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Japan. The 12 in British Columbia at the Vancouver Aquarium and 3 at the Alaska SeaLife Center in Alaska are held for both research and exhibit.

The species is an important subsistence resource for Alaskan natives, who hunt sea lions for food and other uses. Two hundred or more may be taken a year in Alaska.

Steller sea lions may be affected by commercial fi shing directly through incidental catch in nets, by entanglement in derelict debris, by shooting, or indirectly through competition for prey, disturbance, or disruption of prey schools ( Alverson, 1992 ). The number of sea lions caught in trawl nets was high during the 1960s and 1970s but has declined since and is presently at very low levels. Incidental entan-glement probably contributed to population declines in the Aleutian Islands and western Gulf of Alaska in the 1970s and 1980s, but it is not presently considered an important component in the decline. Entanglement in derelict gear is rare and unlikely to have contributed to the decline. In some areas, Steller sea lions were killed deliberately by fi shermen, but it is unclear how such killing affected the world pop-ulation, especially since declines have occurred in areas uncommonly used by commercial fl eets (central and western Aleutian Islands) or where fi shermen rarely have guns (Russia). Commercial fi sheries tar-get on several of the most important prey eaten by Steller sea lions. In combination, these fi sheries remove millions of metric tons of fi sh. However, the complexity of ecosystem interactions and limitations of data and models make it diffi cult to determine whether fi shery remov-als, directly or indirectly, have negatively impacted the populations (e.g., see Rosen and Trites, 2000 ; Fritz and Hinckley, 2005 ) of steller sea lions.

The U.S. government has implemented numerous measures for the conservation. These include prohibitions on shooting, reductions on allowable incidental take in fi sheries, placement of zones around rookeries to restrict commercial fi shing, designation of critical habitat, development of a Steller Sea Lion Recovery Plan, and other meas-ures. Research activities have intensifi ed as scientifi c fi ndings, litiga-tion, and new legislation focused increasing attention on the species ’population decline and concerns over possible impacts by commer-cial fi sheries in Alaskan waters. Additional restrictions were placed on these commercial fi sheries, resulting in the U.S. congress allocat-ing a seven-fold increase in research funding beginning in 2000 with over 125 individual projects planned or implemented. These studies have provided over 750 primary citations, journal articles, progress and technical reports, contract reports, proceedings of conferences and symposia, books, thesis and other manuscripts. More than 50% of the articles were written since 2004 with the majority pertaining to Steller sea lion life history, foraging ecology and vital rates.

See Also the Following ArticlesEared Seals (Otariidae) ■ Ecosytem Effects

References Alverson , D. L. ( 1992 ). A review of commercial fi sheries and the Steller

sea lion ( Eumetopias jubatus ): The confl ict arena . Rev. Aquat. Sci. 6 , 203 – 256 .

Burkanov , V. N. , and Loughlin , T. R. ( 2005 ). Distribution and abundance of Steller sea lions, Eumetopias jubatus , on the Asian coast, 1720s–2005 . Mar. Fish. Rev. 67 , 1 – 62 .

Bickham , J. W. , Patton , J. C. , and Loughlin , T. R. ( 1996 ). High variability for control region sequences in a marine mammal: implications for conservation and biogeography of Steller sea lions ( Eumetopias juba-tus ) . J. Mammal. 77 , 95 – 108 .

Calkins , D. G. ( 1998 ). Prey of Steller sea lions in the Bering Sea . Biosph.Conserv. 1 , 33 – 44 .

Gentry, R. L. (1970). “ Social Behavior of the Steller Sea Lion ” . Ph.D.dissertation , University of California, Santa Cruz, 113 p.

Fritz , L. W. , and Hinckley , S. ( 2005 ). A critical review of the regime shift “ junk food ” nutritional stress hypothesis for the decline of the west-ern stock of Steller sea lion . Mar. Mamm. Sci. 21 , 476 – 518 .

Holmes , E. E. , and York , A. E. ( 2003 ). Using age structure to detect impacts on threatened population: a case study with Steller sea lions .Conserv. Biol. 17 , 1794 – 1806 .

Loughlin, T. R. (1997). Using the phylogeographic method to identify Steller sea lion stocks. In “ Molecular Genetics of Marine Mammals ”(A. Dizon, S. J. Chivers, and W. F. Perrin, eds.) pp. 159–171. Soc.Mar. Mamm. Spec. Publ . 3 , 159–171.

Loughlin , T. R. , Perlov , A. S. , and Vladimirov , V. A. ( 1992 ). Range-wide survey and estimation of total abundance of Steller sea lions in 1989 .Mar. Mamm. Sci. 8 , 220 – 239 .

Loughlin , T. R. , Perez , M. A. , and Merrick , R. L. ( 1987 ). Eumetopias jubatus . Mamm. Spec. 283 , 1 – 7 .

Merrick, R. L. (1995). “ The Relationship of the Foraging Ecology of Steller Sea Lions ( Eumetopias jubatus ) to Their Population Decline. ”Ph.D. dissertation , University of Washington, Seattle. 171 p.

Merrick , R. L. , Chumbley , M. K. , and Byrd , G. V. ( 1997 ). Diet diver-sity of Steller sea lions ( Eumetopias jubatus ) and their population decline in Alaska: a potential relationship . Can. J. Fish. Aquat. Sci. 54 , 1342 – 1348 .

Mitchell , E. D. ( 1968 ). The Mio-Pliocene pinniped Imagotaria . J. Fish. Res. Board Can. 25 , 1843 – 1900 .

Pitcher , K. W. , and Calkins , D. G.. ( 1981 ). Reproductive biology of Steller sea lions in the Gulf of Alaska . J. Mammal. 62 , 599 – 605 .

Rea, L. D., Castellini, M. A., Fadely, B. S., and Loughlin, T. R. (1998). Health status of young of the year Steller sea lion pups ( Eumetopiasjubatus ) as indicated by blood chemistry and hematology. Comp.Biochem. Physiol. , Part A 120 , 617–623.

Rosen , D. A. S. , and Trites , A. W. ( 2000 ). Pollock and the decline of Steller sea lions: testing the junk-food hypothesis . Can. J. Zool. 78 , 1243 – 1258 .

Sinclair , E. , and Zeppelin , T. ( 2002 ). Seasonal and spatial differences in the diet of western stock of Steller sea lions ( Eumetopias jubatus) . J. Mammal. 83 , 973 – 990 .

Springer , A. M. , et al . (8 authors) ( 2003 ). Sequential megafaunal collapse in the North Pacifi c Ocean: an ongoing legacy of industrial whaling ?Proc. Natl. Acad. Sci. 100 , 12223 – 12228 .

Trites , A. W. , Atkinson , S. K. , DeMaster , D. P. , Fritz , L. W. , Gelatt , T. S. , Rea , L. D. , and Wynne , K. M. ( 2006 ). “ Sea Lions of the World . ” Alaska Sea Grant College Program, University of Alaska , Fairbanks , 644 p .

Trites , A. W. , and Larkin , P. A. ( 1996 ). Changes in the abundance of Steller sea lions ( Eumetopias jubatus ) in Alaska from 1956 to 1992: How many were there? Aquat. Mamm. 22 , 153 – 166 .

York , A. ( 1994 ). The population dynamics of northern sea lions, 1975–1985 . Mar. Mamm. Sci. 10 , 38 – 51 .

Stock Assessment JEFFREY M. BREIWICK AND ANNE E. YORK

Amarine mammal stock assessment is a process that seeks to estimate the productivity or growth potential of a stock and predict the future growth in conjunction with management

objectives and conditions, which often includes removals due to incidental catches, directed harvests or natural causes. It also seeks to measure the capacity of the stock to recover from these remov-als. The assessment usually encompasses the status of the stock with

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respect to some reference level, such as the unexploited population size, and the evaluation of the consequences of various management actions. For stocks that are subject to a harvest or experience mortal-ity incidental to fi shing operations, a goal is to determine allowable removal levels (e.g., harvests that will allow the population to recover to some desired level during some time frame). A concise defi nition of a fi sheries stock assessment, equally applicable to marine mam-mals, is that given by Hilborn and Walters (1992) : “ Stock assessment involves the use of various statistical and mathematical calculations to make quantitative predictions about the reactions of fi sh popula-tions to alternative management choices. ”

The components of a stock assessment will vary with the species considered, its stock identifi cation, the quantity and quality of data available, and the methods and mathematical models employed. It is a process whose steps typically include the following: (1) the defi -nition of the geographic and biological extent of the stock, (2) col-lection of appropriate data, (3) choice of assessment model(s) and parameters, (4) specifi cation of performance criteria and evaluation of alternative actions, (5) estimation of model and other parameters, and (6) presentation of results. While these steps were originally for-mulated for fi sheries stock assessments, they are equally applicable to marine mammal stock assessments.

Marine mammal stock assessments are often carried out to deter-mine what level of mortality a stock can sustain. Several type of information are usually required: current as well as historical abun-dance, trends in abundance and estimates of biological parameters (such as age at sexual maturity, natural mortality rate, sex ratio, and pregnancy rate), historical harvests, age distribution, maximum sus-tainable yield level (MSYL), age-specifi c harvest mortality, sustaina-ble or replacement yield, spatial distribution of the stock in question, and other relevant factors that may vary by species and population (see Population Dynamics). In addition to estimates of these quanti-ties, a measure of parameter uncertainty, such as variance or coef-fi cient of variation, is also necessary.

I. Productivity The productivity of a stock is determined by a number of factors,

including abundance, rate of increase, population age structure, sex ratio, and the manner in which density-dependence (see Population Dynamics) operates. The productivity is the amount by which the stock increases over a time interval (usually a year) and is the differ-ence between the number of animals added (by reproduction and immigration) and the number that are lost (due to emigration and from natural causes—all causes not due to harvest). Ideally, immi-gration and emigration are zero or equal, so their effects cancel each other. The amount by which the population increases each year (in the absence of a harvest) is the net production or the replacement yield, and this amount, if harvested, results in the population size at the end of the time period (usually a year) remaining the same size as at the beginning of the year. A related quantity, the sustain-able yield, is the productivity when the stock is stable. This occurs when the various population rates (such as natural mortality and reproduction) have remained constant for suffi cient time and the environment does not change. Fisheries stock assessments generally determine productivity in terms of biomass, whereas marine mam-mal stock assessments most often determine productivity in terms of number of animals. This is not only because marine mammals are diffi cult to weigh but also because they stop growing after reaching physical maturity, whereas most fi sh grow throughout their life. It thus becomes increasingly diffi cult to associate age and size for older animals, especially for cetaceans.

II. Models Most stock assessments employ a mathematical model of the popu-

lation to predict the historical trends in abundance as well as future trends under various removal scenarios and choice of model parame-ters. This approach usually assumes constant environmental conditions and model parameters, and these assumptions are often diffi cult to evaluate. The model parameters are estimated from the available data or fi xed at various plausible values. The more reliable the basic data, the more reliable will be the assessment. A simple population model often used for modeling the dynamics of a population is the discrete, generalized logistic model:

N N R N N K ht t t tz

t� � � � �1 1max ( / )[ ] (1)

where Nt is the population size (in numbers) at the start of year t , Rmax is the maximum per capita growth rate, K is the carrying capac-ity or pre-exploitation abundance of the population, ht is the harvest in year t , and z is a density-dependent exponent which determines at what population level (between 0 and K ) the productivity is maxi-mum. Equation (1) is a difference equation, with the population size at time t � 1 being a function of the population size at time t.

The population level at which the productivity curve is maxi-mum, the maximum net productivity level or MNPL, is considered to be greater than 50% of K for marine mammals. When the har-vest is random with respect to age and sex, MSYL and MNPL are often used interchangeably. The International Whaling Commission (IWC) has usually adopted a value of 60% for the MSYL, which cor-responds to a z of 2.39. A value of z � 1 results in a symmetric pro-ductivity curve with MSYL at 50% of K . This also corresponds to a linear density–dependence relationship between the per capita rate of growth and population density.

This model is simple in that it combines males and females, it ignores age structure and it assumes constant environmental con-ditions and model parameters. It does, however, capture the basic dynamics of the population, including harvesting or other known removals. It has the desirable feature that the recruitment rate is den-sity dependent; it is greatest at small population sizes and decreases as the population increases toward K . The sustainable yield as a function of N for the model shown earlier is given by

SY N R N N K z( ) [ ( / ) ]max� �1 (2)

Productivity, therefore, increases as the population size increases, reaches a maximum when N is equal to the MSYL, a level interme-diate between 0 and K , and then declines to 0 at K . This can be seen in Fig. 1 , which shows the sustainable yield curves for z � 1 (linear density–dependence with MSYL � 50% of K ) and z � 2.39 (nonlin-ear density dependence with MSYL � 60% of K ). By solving for the population size when the productivity is maximum, the MSYL can be shown to be equal to K (1 � z ) � 1/z . Thus, if z � 1, MSYL � K /2 or 50% of K (see also Population Dynamics).

Equation (1) and similar models, often modifi ed to include sex, age, and spatial structure, have been used to model cetacean, pin-niped, and other marine mammal populations. If estimates of Rmax , z , and K are available, along with a time series of removals, then the model can be used to project an initial abundance, N0, forward to any particular year. This procedure can be programmed to fi nd an N0 such that the population trajectory “ hits ” a current abundance estimate. This is a simplifi cation of a technique employed to assess many marine mammal populations. Parameters of the model can be

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estimated by minimizing a measure of discrepancy between observed and model-predicted abundance.

III. Population Status The IWC and the US Government (US Marine Mammal

Protection Act of 1972: MMPA) have based assessments on classifying stocks by their depletion level with respect to pre-exploitation popula-tion size and MNPL. The IWC New Management Procedure (NMP) was based on classifying stocks as Initial Management (IM), Sustained Management (SM), and Protected (P), based on the MSYL and the current depletion level with respect to K . However, for stocks clas-sifi ed as IM or SM, the quota required knowledge of the MSY. The MSY, in turn, depends on, among other things, the level of density-dependence (see Fig. 1 ). The Revised Management Procedure (RMP) addresses shortcomings in the NMP such as the diffi culty of determin-ing MSY for a stock and relies primarily on estimates of abundance and their uncertainty and a simple population model such as Eq. (1) requiring few biological parameters.

The US MMPA called for marine mammal populations to be maintained at an “ optimum sustainable population ” (OSP) level. The US National Marine Fisheries Service defi ned OSP as a popula-tion level between the MNPL and the carrying capacity. The appli-cation of this requires the determination of the current population status with respect to the MNPL. In some cases a range of MNPL was used, while in other cases an estimate was made whether the abundance was either less than or greater than the MNPL. The 1994 amendments to the MMPA required that a Potential Biological Removal (PBR) be determined for marine mammal stocks. The PBR is equal to the maximum number of animals that can safely be removed from the population annually. It is calculated as the product of the minimum population estimate of the stock, one-half the maxi-mum theoretical or estimated net productivity rate and a recovery

factor between 0.1 and 1. The assessment of allowable removals therefore hinges on estimation of abundance and the productiv-ity rate. The PBR is a conservative approach whose goal is to allow stocks to reach or maintain their OSP without having to estimate quantities such as MNPL or K (see Management) which can be dif-fi cult to estimate.

IV. Uncertainty and Other Considerations Uncertainty and how to deal with it is a feature of all stock assess-

ments. The environment and the genetic structure of stocks, as well as the levels of competition and predation may change over time. There is also uncertainty in the underlying population dynamics (termed process error), in the measurement of abundance or indices of abundance (termed measurement error), in the model structure (i.e., is the model correct?), and in the model parameters. Common methods for dealing with some forms of uncertainty include boot-strapping (a method of resampling the data to estimate variability), maximum likelihood (a method for obtaining parameter estimates and their associated variability), model averaging, and Bayesian sta-tistical methods.

Bayesian statistical methods are increasingly being used to deal with uncertainty in stock assessments. Bayesian estimation involves integrating the product of the likelihood of the observed data and the prior probability distribution for parameters of interest to obtain what is termed the posterior distribution for the quantity of interest. Due to the complexity involved in integrating this product it must often be estimated numerically by Monte Carlo methods (based on computer simulations using random numbers). The advantage of the Bayesian methodology is that various sources of information on parameters, including observations from other stocks or species, can be incorporated into the assessment. The end result is not just a simple estimate of the growth rate, for example, but a probability

0 2,000 4,000 6,000 8,000 10,0000

50

100

150

200

250

Population size (N)

Sus

tain

able

yie

ld (

SY

)

z � 1.0

z � 2.39

K � 10,000

Rmax � 0.05

Figure 1 A plot showing sustainable yield as a function of population size [see Eq. (2)] for a hypothetical marine mammal population with Rmax � 0.05, K � 10,000 and two values for the density-dependent exponent, z .

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distribution, showing the probability of different values of the parameter. Disadvantages of the Bayesian method are that it is often diffi cult to construct and obtain agreement on a prior distribution to use in an assessment and the diffi culty of detecting inadmissi-ble combinations of parameters that arise in the prior distributions (Borel’s Paradox).

Most stock assessments deal with uncertainty in model param-eter estimates and management-related quantities, but for the most part they are still based on single-species population models. Some progress has been made in considering marine mammal stocks as part of a larger ecosystem that includes food webs, spatial distribution, and interacting (e.g., competing) species. While it would be preferable to consider a host of interacting factors that infl uence marine mammal stocks, the paucity of available data often precludes the estimation of the parameters necessary to model the various population interactions. It is likely, however, that future stock assessments will increasingly take into account ecosystem considerations.

Environmental factors are an issue that is becoming more impor-tant in fi sheries and marine mammal stock assessment. In the North Pacifi c, for example, decadal oscillations in climate can affect the dis-tribution and abundance of fi sh and marine mammals (by affecting the distribution and abundance of prey species). Large amounts of long-term data are required to be able to assess the effects of climate on marine mammals. Without these data it is very diffi cult to determine whether changes in stock abundance are due to climate, harvesting, or a combination of the two.

V. Examples A. Cetaceans

Recent stock assessments carried out for both the eastern North Pacifi c gray whale ( Eschrichtius robustus ) stock and the Bering-Chukchi-Beaufort Seas stock of bowhead whales ( Balaena mysti-cetus ) have used Bayesian assessment methods ( Wade, 2002 ; Punt, 2006 ). Stock defi nition is not considered an issue for these two stocks, as there is little evidence for sub-stock structure (sub-stock structure has been raised recently with respect to bowhead whales, but the evidence for this is not compelling).

Whales of both of these stocks migrate along the coast where they are counted by shore-based observers. Data collected include counts and sighting distance, which are analyzed to give abundance estimates along with standard errors (measure of uncertainty), and numbers of young and immature animals. Acoustic data are also collected for bow-head whales and integrated with the visual location data to estimate the number of whales passing. Several different assessment models have been used, but all are age- and sex-structured models that incor-porate density-dependence in the reproductive rate. A method often used to estimate the posterior probability distribution of management-related parameters (such as MSYL and RY) involves projecting the population model forwards using as inputs parameter values that are randomly chosen from their prior probability distributions ( Punt and Hilborn, 1997 ). A measure of the discrepancy between the observed abundance estimates and the abundances predicted by the popula-tion model, the likelihood, is then computed. This is repeated a large number of times, and management-related parameters are calculated for each case. These include historic abundance, current abundance, growth rate, MSYL, and RY. From these repeated model runs, a smaller sample is taken with probability proportional to the total likeli-hood computed for each trajectory. This second sample is an estimate of the posterior probability distribution of the management-related parameters. From these distributions the median or mean value can

be obtained as well as other statistics of interest, including the answer to questions such as “ What is the probability that the RY is less than 100? ” or “ What is the probability that the current abundance is greater than the MSYL? ” In practice, a conservative approach has often been adopted by computing such quantities as the lower 5th or 10th per-centile of the RY and other quantities of interest in determining allow-able quotas.

Both the US National Marine Fisheries Service and the International Whaling Commission have assessed these two stocks. A Bayesian analysis using an age- and sex-structured model for gray whales resulted in a lower 10th percentile for Rmax of 0.047. This, cou-pled with a minimum population estimate of 17,752 [lower 20th per-centile of the mean of the 2000/01 and 2001/02 abundance estimates (not signifi cantly different)], and a recovery factor of 1.0, resulted in a potential biological removal (PBR) of 417 animals ( Angliss and Outlaw, 2005 ), well above the average current annual take of less than 180. An assessment based on Bayesian analyses using two different age-struc-tured models ( Wade, 2002 ) resulted in estimates of K of 19,058 and 21,740; N2002 / K of 1.04 and 1.00; and Q 1 , a quantity considered by the IWC to be a more appropriate than RY to use for management advice for populations thought to be above MSYL, of 626 and 669 (Q 1 is defi ned as 0.9MSY for populations above the MSYL, as the minimum of 0.9MSY and the product Nt *MSYR for populations below MSYL, and as zero for populations below Pmin , the population size below which no catches are allowed). These numbers represent medians, but for management advice the IWC used the lower 5th percentile of Q 1 , 463. This number of whales per year was agreed to be sustainable for at least the medium term ( � 30 years).

The PBR for the Western Arctic bowhead whale population was based on a minimum population estimate of 9472, a rate of increase of 3.3% (with a harvest, so an Rmax of 4% was used), and a recovery factor of 0.5 (because the population is increasing in the presence of a known take) ( Angliss and Outlaw, 2005 ). These result in a PBR of 95 animals (9472 0.02 0.5). The development of a PBR for this stock is required by the MMPA even though the Alaska Eskimo subsistence harvest is managed under the authority of the IWC. Thus, the IWC quota takes precedence over the PBR estimate. An assessment submitted to the IWC Scientifi c Committee was based on a Bayesian estimation method to fi t a density-dependent, age-structured population model to available data on abundance ( Punt,2006 ). The maximum population growth rate, Rmax , was estimated to be 0.042. The posterior median for K was 11,120 and for N2002 / K was 0.86. The posterior distribution for replacement yield (RY) was 172 and for Q 1 , 243. The difference between these two quantities occurs because the model estimates that the population is above MSLY and close to K.

In the future, gray whale and bowhead whale quotas will be determined by use of a Strike Limit Algorithm (SLA) that has been developed by the IWC Aboriginal Whaling Management Procedure group. The SLA relies mainly on abundance estimates and their variance as well as historic catches. The SLAs for the two species are different, but both of them were developed after a number of years of extensive testing via computer simulations and are robust to uncertainties in abundance, catch, and other factors.

B. Pinnipeds The population of Steller sea lions ( Eumetopias jubatus ) in west-

ern Alaska has declined sharply since the mid-1970s. No single cause has been implicated in the decline, but human-induced mortality (shootings, incidental takes in fi sheries, small directed harvests) and

Stock Assessment1114

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predators (killer whales) are known to have caused sea lion mortality ( Loughlin and York, 2000 ).

A series of modeling papers has attempted to determine the demo-graphic causes of the decline and how they may have changed over time. York (1994) using two age-structure samples with their esti-mated survival and fecundity rates and counts of Steller sea lions from aerial surveys suggested that the early decline was mostly caused by a decline in juvenile survival. Holmes and York (2003) and Holmes et al . (2007) extended this model by additionally using counts of pups and an index of the number of juveniles developed from photographs using pup counts. The later papers estimated time-varying vital rates that were consistent with the non-pup and pup counts and juvenile index data, assuming that the known vital rates were from the sampled animals at time 0. The later models suggested that over the course of the decline, the demographic causes of the decline have changed from low juvenile survival to a combination of low juvenile survival and low adult survival to an increase in survival now in combination with low fecundity.

Commercial harvests of subadult male northern fur seals (Callorhinus ursinus ) took place on the Pribilof Islands from the time of their discovery in 1786 until 1984. After 1918, the harvest was conducted under the auspices of the Treaty on the Conservation of the Northern Fur Seal (see Northern Fur Seal). The renegoti-ated Treaty of 1957 provided a vehicle for cooperative research among scientists of the party nations and specifi ed that the popula-tion was to be managed to obtain “ maximum sustained productivity. ” Attempts were made to fi t spawner-recruit models to fur seal data and to use them to set the harvest, but these methods largely failed, probably due to high variability in year class survival. Using numbers of young of the year (pups) counted earlier in the century and the pattern of harvests, it was estimated that the harvests, on average, took about 30% of the number of male seals born, or about 15% of the total seals born. When managers of the Pribilof herd learned that age at fi rst reproduction of the Russian herd was, on average, 1 year younger than in the Pribilof herd, they justifi ed a large reduction of females in the Pribilof population with the idea that with a lower herd density age at fi rst reproduction would decrease to the level of the Western Pacifi c population, and a sustainable harvest of the same size would be obtained from a reduced population. That idea was tried and failed, perhaps because the harvesting regime prefer-entially killed those females that tended to reproduce at a younger age. At present, there is no commercial harvest, but a subsistence take for food is permitted. The maximum size of the subsistence take is set by the PBR approach at about 15,000 animals, well above the mean annual take from 2000 to 2004 of 750 animals.

The Northwest Atlantic harp seal ( Pagophilus groenlandicus ) population in Canada and Greenland is currently subject to a har-vest. The current estimate of the population is 5.4 million ( Hammilland Stenson, 2007 ); approximately 18–20% of the population is young of the year. The population model takes into account catches in Canada and Greenland, bycatch in fi shing gear and animals struck and lost in the harvests.

Canada uses a management scheme referred to as “ Objective Based Fisheries Management. ” They have identifi ed upper and lower reference points of 30 and 70% of the historical maximum population. The present management objectives are to maximize economic return while maintaining the population over the 70% ref-erence level, with an estimated probability of at least 80%.

The current catches in Canada have averaged 312,000 for the past 5 years. In 2007, the catch was 225,000 (more than 95% are young of the year). An additional 90,000 are taken by Greenland from the

same population. The current catch level is about 4–5% of the total population or about 20–25% of the young of year population.

See Also the Following Articles Management Population Dynamics

References Angliss , R. P. , and Outlaw , R. B. ( 2005 ). “ Alaska Marine Mammal Stock

Assessments, 2005 . ” U.S. Dep.Comm , NOAA-TM-AFSC - 161 . Anonymous. (1955). “ United States Statement on Estimates of Maximal

Sustainable Productivity for the Pribilof Seal Herd. ” Document 48, presented by the United States during negotiations in Washington, DC, Dec. 19, 1955, preceding ratifi cation of the 1957 Interim Convention on the Conservation of the North Pacifi c Fur Seal.

Brandon , J. R. , and Wade , P. R. ( 2006 ). Assessment of the Bering-Chuckchi-Beaufort Seas stock of bowhead whales using Bayesian model averaging . J. Cetacean Res. Manage. 8 , 225 – 239 .

Butterworth, D. S., David, J. H. M., McQuaid, L. H., and Xulu, S. S. (1987). Modeling the population dynamics of the South African fur seal, Arctocephalus pusillus pusillus. In “ Status, Biology, and Ecology of Fur Seals, Proceedings of an International Symposium and Workshop. ” NOAA Tech. Rep. NMFS 51.

Gerrodette , T. , and DeMaster , D. P. ( 1990 ). Quantitative determina-tion of optimum sustainable population level . Mar. Mamm. Sci. 6 , 1 – 16 .

Goodman , D. ( 1988 ). Dynamic response analysis. I. Qualitative estima-tion of stock status relative to maximum net productivity level from observed dynamics . Mar. Mamm. Sci. 4 , 183 – 195 .

Hammill , M. O. , and Stenson , G. B. ( 2007 ). Application of the precau-tionary approach and conservation reference points to management of Atlantic seals . ICES J. Mar. Sci. 64 , 702 – 706 .

Hilborn , R. ( 1997 ). Uncertainty, risk, and the precautionary princi-ple . In “ Global Trends: Fisheries Management ” ( E. K. Pikitch , D. L. Huppert , and M. P. Sissenwine , eds ) , pp. 100 – 106 . American Fisheries Society , Bethesda, Maryland .

Hilborn , R. , and Walters , C. J. ( 1992 ). “ Quantitative Fisheries Stock Assess-ment: Choice, Dynamics and Uncertainty . ” Chapman and Hall , New York .

Holmes , E. E. , and York , A. E. ( 2003 ). Using age structures to detect impacts on threatened populations: a case study using Steller sea lions . Conserv. Biol. 17 , 1794 – 1806 .

Holmes , E. E. , Fritz , L. W. , York , A. E. , and Sweeney , K. ( 2007 ). Age-structured modeling reveals long-term declines in the natality of western Steller sea lions . Ecol. Appl. 17 , 2214 – 2232 .

International Whaling Commission. (1977). Report of the Scientifi c Committee. Rep. Int. Whal. Commn. 27, 36–51.

Kesteven , G. L. ( 1999 ). Stock assessments and the management of fi sh-ing activities . Fish. Res. 44 , 105 – 112 .

Loughlin , T. R. , and York , A. E. ( 2000 ). An accounting of the sources of mortality of Steller sea lion, Eumetopias jubatus , mortality . Mar. Fish. Rev. 62 , 40 – 45 .

National Research Council ( 1998 ). “ Improving Fish Stock Assessments . ” National Academy Press , Washington, D.C .

Polacheck , T. , Hilborn , R. , and Punt , A. E. ( 1993 ). Fitting surplus pro-duction models: comparing methods and measuring uncertainty . Can.J. Fish. Aquat. Sci. 50 , 2597 – 2607 .

Punt , A. E. ( 2006 ). Assessing the Bering-Chukchi-Beaufort Seas stock of bowhead whales using abundance data together with data on length or age . J. Cetacean Res. Manage. 8 , 127 – 138 .

Punt , A. E. , and Hilborn , R. ( 1997 ). Fisheries stock assessment and deci-sion analysis: the Bayesian approach . Rev. Fish Biol. Fish. 7 , 35 – 63 .

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Stock Identity JOHN Y. WANG

I. Importance of Stock Identity

Determining how a species is divided into stocks (the term “ stocks ” is used here to refer to biological stocks rather than management stocks; see later) is fundamental to the con-

servation of marine mammals. Because evolutionary processes act at the intraspecifi c level, genetic differences and locally adaptive char-acters will accumulate in stocks over time. This reservoir of genetic and phenotypic diversity increases a species ’ ability to persist through environmental changes. Thus, one of the main goals in conservation is to preserve the evolutionary potential of species by maintaining the diversity found in stocks. Another important goal is to maintain spe-cies as functioning elements in their ecosystem by preventing regional overexploitation and depletion. Consequently, knowledge of stock structure of species is integral for developing effective management programs to achieve these goals.

The greatest threats to the survival of marine mammals are human activities. Marine mammals experience various levels and kinds of anthropogenic threats in different regions, and all exhibit life history characteristics (i.e., long-lived, low fecundity, late age of maturity) that make them susceptible to these threats. In order to assess the impact of human activities on marine mammals, it is crucial to identify stocks accurately, establish where the stock boundaries exist, and determine the permeability of the boundaries to genetic exchange with other stocks. This information will infl uence how the biological data needed for assessments are collected and interpreted and how management plans are designed. Inaccurate stock designations can lead to either unnecessary regulation(s) of fi sheries or fallacious management that may result in the depletion of a stock and its accompanying genetic material. For example, if stock structure goes unrecognized and two distinct stocks are incorrectly managed as one, one may inadvertently become depleted.

Understanding stock structure can also help in streamlining the design of other studies, providing insights into evolution and moni-toring illegal activities [e.g., DNA analysis of cetacean meat prod-ucts from Japanese markets found stocks that were prohibited from sale (Baker et al ., 2000)]. Therefore, much effort has been directed toward identifying stocks of marine mammals. However, the task remains problematic, with two major diffi culties: (1) semantic uncer-tainty and disagreement in the defi nition of “ stock ” and (2) studying stock identity with incomplete biological knowledge.

II. Defi nition of Stock The term “ stock ” has been used to refer to both biological and

management entities (although in many cases, they are combined or inseparable). A management stock is a group of conspecifi c indi-viduals that are managed separately. The delineation of these stocks is very much dependent on the goals of managers and may not be based on biological discontinuities (e.g., International Whaling Commission management stock designations for baleen whales). With the exception of the defi nition by Moritz (1994) , who described a “ management unit ” (MU) (which he synonymized with “ stock ” and appears to be equivalent to management stock) as having signifi cant differences in allele frequencies at nuclear or mitochondrial DNA loci, the criteria for determining management stocks may have lit-tle or no biological rationale or consistency and may be infl uenced greatly by political interests. Nevertheless, management stocks have been used widely due to the paucity of biological information and will likely continue to play an important role in conservation. Developments in management strategies for situations with incom-plete biological information should improve the success of conser-vation programs ( Taylor, 1997 ). Although management stocks offer more fl exibility in the sense that they can still be the focus of man-agement programs without evidence of biological distinctiveness, conservation goals (e.g., maintaining genetic diversity) are more likely to be achieved if stocks are based on biological data. Therefore, this article focuses mainly on biological stocks.

Biological stocks are characterized by no or low levels of genetic exchange (which means that members of a biological stock tend to interbreed with each other more often than with other individu-als). An entity with this property has also been called a population, subpopulation, evolutionary signifi cant unit (ESU), deme, and sub-species (the only intraspecifi c taxon recognized by the International Commission on Zoological Nomenclature). When gene fl ow between two groups is absent, there is usually no disagreement that they rep-resent separate biological stocks. However, it is more typical that some level of genetic exchange exists. Even low levels of genetic exchange can obscure stock boundaries and complicate the task of discriminating biological stocks. Although there is no consensus on the threshold level of gene fl ow above which stock status is no longer recognized, several approaches have been developed to make the identifi cation of biological stocks more objective and explicit.

III. Stock Identifi cation Approaches Defi ning stocks is linked inextricably with defi ning species. There

are many concepts that propose species defi nitions, but those advo-cated most commonly today include biological, evolutionary, and phylogenetic species concepts [for a detailed overview of these and other concepts, see Sites and Crandall (1997) and King (1993) ]. However, because these concepts all have major limitations, agree-ment on the best species defi nition still eludes biologists. Like the species concepts, each approach to stock identifi cation has limita-tions and weaknesses. In addition, defi ning stocks can be infl uenced, and therefore complicated further, by the goals of conservation and legislation. For example, one of the goals of the U.S. Endangered Species Act (ESA) is to decrease the loss of genetic variation. Thus, for this purpose, defi ning stocks using genetic criteria [e.g., the ESU of Moritz (1994) ] is a reasonable proposal [however, see Pennockand Dimmick (1997) and Dimmick et al. (1999) ]. Unlike the ESA, the US Marine Mammal Protection Act (MMPA) endeavors to keep biological stocks at or beyond their optimum sustainable levels and functioning in their ecological roles. To accomplish the intent of this