Selectivity was assumed to follow a double half Gaussian selectivity curve:
sg
full
sg
R
sg
full
sg
full
sg
L
sg
full
sg
a
sa
v
sa
sa
v
sa
s
,
,
2,
,
,
2,
,
if
)(
exp
if
)(
exp
2117
where g refers to the commercial fishery (Basin, Shelf-Edge or NF-Gulf). In this model, the age at which fish are
fully selected by the fishery is denoted sg
full
s,. The steepness of the decline away from the age at full selectivity is
governed by the v parameters for the left and right sides of the curve.
The fishery operates throughout much of the year, but for simplicity, we assume the catch is taken during a short
time period half way through the year, an approximation attributed to Pope (Quinn & Deriso 1999). We assume
that the total catch in each year by each fishery ( g
t
C) is known without error. The exploitation rate (proportion
of the vulnerable biomass removed) in each fishery in each year is then:
as asast
sg
a
M
g
t
g
twNse
C
uas
,,,,
,
5.0 ,
where ws,a is the sex specific weights at age.
6.3 Initial conditions
We assume that the population is at an unfished equilibrium population and age structure at the start of the time
period (1961). The calculation of the equilibrium population size is provided in the reference point section
below.
6.4 Predictions from the model
Parameter estimates are obtained from the model by minimizing the discrepancies between the observed data
and predictions from the model. Specifically, we want to obtain predictions of the annual catch per unit effort
(CPUE) of sharks in the three fisheries g
t
I, the predicted length composition of the catch in the three fisheries
and the predicted number of tagged recaptures for each year.
Under the assumption that CPUE is proportional to abundance, the predicted CPUEs of mature and immature
sharks are:
12and11for
,,,
,
5.0
,,
mfast
gas
as
M
ggimmaturet aaNseqI as
and
12and11for
,,,
,
5.0
,,
mfast
gas
as
M
ggmaturet aaNseqI as .
Note that the ages do not correspond directly with the ages of 50% maturity. The mean length at maturity for
male and female porbeagle is roughly 200 cm and the split in the data is on this basis. The ages above
correspond to these lengths. These equations were used in Gibson and Campana (2005), but were modified for
the current model for CPUE by weight by adding weight at age to the right-hand sum and by increasing the
number of q’s (one for each boat in each area and each season).
Following Harley (2002), the sex specific predicted length composition in the catch sg
lt
P,
,is a function of the
population age composition, the selectivity curves and the distributions of length at age:

al ast
s
al
sg
a
aast
s
al
sg
a
sg
lt Nfs
Nfs
P
,,
,
,,
,
,
,.
Here, the sex-specific length proportions at age ( s
al
f) is given by:
2118


2
2
2
exp
2
),( s
a
ss
s
a
s
a
s
a
s
al al lx
lf
where
is the size of the length increment (5 cm in this analysis). Here we used the same growth analysis used
in Campana et al. (2001) and Harley (2002), assuming a von Bertalanffy growth model to model the relationship
between length and age, as well as a linear relationship between s
a
and la. Constants are provided in Table 8.
6.5 The tagged population
We assumed that the dynamics of the tagged population were identical to the untagged population. Denoting the
number of tagged fish of age a that are alive in year t as T
,at
N, the number of tagged fish in the following year
is:
)1()1( T1,1,
T
,
T1,1 kRueNN atat
M
atat a
,
where T
,at
R is the number of tagged fish of age a released in year t and k is the rate of tag loss or mortality
associated with tagging assumed to occur shortly after tagging. The expected number of recaptures Tt,a is then:
at
M
atat ueNT ,
5.0T
,,
.
Here, ut,a is the mean of the rates for the fisheries in the three regions and
is the reporting rate. Reporting rates
of 0.9 were assumed for all years except 2003 and 2004 when (lower) values of 0.75 and 0.70 reflecting
comments from the fishing industry.
6.6 Likelihood equations
The model was fit to the data by minimizing an objective function (O.F.V.) that is the sum of the negative log
likelihoods for the CPUE series ( CPUE
), the tagging data ( tag
) and length compositions in the catches
(compcatch
). We used lognormal error structures for the CPUE time series, a Poisson error structure for the
tagging data and a robust normal error structure (Fournier et al. 1990) for the proportions at length in the catch.
For each fishery, the log-likelihood for the CPUE component of the model is:
2
2
1)(2 )ln
~
(ln
2log
2
1
ln
tg
g
t
g
t
ngg
CPUE II
,
where n is the number of observations in the series, g
is the standard deviation of a normal distribution prior
to exponentiation and g
t
I
~
is the observed CPUE index value in year t and region g. We used a constant value of
0.3 of all g
in this analysis. We also used the standard error of each estimate of g
t
I as an estimate of g
, an
approach that weights the contribution of each year differently based on the precision of the estimate. This
alternative made little difference in the overall fits of the model so we retained the constant value of 0.3. This
equation was appropriately modified when different grouping of the data were used.
From Harley (2002), for a given gear and sex category, the robust normal log-likelihood for proportions at
length in the catch is:
2119



 

 
Y
t
A
lgs
tl
gslt
gstl
gs
tl
Y
t
A
l
nyears
t
gs
tll
gslt
sg complength
A
PP
AA
11 ,,
,
2
,
,
,
,
11 1
,,
,
,.
01.0
/1.02
~
explog
)log())/1.0(2log(5.0
,
where Y is the number with observed proportions at length, A is the number of length categories, gs
t,
is the
sample size and gslt ,
,
is the variance. We set the maximum sample size at 3,000 to keep a few years with very
large samples from dominating the fit, and used the variance of the predicted proportions (Fournier et al. 1990):
)1( ,
,
,
,
,
,gslt
gslt
gslt PP
.
We used a length-frequency distribution of the sexes combined for some years (see the Data section) with
appropriate modifications to the above equations.
The log likelihood for the tagging component of the model is:
at at
at atat
at attag TTTT ,,
,,,
,,)!
~
ln(ln
~
,
where ~ is again used to denote the observed data.
The final objective function is then:
tag
sg
sg
sizesg
sizesg
CPUE compcatch
VFO
,
,
,
,
.
...
We programmed this model using AD Model Builder (Fournier 1996). AD Model builder uses the C++ auto-
differentiation library for rapid fitting of complex non-linear models, has Bayesian and profile likelihood
capabilities, and is designed specifically for fitting these types of models.
6.7 The production model and reference points
We modelled the population dynamics of porbeagle using two equations: a spawner-recruit relationship that
expresses recruitment as a density dependent function of spawner biomass, and the replacement line, the slope of
which is the inverse of the rate at which recruits produce replacement spawners. Here, an implicit assumption is
made that all density-dependent processes occur between spawning and recruitment. The production model also
includes a third component: a yield per recruit relationship. We used the selectivity curves for the Shelf-Edge
fishery in the following analysis. All results are therefore specific to that fishery. Results would vary if other
selectivity curves had been assumed.
The SR model was discussed in the previous section. We modelled the rate at which recruits produce spawners
(the inverse of the slope of the replacement line) by calculating the number of spawners per recruit (SPRF) as a
function of fishing mortality (Shepherd 1982, Mace and Sissenwine 1993, Mace 1994):
max
aga
a
aFM
aF emSPR 1
)(
1
11,F
1,F
5.0 ,
where ga
F,F is the age and gear specific fishing mortality rate for females. Note that the resulting reference
points are specific to the selectivity assumed in the calculation.
The yield per recruit for a given F (YPRF) is found similarly:
2120


s
a
as
gas
FMM
F
max
agas
asas wFeYPR 1,,
)(5.0 1
1
11,
1,, .
For a given value of F, the spawning biomass produced by the number of recruits in year t is
tF RSPRSSN . Equilibrium spawning biomasses and recruitment levels (denoted with asterisks) were
found by solving this equation for Rt, and substituting the result in the spawner-recruit model (Quinn and Deriso
1999):
asy
FR
SSN
SSN
SPR
SSN *
1
**
.
The equilibrium spawning biomass (SSB*) is then:
asyF RSPR
SSN )1(
*
,
and the equilibrium number of recruits (R*) is found by substituting the SSN* in the spawner-recruit model:
asy
R
SSN
SSN
R*
1
*
*
.
The equilibrium catch (C*) is R* multiplied by the yield per recruit for the given value of F:
F
YPRRC ** .
Reference points from the spawning biomass per recruit and yield per recruit analyses were found using a grid
search across a set of F's {0 to 2.0; increment of 0.0025}. We calculated YPRF and SPRF for each value of F,
and reference points were then estimated by selected the fishing mortality rate corresponding to the appropriate
reference point criterion. The SPRx% reference points were found by selecting the fishing mortality rate where
the SPRF was x% that of SPRF=0.
We estimated five reference points from the production model. The equilibrium spawning biomass in the
absence of fishing, SSNeq, was estimated directly from the production model. A spawning biomass of 20% SSNeq
is sometimes used as a minimum threshold population size (Beddington and Cooke 1983, Goodyear 1993).
SSN20% was calculated as 20% the equilibrium female spawner abundance in the absence of fishing:
asyF RSPR
SSN )1(
2.0 0
%20
The grid searches were used to find the fishing mortality rate that produces maximum sustainable yield (FMSY),
the corresponding spawner biomass that produces maximum sustainable yield (SSNMSY) and the fishing mortality
rate that drives the population to extinction (Fcol). We estimated FMSY by calculating C* for each value of F, and
selecting the value of F where C* was maximized. SSBMSY, the spawning biomass at MSY, was found similarly.
The equilibrium fishing mortality rate at which the population goes extinct, Fcol, is determined by the slope of
the SR relationship at the origin
, and is the value of F where
F
/1 SPR .
6.8 Population viability analysis
2121
To assess recovery and timelines for recovery, recovery targets are required. Recovery targets have not yet been
established for porbeagle. Here, we assess how differing levels of incidental harm (mortality associated with by-
catch in fisheries not targeting porbeagle) affects the recovery timelines relative to two commonly used fishery
reference points SSN20% and SSNMSY. These are not recovery targets, but are reference points against which
population growth can be evaluated.
Population viability analysis is an important tool which can be used to evaluate recovery potential, recovery
trajectories and recovery times. In a PVA, a population dynamics model is used to determine how the probability
of persistence is affected by current conditions and future perturbations (Beissinger and McCullough 2002). The
goals of a PVA are to 1) determine the current viability of a population, 2) identify threats to persistence, and 3)
provide a defensible structure for management and legal action. Typically, there are several other benefits of
PVA such as identifying information gaps, and directing future research.
A disadvantage of PVA is that it is data intensive and the minimum data required is only available for a few
species. For porbeagle, we have estimates of reproductive rates (as characterized via the spawner-recruit model),
maturity schedules and mortality rates. However, we do not presently have estimates of variances for these life
history parameters or their temporal autocorrelation, two factors than can effect recovery times and population
viability. Therefore, we projected the population forward deterministically (no variability added) from the
estimated 2009 population size and age-structure using the estimated life history parameters and an assumed by-
catch rate. We used the selectivity parameters from the Shelf-Edge fishery for these simulations. Simulations
were carried out for 17 levels of by-catch mortality (defined as the proportion of the vulnerable biomass taken as
by-catch) ranging from 0.0 to 0.1. Population projections were 100 years in length.
7. Results
Initial model fitting indicated that, as is often the case with these types of models, estimation of natural mortality
was confounded with estimation of selectivity. Additionally, none of the models achieved a robust fit (hessian),
so we do not have measures of uncertainty to qualify model results. We are therefore presenting 4 models fit to
the data, each representing a different scenario:
Model 1: integrated CPUE by weight; constant M: M=0.1 and 0.2 for immature and mature porbeagle
respectively;
estimated in the model
Model 2: integrated CPUE by weight; M= 0.1 and 0.2 for immature and mature porbeagle respectively;
constant
=2.0 (lower productivity scenario).
Model 3: integrated CPUE by weight; M= 0.1 and 0.2 for immature and mature porbeagle respectively;
constant
=2.5 (intermediate productivity scenario).
Model 4: integrated CPUE by weight; M= 0.1 and 0.2 for immature and mature porbeagle respectively;
constant
=3.2 (higher productivity scenario).
Models 2-4 used the same model structure as those of the same name in Gibson and Campana (2005), but Model
1 in the current assessment is different than Model 1 in Gibson and Campana (2005). In the latter, Model
1differed by not integrating CPUE and by using the length frequency twice (once for length composition, and a
second time for determining CPUE by maturity stage). For these reasons, Model 1 from Gibson and Campana
(2005) was the least preferred model at the time.
7.1 Fits to the data
Based on the maximized likelihoods (Table 9), Model 1 is the most plausible scenario, followed by Model 4.
Model 2 is the least plausible of these models. The estimated selectivity of the three fisheries is roughly similar
among the four models (Figure 18; Table 9), with similar parameter estimates for all four models (Table 9).
Differences in fits to the data are also subtle among the models. The predicted CPUE series for porbeagle are
similar among the integrated models, although the data show considerable variability around the fitted
relationship (Figures 19.1 to 19.7). Fits to the catch at length data are shown in Figures 20.1 to 20.8, and are
again virtually indistinguishable among models. Although no trend is apparent in the catch at length residuals
(Figures 21.1 to 21.3), the model apparently under-predicts the proportion of larger fish in early years, and the
proportion of smaller fish in the later years (Figure 22), although as shown in Figures 21.1 to 21.3, the
magnitudes of the residuals are relatively small.
2122
Residual patterns for the tagging recaptures are also similar among models (Figure 23). In all models, the catch
of younger (< age-4), tagged porbeagles is overestimated, whereas the catch of tagged, older porbeagles is
underestimated. Comparison of the log likelihoods (Figure 23) indicates that higher productivity models 1 and 4
provide better fits than low-medium productivity Models 2 and 3.
The implications of flat-topped rather than dome-shaped selectivity patterns were also explored. The fit of the
flat-topped selectivity model was considerably worse (objective function value of 16277 versus the original
13212), and there were extreme residual patterns in proportions at length, indicating that the model was
inappropriate. Although the resulting fishing mortality estimates were reduced by about half, and fishable
biomass doubled, all fishing mortality reference points were reduced accordingly, producing little net change in
recovery trajectory or time.
7.2 Population dynamics
Estimates of
were fixed using life history characteristics in Models 2-4, but was estimated to be 3.6 using
Model 1 (Table 9). Values of 2, 2.5 and 3.2 were used in the remaining models, and were thought to span the
range of plausible values for porbeagle based on life history characteristics (see Discussion). The estimate of the
maximum lifetime reproductive rate ( 0*SPRF
) from Model 1 is: 2.9 spawners per spawner, and the
assumed values from models 2 to 4 range from 1.6 to 2.6. As expected for sharks, these values are at the lower
end of the range for fish populations (Myers et al. 1999), and are indicative of very low population growth rates.
7.3 Reference points
Estimates of FMSY from the four models range from 0.036 to 0.075 (Table 9), and of Fcol from 0.075 to 0.160.
Estimates of SSNMSY decreased with estimated or assumed productivity from 40,089 females for an
of 2.0 to
27,945 females for an
of 3.6. The spawning biomass per recruit reference points F35% and F45% met or
exceeded Fcol in most model runs and are not safe reference points for porbeagle fisheries. These reference
points were calculated using the selectivities for the Shelf-Edge fishery, but given the similarity to the
selectivities for the Basin fishery, reference points for the Basin would likely be close to the values for the Shelf-
Edge. Reference points for the NF-Gulf fishery would likely differ, although little fishing is presently occurring
in that region (Table 4).
7.4 Trends in abundance and exploitation
Trends in abundance are also roughly similar between the models (Figure 24). Estimates of the number of
spawners in 1961 were highest from Model 2. All models suggest an increase in spawner abundance in the late
1970s and early 1980s, although the increase is small. The estimated total number of porbeagle also increases
only slightly during the 1980s (Figure 24). Although abundance has been relatively stable since 2002, there has
been a very slight increase in abundance of both spawners and recruits since 2006.
Estimates of exploitation rate are also similar among the models (Figure 25). All models estimate exploitation in
the Basin region to be 1% or less since 2007 (Table 10). Estimates of the exploitation rate in 2008 for the Shelf-
Edge fishery are the same from all models (0.021), which is less than the values expected to produce MSY for
any model.
7.5 Population status
Estimates of the population size in 2009 (Table 11) range from 196,911 to 206,956 sharks. The estimated
number of mature females range from 11,339 to 14,207 (Table 11), or about 6% of the population. The models
indicate that the population is about 22% to 27% its size in 1961 (Table 11), and that female spawner abundance
is about 12% to 16% of its 1961 level. The models indicate that the reduced quotas since 2002 have more or less
halted the decline in population size.
The total biomass was estimated at around 10,000 t in 2009 (Table 11). Such a biomass would place the 2009
value at between 20-24% of its value in 1961, and 4-22% higher than it was in the year 2001.
2123
Estimates of the vulnerable biomass in 2009 differ depending on the assumed selectivity as well as among
models (Table 12). Assuming the Shelf-Edge selectivity, the models place the vulnerable biomass in 2009 (mid-
year) at about 4,700-5,100 metric tonnes.
7.6 Recovery trajectories
All models indicate that the northwest Atlantic porbeagle population can recover if levels of human induced
mortality are kept low (Figure 26), with recovery to SSN20% predicted to occur circa 2012 at harvest rates less
than 4%. Estimated recovery times to SSNMSY vary depending on the assumed productivity and harvest rate.
Based on lower productivity Models 2 and 3, in the absence of human-induced mortality, recovery to SSNMSY is
expected to occur between 2040 and 2060, whereas higher productivity Models 1 and 4 predict recovery as early
as 2028. An incidental harm rate of 4% of the vulnerable biomass is expected to delay recovery to SSNmsy to
somewhere between 2041 (Model 1, best case scenario) and the 22nd century (Model 2, worst case scenario).
Model 1 provides the most optimistic scenario, in part due to the higher estimated productivity and the lower
estimated reference points.
8. Discussion
All of our analyses indicate that the abundance of porbeagle in the northwest Atlantic declined during the late
1960s, increased slightly during the late 1970s and early 1980s, and decreased again during the late 1990s. The
decline in total and spawner abundance appears to have halted sometime after the quota reductions in 2002, and
may have entered the initial stages of recovery. Population size is expected to increase now that exploitation
rates have been lowered, but that recovery times will be slow.
Of the four models presented in this document, statistical considerations (OFV) suggest that Model 1 is the
preferred model. Model 1 is also the only model in which
was estimated. Since the
estimate from Model
1 was similar to the fixed value of
incorporated into Model 4, the two models understandably produced
similar output. However, these models were also the least precautionary, given that they assumed the highest
productivity (highest values of
). In contrast, Model 2 (with the poorest model fit) assumed the lowest
productivity, and thus was the most precautionary. All four values of
used in the models were thought to be
plausible based on life history characteristics, so there is no obvious means to select among them based on
external information. From the perspective of assessing the effects of human-induced mortality, the higher
productivity model (Model 1) would result in a higher catch quota than would the more precautionary, lower
productivity model (Model 2).
The values of
used in the population models compare favourably with published estimates of juvenile
survival in sharks. If a mean litter size of 3.9 is assumed, a value of
of 2 equates to a survival rate of 0.51
between birth and age-1. Using a depletion method with a marked population, Gruber et al. (2001) estimated
annual survival of juvenile lemon sharks to vary between 0.38 and 0.65. Most sharks in their study were marked
at age-0 although some age-1 and age-2 sharks were also included. Our assumed values include deaths at time of
birth and onset of feeding that would not be a part of the Gruber et al. study, so a survival estimate to the lower
end of their range is not implausible given the differences in our studies.
The maximum intrinsic rate of increase (rmax) for NW Atlantic porbeagle is low relative to estimates for some
other sharks. Using the Leslie matrix method (Krebs 1985) and the demographic parameters from Models 2 and
4, rmax is estimated to be 0.032 and 0.061 respectively. These values bracket the value of 0.051 estimated by
Campana et al. (2001). Cortes (2002) estimated a lower value of rmax for porbeagle (0.022) due to differences in
the assumed natural mortality and longevity. McAllister et al. (2001) derived priors for rmax for sandbar shark
with medians in the range of 0.07 to 0.09 and for blacktip shark with a median of about 0.125. Smith et al.
(1998) estimated rmax for several shark species, although due to methodological differences, their results and
ours are not directly comparable (our estimate is low relative to their values for most other species). If
productivity is being overestimated in our study, the results from Model 2 would be most conservative. Note
however, that although a productivity scenario cannot be selected on the basis of model fit, the estimates of the
vulnerable biomass in 2009 are similar among the integrated CPUE models.
As is the case with any complex population model, model verification is often limited to assessing the
distribution of the residuals with respect to each factor. Residuals were generally randomly distributed in this
model, although the residuals around the tagging data indicated that actual survival and abundance may be
2124
higher than predicted by the models. As such, management advice based on the models would be precautionary.
However, a comparison of along-cohort catch rates (Paloheimo Z) from Campana et al. (2001) with those of
Gibson and Campana (2005) provided a test of model accuracy that was almost independent of the 2005 model
results. Those comparisons suggested that the higher productivity scenarios might be closer representations of
the porbeagle population than the more conservative model runs. A more rigorous test of model accuracy will
become possible when the results of the 2009 shark survey become available, and are compared with the
abundance and size composition estimates from the 2007 survey.
Our analyses indicate that the estimated number of mature females is in the range of 11,000 to 14,000
individuals, and in the range of 12% to 16% of its 1961 level. The total population size is thought to be about
22% to 27% its size in 1961 and about 95% to 103% its size in 2001. The total biomass was estimated to be
about 10,000 t in 2009, which is 20-24% of its value in 1961, and 4-22% higher than it was in the year 2001.
Spawner abundance in 2009 is about 83% to 103% of its 2001 value. These results are somewhat more
optimistic than those reported in Gibson and Campana (2005) for two reasons. First, the current model results
reflect 4 additional years of population growth under reduced exploitation. Indeed, landings since 2004 were
less than the 4% harvest rate predicted at the time, due to low market prices. This reduced exploitation provided
benefits in terms of stock recovery, albeit marginal. Secondly, the higher CPUE values first observed between
2002 and 2004 have continued to the present, which produced a more lasting effect on modelled abundance.
With CPUE being the only index of abundance for model calibration, continued high catch rates should be a
good sign. However, an important caveat exists with the contraction of the fishery to the shelf edge and basins
where porbeagle density is greatest. Although the incorporation of three separate regions in the model structure
was designed to deal with the elimination of the NF-Gulf region of the fishery after the year 2000, it continues to
assume that catch rates within the shelf edge and basin regions are randomly distributed in space; if that
assumption is false, model output may be overly optimistic. We note however, that the 2007 shark survey does
not suggest that overall population distribution has unduly contracted, or that areas of high porbeagle density are
restricted to the area now being fished.
All analyses indicate that this porbeagle population can recover at modest fishing mortalities, but that the time
horizon for recovery is sensitive to the amount of human-induced mortality. All population models predict
recovery to SSN20% in less than 5 years in the absence of human-induced mortality, and to occur before 2014 if
the human-induced mortality rate is 4% of the vulnerable biomass. Of the four models, Model 2 is the least
optimistic due to the lower assumed productivity. This model predicts that recovery will occur if human-induced
mortality is less than 4% of the vulnerable biomass, but not at 8%. Under this model, recovery to SSNMSY is
predicted to take over 100 years at exploitation rates of 4% of the vulnerable biomass. These estimates are
conditional on the assumed selectivity. Assuming the Shelf-Edge selectivity, Models 1, 3 and 4 (all of which fit
better than Model 2) predict that keeping the rate of human-induced mortality to less than 4% of the vulnerable
biomass would be precautionary and would keep expected recovery times to SSNMSY on the order of decades.
Analyses presented herein indicate the current population is not so small that random factors will threaten the
population. Although the recent trajectory of the stock is nearly flat, the expectation is that abundance will
increase as spawner abundance increases due to maturity of juveniles, so that survival or recovery is not in
jeopardy in the short term. The known sources of human-induced mortality (by-catch) for this population are
under management control and, assuming they can be monitored and enforced, are unlikely to increase during
the near term. As a result, a low level of human-induced mortality will still allow the population to increase
towards recovery thresholds, and if appropriately controlled, will not jeopardise the survival or recovery of the
species. Unknown, and hence unregulated, catches of porbeagle on the high seas remain the wild card in the
recovery of this population.
9. References
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2125
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the northwest Atlantic. Fish. Oceanogr. 13:52-64.
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porbeagle shark (Lamna nasus) population in the northwest Atlantic. CSAS Res. Doc. 99/158.
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Campana, S., Joyce, W., Marks, L., Natanson, L.J., Kohler, N.E., Jensen, C.F., Mello, J.J., Pratt Jr. H.L. and
Myklevoll, S. 2002a, Population dynamics of the porbeagle in the northwest Atlantic Ocean. North Am. J.
Fish. Management 22:106-121.
Campana, S.E., Natanson, L.J. and Myklevoll, S. 2002b, Bomb dating and age determination of large pelagic
sharks. Can. J. Fish. Aquat. Sci. 59:450-455.
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northwest Atlantic in the context of species at risk. CSAS Res. Doc. 2003/007.
Campana, S.E., Joyce, W., Marks, L., Hurley, P., Natanson, L., Kohler, N.E., Jensen, C.F., Mello, J.J., Pratt Jr,
H.L., Myklevoll, S. and Harley, S. 2008, The rise and fall (again) of the porbeagle shark population in the
Northwest Atlantic. P. 445-461. In Sharks of the Open Ocean: Biology, Fisheries and Conservation. [eds.
M.D. Camhi, E.K. Pikitch and E.A. Babcock]. Blackwell Publishing, Oxford, U.K.
Cassoff, R.M., Campana, S.E., and Myklevoll, S. 2007, Changes in baseline growth and maturation parameters
of northwest Atlantic porbeagle, Lamna nasus, following heavy exploitation. Can. J. Fish. Aquat. Sci.
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Cortes, E. 2002, Incorporating uncertainty into demographic modeling: application to shark populations and
their conservation Cons. Biol. 16:1048-1062.
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Committee on the Status of Endangered Wildlife in Canada. Ottawa. viii + 43 pp.
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Research Ltd., Nanaimo, BC, Canada.
Fournier, D., Sibert, J.R., Majkowski, J. and Hampton, J. 1990, Multifan a likelihood-based method for
estimating growth parameters and age composition from multiple length frequency data sets illustrated
using data for southern bluefin tuna. Can. J. Fish. Aquat. Sci. 47: 301-317.
Francis, M.P., Campana, S.E., and Jones, C.M. 2007, Age under-estimation in New Zealand porbeagle sharks
(Lamna nasus): Is there an upper limit to ages that can be determined from shark vertebrae? Mar. Freshw.
Res. 58:10-23.
Francis, M.P. and Stevens, J.D. 2000, Reproduction, embryonic development, and growth of the porbeagle
shark, Lamna nasus, in the southwest Pacific Ocean. Fish. Bull. 98:41-63.
Gibson, A.J.F. and Campana, S.E. 2005, Status and recovery potential of porbeagle shark in the northwest
Atlantic. CSAS Res. Doc. 2005/053.
Gibson, A.J.F., and Myers, R.A. 2003a, A meta-analysis of the habitat carrying capacity and the maximum
lifetime reproductive rate of anadromous alewife in eastern North America. p. 211-221. In K. E. Limburg,
and J.R. Waldman [ed.] Biodiversity, Status, and Conservation of the World’s Shads. American Fisheries
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pseudoharengus) Fisheries in Atlantic Canada. Can. Tech. Rep. Fish. Aquat. Sci. No. 2468. 50p.
Gibson, A.J.F., and Myers, R.A. 2004, Estimating reference fishing mortality rates from noisy spawner-recruit
data. Can. J. of Fish. Aquat. Sci. 61: 1771-1783.
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p. 67-82. In S. J. Smith, J. J. Hunt and D. Rivard [ed.] Risk evaluation and biological reference points for
fisheries management. Can. Spec. Publ. Fish. Aquat. Sci. 120.
Gruber, S.H., de Marignac, J.R.C. and Hoenig, J.M. 2001, Survival of juvenile lemon sharks at Bimini,
Bahamas, estimated by mark-depletion experiments. Trans. Am. Fish. Soc. 130:376-384.
2126
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porbeagle shark (Lamna nasus) in the western North Atlantic Ocean. Fish. Bull. 100:727-738.
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stomach contents of the porbeagle shark (Lamna nasus) in the northwest Atlantic. ICES J. Mar. Sci.
59:1263-1269.
Krebs, C.J. 1985, Ecology: the experimental analysis of distribution and abundance. 3rd ed. Harper and Row,
New York.
Mace, P.M. 1994, Relationships between common biological reference points used as thresholds and targets of
fisheries management strategies. Can. J. Fish. Aquat. Sci. 51: 110-122.
Mace, P.M. and Sissenwine, M.P. 1993, How much spawning per recruit is enough? p. 101-118. In S. J. Smith,
J. J. Hunt and D. Rivard [ed.] Risk evaluation and biological reference points for fisheries management.
Can. Spec. Publ. Fish. Aquat. Sci. 120.
McAllister, M.K., Pikitch, E.K. and Babcock, E.A. 2001, Using demographic methods to construct Bayesian
priors for the intrinsic rate of increase in the Schaefer model and implications for stock rebuilding. Can. J.
Fish. Aquat. Sci. 58: 1871-1890.
Maunder, M.N. 2001, A general framework for integrating the standardization of catch per unit of effort into
stock assessment models. Can. J. Fish. Aquat. Sci. 58: 795-803.
Maunder, M. N. and Punt, A.E. 2004, Standardizing catch and effort data: a review of recent approaches. Fish.
Res. 70: 141-159.
Myers, R. A., J. Bridson, and N. J. Barrowman. 1995. Summary of worldwide stock and recruitment data. Can.
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Myers, R.A., MacKenzie, B.R., Bowen, K.G. and Barrowman, N.J. 2001, What is the carrying capacity of fish
in the ocean? A meta-analysis of population dynamics of North Atlantic cod. Can. J. of Fish. Aquat. Sci. 58:
1464-1476.
Myers, R.A., Bowen, K.G. and Barrowman, N.J. 1999, The maximum reproductive rate of fish at low
population sizes. Can. J. Fish. Aquat. Sci. 56: 2404-2419.
Natanson, L.J., Mello, J.J. and Campana, S.E. 2002, Validated age and growth of the porbeagle shark, Lamna
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MD. Public Document. pp. 343.
O’Boyle, R., Fowler, G.M., Hurley, P., Showell, M. and Stobo, W. 1996, Observations on porbeagle shark
(Lamna nasus) in the North Atlantic. DFO Atl. Fish. Res. Doc. 96/24.
O’Boyle, R.N., Fowler, G.M., Hurley, P.C.F., Joyce, W. and Showell, M.A. 1998, Update on the status of
NAFO SA 3-6 porbeagle shark (Lamna nasus). CSAS Res. Doc. 98/41, Fisheries and Oceans, Canada.
Quinn, T.J. II and Deriso, R.B. 1999, Quantitative Fish Dynamics. Oxford University Press. New York.
Shepherd, J.G. 1982, A versatile new stock-recruitment relationship of fisheries and construction of sustainable
yield curves. J. Cons. Perm. Int. Explor. Mer 40: 67-75.
Smith, S.E., Au, D.W. and Show, C. 1998, Intrinsic rebound potentials of 26 species of Pacific sharks. Mar.
Freshwater Res. 49:663-678.
Stevens, J.D. 1990, Further results from a tagging study of pelagic sharks in the north-east Atlantic. J. Mar. Biol.
Ass. U.K. 70:707-720.
2127
Table 1. Reported landings (metric tonnes) by country for NAFO areas 2 to 6. Canadian landings have been converted to
live equivalent weight, which differs in some cases from the live weight recorded in the statistics.
Year Canada Faroe Is France Iceland Japan Norway Spain USSR USA Total
1961 0 100 1824 1924
1962 0 800 2216 3016
1963 0 800 5763 6563
1964 0 1214 7 8060 9281
1965 28 1078 4045 5151
1966 0 741 1373 2114
1967 0 589 36 625
1968 0 662 137 269 1068
1969 0 865 208 1073
1970 0 205 674 879
1971 0 231 221 452
1972 0 260 87 347
1973 0 269 269
1974 0 0
1975 0 80 80
1976 0 307 307
1977 0 295 295
1978 1 121 122
1979 2 299 301
1980 1 425 426
1981 0 344 3 347
1982 1 259 1 261
1983 9 256 0 265
1984 20 126 1 17 164
1985 26 210 0 236
1986 24 270 5 1 300
1987 59 381 16 0 12 468
1988 83 373 9 3 32 500
1989 73 477 9 3 4 566
1990 78 550 8 9 19 664
1991 329 1189 20 12 17 1567
1992 814 1149 7 8 13 1991
1993 920 465 6 2 39 1432
1994 1573 2 3 1578
1995 1348 7 4 5 1364
1996 1043 40 9 8 1100
1997 1317 13 2
3
2 1337
1998 1054 20 0
9
12 1095
1999 955 6
3
3967
20008991324
5
941
2001 499 2 25
3
528
2002 229 1 0
5
0236
2003 139 2 0
2
0143
2004 218 4 0
5
1228
2005 203
7
0210
2006 190
9
0199
2007 93
6
99
2008 125 37 162
Notes:
France data is from FAO Statistics (1998), 2000-2006 from FAO Fishstat Plus v 2.32.
Northwest Atlantic Data for 1950 - 60 is from FAO (ICCAT Report of Shark Working Group, Miami, 26-28 February 1996).
Canada for 1961-90 is from NAFO.
Canada for 1991-2002 is from DFO Zonal Statistics File, corrected to appropriate live equivalent weight.
Canada for 2003-2008 is from DFO MARFIS.
Faroe Is for 1961-63 is from FAO (ICCAT Report of Shark Working Group, Miami, 26-28 February 1996).
Norway from 1961-86 is from NAFO.
Northwest Atlantic Data for 1964-86 is from NAFO.
Northwest Atlantic Data for 1987-2004 is from Scotia-Fundy & NF IOP (includes landings and discards).
Northwest Atlantic Data (US/ 1961-94) is from FAO (ICCAT Report of Shark Working Group, Miami, 26 - 28 February 1996).
Northwest Atlantic Data for 2000-2008 from FAO Fishstat Plus v 2.32 Capture Production March 2008.
NAFO Database 21B or ICCAT Task 1 Dataset 2009.
Northwest Atlantic Data for 2000-2006 (Japan) from NAFO Database 21B, catch for code 469, large sharks.
NAFO catch data for Spain for 2005 (231 t) and 2006 (230 t) were errors, and not reported here.
2128
Table 2. Porbeagle by-catch (kg) in Canadian Scotia-Fundy fisheries.
Yea
r
2000 2001 2002 2003 2004 2005 2006 2007 2008
TAC 850,000 850,000 250,000 250,000 250,000 250,000 185,000 185,000 185,000
Groundfish fixed gear 45-65 997 789 958 2400 2031 1196 509 851 848
Groundfish fixed gear <45 4743 6925 13141 13041 14344 15286 9,870 18,258 14,409
Groundfish inshore 56 197 687 100 170
Groundfish midshore 461 518 697 1384 101 166 780 448
Groundfish offshore 191 285 220 600 1131 594 323 288
Groundfish unspecified 456 1059 1184 1105 1010 2747 3,908 1,597 317
Total Groundfish 6848 9576 15980 18150 18141 20723 15,568 21,909 16,481
Directed porbeagle 870741 476703 172001 86059 172520 161997 123,913 49,965 87,637
Swordfish 5482 9582 18939 29160 22155 11641 14,157 9,120 10,533
Tuna 1266 577 18435 5558 6156 8569 36,221 12,245 10,137
Herring 256 23
Total 884337 496694 225355 138927 218995 202930 189,859 93,239 124,788
Total from bycatch 13596 19991 53354 52868 46475 40933 65,946 43,274 37,151
Percent total from bycatch 2% 4% 24% 38% 21% 20% 35% 46% 30%
Table 3. Porbeagle catch (kg) in Canadian fisheries outside of Scotia-Fundy.
Year 2000 2001 2002 2003 2004 2005 2006 2007 2008
Newfoundland fixed gear 141 946 1,851 1,071 142 27 105
Newfoundland mobile gear 40
Gulf (all gears) 18,976 1,192 11,566 2,565 12,968 52 691 55
Gulf (unspecified shark)
1
8,378 6,945 8,799 5,090 3,512 3,347
USA (all gears)
2
3,595 785 1,813
1 May include Porbeagle.
2 Landings only.
2129
Table 4. Proportion of the reported, directed porbeagle landings from each of three regions.
Year Basin NF-Gulf Shelf-Edge
1988 0.03 0.33 0.64
1989 0.09 0.35 0.56
1990 0.32 0.25 0.43
1991 0.18 0.42 0.40
1992 0.12 0.49 0.39
1993 0.12 0.42 0.46
1994 0.20 0.27 0.53
1995 0.08 0.43 0.48
1996 0.14 0.33 0.54
1997 0.14 0.32 0.54
1998 0.08 0.34 0.58
1999 0.15 0.22 0.63
2000 0.17 0.39 0.44
2001 0.11 0.24 0.66
2002 0.43 0.22 0.35
2003 0.51 0.02 0.47
2004 0.20 0.02 0.78
2005 0.31 0.00 0.69
2006 0.54 0.00 0.45
2007 0.48 0.09 0.43
2008 0.17 0.01 0.82
Average 0.22 0.25 0.54
2130
Table 5. Estimated total discards of porbeagle by Canadian large pelagic longliners, July-December.
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Target fish kept catch (mt) from observers 33.6 102.4 95.4 105.6 40.3 152.4 312.4 126.3 51.4 78.4 142.2 80.0 76.3
Porbeagle (discarded) from observers 0.2 0.1 0.2 2.0 1.0 3.8 2.6 2.4 1.1 1.2 3.4 2.3 1.5
Porbeagle proportion (observed) 0.01 0.00 0.00 0.02 0.02 0.02 0.01 0.02 0.02 0.02 0.02 0.03 0.02
Target fish catch (mt) landed in fishery 886 1163 990 1162 1128 1085 1279 1195 1424 1642 1582 1382 1254
Estimated porbeagle discarded in fishery (mt) 5 1 2 22 27 27 10 22 32 26 37 40 25
2131
Table 6.1. Distribution of sets that have reported catch (weight) and effort, by vessel and year, in the Basin area. Totals are the number of sets.
CFV 1981 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Total
1 XXX 64
2XXXXXXX 110
3 X 1
4 XX 29
5 XX 8
6 X 3
7 XXXX X 42
8 XXXXX 95
9 XXXXXXXXX 100
10 XXXXXXXX XX 89
11 X 27
12 XX 6
13 XX 27
14 XX 14
15 X X 7
16 X 1
17 X 2
18 XX 4
19 X XXX 13
20 X 2
21 XXXXXXX X X 52
22 XX 18
23 X 3
24 X 4
25 X X 2
26 XXXXXXX X 55
27 XXXXXXXXXXX 153
28 XXXXX X 111
29 XXX XX X 37
30 X XXX 24
31 XXXXXX 34
32 XX 3
33 X 1
34 X 1
35 XXXXX 114
36 X 2
Total 6 2 3 35 93 74 66 88 47 94 146 94 118 108 66 37 15 26 37 60 31 12 1258
2132
Table 6.2. Distribution of sets with reported catch (weight) and effort, by vessel and year, in the NF-Gulf area. Totals are the number of sets.
CFV 1981 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Total
1 XXX 202
2XXXXXXXX 415
3 X 17
4 XXXXXXXXXX 395
5 X 6
6 X X 9
7 XXXXXXXXXX 676
8 XXXXX 241
Total 8 61 67 55 68 167 306 245 187 209 78 122 116 88 138 33 13 1961
2133
Table 6.3. Distribution of sets with reported catch (weight) and effort, by vessel and year, in the Shelf Edge area. Totals are the number of sets.
CFV 1981 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Total
1 XXX 173
2X 19
3XXXXXXXX 499
4 X 1
5 X X X 23
6 X 2
7 X 12
8 X 1
9 XXXXXX 88
10 XXXXXXXXXX 656
11 XXXXXX X 116
12 X 5
13 XX 3
14 XX 8
15 X 10
16 X X 17
17 X 1
18 XX X 4
19 X 1
20 XXXXXXX XXX 214
21 X 12
22 XXXXXXXXXX 467
23 X X 5
24 XXXX 43
25 X XX X 19
26 X 2
27 XXX XX 16
28 XX XX 15
29 X 1
30 X 11
31 XXXXX 207
86 58 69 62 58 134 203 192 199 171 220 218 265 269 175 147 22 8 33 15 22 12 13 2651
2134
Table 7. Number of porbeagle sharks tagged in the U.S. and Canadian tagging programs between 1980 and 1999 and the number and timing of recaptures of porbeagle that
were tagged when under 125 cm in fork length (from Gibson and Campana 2005).
Year Number Tagged Year recaptured
Tagged Total <125cm FL 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 Total
USA 80 1 0
81 5 0
82 5 1 1
83 3 0
84 5 0
85 7 0
86 20 1 1 1 3
87 83 25 1 1 2
88 55 11 2 1 3
89 1 1 1
90 0 0
91 10 1 1
92 16 1 1 1 1 4
93 132 106 3 2 1 5 2 3 16
94 135 131 2 10 6 6 4 5 2 35
95 118 116 4 3 4 11
96 44 37 2 1 3
97 135 99 1 4 2 7
98 91 53 1 1 2
99 151 148 3 2 5
USA Total 944 801 0 0 1 0 1 1 1 2 0 1 2 2 6 14 11 17 7 21 7 94
Canada
94 40 40 1 3 4
95 179 179 4 3 6 6 19
96 37 37 1 1 1 3
97 23 23 1 1
98 5 5 0
Can. Total 284 284 0 1 4 7 6 7 2 27
2135
Table 8. Constants used in the assessment model (from Gibson and Campana 2005).
Component Parameter Females Males
Growth
L 309.8 257.7
(Von Bertalanffy) t0 0.061 0.080
k -5.90 -5.78
Growth variability b0 12.05 11.05
(linear) b1 4E-4 0.0048
Length to weight bi 5E-5 5E-5
conversion bii 2.713 2.713
Maturity A50 13 8
(logistic) a -13.57 -6.07
b 1.042 0.75
Age for splitting CPUE 11 12
2136
Table 9. Parameter maximum likelihood estimates and reference points obtained from four models fit to the porbeagle
data. The models differ in the assumed productivity. Reference points are calculated using the selectivity curves for the
Shelf Edge fishery.
Model 1 Model 2 Model 3 Model 4
Differing assumptions:
estimated
=2.0
=2.5
=3.2
OFV 13,139 13,269a 13,212a 13,160a
Spawner - Recruit Rasym 135,525 280,675 195,399 149,018
alpha 3.6 2a 2.5a 3.2a
SPRF0 0.808 0.808 0.808 0.808
Selectivity (Basin) B_SfullF 2 (bound) 2 (bound) 2 (bound) 2 (bound)
B_SfullM 2.063 2.072 2.068 2.064
B_varLestF 0.243 0.254 0.248 0.243
B_varLestM 0.979 1.014 0.987 0.968
B_varRestF 33.040 29.534 30.926 32.550
B_varRestM 216.007 168.370 185.564 207.195
Selectivity (N.-Gulf) N_SfullF 10.486 9.970 10.148 10.375
N_SfullM 15.725 14.277 14.739 14.728
N_varLestF 35.153 34.331 34.51 35.008
N_varLestM 65.126 58.842 60.370 57.423
N_varRestF 23.262 24.208 23.881 23.510
N_varRestM 2.873 9.975 7.517 8.048
Selectivity (Shelf
Edge) E_SfullF 2 (bound) 2 (bound) 2 (bound) 2 (bound)
E_SfullM 10.032 9.648 9.663 9.850
E_varLestF 0.314 0.338 0.326 0.316
E_varLestM 95.230 97.473 93.360 93.467
E_varRestF 53.125 45.45 48.283 51.573
E_varRestM 23.483 22.086 24.159 24.678
Catchability logqCPUE -8.388b -8.473b -8.433b -8.401b
Tag loss/mort. proportion 0.608 0.591 0.601 0.607
Reference SSNeq 71,858 86,447 79,722 73,838
Population Sizes 20% SSNeq 14,372 17,290 15,945 14,768
Req 88,933 106,989 98,667 91,384
SSNMSY 27,945 40,089 34,573 30,009
Reference FMSY 0.075 0.036 0.051 0.067
Fishing Mortality Rates Fcol 0.160 0.075 0.108 0.142
F35% 0.157 0.166 0.163 0.157
F45% 0.119 0.125 0.122 0.119
aconstants (not estimated); baverage q’s for 59 CPUE series.
2137
Table 10. Estimates of recent exploitation rates (proportion of vulnerable biomass taken by the fishery).
Year Model 1 Model 2 Model 3 Model 4
Basin 2006 0.022 0.023 0.022 0.022
2007
0.009 0.010 0.010 0.009
2008
0.004 0.005 0.005 0.005
NF Gulf 2006 0.000 0.000 0.000 0.000
2007 0.002 0.002 0.002 0.002
2008 0.000 0.000 0.000 0.000
Shelf 2006
0.018 0.018 0.018 0.018
2007
0.008 0.009 0.008 0.008
2008
0.021 0.021 0.021 0.021
2138
Table 11. Estimates of population size and total biomass (metric tonnes) obtained from four models fit to the
porbeagle data. See text for model descriptions.
Model 1 Model 2 Model 3 Model 4
Differing
assumptions:
estimated
=2.0
=2.5
=3.2
1961 SSN 71,858 86,447 79,722 73,838
N 760,620 915,048 843,866 781,582
Biomass 41,744 50,219 46,312 42,894
1971 SSN 17,439 33,087 25,947 19,868
N 291,174 422,212 362,599 310,002
Biomass 11,958 19,541 16,048 13,013
1981 SSN 20,842 35,013 28,561 22,759
N 284,362 383,292 339,358 299,446
Biomass 14,292 20,404 17,672 15,220
1991 SSN 20,935 30,661 26,385 22,516
N 347,711 397,555 374,428 354,463
Biomass 16,587 20,335 18,636 17,131
2001 SSN 10,999 17,031 14,377 12,062
N 190,024 206,680 198,163 192,162
Biomass 8,082 9,664 8,908 8,299
2009 SSN 11,339 14,207 12,886 11,809
N 206,956 196,911 198,970 204,482
Biomass 9,890 10,078 9,903 9,891
2009/1961 SSN 0.119 0.164 0.162 0.160
N 0.272 0.215 0.236 0.262
Biomass 0.237 0.201 0.214 0.231
2009/2001 SSN 1.031 0.834 0.896 0.979
N 1.089 0.953 1.004 1.064
Biomass 1.223 1.043 1.112 1.192
2139
Table 12. Estimates of the mid-year vulnerable biomass (metric tonnes) for 2009 from the four models and three
fishery selectivities. Note that the vulnerable biomass is conditional on the selectivity, and assumes that a
selectivity is applicable to the entire population. The values do not apply separately to each region.
Model 1 Model 2 Model 3 Model 4
Differing assumptions:
estimated
=2.0
=2.5
=3.2
Differing data CPUE by weight,
integrated CPUE by weight,
integrated CPUE by weight,
integrated CPUE by weight,
integrated
Biomass removed using:
Basin selectivity 4,894 4,406 4,562 4,801
NF Gulf selectivity 4,416 4,747 4,603 4,562
Shelf selectivity 5,093 4,747 4,856 5,030
Figure 1. Map of eastern Canada showing NAFO Divisions and fishing banks.
2140
Figure 2. Summary of porbeagle tag movements from tagging location (line origin) to recapture location
(arrowhead) between 1961 and 2008. Norwegian tags in green; U.S. tags in grey; Canadian tags in red.
2141
Figure 3. Growth curve for porbeagle shark, showing a reduction in growth rate for both sexes at the age of
sexual maturity. Fitted lines are LOESS by sex. The age-length table is based on the von Bertalanffy growth
model, substituting observed lengths for ages 0 and 1. Ages have been validated to age 11.
2142
Figure 4. Maturity ogive for porbeagle shark, based on examination of 393 males and 382 females. Fitted lines
are from logistic regression.
2143
Figure 5. Known mating grounds for porbeagle shark in the NW Atlantic (ovals). Symbols shown capture
locations for pregnant females.
2144
Figure 6. Porbeagle catch and associated temperature at mid-gear depth for 1999 (from Campana and Joyce
(2004)).
max = 7.0
2145
Figure 7. Porbeagle shark survey catch rates in relation to water temperature at depth.
2146
Figure 8. Porbeagle landings in northwest Atlantic (NAFO 2-6) from 1961 to 2008.
2147
Figure 9. Porbeagle catch locations 2005-2008.
2148
Figure 10. Young of the year, juvenile and adult porbeagle distribution by decade as observed by the DFO
Observer Program.
2149
Figure 11. Porbeagle distribution by life history stage as observed by the U.S. Pelagic Observer Program and
the U.S. Cooperative Tagging Program between 2000 and 2007. Map and data from NMFS (2008)
http://sharpfin.nmfs.noaa.gov/website/EFH_mapper/HMS/map.aspx
YOY
Juveniles
Juveniles
2150
Figure 11. Continued.
Adults
2151
Figure 12. Juvenile (FL<120 cm) porbeagle distribution as observed by the U.S. Pelagic Observer Program
between 2000 and 2007. Data courtesy of Enric Cortés, NMFS.
2152
Figure 13. Porbeagle length frequencies in commercial catch.
Fork length (cm)
2602402202001801601401201008060
N
um
b
e
r
2500
2000
1500
1000
500
0
Std. Dev = 21.82
Mean = 147
N = 9293.00
2005-2008
Fork length (cm)
2602402202001801601401201008060
Number
6000
5000
4000
3000
2000
1000
0
Std. Dev = 28.67
Mean = 140
N = 32520.00
2000-2004
Fork length (cm)
2602402202001801601401201008060
N
um
b
e
r
14000
12000
10000
8000
6000
4000
2000
0
Std. Dev = 31.88
Mean = 152
N = 108735.00
1990-1999
2153
Figure 14a. Error bar plots (mean and 95% CI) showing porbeagle CPUE by area in terms of ln-transformed
kg/hook. Note that the years differ between the graphs.
5133833251530401069886596245856668753526N =
Basin
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1988
1981
CPUE (LN kg/hook)
4
2
0
-2
133121821125920918723430316768556760N =
NFGulf
2002
2001
2000
1999
1998
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
CPUE (LN kg/hook)
4
2
0
-2
21013153082213216325324820021016319217917412358695067N =
Sh
e
lf
e
d
ge
YEAR
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1988
1987
1981
CPUE (LN kg/hook)
4
2
0
-2
2154
Figure 14b. Error bar plots (mean and 95% CI) showing porbeagle CPUE by area and maturity stage in terms
of ln-transformed number/hook. Note that the years differ between the graphs.
2155
Figure 15. Distribution of porbeagle CPUE by year.
2156
Figure 15. Continued.
2157
Figure 15. Continued.
2158
1980 1985 1990 1995 2000 2005 2010
0
5
10
15
!
"
$$
%
&
(
BASIN
1980 1985 1990 1995 2000 2005 2010
0
2
4
6
8
10
#%
'
SHELFEDG
1980 1985 1990 1995 2000 2005 2010
0
1
2
3NFGULF
Year
C.P.U.E. (kg/h)
Figure 16. Comparison of the grand mean of the CPUE (kg/hook) with the mean CPUE for each
vessel.
2159
1980 1985 1990 1995 2000 2005 2010
0
5
10
15 BASIN
1980 1985 1990 1995 2000 2005 2010
0
2
4
6
8
10 SHELFEDG
1980 1985 1990 1995 2000 2005 2010
0
1
2
3NFGULF
Year
C.P.U.E. (kg/h)
grand mean
Jan - Mar
Apr - June
July - Dec
Figure 17. Comparison of the grand mean of the CPUE (kg/hook) with the seasonal mean CPUEs.
2160
5 101520
0.0
0.2
0.4
0.6
0.8
1.0 Basin
Females
5 101520
0.0
0.2
0.4
0.6
0.8
1.0 NFGulf
5 101520
0.0
0.2
0.4
0.6
0.8
1.0 Shelf Edge
5101520
0.0
0.2
0.4
0.6
0.8
1.0 Basin
Males
5101520
0.0
0.2
0.4
0.6
0.8
1.0 NFGulf
5101520
0.0
0.2
0.4
0.6
0.8
1.0 Shelf Edge
Model 1
Model 2
Model 3
Model 4
Age
Selectivity
Figure 18. Estimated selectivity curves for porbeagle fisheries in three regions obtained from the
four models (see text).
2161
1980 1985 1990 1995 2000 2005 2010
0.0 0.5 1.0 1.5 2.0
series = 1
1980 1985 1990 1995 2000 2005 2010
024681012
series = 2
1980 1985 1990 1995 2000 2005 2010
012345
series = 3
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 4
1980 1985 1990 1995 2000 2005 2010
024681012
series = 5
1980 1985 1990 1995 2000 2005 2010
01234
series = 6
1980 1985 1990 1995 2000 2005 2010
0246
series = 7
1980 1985 1990 1995 2000 2005 2010
01234
series = 8
1980 1985 1990 1995 2000 2005 2010
024681012
series = 9
Figure 19.1. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE
series (a single vessel fishing in a single area during a single season). The light line is the annual geometric
mean of the data. The dark line is the model fit obtained from Model 3.
C.P.U.E.
Yea
r
2162
1980 1985 1990 1995 2000 2005 2010
024681012
series = 10
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 11
1980 1985 1990 1995 2000 2005 2010
02468
series = 12
1980 1985 1990 1995 2000 2005 2010
01234
series = 13
1980 1985 1990 1995 2000 2005 2010
02468
series = 14
1980 1985 1990 1995 2000 2005 2010
024681012
series = 15
1980 1985 1990 1995 2000 2005 2010
0246
series = 16
1980 1985 1990 1995 2000 2005 2010
0246810
series = 17
1980 1985 1990 1995 2000 2005 2010
02468101214
series = 18
Figure 19.2. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE
series (a single vessel fishing in a single area during a single season). The light line is the annual geometric
mean of the data. The dark line is the model fit obtained from Model 3.
C.P.U.E.
Yea
r
2163
1980 1985 1990 1995 2000 2005 2010
024681012
series = 19
1980 1985 1990 1995 2000 2005 2010
01234
series = 20
1980 1985 1990 1995 2000 2005 2010
01234
series = 21
1980 1985 1990 1995 2000 2005 2010
0246
series = 22
1980 1985 1990 1995 2000 2005 2010
0246
series = 23
1980 1985 1990 1995 2000 2005 2010
012345
series = 24
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 25
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 26
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 27
Figure 19.3. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE
series (a single vessel fishing in a single area during a single season). The light line is the annual geometric
mean of the data. The dark line is the model fit obtained from Model 3.
C.P.U.E.
Yea
r
2164
1980 1985 1990 1995 2000 2005 2010
0246
series = 28
1980 1985 1990 1995 2000 2005 2010
0.0 0.5 1.0 1.5 2.0
series = 29
1980 1985 1990 1995 2000 2005 2010
0246810
series = 30
1980 1985 1990 1995 2000 2005 2010
02468
series = 31
1980 1985 1990 1995 2000 2005 2010
02468
series = 32
1980 1985 1990 1995 2000 2005 2010
0246810
series = 33
1980 1985 1990 1995 2000 2005 2010
0102030
series = 34
1980 1985 1990 1995 2000 2005 2010
0 5 10 15 20 25
series = 35
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 36
Figure 19.4. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE
series (a single vessel fishing in a single area during a single season). The light line is the annual geometric
mean of the data. The dark line is the model fit obtained from Model 3.
C.P.U.E.
Yea
r
2165
1980 1985 1990 1995 2000 2005 2010
0.0 1.0 2.0
series = 37
1980 1985 1990 1995 2000 2005 2010
01234
series = 38
1980 1985 1990 1995 2000 2005 201
0
0.01.02.03.0
series = 39
1980 1985 1990 1995 2000 2005 2010
012345
series = 40
1980 1985 1990 1995 2000 2005 2010
0123
series = 41
1980 1985 1990 1995 2000 2005 201
0
02468
series = 42
1980 1985 1990 1995 2000 2005 2010
0246
series = 43
1980 1985 1990 1995 2000 2005 2010
0.0 0.2 0.4 0.6 0.8
series = 44
1980 1985 1990 1995 2000 2005 201
0
012345
series = 45
Figure 19.5. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE
series (a single vessel fishing in a single area during a single season). The light line is the annual geometric
mean of the data. The dark line is the model fit obtained from Model 3.
C.P.U.E.
Yea
r
2166
1980 1985 1990 1995 2000 2005 2010
024681012
series = 46
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 47
1980 1985 1990 1995 2000 2005 2010
0.0 0.5 1.0 1.5 2.0
series = 48
1980 1985 1990 1995 2000 2005 2010
024681012
series = 49
1980 1985 1990 1995 2000 2005 2010
02468
series = 50
1980 1985 1990 1995 2000 2005 2010
0246810
series = 51
1980 1985 1990 1995 2000 2005 2010
02468
series = 52
1980 1985 1990 1995 2000 2005 2010
0246
series = 53
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 54
Figure 19.6. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE series
(a single vessel fishing in a single area during a single season). The light line is the annual geometric mean of
the data. The dark line is the model fit obtained from Model 3.
C.P.U.E.
Yea
r
2167
Figure 19.7. Observed (points) and fitted (lines) catch per unit effort by weight for each porbeagle CPUE series
(a single vessel fishing in a single area during a single season). The light line is the annual geometric mean of
the data. The dark line is the model fit obtained from Model 3.
1980 1985 1990 1995 2000 2005 2010
0246810
series = 55
1980 1985 1990 1995 2000 2005 2010
0246810
series = 56
1980 1985 1990 1995 2000 2005 2010
0123456
series = 57
1980 1985 1990 1995 2000 2005 2010
024681012
series = 58
1980 1985 1990 1995 2000 2005 2010
0 5 10 15
series = 59
C.P.U.E.
Yea
r
2168
Figure 20.1. Observed (points) and fitted (lines) catch-at-length proportions by sex in the Basin region. Line
symbolism is the same as Figure 19. All fits are virtually identical.
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1995
n = 209
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1995
n = 360
Basin - by sex
Proportion
Length (cm)
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1998
n = 412
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1998
n = 731
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1999
n = 1240
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1999
n = 1700
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2000
n = 831
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2000
n = 1115
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2001
n = 1335
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2001
n = 1402
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2002
n = 938
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2002
n = 1136
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2003
n = 436
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2003
n = 480
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2004
n = 476
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2004
n = 510
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2005
n = 435
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2005
n = 534
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2006
n = 509
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2006
n = 576
2169
Figure 20.1 Continued.
Figure 20.2. Observed (points) and fitted (lines) catch-at-length proportions by sex in the NF-Gulf region up to
1995. Line symbolism is the same as Figure 19. All fits are virtually identical.
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2007
n = 81
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2007
n = 86
Basin - by sex
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 2008
n = 240
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 2008
n = 265
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1961
n = 402
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1961
n = 753
NFGulf - by sex
Proportion
Length (cm)
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1963
n = 74
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1963
n = 35
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1988
n = 844
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1988
n = 697
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Females 1989
n = 1192
100 150 200 250
0.0
0.05
0.10
0.15
0.20 Males 1989