NOAA Technical Report NMFS 63

Stock Assessment of the

Atlantic Menhaden,

Brevoortia tyrannus, Fishery

Douglas S. Vaughan

Joseph W. Smith

January 1988

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service
NOAA TECHNICAL REPORT NMFS

The major responsibilities of the National Marine Fisheries Service (NMFS) are to monitor and assess the abundance and geographic distribution of fishery resources, to

underSlJlnd and predict fluctuations in the quantity and distribution of these resources, and to eSlJlblish levels for their optimum use. NMFS is also charged with the development

and implemenlJltion of policies for managing national fishing grounds, development and enforcement of domestic fisheries regulations, surveillance of foreign fishing off United

SlJItes coaSlJll waters, and the development and enforcement of international fishery agreements and policies. NMFS also assists the fishing industry through marketing service

and economic analysis programs, and mortgage insurance and vessel construction subsidies. It collects, analyzes, and publishes slJltistics on various phases of the industry.

The NOAA Technical Report NMFS series was eSlJlblished in 1983 to replace two subcategories of the Technical Reports series: "Special Scientific Report-Fisheries" and

"Circular." The series conlJlins the following types of reports: Scientific investigations that document long-term continuing programs of NMFS; intensive scientific reports on

studies of restricted scope; papers on applied fishery problems; technical reports of general interest intended to aid conservation and management; reports that review in considerable delJlil and at a high technical level certain broad areas of research; and technical papers originating in economics studies and from management investigations. Since

this is a formal series, all submitted papers receive peer review and those accepted receive professional editing before publication.

Copies of NOAA Technical Reports NMFS are available free in limited numbers to governmenlJlI agencies, both Federal and SlJIte. They are also available in exchange for

other scientific and technical publications in the marine sciences. Individual copies may be oblJlined from: U.S. Department of Commerce, National Technical Information Service,

5285 Port Royal Road, Springfield, VA 22161. Although the contents have not been copyrighted and may be reprinted entirely, reference to source is appreciated.

13. Guidelines for reducing porpoise mortality in tuna purse seining, by James M.

Coe, David B. Holts, and Richard W. Butler. September 1984, 16 p.

14. Synopsis of biological data on shortnose sturgeon, Acipenser brevirostrum

leSueur 1818, by Michael 1. Dadswell, Bruce D. Taubert, Thomas S. Squiers, Donald

Marchette, and Jack Buckley. October 1984, 45 p.

15. Chaetognatha of the Caribbean sea and adjacent areas, by Harding B. Michel.

October 1984, 33 p.

16. Proceedings of the Ninth and Tenth IJ S.-Japan Meetings on Aquaculture, by

Carl J. Sindermann (editor). November 1984, 92 p.

17. Identification and estimation of size from the beaks of 18 species of cephalopods

from the Pacific Ocean, by Gary A. Wolff. November 1984, 50 p.

18. A temporal and spatial study of invertebrate communities associated with hardbottom habitats in the South Atlantic Bight, by E. L. Wenner. P. Hinde, D. M. Knott,

and R. F. Van Dolah. November 1984, 104 p.

19. Synopsis of biological dalJl on spotlJlil pinfish, Diplodus holbrooki (Pisces:

Sparidae), by George H. Darcy. January 1985, II p.

20. Ichthyoplankton of the Continental Shelf near Kodiak Island, Alaska, by Arthur

W. Kendall, Jr., and Jean R. Dunn. January 1985, 89 p.

21. AnnOlJlted bibliography on hypoxia and its effects on marine life, with emphasis

on ti,e Gulf of Mexico, by Maurice L. Renaud. February 1985, 9 p.

22. Congrid eels of the eastern Pacific and key to their Leptocephali, by Solomon

N. Raju. February 1985, 19 p.

23. Synopsis of biological dalJl on the pinfish, Lagodon rhomboides (Pisces:Sparidae),

by George H. Darcy. February 1985, 32 p.

24. Temperature conditions in the cold pool 1977-81 : A comparison between southern

New England and New York transects, by Steven K. Cook. February 1985, 22 p.

25. Parasitology and pathology of marine organisms of the world ocean, by William

J. Hargis, Jr. (editor). March 1985, 135 p.

26. SynopsIs of biological dalJl on the sand perch, Diplectrum formosum (Pisces:

Serranidae), by George H. Darcy. March 1985,21 p.

27. Proceedings of the Eleventh U.S.-Japan Meeting on Aquaculture, Salmon

Enhancement, Tokyo, Japan, October 19-20, 1982, by Carl 1. Sindermann (editur).

March 1985, 102 p.

28. Review of geographical stocks of tropical dolphins (Stenel/a spp. and Delphinus

delphis) in the eastern Pacific, by William F. Perrin, Michael D. Scott, G. Jay Walker,

and Virginia L. Casso March 1985, 28 p.

29. Prevalence, intensity, longevity, and persistence of Anisakis sp. larvae and Laeisrorhynchus lenuis metacestodes in San Francisco striped bass, by Mike Moser, Judy

A. Sakanari, Carol A. Reilly, and Jeannette Whipple. April 1985,4 p.

30. Synopsis of biological da:a on the pink shrimp, Pandalus borealis Kr6yer, 1838,

by Sandra E. Shumway, Herbert C. Perkins, Daniel F. Schick, and Alden P. Stickney.

May 1985, 57 p.

31. Shark catches from selected fisheries off the U.S. east coast, by Emory D. Andersun, John G. Casey, John J. Hoey, and W. N. WitzelI. July 1985, 22 p.

32. Nutrient Distributions for Georges Bank and adjacent waters in 1979, by A. F.

J. Drax1er, A. Matte, R. Waldhauer, and J. E. O'Reilly. July 1985,34 p.

33. Marine flora and fauna of the Northeastern United SlJItes. EchinodermalJl:

Echinoidea, by D. Keith Serafy and F. Julian Fell. September 1985, 27 p.

34. Additions to a revision of the shark genus Carcharhinus: Synonymy of Aprionadon and Hypopriun, and description of a new species of Carcharhinus (Carcharhinidae),

by J. A. F. Garrick. November 1985,26 p.

35. Synoptic review of the literature on the Southern oyster drill Thais haemasroma

jloridana. by Philip A. Butler. November 1985, 9 p.

36. An egg production method for estimating spawning biomass of pelagic fish:

Application to the northern anchovy, Engraulis mordax, by Reuben Lasker (editor).

December 1985, 99 p.

37. A histopathologic evaluation of gross lesions excised from commercially important North Atlantic marine fishes, by Robert A. Murchelano, Linda Despres-PalJlnjo,

and John Ziskowski. March 1986, 14 p.

38. Fishery atlas of the northwestern Hawaiian [slands, by Richard N. Uchida and

James H. Uchiyama (editors). September 1986, 142 p.

39. Survey of fish protective facilities at water withdrawal sites on the Snake and

Columbia Rivers, by George A. Swan, Tommy G. Withrow, and Donn L. Park. April

1986, 34 p.

40. Potential impact of ocean thermal energy conversion (OTEC) on fisheries, by

Edward P. Myers, Donald E. Hoss, Walter M. Matsumoto, David S. Peters, Michael

P. Seki, Richard N. Uchida, John D. Ditmars, and Robert A. Paddock. June 1986,

33 p.

41. A slJltionary visual census technique for quantitatively assessing community structure of coral reef fishes, by James A. Bohnsack and Scott P. Bannero!. July 1986, 15 p.

42. Effects of temperature on the biology of the northern shrimp, Pandalus borealis,

in the Gulf of Maine, by Spencer Apollonio, David K. Stevenson, and Earl E. Dunton,

Jr. September 1986, 22 p.

43. Environment and resources uf seamounts in the North Pacific, by Richard N.

Uchida, Sigeitl Hayasi, and George W. Boehlert (editors). September 1986, 105 p.

44. Synopsis of biological data on the porgies, Calamus arctifrons and C. proridens

(Pisces: Sparidae), by George H. Darcy. September 1986, 19 p.

45. Meristic variation in Sebastes (Scorpaenidae), with an analysis of character association and bilateral pattern and their significance in species separation, by Lo-chai Chen.

September 1986, 17 p.

46. Distribution and relative abundance of pelagic nonsalmonid nekton off Oregon

and Washington 1979-84, by Richard D. Brodeur and William G. Pearcy. December

1986, 85 p.
NOM Technical Report NMFS 63

Stock Assessment of the

Atlantic Menhaden,

Brevoortia tyrannus, Fishery

Douglas S. Vaughan

Joseph W. Smith

January 1988

U.S. DEPARTMENT OF COMMERCE

C. William Verity, Jr., Secretary

National Oceanic and Atmospheric Administration

Anthony J. Calia, Administrator

National Marine Fisheries Service

William E. Evans, Assistant Administrator for Fisheries
The National Marine Fisheries Service (NMFS) does not approve, recommend

or endorse any proprietary product or proprietary material mentioned in this

publication. No reference shall be made to NMFS, or to this publication furnished

by NMFS, in any advertising or sales promotion which would indicate or imply

that NMFS approves, recommends or endorses any proprietary product or proprietary material mentioned herein, or which has as its purpose an intent to cause

directly or indirectly the advertised product to be used or purchased because of

this NMFS publication.

11
CONTENTS

Introduction

Description of the Fishery 3

Virtual Population Analyses 4

Size-At-Age and Growth Analyses 8

Surplus Production Models II

Spawner-Recruit Relationships 12

Yield-Per-Recruit Analyses 15

Management Implications 17

Acknowledgments 18

Citations 18

iii

Stock Assessment of the

Atlantic Menhaden,

Brevoortia tyrannus,

Fishery

DOUGLASS. VAUGHAN

JOSEPH W. SMITH

Beaufort Laboratory

Southeast Fisheries Center

National Marine Fisheries Service. NOAA

Beaufort. North Carolina 28516-9722

ABSTRACT

A stock assessment of the Atlantic menhaden, BrevoortiLl tyrannus. fishery was

conducted with purse-seine landings data from 1940 to 1984 and port sampling

data from 1955 to 1984. These data were analyzed to determine growth rates,

maximum sustainable yield (MSY), spawner-recruit relationships, and yield per

recruit. Virtual population analysis was used to estimate stock size, year class

size, and fishing mortality rates.

Surplus production models produced estimates of MSY from 450 to 490 kmt

compared with yields of 416to 436 kmt based roughly on maximum recruitment

from a weak spawner-recruit relationship. Recruitment to age-I ranged from 1.2

to 14.8 billion fish for year classes 1955-81. Recent mean recruitment to age-I for

the 1975-81 year classes averaged 5.7 billion fish and compared favorably with

the mean of7.7 billion age-I fish recruited during the late 1950's. Mean recruitment from recent years suggests possible coastwide yields of 416 to 481 kmt.

Continued dominance of late age-2 spawners among the spawning stock is of

concern, since the stock is at greater risk through poor recruitment if recent

favorable environmental conditions change.

Yield-per-recruit estimates ranged from 46 g to 59 g since 1970. The high

dependency of the modern fishery on prespawners has increased concerns about

fluctuations in year-to-year availability and catches. To increase yield and enhance the stability of the resource, the number of age classes contributing significantly to the fishery should be increased, creating a butTer against future poor

recruitment years and lessening the year-to-year fluctuations in landings.

Introduction _

The Atlantic menhaden, Brevoortia tyrannus. is a euryhaline species found in coastal and inland tidal waters from Nova Scotia,

Canada, to West Palm Beach, Florida (Fig. I) (Reintjes 1969).

They form surface schools off Florida, Georgia, and the Carolinas

in April and Mayas the waters warm, and move slowly northward,

stratifying by age and size during the summer (older and larger fish

are generally found farther north). A southern migration begins in

early fall, with surface schools disappearing in late December or

early January off the Carolinas. Spawning occurs principally at sea

and in larger bays and sounds from May to October in the North

and Middle Atlantic areas and from October to April in the

Chesapeake Bay and South Atlantic areas. Eggs hatch at sea and

the larvae are moved to estuaries by ocean currents (Nelson et al.

1977) where they metamorphose and develop into juveniles. In late

fall and early winter, the juveniles leave the estuaries and move

into large bays or the open sea. Adult Atlantic menhaden are filter

feeders (feeding primarily on phytoplankton) and, in turn, support

predatory food fishes.

A commercial fishery for Atlantic menhaden has existed since

colonial times, but purse seines, now the principal gear, were

introduced by 1845 (Frye 1978). Large carrier vessels are equipped

with a pair of purse boats for setting the seines around the schools

of fish. In 1984, eight active reduction plants at five ports on the

Atlantic coast (Fig. I) produced fish meal and solubles used in

poultry and livestock feeds, and oil used in paints and as an edible

oil in Europe. Landings increased rapidly through the 1940's and

early 1950's as fishing effort (measured in vessel weeks) increased

(Fig. 2). After several years of high landings and fishing effort in

the late 1950's, a sharp decline was observed in landings in the

early and mid-1960's. Fishing effort similarly declined during the

1960's. Landings have recovered somewhat since the late 1960's,

and represent 38% by weight of the U.S. Atlantic coast commercial fish landings in 1984 (U.S. National Marine Fisheries Service

1985).

The menhaden research program of the National Marine Fisheries Service has maintained records of daily vessel landings and

fishing activity since 1955, supplemented in recent years by information from captains' daily fishing reports. Samples of catches for

weight, length, and age composition have been used in conjunction

with vessel landings to estimate number of fish landed at each age

by plant and area, to determine growth rates, and to estimate

fishing mortality (Chester 1984). Additional information has also

been obtained on fecundity (Higham and Nicholson 1964; Dietrich

1979) and on selected environmental variables (Nelson et al.

1977). Juveniles have been tagged each fall to study movements

and to estimate natural mortality (Kroger and Guthrie 1973). An

overview of the life history and stock structure of the Atlantic

menhaden is presented in Ahrenholz et al. (1987).

The major purpose for this report is to update the analyses

presented in Ahrenholz et al. (1987) with three additional years of

data (1982-84 fishing years). These analyses include (I) application of virtual population analysis to obtain estimates of population

sizes and fishing mortality; (2) analyses of growth to confirm an

inverse relationship with population size and use in population

models; (3) development of surplus production models to estimate

maximum sustainable yield (MSY); (4) development of spawnerrecruit models to determine adequacy of recent recruitment and

spawning stock; and (5) application of yield-per-recruit approach

to determine if greater yields are available given recent levels of

recruitment.
1955 1984

Figure I

Geographic fishing areas for the Atlantic menhaden purse-seine fishery, and landing ports for 1955 and 1984 fishing years. The number of plants operating at each

port is given in parentheses when greater than one.

2
w 800 4000

z __ Landings I0 c:::

I- ______ Effort 0

() 3000

u.. w

a: 600 u..~

I- Ww

W "w

z~-I

0 400 2000 I...J

0 ww

0 -wu.. w

en ...J w f --- «> " 200 f '-~ 1000

z , z

is

z 0 « z ...J

40 45 70 75 80 85

FISHING YEARS

Figure 2

Catch of Atlantic menhaden in thousands of metric tons and fishing elTort in vessel weeks for fishing years 1940-84.

Description of the fishery Table 1

Number of purse-seine vessels that landed Atlantic menhaden during

For purposes of summarization and analysis, June and Reintjes each fishing year by area, 1955-84.

(1959) divided the Atlantic coast into four geographic fishing areas

and one temporal fishing area (Fig. I). With only a change in the Nonh Middle Chesapeake Soulh Fall

boundary line between the South Atlantic and Chesapeake Bay Year Allantic' Allantic Bayb AtlanticC Totald fishery

areas (Nicholson 1975), the divisions are: 1955 39 48 20 34 150 51

1956 40 47 24 30 149 63

North Atlantic Area (Area I) Waters along the southern coast of 1957 33 46 25 31 144 64

Long Island, east of a line due south of Moriches Inlet (lat. 40° 46' 1958 23 44 28 26 130 63

N. and long. 72° 44' W.), and waters northward. 1959 34 45 31 25 144 59

1960 19 47 22 20 115 37

1961 21 47 23 20 117 44 Middle Atlantic Area (Area 2) Waters west of a line running due 1962 20 47 29 15 112 49

south of Moriches Inlet, on the southern coast of Long Island, 1963 10 46 36 16 112 46

southward to Great Machipongo Inlet, VA (lat. 37" 22' N. and 1964 9 37 38 16 III 51

long. 75° 43' W.). 1965 6 13 38 19 84 46

1966 5 10 36 16 76 43

Chesapeake Bay Area (Area 3) Chesapeake Bay proper and 1967 0 4 32 16 64 46

1968 2 4 25 16 59 45

coastal waters south of Great Machipongo Inlet, VA, to lat. 35° 20' 1969 3 4 22 16 51 36

N. on the North Carolina coast. 1970 4 I 18 II 54 37

1971 5 2 20 II 51 32

South Atlantic Area (Area 4) Coastal waters south of lat. 35° 20' 1972 9 4 19 II 51 5

N. on the North Carolina coast to Cape Canaveral, FL. 1973 10 6 23 II 58 4

1974 12 6 22 12 63 12

North Carolina Fall Fishery (Area 5) A temporal fishing area 1975 9 5 22 14 61 17

1976 12 4 21 12 62 13

consisting of waters from Cape Hatteras, NC, south to the southern 1977 12 5 24 10 64 16

border of North Carolina, beginning sometime between the last 1978 13 5 22 II 53 18

week of October and the second week of November, depending on 1979 II 4 22 13 54 18

the arrival of migratory menhaden from more northerly waters, to 1980 5 6 24 r2 51 19

1981 8 7 23 13 57 19

the end of February of the next calendar year (fishing usually stops 1982 9 0 22 3 47 18

by mid-January). For standardized data summary, the week of each 1983 7 0 24 10 41 17

season which ends between Nov. 8 and Nov. 14 is taken to be the 1984 6 0 26 6 38 12

first week of the fall fishery. 'Yessels fishing from New England pons in recent years are all trawlers that

conven 10 purse seine in summer. some fish regularly and others sporadiTwenty-three plants operated at 16 ports along the U. S. Atlantic cally.

coast from Maine to Florida during 1955, while only eight plants bYessels that fished only in regular season. Does not include vessels added

operated at five ports during 1984 (Fig. I). The number of vessels in October and November.

eJncludes only vessels thaI landed regularly in Ihe summer fishery. landing fish declined from 150 during the 1955 fishing season to dlncludes all vessels thaI landed fish during the year.

a low of 38 during the 1984 fishing season (Table I). Much of this

3
decline has occurred in the North and Middle Atlantic areas. For

example, during 1955 there were 77 vessels operating out of the

North and Middle Atlantic areas and 54 vessels out of the

Chesapeake Bay and South Atlantic areas compared with only 6

and 32 vessels, respectively, during 1984. During the 1984 fishing

year, two small plants operated in the North Atlantic area, none

operated in the Middle Atlantic area, two large plants operated in

the Chesapeake Bay area, and three small plants operated in the

South Atlantic area during the summer season. Two small plants

and one large plant operated in Beaufort, North Carolina, during

the 1984 North Carolina fall fishery. However, modernization and

increased vessel size, coupled with technological innovations to

the fishing operations themselves, have substantially increased the

potential fishing power of individual vessels (Reintjes 1969;

Nicholson 1971).

Virtual population analyses _

Estimates of population sizes and fishing mortality rates by age are

obtained from virtual population analyses (VPA) as developed by

Murphy (1965) and modified by Tomlinson (1970). Tomlinson's

computer program MURPHY (Abramson 1971) was used for these

calculations which are obtained independently of catch-per-uniteffort (CPUE). Backward sequential computations (oldest age to

youngest age) were used because they tend to converge on the

same (i.e., true) estimates, while forward calculations tend to

diverge unless the true starting value was used.

A major component of the input data for these analyses is catch

in numbers-at-age. These data are summarized annually (1955-64)

and quarterly (1965-84) (Smith et al. 1987) from daily estimates by

sampling methods outlined in Nicholson (I 978a). The fishing year

is divided into four approximately equal periods beginning March

I (Table 2). The annual instantaneous natural mortality rate (M)

was obtained from Ahrenholz et al. (1987). This estimate (0.45 per

year or 0.1125 per quarter) was assumed constant for all ages

(greater than 0.5) and years. In the historical data set (1955-84)

Atlantic menhaden greater than age-8 were pooled with age-8 fish

(Smith et al. 1987).

Three sets of VPA's were conducted on the Atlantic menhaden

catch-at-age data. First, a set of annual VPA's was conducted on

all year classes from 1947 through 1981. These provided estimates

of annual instantaneous fishing mortality rate by age and population size of each age class at the start of each fishing year (March

I). Second, a set of "partial-quarterly" VPA's was conducted on all

year classes from 1947 through 1964 based on the assumptions

outlined in Ahrenholz et al. (1987). These VPA's, which are

actually annual VPA's offset by one quarter, are used to estimate

population size-at-age at the start of the fourth quarter (December

I), prior to the onset of the major spawning period from December

through February. Finally, a set of quarterly VPA's could be conducted only on year classes from 1965 through 1984. Estimates of

instantaneous fishing mortality rates and population sizes are obtained for each age at the start of each quarter.

Results from these VPA's differed slightly from those of Ahrenholz et al. (1987) for two reasons. First, the port sampling data for

size and age (1970-84) were examined for errors using recently

developed editing programs. Corrections were made to the data set

where appropriate based on an examination of the original records.

Second, a new method was used to estimate the terminal F used as

the starting value in the VPA procedure (Table 3). This estimation

4

Table 2

Quarterly time increments used in stock assessment

analysis of Atlantic menhaden.

Beginning week Ending week

Quarter ending date ending date

I > 2/29 < 6/01

2 > 5/30 < 8/30

3 > 8/29 <11/29

4 >11/28 < 2/29'

'February of next calendar year, but same season.

Table 3

Minimimum variance unbiased estimates (MVUE) of

terminal F for use in annual virtual population analyis

(VPA) of Atlantic menhaden, source of estimate, and

ages involved by year class.

Year class Terminal F VPA Ages MVUE Ages'

1947 0.4862b 8

1948 1.3134b 7-8

1949 0.6673 6-8 6-8

1950 05993 5-8 5-8

1951 06607 4-8 4-8

1952 0.6821 3-8 3-8

1953 0.8273 2-8 2-8

1954 1.3446 1-8 2-8

1955 1.5300 0-8 2-8

1956 0.8683 0-8 2-8

1957 I. 1333 0-8 2-8

1958 1.0425 0-8 4-8

1959 0.7456 0-7 2-7

1960 1.4883 0-6 2-6

1961 1.6770 0-6 2-6

1962 1.7335 0-6 2-6

1963 1.9690 0-6 2-6

1964 13676 0-5 2-5

1965 2.1564 0-5 3-5

1966 1.8880 0-5 2-5

1967 1.2648 0-5 2-5

1968 1.2656 0-5 2-5

1969 2.5027 0-6 3-6

1970 2. 1135 0-5 2-5

1971 2.5530 0-6 2-6

1972 2.3138 0-5 2-5

1973 2.1339 0-6 2-6

1974 1.8871 0-6 2-6

1975 15931 0-8 2-8

1976 1.4942 0-6 2-6

1977 1.4363 0-6 2-6

1978 15324 0-6 2-6

1979 1.2241 0-5 2-5

1980 1.8381 0-4 2-4

1981 1.8962 0-3 2-3

'Ages used in calculating terminal Fusing MVUE.

bMean from VPA results (see Ahrenholz el al. 1987).
procedure, which obtains the Chapman-Robson survival estimate

(Seber (973), has the desirable statistical properties of being minimum variance and unbiased (MVUE). When estimating the instantaneous total mortality rate (Z) from survival (5), Chapman

and Robson (1960) provide a modified estimator:

Z* = -In 5 - (n-l)(n-2)/[n(n+X-I)(X+I)] , (I)

where 5 = XI(n +X - I); n = sum of all menhaden from a cohort

in the landings greater than a given age (usually greater than

age-I); X = sum of product of coded age (e.g., 0 for age-2, I for

age-3, etc.) with catch in numbers-at-age.

In addition to these VPA's, further estimates of population size

at age-O. 5 were made for year classes 1965 through 1981 based on

different assumptions as to the catch of age-O menhaden versus the

landings of age-O menhaden which are sampled at the plants. One

of the reasons for raising this issue is the statement "[i]t is generally

acknowledged [that] the fishing process will sometimes kill additional numbers of small fish" (AMAC 1982). Robert W. Smith,

then President of Seacoast Products Inc., states in reference to

catching of age-O menhaden by purse-seine (letter to Joseph W.

Grimsley, Secretary of North Carolina's Department of Natural

Resources and Community Development, 6 April 1982) that

"because of the small size of the fish, the rule of thumb is that as

many fish are wasted as are landed." Furthermore, Chester (1984)

has demonstrated that in the North Carolina fall fishery, when most

age-O fish are landed, there is a bias towards underestimating the

numbers of age-O fish in the landings. In both cases the question

arose as to what possible effect the underestimation of age-O fish

in the catches might have on the conclusions of this and previous

stock assessments. Hence, three sets of quarterly VPA's were

conducted such that the number of age-O's estimated in the landings were multiplied by 1.5,2, and 4 to reflect increasing levels of

underestimation of age-O's in the estimated catch in numbers-atage. Only estimates of population size and fishing mortality for

age-O fish are altered in this analysis.

Landings in the Atlantic menhaden fishery historically have

depended primarily on age-l and age-2 fish in terms of numbers

(Fig. 3). However, there are exceptions. In 1961 and 1962 large

landings of age-3 and age-4 fish, respectively, resulted from the

large 1958 year class (note age-I fish landed in 1959 and age-2 fish

landed in 1960). In 1979, 1981, 1983, and 1984 landings of age-O

fish (or "peanuts") exceeded landings of age-l fish (and age-2 fish

as well in 1984). Most Atlantic menhaden landed by the North

Carolina fall fishery are age-O fish (Fig. 4), and late-season fishing

(after the Virginia season closes in November) off North Carolina

by boats from Virginia plants in 1983 and 1984 contributed significant numbers of age-O fish to South Atlantic catches (Fig. 5). This

increased dependence on age-O fish relative to total landings (four

of the last six years) has increased the concern about "growth

overfishing" in the Atlantic menhaden fishery, a concept that refers

to the trade off between catching greater numbers of younger and

smaller fish or catching fewer numbers of older and larger fish.

The trade off depends both on the rate of growth of individual

fish and the natural mortality rate of the stock. This concept will

be discussed in greater detail in the section on yield-per-recruit

analyses.

Figure 3

Contribution in percent of total numbers of Atlantic menhaden landed by age group for fishing years 1955-84.

100

80

AGE

I- 60 r z

w

u

a:

w . 0 40 a.

20

IZ

w

U

a:

w

a.

FISHING YEAR

Age

Figure 4

Contribution in percent of total numbers of Atlantic menhaden

landed in the North Carolina fall fishery (Area 5) by age group

for fishing years 1970-84.

5
IZ

W

(,)

CI:

w

c..

Figure 5

Contribution in percent of total numbers of Atlantic menhaden

caught in the South Atlantic (Area 4) by age group for fishing

years 1970-84.

FISHING YEAR

Age

Recruits to age-I obtained from the second ("partial-quarterly")

and third (quarterly) sets of VPA's for 1955-81 year classes range

from 1.2 billion recruits in 1968 from the 1967 year class to 14.8

billion recruits in 1959 from the 1958 year class (Table 4). Recruitment was high for the 1956 and 1957 fishing years, exceptionally

high for the 1959 fishing year, and low for the 1960-71 fishing

years. Recruitment rose for the fishing years during the early

1970's, and has been generally high for fishing years since 1976,

averaging over 5.7 billion recruits to age-I. Recent high recruitment values would seem to indicate a sufficient number of potential spawners and good survival prior to recruitment to the fishery.

These implications will be discussed later in the section on

spawner-recruit relationships. Similar trends are noted in recruitment to age-0.5 (fin Table 4 indicates the factor by which landings

of age-O fish have been multiplied). The effect of the multiplicative

factor on estimates of recruitment to age 0.5 depends on the relative number of age-O Atlantic menhaden in the landings for the

year class (compare Table 4 with Figure 3). For instance, in 1961,

when almost no age-O fish were landed, no change is observed in

the estimated recruitment to age 0.5 with increasing multiplicative

factor,f. However, in 1979, when almost 40% of the menhaden

landed were age-O fish (f = 1.0), the estimate of recruitment to

age-0.5 increases by over 50% for the multiplicative factor, f,

equal to 4.0. Results would be expected to be similar for the 1984

year class.

Estimates of population size (based on age-I and older Atlantic

menhaden on I March) range from 2. I billion fish in 1968 to 16.9

billion fish in 1959 (Table 5 and Fig. 6). The population size for

the period 1976-82 averaged about 8.6 billion fish. This value is

similar to those for population sizes between 1955 and 1961 (excluding the very large population size present in 1959).

Population exploitation rates (u, based on age-I and older fish)

ranged from 30% to 51 % of the population removed by fishing

each year (Table 5). Since 1975, the population exploitation rate

has averaged 34% for age-I and older fish, which is less than the

average of 38% for 1955-82. Age-specific exploitation rates range

from 16% to 89% removal of an age class for the fully recruited

adult age classes (age-2 and older) (Fig. 7). Exploitation rates for

age-I Atlantic menhaden range from 13% to 40%, while the exploitation rates for age-O (based on recruits to age-0.5) ranged from

essentially 0% (in 1961) to 12% (in 1979). For fishing years

1955-81, an average 25% of age-l fish and 65% of age-2 and older

fish were taken by the fishery annually, with 30% and 20%, respectively, being lost to natural causes annually.

6

Table 4

Estimated number of Atlantic menhaden spawners that produced the year

classes 1955-84, estimated egg production from the spawning stock,

estimated numbers of recruits by year class at age-0.5 and age-I, and

estimated egg production by the recruits.

Spawnersa Recruits (109)

Age-0.5b

Year No. Eggs Eggs

class (109) (1012) f=1.0 f=1.5 f=2.0 f=4.0 Age-l (10 12 )

1955 1.89 214.0 787 829 871 1040 5.60 524

1956 1.37 148.5 899 9.01 9.03 9.11 715 119.0

1957 0.72 84.9 442 4.59 4.75 542 3.26 551

1958 0.55 58.1 18.62 18.68 18.73 18.98 14.77 195.3

1959 1.30 89.1 2.72 2.73 2.74 2.76 2.16 33.2

1960 0.79 765 3.79 3.83 3.87 403 2.96 15.6

1961 2.96 155.8 2.77 2.77 2.77 2.77 2.21 13.9

1962 1.29 106.6 2.84 287 2.90 3.01 2.22 114

1963 043 374 2.30 2.36 241 263 1.75 8.0

1964 026 214 276 2.93 3.10 3.77 1.94 196

1965 0.19 13.8 2.07 2.21 2.35 292 1.43 10.0

1966 0.12 76 2.88 306 3.25 3.99 2.00 12.9

1967 021 17.0 1.52 1.53 1.53 154 1.21 138

1968 017 12.9 2.32 241 2.50 2.85 1.71 12.6

1909 014 10.5 345 3.53 3.62 3.98 261 24.2

1970 015 11.7 1.75 1.76 1.78 1.83 1.38 5.2

1971 0.21 150 4.54 4.58 4.62 479 3.56 58

1972 0.30 25.7 356 359 3.62 3.73 2.79 7.7

1973 008 7.0 3.94 3.97 4.01 4.14 310 10.5

1974 0.09 5.7 5.20 5.39 5.57 6.30 386 148

1975 0.12 7.1 9.07 9.24 941 10.10 696 23.2

1976 0.16 8.1 6.90 7.06 7.22 7.86 5.25 234

1977 025 12.2 6.60 688 7.17 8.31 481 222

1978 0.57 19.5 5.96 622 648 7.53 4.34 142

1979 0.53 18.8 10.38 11.25 12.13 15.63 6.88 262

1980 0.64 26.0 6.18 6.23 6.28 649 4.85

1981 0.52 20.8 9.51 10.19 10.88 13.63 649

1982 0.80 19.5

1983 0.51 16.7

1984 0.70 25.9

aSpawners presenl on I December prior 10 the year 10 which the year class was

assigned (X.75 wilh X>I).

bFactor if) by which landings of age-O fish are multiplied in special virtual

populalion analyses (see text).

eNOl estimable (require data from 1985 and later fishing years).
Figure 6

Population total (age-I and older Atlantic menhaden) on 1 March and recruits to age-I for fishing years 1955-82_

FISHING YEAR

1956 1960 1964 1968 1972 1976 1980

18

16

'"0 14

x

rJ)

0::

UJ 12 10

::E

::l

Z 10

UJ

':::!

rJ)

z

0

<>::

...J

::l

ll.

0

ll.

0.80

0.60

0.40

z

0 0.20

<>::

I-

<5

...J 0 ll.

X

UJ

LL 0.80 0

UJ

I-

<>::

0::

Table 5

Annual estimates of Atlantic menhaden population size and catch in numbers

(age-J to maximum observed in millions), population exploitation rates (u),

landings in thousands of metric tons, effort in vessel weeks (VW), population

F, and proportion of age-O fish in landings as numbers.

Pop. Calch Calch Effon Pop. Landings

Ycar sizea (n) /I (103 MT) (VW) F Age 0/0-8

1955 6.846.1 2357.4 0.344 641.4 2748 0543 0.244

1956 8.192.4 3528.4 0.431 712.1 2878 0.736 0.010

1957 9.686.0 3212.1 0.332 602.8 2775 0.518 0.085

1958 7.012.4 2613.2 0.373 510.0 2343 0.603 0.039

195~ 16.866.6 5342.2 0.317 659.1 2847 0.489 0.002

1960 9.047.0 2702.9 0.299 5298 2097 0.454 0.026

1961 6.700.4 2598.1 0388 575.9 2371 0.636 b

1962 4.514.8 2048.3 0.454 537.7 2351 0.793 0.025

1963 3.581.0 1667.6 0.466 346.9 2331 0.824 0.055

1964 2.777.4 1426.5 0.514 2692 1807 0958 0.175

1965 2,631.5 1260.4 0.479 273.4 1805 0.859 0.165

1966 2.149.5 9912 0.461 219.6 1386 0.811 0.176

1967 2,598.5 977.2 0.376 193.5 1316 0.610 0.007

1968 2.097.3 993.7 0.474 2348 1209 0.846 o 134

1969 2.280.7 710.0 0311 161.6 995 0.477 0.182

1970 3.505.6 1381.5 0.394 259.4 906 0.650 0.015

1971 2.548.7 896.2 0352 250.3 897 0.559 0.075

1972 4,486.3 1663.8 0.371 365.9 973 0.590 0.029

1973 4.339.3 1787.4 0.412 346.9 1099 0.691 0.030

1974 4,465.3 1675.1 0.375 292.2 1145 0.608 0.159

1975 5,415.7 1863.7 0.344 250.2 1218 0.543 0.138

1976 8.963.8 3009.2 0.336 340.5 1163 0.526 0.084

1977 8.628.6 3189.1 0370 341.2 1239 0.597 0.132

1978 7.817.5 2627.8 0.336 344.1 1210 0.526 0.148

1979 7.278.2 2377.7 0.327 375.7 1198 0.508 0.386

1980 9.652.9 3244.0 0.336 401.5 1158 0.526 0.026

1981 8,421.6 2796.4 0.332 381.3 1133 0.518 0.298

1982 9.660.8 3061.6 0.317 382.4 948 0.489 0.036

1983 2977.7 418.6 995 0.245

1984 2253.8 326.3 892 0.365

'At stan of fishing year on I March (X .0).

bTrace (0.0001).

eNot eSlimablc.

FISHING YEAR

Figure 7

Estimates of annual rates of exploitation of Atlantic menhaden, ages 0-5,

7
Size-at-age and growth analyses _

where Lin!, k, and 10 are parameters to be estimated. The computer

program BGC3 (Abramson 1971) was used to obtain parameter

estimates for Eq. (2). This program employs a nonlinear regression

algorithm (Vaughan and Kanciruk 1982). Weight (WI' in grams) is

then estimated from the weight-length relationship expressed in the

linear form of the power function,

Estimates of length- and weight-at-age, summarized in Nicholson

(1975) and Smith et al. (1987), are needed for estimating fishing

yield, primarily from yield-per-recruit analyses. Estimates of

length-at-age are also used to test an hypothesis concerning

density-dependent growth (AMMB 1981) and to reconstruct potential egg production from spawners and recruits for use in developing spawner-recruit relations. Fork length (L" in millimeters) is

estimated from age (I, in years) on the basis of the von Bertalanffy

(1938) growth function,

Table 6

Weight-length regression parameters

for Atlantic menhaden, 1970-84 (In W = In a+b In L).

Year In a b ,2

1970 -11.7\2 315\ 0994

\97\ -11.436 3092 0.993

1972 -11.690 3\33 0.992

1973 -11.313 3.070 0.980

1974 -11.795 3.\56 0.988

1975 -11.908 3.\80 0.991

1976 - 12.419 3.279 0.99\

1977 -12.618 3.3\9 0.992

1978 -\2.36\ 3.270 0992

1979 -\2.498 3.296 0992

1980 -\2.474 3.293 0.993

\981 -\2.582 3.309 0992

\982 -11.689 3.\48 0.985

1983 -11.621 3.\25 0.992

1984 -11.554 3.\21 0.987

8

mean lengths-at-age are aligned by year class (or cohort) so that

resultant growth curves represent the growth of a year class

through its life span, rather than across several cohorts during a

single fishing year. Mean lengths are assumed to represent the

middle of the quarterly interval, so that age-X .125 is assigned for

the mean length of the first quarter and so forth for the remaining

quarters. Estimated parameters for the five NMFS fishing areas are

given for year classes 1965-81 (Table 7), and are used to estimate

fish length and weight at the start of each quarter by area (see

section on yield-per-recruit analysis).

Corresponding coastwide estimates of the von Bertalanffy

parameters were made for year classes 1965-81 by obtaining

weighted averages of mean lengths-at-age across the five NMFS

fishing areas (weighting based on catch in numbers-at-age for each

area as in Ahrenholz et al. 1987). For those instances when the von

Bertalanffy fitting procedure failed to converge, a linear regression

of length (L) on age (I) was used. These growth curves are used

only in the yield-per-recruit analyses, where they are appropriate

only for interpolation within the range of ages from which the

growth parameters were estimated. They are not appropriate for

extrapolating beyond the range of ages for which data were available.

The size of age-0.5 and age-0.75 Atlantic menhaden were found

by Ahrenholz et al. (1987) to be biased upwards. Therefore, we

deleted lengths at these ages when fitting the von Bertalanffy

growth equation to coastwide lengths-at-age for year classes 1965-

81 (Table 8) for development of estimates of spawners and recruits

as eggs (Table 4). In addition, we used fourth-quarter data from

fishing area 5, as did Ahrenholz et al. (1987), to obtain parameter

estimates for year classes 1955-64 (Table 8).

Estimates of annual weighted mean weights by age for Atlantic

menhaden in purse-seine catches were calculated to indicate potential trends in yield-per-recruit that could be expected from the

fishery (Fig. 8). These trends were affected by changes in fishing

patterns both geographically and seasonally, so that part of the

decline noted since 1970 is due to the shift of the center of fishing

southward to smaller fish of the same age. Part of this decline can

also be explained by the inverse relationship noted between firstyear growth of Atlantic menhaden and year-class strength (AMMB

1981; Reish et al. 1985). Ahrenholz et al. (1983) obtained significant correlations for recruitment to age-0.5 with mean length at

age-0.5 (Chesapeake Bay area) and with mean length at age-0.75

(North Carolina fall fishing area). Similar results have been obtained using data from the 1965-81 year classes, with 64% of the

variability in lengths at age-0.5 from Chesapeake Bay area explained by population size (Fig. 9a), and 25% of the variability in

lengths at age-O. 75 from North Carolina fall fishing area explained

by population size (Fig. 9b).

(3)

(2)

In W, = a + b In L, ,

L, = Linll - exp(-k(I-lo») ,

where a and b are estimated parameters, and the bias from transforming from a normal to a lognormal variate (Miller 1984) is

insignificant because of the small variance about the transformed

variate. Annual estimates of a and b for fishing years 1970-84 were

made (Table 6), with the percentage of variability explained by

each of these annual regressions ranging from 98.0 to 99.4%.

Estimates of a range from -11.3 to -12.6, and estimates of b

range from 3.1 to 3.3. Based on these results, the weighted averages of these parameters were used in the following analyses when

calculating weight from length (a = -12.1, b = 3.2).

Use of only coastwide estimates of mean length-at-age in size

and growth analyses is inappropriate in an analysis of yield-perrecruit because of the distribution of Atlantic menhaden along the

coast by age and size (Nicholson 1972, 1978b). Hence, mean

lengths-at-age are calculated directly from the port sampling data

by NMFS fishing area caught (e.g., North Atlantic, Middle Atlantic) and by season (or quarter, Table 2). These area-specific
Table 7

Area.specific von BertalanfTy parameters (includes 3rd· and 4th-quarter data from age-O fish)

for Atlantic menhaden, 1965-81. (These values are no/ suitable for general use-see text).

Year Year

class Lmf K '/0 n class Lm! K 'to n

Area I Area 4

1965 216.6 23.1 O' 5 1965 221.2 0.7641 -0.6596 8

1966 340.9 06286 -0.654 6 1966 27694.7 0.0011 - 3. 7288 7

1967 315.9 2.3476 \.1371 6 1967 109.0 34.7 O' 7

1968 334.1 0.9195 0.6251 5 1968 127.2 29.8 O' 8

1969 331.6 \.4831 0.7039 8 1969 75108.7 0.0006 -\.8791 9

1970 35\.4 0.2773 -4.2640 6 1970 272.5 0.3233 -1.8040 7

1971 310.3 1.3572 \.1158 9 1971 94.1 49.8 O' 10

1972 297.6 1.0889 06424 8 1972 249.5 \.0191 0.2356 8

1973 318.9 0.4255 -\.2752 10 1973 198.1 3.3924 0.7673 6

1974 322.6 0.3752 -\.1375 12 1974 286.8 0.4411 -0.5467 9

1975 467.9 0.0935 -4.9384 13 1975 55233.0 0.0004 -5.8115 10

1976 330.2 0.3432 -0.9397 13 1976 314.6 0.3054 -0.5076 12

1977 317.6 0.5483 0.1540 12 1977 227.0 0.7426 0.1026 9

1978 299.2 0.5053 -0.7047 13 1978 117.1 27.4 O' 12

1979 447.0 0.1078 -3.9287 10 1979 283.6 0.3159 -0.6564 14

1980 312.0 0.4756 -0.1\55 7 1980 222746.2 0.0002 -2.6669 II

1981 265.2 2.0023 \.4917 4 1981 276.8 0.4121 -0.3615 10

Area 2 Area 5

1965 313.2 1.0060 0.4384 6 1965 407.4 0.3017 -0.5882 10

1966 348.6 0.5701 -0.3618 7 1966 37\.7 0.4546 -0.1573 10

1967 353.5 0.4739 -0.5379 8 1967 382.3 0.4508 -0.0262 7

1968 429.0 0.1979 -2.7051 7 1968 163415.9 0.0004 -0.9768 8

1969 399.0 0.2903 -\.8364 9 1969 107.6 53.4 O' 8

1970 285.4 4.383 \.0415 7 1970 332.4 0.5331 -0.0235 8

1971 359.9 0.2831 -\.8545 9 1971 882.2 0.0814 -\.2732 6

1972 319.0 0.4460 -0.8359 9 1972 336.4 0.4772 -0.0614 6

1973 309.8 0.5135 -0.6848 II 1973 38\.8 0.2691 -0.5751 8

1974 277.0 0.9954 0.8215 10 1974 328.9 0.4079 -0.0904 8

1975 435.4 0.1351 -2.8239 12 1975 394.5 0.2149 -1.0058 9

1976 315.4 0.4103 -0.6078 II 1976 375.1 0.2332 -0.7452 9

1977 11246.7 0.0011 -17.4552 7 1977 35\.5 0.3118 -0.3058 9

1978 174.6 18.6 O' 8 1978 355.4 0.2575 -0.8781 10

1979 148.4 27.5 O' 7 1979 355.2 0.2682 -0.4681 10

1980 147.6 29.4 O' 7 1980 431.6 0.1814 -0.9713 9

1981 128.3 33.2 O' 7 1981 7522.8 0.0069 -1.3908 8

Area 3 Coastwide

1965 483.3 0.1686 -1.7049 II 1965 592.4 0.1292 -1.4512 18

1966 345.8 0.4604 -0.7233 II 1966 42\.7 0.2525 -0.9604 20

1967 429.7 0.2283 -1.3710 II 1967 502.6 0.1887 -0.9369 17

1968 477.3 0.1708 -\.9694 12 1968 1040.1 0.0539 -2.2117 18

1969 3628 0.4493 -0.7612 II 1969 393.6 0.3117 -0.8714 19

1970 292.6 0.8165 -0.5528 8 1970 36\.6 0.4248 -0.2902 17

1971 455.6 0.1898 -1.3816 10 1971 353.2 0.3701 -0.5432 19

1972 317.1 0.5361 -0.1293 10 1972 317.8 0.5630 -0.0034 18

1973 472.3 0.1779 -1.0721 1\ 1973 345.2 0.3607 -0.4743 22

1974 104194.1 0.0004 -2.4294 14 1974 348.3 0.3059 -0.7790 24

1975 353.0 0.2084 -1.3885 13 1975 392.1 0.2018 -\.1137 24

1976 252.8 0.4815 -0.7961 13 1976 359.2 0.2774 -0.4864 23

1977 279.0 0.3541 -\.0517 12 1977 389.9 0.2379 -0.6938 21

1978 225.2 0.6874 -0.6645 10 1978 360.5 0.2490 -0.8338 22

1979 245.2 0.3679 -1.4871 II 1979 520.9 0.1160 -1.3361 21

1980 215.5 0.8646 -0.2870 10 1980 1302.1 0.0371 -\.9474 17

1981 292.8 0.2760 -1.6498 10 1981 90.8 43.4 O' 15

'Von Benalanffy model did nol converge. MAREA input obtained from L = a +bl, I in years-of-age;

a under Linf• b under k. and 0 under (0'

9

Table 8

Estimated von BertalanfTy growth parameters for Atlantic

menhaden, year classes 1955-81 (general use estimates).

Year n

class Lin! K to (means)

1955a 339.49 0.5401 0.1234 7

1956 343.67 0.4598 0.0245 7

1957 324.49 0.6260 00707 7

1958 363.73 0.3637 -0.1163 7

1959 355.64 0.3631 -0.4709 6

1960 354.69 0.4009 -0.1481 5

1961 340.52 0.4514 -0.3506 5

1962 376.35 0.4012 -0.1122 5

1963 370.04 0.3494 -0.4652 6

1964 33\.17 0.6138 00606 5

1965b 42\.17 0.2876 -0.4345 16

1966 371.75 0.4144 -0 1762 18

1967 377.20 0.4472 0.1676 16

1968 526.34 0.1679 -\.0108 16

1969 359.98 0.4923 -0.1047 17

1970 338.67 0.5948 0.1385 16

1971 344.49 0.4253 -0.2948 18

1972 317.80 0.5630 -0.0034 18

1973 334.14 0.4253 -0.1985 21

1974 326.53 0.4256 -0.1759 22

1975 380.Q3 0.2250 -0.8858 23

1976 339.80 0.3393 -0.1814 22

1977 361.79 0.3028 -0.3265 20

1978 362.65 0.2440 -0.8696 21

1979 54763 0.1062 -1.4349 20

1980 894.42 0.0598 -\.6918 16

1981 764.67 0.0818 -1.2050 13

aYear classes 1955-64 represented by filled values for 4lh

quaner, Area 5 (see Ahrenholz et al. 1987).

bYear classes 1965-78 represented by filled values for weighted

quanerly mean lenglhs.
600...----------------------,

o 1956 1960 1964 1968 1972 1976 1980 1984

YEAR

Figure 8

Weighted mean annual weight of purse-seine landed Atlantic menhaden,

ages·l, 2, and 3, for fishing years 1955-84.

I I

r 2 =0.247

r 2 =0.643

180

E 160

.5

J:

.... 140

"

Z

W

...J

120

100

160 ,.,.

E

.5

J: 140 ....

"

Z

W

...J 120

100 2 4 6

I

8 10

(8)

(b)

12

RECRUITS TO AGE 0.5 (billions)

Figure 9

(a) Estimates of year·c1ass recruitment at age-O.5 against mean length at age·O.5

(third quarter) for Atlantic menhaden caught in Chesapeake Bay area.

(b) Estimates of year-class recruitment at age·O.75 against mean length at age·

0.75 (fourth quarter) for Atlantic menhaden caught by North Carolina fall

fishery.

10
Surplus production models _

Surplus production models are typically used to obtain estimates of

maximum sustainable yield (MSY) from yield and fishing-effort

data (Vaughan et al. 1984). Ricker (1975) defines MSY as "[t]he

largest average catch or yield that can continuously be taken from

a stock under existing environmental conditions. (For species with

fluctuating recruitment, the maximum might be obtained by taking

fewer fish in some years than in others.)" When using surplus

production models, catch-per-unit-effort is assumed to be proportional to population abundance and fishing effort proportional to

fishing mortality. Theoretically, plotting catch against fishing effort should give a dome-shaped curve (Vaughan et al. 1984),

which is not the case with Atlantic menhaden data (Fig. 10). When

relating fishing effort (E) to the instantaneous fishing mortality rate

(F), the catchability coefficient (q) is assumed to be constant; i.e.,

F = q E , (4)

0.0008

0.0006

0.0004

0.0002

1956 1960 1964 1968 1972 1976 1980 1984

FISHING YEAR

Figure 11

Catchability coefficient (fishing mortality per vessel-week) of Atlantic menhaden at age-I and older for fishing years 1955-82.

Figure 12

Estimates of the Atlantic menhaden population catchability coefficient (q) for

fishing years 1955-82, ploUed against the estimated population size (excluding

age-O fish).

73

'71 "72

·66

.64 • 74 8.2

POPULATION NUMBERS (millions)

·77 .75 81·. '80

79 78 76

20000

·59

10000 15000

61.

5'8 ·56

·60 '55 '57

5000

·70

63' '62

68'

0.0008

Iz 0.0007 w

<3

u:: 0.0006 u..

w

0

() 0.0005

>- I- 0.0004 :J

m<>: 0.0003 I

()

I-

<>: 0.0002 ()

0.0001

0

where the unit of fishing effort, E, is defined as vessel-weeks for

Atlantic menhaden. As noted in Ahrenholz et al. (1987), the above

unit of fishing effort, referred to as nominal effort, is not a reliable

measure of fishing mortality. A unit of fishing effort that is a

reliable measure of fishing mortality is referred to as "effective"

effort. The difficulty in directly obtaining a reliable unit of fishing

effort results from the schooling nature of menhaden, since menhaden and other schooling clupeids are more susceptible to fishing

effort than non-schooling species [see discussion of "dynamic aggregation process" in Clark and Mangel (1979)].

To demonstrate that the population catchability coefficient, q,

for Atlantic menhaden is not constant but dependent upon the

population size, it was estimated by solving Eq. (4) for q (=F/E)

for each fishing year from 1955 through 1982 (Fig. II) and compared with the population size for the same fishing year (Fig. 12).

To calculate the population instantaneous fishing mortality rate

(F), it was first necessary to compute the population exploitation

rate (u) by comparing numbers caught in a fishing year (for all ages

1-8) with the population size (for all ages 1-8) on I March for that

year (Table 5). The population F is then calculated iteratively from

NOMINAL FISHING EFFORT (vessel-weeks)

Figure 10

Atlantic menhaden landings (1000 metric tons) vs. nominal fishing effort

(vessel-weeks) for fishing years 1940-84.

'.

where u and M (=0.45/year) are known. Estimates of q range from

0.OOOI7·year·vessel-week in 1959 when the population size was

16.9 billion (age-I and older fish) to O.OOOn·year·vessel-week in

1970 when the population size was 3.5 billion. As noted in Ahrenholz et al. (1987), there is a pronounced inverse relationship between the catchability coefficient and population size (Fig. 12).

Furthermore, the historical trend that they noted continues to be

evident with the addition of three more years of data; that is, there

appear to be two functional curves, 1955-69 and 1970-82. As

described in Ahrenholz et al. (1987), the catchability coefficient

increased beginning in 1959 with decreasing population size and an

increasingly more efficient fleet due to various innovations. With

increasing population size following 1971, the catchability coefficient declined to a level over twice that in 1959, which reflects the

greater efficiency of the fleet in the 1970's and early 1980's compared with the 1950's and 1960's.

F = u (F+M)/(I - exp(-(F+M») (5)

the following equation:

1500 2000 2500 3000

I

1000

800

;: 700 :::E

0

0 600 0

(f) 500 (f)

<l:

:::E 400

0

iii

300

I

() 200 I-

<l:

() 100

500

II
To adjust nominal fishing effort to account for variations in q,

we calculated a mean value of q for the period 1955-82 (qa) and

adjusted nominal effort (E) so that q is made constant (qa); i.e.,

where E' is now a unit of "effective" fishing effort.

The computer program PRODFIT (Fox 1975), which accounts

for nonequilibrium conditions, is used to estimate parameters for

different surplus production models depending on the value of m

in the following equation:

In(EGGS) = 0.315 + 0.0176 L , (8)

Figure 13

Catch of Atlantic menhaden in thousands of metric tons against estimates of

population F for fishing years 1955-82. Solid curve is the parabolic (Schaefer)

production model, and dashed line is the Pella-Tomlinson generalized production

model.

where EGGS equals thousands of eggs produced per female, and

L equals estimated fork length (mm). Mean length-at-age for the

third quarter (Table 10) was calculated from the von Bertalanffy

growth curves given in Table 8. To fill in missing values, we used

either the observed mean length-at-age for the fourth quarter or the

means from the adjacent three year classes. The expected egg

production per female of a given age was calculated using Eq. (8)

and the lengths given in Table 10. Assuming a 50:50 sex ratio,

multiplying population numbers-at-age (Table 9) by one-half, the

expected egg production per female-at-age gives the potential egg

production per individual-at-age (Table II). Summing across ages

for the same fishing year gives the numbers of spawners as potential eggs (Table 4). Summing across ages for the same year class

(or cohort) gives the numbers of recruits as potential eggs; i.e.,

recruits as eggs for a year class are calculated from the number of

eggs estimated as actually produced by that year class during its

lifetime (Table 4). The number of eggs produced by a year class

does not differ, whether referring to recruits to age-0.5 or age-I,

or referring to recruits based on the increasing multiplicative

factor.

An important question in population dynamics and in fisheries

management concerns the degree of dependency between the number of spawners and the number of subsequent recruits to the stock.

If there is no such dependency, then there is little that a manager

can do to control the number of recruits (and hence future stock

sizes) other than to assure sufficient spawners to produce subsequent recruits to the population and to preserve the quality of the

habitat utilized by prerecruit larvae ·and juveniles. If there is a

quantifiable relationship between spawners and recruits, then management can be designed to maximize the landings based on this

relationship. Such a relationship was examined using the Ricker

(1954) model (Schaaf and Huntsman 1972; Nelson et al. 1977;

Schaaf 1979; Reish et al. 1985; Ahrenholz et al. 1987).

Estimation of the number of recruits to age-O (for four multiplicative factors:! = 1.0, 1.5,2.0, and 4.0) and to age-I has been

described in the section on virtual population analyses (Table 4).

Estimation of spawners follows the description given in Ahrenholz

et al. (1987). The number of mature spawners for each fishing year

is given by age (Table 9), where peak spawning is assumed to

occur during the fourth quarter (between I December and 29

February) of each fishing year (hence the use of age-X .75). The

total number of spawners for each recruitment year is given by the

sum from age-2.75 through age-8.75 (Table 4).

Indices of spawners and recruits have also been estimated as

potential egg production. Estimates of egg production as a function

of fish length were obtained from the equations used by Nelson et

al. (1977) which were derived from data in Higham and Nicholson

(1964). Ahrenholz et al. (1987) used the same expression:

Spawner-recruit relationships _

(7)

(6)

1.0 1.2 1.4

1\

\

"\'pella-Tomlinson

'/

"-,

"'-'

................. ,-

0.8

,

,

,

\ Schaefer

\/

\

\

POPULATION F

0.6

E'=Eqlqa,

0.4

U=(A +BE')I/(m-l) ,

500

I- 400 ::;:

0

0

300

ui

Cl

z

0

z

«

..J

where U is catch-per-unit-effort, and A , B, and m are parameters

to be estimated. The generalized production model of Pella and

Tomlinson (1969) is obtained when m is allowed to be estimated

freely. However, when m is forced equal to 2.0, the Schaefer

model (Schaefer 1954, 1957) is obtained; when m is forced equal

to 1.0, the GompeI1Z model (Fox 1970) is obtained. The program

PRODFIT also allows the analyst to enter the number of significant

age classes to be entered in the analysis (i .e., this is used in

estimating parameters under nonequilibrium conditions). Those

age classes contributing at least 10% to the landings in numbers

served as the basis for determining the number of significant age

classes for each fishing year in the analysis (1955-82). Estimates

of MSY range from 448.9 kmt when m is forced equal to 2.0

(Schaefer model) to 459.3 kInt when m is estimated freely (1.59;

Pella-Tomlinson model).

Ahrenholz et al. (1987) suggested a more direct method by

utilizing estimates of population F for the independent variable

instead of adjusting fishIng effort. Using this approach, estimates

of MSY range from 455.4 kInt at F = 0.53 when m is forced equal

to 2.0, to 487.2 kInt at F = 0.42 when m is estimated freely (1.33)

(Fig. 13). Since 1975, population fishing mortality rates have

averaged 0.53 (Table 5) and observed landings have averaged 356

kIn!.

With MSY estimates ranging about 470 kInt, one would expect

that this level of landings could be obtained with current levels of

vessel and plant capacity. However, changes in fishing patterns

since the 1950's and loss of reduction plants primarily to the north

restrict the industry's ability to attain MSY. The next section

provides some insight into whether there is sufficient spawning

stock to guard against recruitment failure or whether there are

sufficient numbers of recruits to sustain the stock.

12
Table 9

Estimates of spawning stock size (103) for Atlantic menhaden, 1954-81 seasons, at start of 4th

quarter (resultant year class is year +I).

Age in years

Year 2.75 3.75 4.75 5.75 6.75 7.75 8.75

1954" 717,088.4 976.389.5 141.718.5 43,441.7 10,451.6 2,689.0

1955 750.544.7 218,095.6 329.260.0 52,045.7 13,751.9 3,463.6 931.0

1956 284,846.4 213,233.7 103,337.2 101,485.8 12.174.1 3,589.2 593.9

1957 315,980.1 98,471.5 72,620.9 35,778.3 21,458.0 1,817.2 1,016.6

1958 1,060,636.0 141,757.4 45,782.9 29,083.3 11,453.0 6,505.8 433.1

1959 330,9780 366.103.3 63.751.7 19.264.4 7,895.4 2,366.1 1,973.7

1960 2,660.856.3 144,374.9 124,950.2 19.0069 5,398.5 1.352.8 866.0

1961 433,025.0 736,605.6 69.969.6 46,336.2 5.792.6 1.203.7 153.2

1962 216,040.7 84,780.9 98,030.7 19,041.5 6,568.7 1,250.8 200.0

1963 173.767.0 43,462.7 18,212.7 15,720.6 2,790.7 985.3 197.9

1964 151,144.3 26,765.7 4,380.3 2,345.2 1,118.1 177.3 190.0

1965 101,328.0 12,859.4 1,425.9 176.7 265.5 56.4 25.2

1966 194,344.5 18,778.4 1,407.3 18.6 25.4 80.3 7.0

1967 133,382.8 36,082.5 2,859.1 210.4 2.2 0 0

1968 121,343.1 16,252.6 1.270.9 199.1 10.0 0 0

1969 124,839.7 26.039.2 772.1 41.5 1.2 0 0

1970 174,942.4 33,984.2 5.670.2 55.0 0 0 0

1971 263,705.9 28,407.7 3,879.2 446.6 0 0 0

1972 60,802.2 13,899.5 699.9 620.1 0 0 0

1973 84,517.1 3.904.4 2,005.3 125.9 0 0 0

1974 106,351.6 10,127.0 3443 142.6 0 0 0

1975 144,107.8 15,026.2 617.9 22.8 7.4 0 0

1976 214,064.8 37,623.1 2,234.4 162.0 0 0 0

1977 507,498.8 58,2555 5,320.5 130.4 8.0 0 0

1978 429,083.4 87,302.1 13.136.7 732.1 0 0 0

1979 470,146.6 139.849.9 30,565.0 2,486.7 11.6 0 0

1980 382,506.6 93,321.7 32.021.3 7,390.2 727.9 0 0

1981 751,194.3 36.971.6 8,452.4 889.5 1,911.0 0 0

1982 361,689.3 138,577.5 12.155.3 1,319.1 127.3 948.0 0

1983 507,265.7 126.378.8 61,097.6 2,375.1 59.6 0 604.5

'Derived from I Mareh 1953 estimale (Ahrenholz et al. 1987).

bNol eSlimable.

Spawners as numbers of adults on I December (Table 4) ranged

between 76.0 million in 1972 (producing the 1973 year class) and

2,956.8 million in 1960 (producing the 1961 year class). Spawners

as potential eggs on I December ranged between 5.7 trillion eggs

in 1973 (producing the 1974 year class) and 214.0 trillion eggs in

1954 (producing the 1955 year class). Low spawning stock size

was the rule from 1964 to 1977, and a medium-to-high spawning

stock size from 1955 to 1963 and 1978 to 1984. High recruitment

in 1958 resulted in large spawning stocks in 1960 (as age-2 fish)

and in 1961 (as age-3 fish). High recruitment in 1952 and 1956

resulted in large spawning stocks (as age-2 fish) in 1954 (producing the 1955 year class) and 1958 (producing the 1959 year class).

During the late 1950's and early 1960's, the contribution of late

age-2 spawners to the spawning stock was highly variable, ranging

between 35% and 90% in numbers and between 20% and 75% as

eggs (Fig. 14). Since the mid-1960's, the contribution of late age-2

spawners to the spawning stock has averaged about 80% in numbers and about 70% as eggs.

Parameters of the Ricker model were estimated by nonlinear

regression from the following equation:

R = as exp( -bS) , (9)

13

where R equals recruits (numbers at age-0.5 or age-lor potential

eggs), S equals spawners (number of adults or potential eggs), and

a and b are parameters to be estimated. Six regressions were

calculated from the data presented in Table 4. Five regressions

were calculated using spawners in numbers versus the five indices

of recruits in numbers (four multiplicative factors for recruits to

age-0.5 and also recruits to age-I). An additional regression was

calculated with both spawners and recruits as potential eggs. In all

cases, parameter estimates for both a and b were significantly

greater than zero, indicating a statistically significant relationship.

These parameters do not vary appreciably with increasing multiplicative factor based on recruits to age-I. Parameter a increases

from 29 to 32, and parameter b increases from 0.0014 to 0.0015

while increasing the multiplicative factor from I to 4. Depending

on the level of the multiplicative factor if), estimates of maximum

recruitment to age-0.5 obtained from spawner-recruit relations

based on spawners and recruits to age-5 in numbers range from 7.6

if = I) to 9.0 if = 4) billion menhaden. This range of estimates is

similar to estimates of mean recruitment to age-O for the period

1976-81 , ranging from 7.6 if = 1) to 9.9 if = 4) billion menhaden.

Increasing the number of age-O menhaden presumed killed (increasing!), results in an increase in the estimated fishing mortality

rate for age-O menhaden during the third and fourth quarters and in

the estimated recruits to age-0.5 (but not age-I).
Table 10

Estimated mean length-at-age for Atlantic menhaden spawning stock by year

(year class produced is tabular year +I).

Age in years

Year 2.75 3.75 4.75 5.75 6.75 7.75 8.75

1954' 264.3 299.3 309.5 315.8 318. I 327.8

1955 268.4 2970 306.5 3168 321.0 327.8 338.0

1956 267.2 297.8 307.8 312. I 312.7 326.2 315.0

1957 257.3 303.2 314.2 318.5 320.5 326.0 340.0

1958 245.5 291.6 314.8 3~2.2 3296 331.0 341.0

1959 263.9 2817 311.6 323. I 327.4 329.5 341.0

1960 235.5 292.1 304.5 323.2 328.3 335.3 342.0

1961 245.2 274.6 307.2 319.0 330.0 334.4 33~.6

1962 243.7 278.8 301.8 315.2 328. I 334.0 338.6

1963 256.3 280.4 302.2 320.7 3195 333.8 336.3

1964 257.0 287.0 304.9 318.5 333.8 321.8 3375

1965 249.7 269.4 306.5 321.4 3298 342.9 323. I

1966 2676 2852 322.8 3188 332.4 337.7 349.3

1967 252.6 296.8 310.2 340.5 326.7

1968 261.2 2948 312.5 3279 352.4

1969 258.3 298.7 326.4 321. I 340.3

1970 246.4 301.2 323.5 350.1

1971 2717 289.7 328.6 3399 - 1972 267.0 306.0 326.2 346.1

1973 250.1 299 I 327.0 357.2

1974 250.4 2828 316.9 339.8

1975 238.8 279.4 304.2 326.6 347.7

1976 232.5 271.8 295.9 318.1

1977 212.3 265.1 293.4 3053 327.3

1978 214. I 246. I 286.4 307.5

197') 219.2 250.3 273.1 300.3 316.7

1980 212.7 256.5 276.0 294.6 309.4

1981 196.4 245.2 284.0 294.4 311.8

1982 208.5 231.8 270.6 304.3 307.4 325.6

1983 211.3 2483 263.6 290.6 319.3 336.5

'Estimated mean lengths-at-age for years 1954-64 from Ahrenholz et aL (1987).

Table II

Potential egg production (1012) by year, 1954-83, for Atlantic menhaden

by age (resultant year class is year +I).

Age in years

Year 2.75 3.75 4.75 5.75 6.75 7.75 8.75

1954 51.46 129.74 22.53 7.72 1.93 0.59 0

1955 57.90 27.83 49.68 9.41 2.68 0.76 0.24

1956 21.51 27.59 15.95 16.89 2.05 0.77 0.10

1957 20.05 14.01 12.54 6.67 4.14 0.39 0.28

1958 5468 16.45 7.99 5.78 2.59 1.51 0.12

1959 23.59 35.69 10.52 3.89 1.72 0.53 0.55

1960 115.03 16.90 18.19 3.85 1.19 0.34 0.24

1961 22.20 63.37 10.68 8.71 1.32 0.30 0.04

1962 10.79 7.85 13.61 3.35 1.45 0.30 0.04

1963 10.83 4.14 2.55 3.04 0.53 0.24 0.05

1964 9.54 286 0.64 0.44 0.27 0.Q3 005

1965 5.62 1.62 0.22 0.03 0.06 0.Q2 0.01

1966 14.78 1.95 0.28 . 001 002 . 1967 7.79 459 0.46 006 · 0 0

1968 8.25 2.00 0.21 0.04 · 0 0

1969 8.06 3.42 0.16 001 · 0 0

1970 9.16 4.69 1.15 0.Q2 0 0 0

1971 21.56 3.19 0.86 0.12 0 0 0

1972 4.58 2.08 0.15 0.19 0 0 0

1973 4.72 0.52 0.43 0.05 0 0 0

1974 5.98 1.01 0.06 0.04 0 0 0

1975 6.60 1.41 0.09 0.01 · 0 0

1976 8.78 3.08 0.28 0.Q3 0 0 0

1977 14.58 4.24 0.64 0.Q2 · 0 0

1978 12.73 4.55 1.39 0.1 I 0 0 0

1979 15.26 7.84 2.56 0.34 · 0 0

1980 11.07 5.84 2.82 0.90 0.12 0 0

1981 16.32 1.90 0.86 0.1 I 0.32 0 0

1982 9.72 5.61 0.97 0.19 0.02 0.20 0

1983 14.23 6.84 4.33 0.27 0.01 0 0.15

'Trace «0.005).

100

Numbers

()

0 80 1\

l- 1\

m "\ /\ 1

0 / / \ 1 , 1

Z I \ 1 ,

, I

ZC\j 60 I V ,I I

~I I

<w I

c..o I

m< / ...."E99S l1..1- 40

0< I

I I

l- I I I

Z I II

W 20 t' ()

a:

w

c..

1956 1960

YEAR

Figure 14

Contribution of lale age-2 spawners (%) to total spawning stock (numbers) and to total egg production (eggs) of Atlantic menhaden for fishing years 1955-84.

14
'58

14

Yield-per-recruit analyses _

The yield-per-recruit approach compares the rates of growth and

mortality (natural and fishing) to determine whether the same yield

is obtained from the fishable population as can be given the observed number of recruits. Yield-per-recruit is simply the expected

yield in biomass from a year class or cohort (surviving fish from

all spawning that occurs in a given year) during its fishable life

span divided by the initial size of the cohort in numbers (i.e.,

recruits).

The computer program employed in this analysis (MAREA,

Epperly et al. 1986) was modified from a multiple-gear extension

(MGEAR, Lenarz et al. 1974) of the Ricker-type yield-per-recruit

model to accommodate a multiple-area fishery, and utilizes areaspecific estimates of growth (based on von Bertalanffy growth

equations sununarized in Table 7) and fishing mortality rates obtained from virtual population analysis. Ricker (1975) subdivided

the exploited phase into a number of segments during which mortality and growth rates can be assumed constant. Ricker's approach

permits instantaneous natural and fishing mortality rates to vary

during the fishable life span and permits a general growth pattern

to be used. Total equilibrium yield-per-recruit is then obtained by

summing the catches in each segment over the total number of

segments in the fishable life span.

Several assumptions inherent to yield-per-recruit modeling

(Vaughan et al. 1984) are accounted for in this analysis. First,

although the entire Atlantic menhaden stock is included in our

analysis, the computer program MAREA permits the estimation of

area-specific yield-per-recruit. Second, the poor relationship of

spawners to recruits suggests that mortality is relatively independent of population density and will not significantly impact on our

yield-per-recruit analysis. Finally, the use of the multiplicative

factor to increase numbers of age-O fish, so as to adjust for those

age-O fish killed but not landed during the purse-seine operation,

will in part account for the lack of perfect retention by fishing gear

above a critical size or age (knife-edge selection).

The end product of a yield-per-recruit analysis for fisheries

management is an isopleth diagram which presents the yield-perrecruit for different ages at entry to the fishery and instantaneous

fishing mortality rates (F or F -multiples). An example is shown for

estimated growth and mortality rates for the 1981 fishing year (Fig.

16). Yield-per-recruit for this fishing year is 46.0 g with an age at

entry of 0.5 years and F multiple of 1.0/year (Table 12). A goal of

the fishery manager from a biological perspective is to maximize

the yield-per-recruit for a fishery, while allowing sufficient recruitment to maintain stock. When natural mortality is large compared

with the growth rate of an individual fish, then the cohort biomass

decreases with time, and fish should be caught at a relatively young

age. Conversely, when natural mortality is small compared with

the growth rate of an individual fish, then the cohort biomass

increases with time, and the age-at-entry to the fishable stock

should be delayed. Usually the rate of growth declines with age so

that there is an intermediate age such that cohort biomass is at a

maximum. The isopleth diagram permits a comparison of the total

yield from fewer, larger fish to that from more, smaller fish based

on the same number of recruits to the year class. Hence, the

manager may consider various strategies for attaining maximum

yield-per-recruit by altering the age-at-entry or the instantaneous

fishing mortality rate.

Estimates of yield-per-recruit for Atlantic menhaden have been

calculated using MAREA for the fishing years 1976-81 (the years

1976-78 have been averaged to permit comparison with estimates

R= 28.9S exp(-1.4S)

R,S in billions

,55

78

71

6,2

2 6,664 '59

'68'63

,65

'70

1 67

SPAWNERS (billions)

'57

3 ' 73 '60

'72

89

6

5

O~-~--~--+---~-~ o 5

w

(!)

<

o

en

5

a:

()

w

a:

7 75

15,....-------------........,

As illustrated in Fig. 15 for the Ricker curve based on spawners

in numbers and recruits to age-I, considerable scatter (or unexplained variability) remains due to environmental conditions or

measurement error. Given the scatter evident from these regressions, their use is of limited value; e.g., not useful for predicting

future absolute population sizes. However, these relationships are

statistically significant, so that the number of future recruits does

depend to some extent upon the size of the spawning stock which

produced them, consisting primarily of late age-2 spawners since

the late 1960's (Fig. 14).

Hence, although recruitment has been high since the late 1970's,

it potentially depends largely upon environmental conditions (as

evidenced in part by the unexplained scatter in Fig. 15) which are

usually beyond the control of management. To the extent that

recruitment does depend upon the spawning stock, the dependency

has rested since the late 1960's primarily on late age-2 spawners.

The concern of management is that several poor environmental

years leading to several poor recruitment years could put the Atlantic menhaden population at risk. Thus, there is need to increase

the proportion of older fish (age-3 and older) in the spawning

stock.

Figure IS

Numbers of Atlantic menhaden recruits (R, in billions) plotted against numbers

of spawners (5, in billions) for year classes 1955-81. Curve represents the fitted

Ricker function.

15
Figure 16

Overall yield-per-recruit of Atlantic menhaden under current conditions (Fmultiple of 1.0 and age-at-entry of 0.5) using average fishing mortality values by

quarter for the 1981 fishing season.

60-

80-r-----------,...

Table 13

Yield-per-recruit from the Atlantic

menhaden fishery for fishing years

1976-81 and by multiplicative factor

increasing the number of age-O menhaden assumed caught or killed by

the purse-seine neet.

Multiplicative factor

Fishing

year 1.0 1.5 20 4.0

1976-78 58.6 57.3 56.1 521

1979 530 50.8 48.9 43.2

1980 53.8 53.6 53.4 52.5

1981 45.9 44.4 43.0 38.8

by Ahrenholz el al. 1987). During these fishing years, yield-perrecruit ranged from 46 g in 1981 to 59 g for Ihe period 1976-78.

In general, yield-per-recruit increases wilh increasing age-at-entry

up to age-3 fish. Greater yield-per-recruil would be obtained for an

F-mulliple of 0.6 (60% of fishing mortality rate for that fishing

year) with an age-al-entry of 0.5 years than at the current levels of

F and age-at-entry. Maximum yield-per-recruit for the range of

ages-at-entry and F -multiples given occurs at age-3 and an Fmultiple of 1.8. Fishing year 1979 is an exception to these general

statements. Gains from increasing the age-at-entry to 1.0 year

(eliminate the harvest of age-O fish) range from 0.9% in 1980

(when very few age-O fish were landed; Fig. 3) to 11.1 % in 1979

(when record numbers of age-O fish were landed). Changes in

yield-per-recruit are more variable when reducing fishing mortality

by 40% (i.e., F -mulliple=0.6), ranging from a loss of 0.2% in

1979 to a gain of 9.3% in 1981.

Yield-per-recruit declines with increasing numbers of age-O

menhaden killed by the fishing fleet compared with estimated as

landed (mulliplicative factor, f) (Table 13). However, greater

gains from increasing age-at-entry to the fishable stock are available than suggested in Table 12. When large numbers of age-O

menhaden were landed in 1979 and 1981 (Fig. 3), the decline in

yield-per-recruit with increasing multiplicative factor was most

pronounced. When few age-O menhaden were landed in 1980, the

decline in yield-per-recruit with increasing multiplicative factor

was insignificant (53.8 to 52.5). Changes in availability of age-O

menhaden can vary significantly from year to year, depending on

the timing of juvenile migrations out of nursery areas in the late

fall. Hence, gains in yield-per-recruit from raising the age-at-entry

to the fishable stock will also vary significantly from year to year.

A series of MAREA computer runs was made for each fishing

year from 1970 through 1981. The decline in yield-per-recruit

(Fig. 17) since 1970 can be attributed largely to a comparable

decline in the average weight of fish landed during this period (Fig.

7). The decline of the Atlantic menhaden fishery in the North and

Middle Atlantic areas and increased importance of fishing farther

south has led to an increased dependence on younger and smaller

fish (Fig. 8). Especially important is the increased dependency on

age-O fish in the North Carolina fall fishery (Fig. 4).

-60

-80

~~-"-40

--------- -20

40-

Table 12

Estimates of yield-per-recruit for Atlantic menhaden for the

years 1976-81 by age-at-entry to the fishery and F -multiple. For

each year yield-per-recruit given in grams for actual conditions

(age-at-entry = 0.5; F -multiple = 1.0); remaining values are

percent change from yield-per-recruit estimates.

F-multiple

Age-alenlry 0.2 0.6 1.0 1.4 1.8

Mean 1976-78 fishing years

0.5 -13.3 +6.0 58.62 g -6.2 -11.2

1.0 -12.6 +9.2 +4.9 +0.1 -3.8

2.0 -11.8 + 15.6 + 15.0 + 13.1 +11.6

3.0 -21.8 +21.1 +295 +31.9 +32.7

1979 fishing year

0.5 -320 -02 53.04 g -4.6 -97

1.0 -31.1 +6.1 +11.1 + 10.2 +8.1

2.0 -31.9 +8.8 + 16.9 + 18.4 + 18.4

3.0 -49.7 -72 +7.7 + 14.4 +18.0

1980 fishing year

0.5 -18.2 +4.1 53.84 g -5.5 -10.2

1.0 -18.1 +4.7 +0.9 -4.4 -8.9

2.0 -17.0 + 13.0 + 14.3 +130 + 11.7

3.0 -27.6 + 14.3 +24.8 +28.7 +30.6

1981 fishing year

05 -3.3 +9.3 45.95 g -73 -12.6

1.0 -1.8 + 15.2 +8.6 +3.4 00

2.0 -1.5 + 18.4 + 12.7 +7.6 +4.1

3.0 -2.4 +36.4 +40.6 +41.0 +41.0

16

'1Q~ /

'11' ":?

1-1'-9 'J..~

)- ...~' ':'----,-----,---,.-.----"""1.-.-"-.-...--1

0.2 0.6 1.0 1.4 1.8

F-MULTIPLE

5

a::

u

w

a::

a::

w

ll.

o

...J

W

>=
110

Management implications _

the great importance of late age-2 spawners to the spawning stock

(Fig. 14) they suggest that increasing the number of older (age-3 +)

spawners would aid in guarding against a possible stock collapse

brought on by heavy fishing during a period of poor recruitment.

While parameters obtained from the Ricker model for spawners

and recruits to age-0.5 vary little in numbers with increasing multiplicative factor, estimated recruits to age-D.5 range from 7.6 to

9.0 billion fish. When multiplied by the average coastwide yieldper-recruit (1976-81) with an age-at-entry of 0.5 (54.8-48.5 g.)

(Table 13), a rough estimate of yield from recent cohorts ranges

from 416.2 to 436.3 kmt, depending on the level of the multiplicative factor. Similarly, multiplying mean recruitment for the same

period (1976-81) by average coastwide yield-per-recruit provides

a range in estimated yield of 415.7 to 480.6 kmt. The range of

MSY estimates from the surplus production approach (450 to 490

kmt) is slightly greater than the range in estimated yields based on

maximum recruitment from the spawner-recruit relationships, and

overlaps the range based on the mean of recent recruitment. The

upper end of the estimated ranges using recruitment assumes 2 to

4 times as many age-O menhaden were killed than estimated as

landed.

The decline in yield-per-recruit since 1970 (Fig. 17) has been

attributed largely to the decline in average weight-at-age of fish

landed during this period (Fig. 8). The general shift in activity of

the fishery to more southern waters (Chesapeake Bay and South

Atlantic areas and the North Carolina fall fishery) also explains

some of the observed decline (Fig. I). Since 1976, however, no

trend in yield-per-recruit is obvious. In general, increasing the

age-at-entry causes an increase in the yield-per-recruit, except for

small F-multiples; e.g., F-multiple = 0.2 (Table 12). On the other

hand, decreasing the F-multiple to F-multiple = 0.6 generally

causes a decrease in yield-per-recruit, except for the 1979 fishing

year. Greater declines or any increases in the F-multiple generally

cause a decrease in yield-per-recruit at the current age-at-entry. If

greater numbers of age-O menhaden are killed than estimated as

landed (multiplicative factor greater than one), then current levels

of yield-per-recruit are lower, and greater gains in yield-per-recruit

are available by raising the age-at-entry to the fishable stock. Gains

in yield-per-recruit depend on the year-to-year availability of age-O

menhaden, which varies with the timing of migration by juveniles

from their nursery areas in the late fall. These results suggest that

the fishery is harvesting the Atlantic menhaden stock at too young

an age, and that the age-at-entry should be raised to increase

potential yield from the stock.

In summary, the modem fishery has a high dependency on

prespawners (age-2 and younger fish), so large fluctuations in

year-to-year availability and catches are to be expected. To increase yield and enhance the stability of the resource, it is desirable

that the number of age classes significantly contributing to the

fishery be increased. This would create a buffer against future poor

recruitment years and lessen the year-to-year fluctuations in landings. Furthermore, greater yields should be attainable from the

stock. Whether MSY estimates of 450-490 kmt are attainable may

be questioned because of changes in plant locations and fishing

patterns. However, gains in yield-per-recruit are possible by adjusting the age-at-entry.

Chesapeake

Bay

Entire

Fishery

North

Atlantic

--/ Middle

, ------ ---/'Atlantic

FISHING YEARS

60

50

40

30

20

South

20 Atlantic

10 /', I

~Flshery

...... Fall

1970 72 74 76 78 80

to-

:5

a:

(,)

w

a:

a:

w

aa

...J

w

>-

rtl

E

'"2

Figure 17

Estimated yield-per-recruit of Atlantic menhaden for fishing pallerns and

growth prevalent during fishing years 1970-81.

Although landings have recovered somewhat from the depressed

levels during the 1970's, they have not returned to the levels

attained during the late 1950's when they averaged 625 kmt during

the 1955-59 fishing years (Fig. 2). Even though estimates ofMSY

of 450-490 kmt at a population F of 0.5/year were obtained from

the surplus production models (Fig. 13), those levels are unlikely

to be attained over an extended period given the present structure

of the fishery. However, recent landings averaging 356 kmt with

a population F averaging D.53/year since 1975 raises the question

why MSY has not been attained. Estimates of MSY from the

surplus production approach represent an historical average. Cycles or patterns of recruitment within this historical period (Table

4) suggest that greater yields than MSY are available at times, and

smaller yields than MSY are available at other times. The crux of

the problem for management is associated with predicting in advance the level of recruitment (primarily controlled by environmental factors) so that management and the fishing fleet can respond appropriately. Such a predictive tool is not yet available for

Atlantic menhaden.

As discussed in the section on spawner-recruit relationships,

sufficient recruitment has been available since 1975 to attain MSY.

Since considerable scatter about the fitted spawner-recruit curves

exists (Fig. 15), it appears that managing the fishery to maintain

large numbers of spawners would prove fruitless and that environmental conditions may outweigh the availability of spawners in

controlling subsequent recruitment. However, the Ricker spawnerrecruit relationships are marginally significant, and combined with

17
Acknowledgments _

Thanks are due to the many past and present employees of the

Beaufort Laboratory, Southeast Fisheries Center, NMFS, NOAA,

who were involved in the many aspects of the menhaden program,

especially Donnie Dudley and Ethel A. Hall. We are grateful to

Charles W. Krouse for his assistance in preparing the computerized

data sets for analysis and for other programming help. We would

also like to thank Dean W. Ahrenholz, Sheryan P. Epperly, James

R. Waters, John V. Merriner, and two anonymous reviewers for

their helpful comments, Nancy D. Vaughan for entering the tables

and figures on microcomputer, and Herbert R. Gordy for drafting

final figures.

Citations _

ABRAMSON, N. J

1971 Computer programs for fish stock assessment. FAO Fish. Tech. Pap.

101:1-154.

AHRENHOLZ. D. w., J. F. GUTHRIE, and C. W KROUSE

1983. Early relative abundance studies ofjuvenile menhaden. Beaufon Lab.,

Southeast Fish. Cent., Natl. Mar. Fish. Serv., NOAA, Beaufon, !'IC 28516.

Unpubl. manuscr., 42 p.

AHRENHOLZ, D. W., w. R. NELSON, and S. P. EPPERLY

1987. Population and Fishery Characteristics of Atlantic menhaden, Brevoorlio tyrannus. Fish. Bull., U.S. 85:569-600.

(AMAC) ATLANTIC MENHADEN ADVISORY COMMITTEE.

1982. Status and management recommendations for the purse-seine fishery;

repon to the Atlantic Menhaden Implementation Subcommittee (AMIS).

Atl. States Mar. Fish. CO'llm., Wash., D.C., 15 p.

(AMMB) ATLANTIC MENHADEN MANAGEMENT BOARD

1981. Fishery management plan for Atlantic menhaden Brevoorlia tyrant/us

(Latrobe). Atl. States Mar. Fish. Comm., Wash., D.C., 134 p.

CHAPMAN, D G., and D. S. ROBSON.

1960. The analysis of a catch curve. Biometrics 16:354-368.

CHESTER, A 1.

1984. Sampling statistics in the Atlantic menhaden fishery. NOAA Tech.

Rep. NMFS 9, 16 P

CLARK, C. W., and M. MANGEL.

1979. Aggregation and fishery dynamics: A theoretical study of schooling

and the purse seine tuna f.sheries. Fish. Bull., U.S. 77:317-337.

DIETRICH, C. S., Jr.

1979. Fecundity of the Atlantic menhaden, Brevoorria tyrallllus. Fish. Bull.,

U.S. 77:308-311.

EPPERLY, S. P., w. H. LENARZ, L. L. MASSEY, and W. R. NELSON.

1986. A generalized computer program for yield per recruit analysis of a

migrating population with area-specific growth and monality rates. NOAA

Tech. Memo. NMFS-SEFC-180, 26 p. Southeast Fish. Cent., Natl. Mar.

Fish. Serv., NOAA, Miani, FL 33149.

FOX, w. W., Jr.

1970. An exponential surplus-yield model for optimizing exploited fish populations. Trans. Am. Fish. Soc. 99:80-88.

1975. Fitting the generalized stock production model by least-squares and

equilibrium approximation. Fish. Bull., U.S. 73:23-37.

FRYE, J.

1978. The men all singing. Donning Co., Virginia Beach, VA, 242 p.

HIGHAM, J. R., and W R. NICHOLSON.

1964. Sexual maturation and spawning of Atlantic menhaden. Fish. Bull.,

U.S. 63':255-271.

JUNE, F. c., and J. W. REINTJES.

1959. Age and size composition of the menhaden catch along the Atlantic coast

of the United States, 1952-55; with a brief review of the commercial fishery.

U.S. Fish Wildl. Servo Spec. Sci. Rep. Fish. 317, 65 p.

KROGER, R. L., and J F GUTHRIE.

1973. Migrations of taggec juvenile Atlantic menhaden. Trans. Am. Fish.

Soc. 102:417-422.

18

LENARZ, w. H., w. W. FOX, Jr, G. T. SAKAGAWA, and B 1. ROTHSCHILD.

1974. An examination of the yield per recruit basis for a minimum size regulation for Atlantic yellowfin tuna, Thullnus albacares. Fish. Bull .. U.S.

72:37-61.

MILLER, D. M.

1984. Reducing transformation bias in curve fitting. Am. Statistician

38(2): 124-126.

MURPHY, G. I.

1965. A solution of the catch equation. J. Fish. Res. Board Can. 22: 191-201 .

'ELSO , W. R., M. C. INGHAM, and W. E. SCHAAF.

1977. Larval transpon and year-class strength of Atlantic menhaden, Brevoortia tyrannus. Fish. Bull., U.S. 75:23-41.

NICHOLSON, W. R.

1971. Changes in catch and effon in the Atlantic menhaden purse-seine fishery

1940-68. Fish. Bull., U.S. 69:765-781.

1972. Population structure and movements of Atlantic menhaden, Brevoorria

tyral/nus, as inferred from back-calculated length frequencies. Chesapeake

Sci. 13:161-174.

1975. Age and size composition of the Atlantic menhaden, Brevooriia tyral/-

nus, purse seine catch, 1963-71, with a brief discussion of the fishery.

NOAA Tech. Rep. NMFS SSRF-684, 28 p.

1978a. Gulf menhaden, Brevoorria patronus, purse seine fishery: Catch, fishing activity, and age and size composition, 1964-73. NOAA Tech. Rep.

MFS SSRF-722, 8 p.

1978b. Movements and population structure of Atlantic menhaden indicated by

tag returns. Estuaries 1:141-150.

PELLA, J. J., and P. K. TOMLINSON.

1969. A generalized stock production model. Inter-Am. Trop. Tuna Comm.

Bull. 14:420-496.

REINTJES, J. W.

1969. Synopsis of biological data on Atlantic menhaden, Brevoorria tyrallnus.

U.S. Fish. Wild I. Serv., Circ. 320, 30 p.

REISH, R. L., R. B. DERISO, D. RUPPERT, and R. J. CARROLL.

1985. An investigation of the population dynamics of Atlantic menhaden (Brevoorria tyranllus). Can. J. Fish. Aquat. Sci. 42:147-157.

RICKER, W E.

1954. Stock and recruitment. J. Fish. Res. Board Can. 11:559-623.

1975. Computation and interpretation of biological statistics of fish populations. Bull. Fish. Res. Board Can. 191,382 p.

SCHAAF, W. E.

1979. An analysis of the dynamic response of Atlantic menhaden, Brevooriia

tyrannus, to an intensive fishery. Rapp. P.V. Reun. Cons. Int. Explor. Mer

177:243-251.

SCHAAF, W. E., and G. R. HUNTSMAN.

1972. Effects of fishing on the Atlantic menhaden stock: 1955-1969. Trans.

Am. Fish. Soc. 101:290-297.

SCHAEFER, M. B.

1954. Some aspects of the dynamics of populations imponant to the management of the commercial marine fisheries. Inter-Am. Trop. Tuna Comm.

Bull. 1:27-56.

1957. A study of the dynamics of the fishery for yellowfin tuna in the eastern

tropical Pacific Ocean. Inter-Am. Trop. Tuna Comm. Bull. 2:247-268.

SEBER, G. A. F.

1973. The estimation of animal abundance. Charles Griffin & Co., London,

506 p.

SMITH, 1. W., w. R. NICHOLSON, D. S VAUGHAN, D. L. DUDLEY, and

E.A. HALL.

1987. Atlantic menhaden, Brevoorria tyrannus, purse seine fishery, 1972-

1984, with a brief discussion of age and size composition of the landings.

NOAA Tech. Rep. NMFS 59, 23 P

TOMLINSOr;, P. K.

1970. A generalization of the Murphy catch equation. J. Fish. Res. Board

Can. 27:821-825.

U.S. !'IATIONAL MARINE FISHERIES SERVICE.

1985. Fisheries of the United States, 1984. Curro Fish. Stat. 8360, Natl.

Mar. Fish. Serv., NOAA, 121 p.

VAUGHAN, D. S. and P. KANCIRUK.

1982. An empirical comparison of estimation procedures for the von Benalanffy growth equation. J. Cons., Cons. Int. Explor. Mer 40:211-219.

VAUGHAN, D S., R. M. YOSHIYAMA, 1. E. BRECK, and D. L. DE ANGELIS.

1984. Modeling approaches for assessing the effects of stress on fish populations. In Cairns, V. W., P. V. Hodson, and J. O. Nriagu (eds.), Contaminant effects on fisheries, p. 259-278. John Wiley, New York.

VON BERTALANFFY, L.

1938. A quantitative theory of organic growth. Human BioI. 10:181-213.