NOAA Technical Report NMFS 58

Stock Assessment of

the Gulf Menhaden,

Brevoortia patronus ,

Fishery

Douglas S. Vaughan

September 1987

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service
NOAA TECHNICAL REPORT NMFS

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

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States coastal 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 statistics on various phases of the industry.

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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 monality 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 J. Dadswell, Bruce D. Taubert. Thomas S. Squiers, Donald

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

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

October 1984, 33 p.

16. Proceedings of the Ninth and Tenth U.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 cep.lalopods

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, ]04 p.

19. Synopsis of biological data on spottail pinfish, Dlp/odus hC'/brooJ.i (Pisces:

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

20. Ichthyoplankton of the Contmental Shelf near Kodiak Island, Alaska, bl Arthur

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

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

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

22 Congrid eels of the eastern Pacific and key 10 their Leptocephali, by Solomon

N Raju. February 1985, 19 r.

23. Synopsis of biological data 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 "outhern

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 data on the sand perch, Diplectrum !wmosum (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 J. Sindermann (editor).

March 1985, 102 p.

28. Rev iew of geographical stocks of tropical dolphins (Stenella 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, inten.ity, longevity, and persistence of Anisakis sp. larvae and Laeistorhynchus tenuis 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 data 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. Anderson, John G. Casey, John J. Hoey, and W. N. Witzell. July 1985,22 p.

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

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

33. Marine flora and fauna of the Northeastern United States. Echinodermata:

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

34, Additions to a revision of the shark genu. Carcharhinus: Synonymy of Aprionodon and Hypoprion, 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 haemastorna

floridana, 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, Engraulls mordax, by Reuben Lasker (editor).

December 1985, 99 p.

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

and John Ziskowski. March 1986, 14 p.

38, Fishery atlas of the northwestern Hawaiian Islands, 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 imp.,t elf 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 stationary 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, Pandolus 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 of seamounts in the North Pacific, by Richard N.

Uchida, Sigeiti 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. De~elllber

1986, 85 p.
NOAA Technical Report NMFS 58

Stock Assessment of the

Gulf Menhaden, Brevoortia patronus,

Fishery

Douglas S. Vaughan

September 1987

U.S. DEPARTMENT OF COMMERCE

C. William Verity, Jr., Secretary

National Oceanic and Atmospheric Administration

Anthony J. Calio, 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.

II
CONTENTS

Introduction

Virtual population analyses 3

Size-at-age and growth analyses 4

Yield-per-recruit analyses 8

Surplus production models 9

Spawner-recruit relationships 13

Population simulation models 15

Management implications 16

Acknowledgments 17

Citations 18

iii

Stock Assessment of the

Gulf Menhaden, Brevoortia

patronus, Fishery

Douglas S. Vaughan

Beaufort Laboratory

Southeast Fisheries Center

National Marine Fisheries Service. NOAA

Beaufort. North Carolina 28516-9722

ABSTRACT

A stock assessment of the gulf menhaden. Brevoortia patronus , fishery was conducted with data on purse-seine landings from 1946 to 1985 and port sampling

data from 1964 to 1985. These data were analyzed to determine growth rates,

yield-per-recruit, spawner-recruit relationships, and maximum sustainable yield

(MSY). Virtual population analysis was used to estimate stock size, year-class

size, and fishing mortality rates. During the period studied, an average of 27%

of age-l fish and 55% of age-2 and age-3 fish were taken by the fishery, and 54%

for age-I and 38% for age-2 and -3 fish were lost annually to natural causes.

Annual yield-per-recruit estimates ranged from 6.9 to 19.3 g, with recent

mean conditions averaging 12.2 g since 1978. Surplus production models produced estimates of MSY from 620 to 700 kilometric tons. Recruits to age-I

ranged from 8.3 to 41.8 billion fish for 1964-82. Although there was substantial

scatter about the fitted curves, Ricker·type spawner-recruit relationships were

found suitable for use in a population simulation model. Estimates of MSY from

population simulation model runs ranged from 705 to 825 kilometric tons with

F -multiples of the mean rate of fishing ranging from 1.0 to 1.5.

Recent harvests in excess of the historical MSY may not be detrimental to the

gulf menhaden stock. However, one should not expect long-term harvesting

above the historical MSY because of the short life span of gulf menhaden and

possible changes from currently favorable environmental conditions supporting

high recruitment.

Introduction _

Gulf menhaden, Brevoortia patronus, is a euryhaline species

found in coastal and inland tidal waters from the Yucatan Peninsula

in Mexico to Tampa Bay, Florida (Christmas et al. 1983; Nelson

and Ahrenholz 1986). Adult menhaden are filter feeders (feeding

primarily on phytoplankton) and. in tum, support predatory food

fishes. Gulf menhaden form large surface schools which appear in

the nearshore Gulf waters from about April to November. Although no extensive coastwise migrations are known to occur.

there is evidence that older fish move towards the Mississippi

River delta (Ahrenholz 1981). Spawning occurs in offshore waters

during winter, peaking during December and January (Lewis and

Roithmayr 1981). Eggs hatch at sea and the larvae are carried to

estuaries by ocean currents where they develop into juveniles.

Juveniles migrate offshore during winter and move back to coastal

waters the following spring as age-I adults.

Gulf menhaden are subject to an extensive purse-seine fishery in

the northern Gulf of Mexico (Fig. I) from mid-April through

mid-October as regulated by interstate compact (Christmas and

Etzold 1977; Nelson and Ahrenholz 1986). Since 1964 the National Marine Fisheries Service (formerly Bureau of Commercial

Fisheries) has maintained a sampling program for gulf menhaden.

During this period the number of active reduction plants, where

menhaden are processed for meal and oil, has varied between 10

and 14, except in 1985 when it fell to 7 plants (Table I). The

number of purse-seine vessels has varied between 66 and 92, with

73 vessels active during the 1985 fishing season. Annual landings

and nominal fishing effort (vessel-ton-week), available since 1946,

show an upward trend with record high landings during the 1984

fishing season (Fig. 2). Since 1964 detailed information on daily

vessel landings and fish sampled for length. weight, and age (from

scales) are available. This information is used to estimate the

number of fish landed at age. 1964-85 (Table 2). The fishery

depends primarily on age-l fish (comprising from 47.2% to 92.0%

of the landings) and to a lesser extent on age-2 fish (7.3% to

45.2%) (Fig. 3). The remaining ages (age-O, -3, and -4+) generally contribute insignificantly to the landings (0.6% to 12.7%),

although age-3 fish contributed 10.2% to the landings in 1975.

Nelson and Ahrenholz (1986) analyzed the gulf menhaden data

for the 1964-78 fishing years, and recent landings (700-980 kilometric tons (kmt) since 1975) exceed reported estimates for MSY

(540 to 640 krnt). The purpose of this report is to reevaluate the

gulf menhaden stock with data included from seven more fishing

years. As shown by the catch data (Table 2 and Fig. 3), gulf

menhaden are a short-lived species, requiring constant stock monitoring through annual data collection and frequent assessments.

The analyses that follow closely parallel those presented in Nelson

and Ahrenholz (1986). Estimates of population numbers and fishing mortality rates by age are obtained from virtual population

analysis (VPA). Growth in length is obtained by considering mean

length-at-age by year class and fitting the von Bertalanffy growth

function to these data to obtain parameter estimates; growth in

weight is obtained by relating weight to length by fishing year.

Yield-per-recruit is obtained for each year class and for two sets of

mean conditions (1964-85 fishing years and 1978-85 fishing

years). By adjusting nominal fishing effort for variability in the

catchability coefficient to obtain estimates of effective effort for

1964-83, parameters for the Schaefer and Pella-Tomlinson surplus

production models are estimated from yield and fishing effort data

from 1946 to 1985. Estimates of maximum sustainable yield

(MSY) are also obtained from these models. Population simulation
98· 96· 94· 92· 90· 88· 86· 84· 82·

LOUISIANA FLORIDA

TEXAS , , 3D· - : Cameron . '" 3D·

~~r <> Dulac(2) (.

1/ Morgan City '- - .

Empire

(2)

28· 28·

GULF OF MEXICO

\\

26· 26·

LOUISIANA MISS..ALA.; FLORIDA

TEXAS Intracoastal MOSSP~

City ~(~) _ V

3D· Cameron j

~' 3D·

2) <:> Dulac .

. , .-, /

Empire

28° 28°

GULF OF MEXICO

\~

26· 26·

98· 94° 92° 90· 82°

Figure 1

Map of northern Gulf of Mexico showing port locations for active plants in 1964 (upper) and in 1985 (lower),

t-=Cf)

800 mu.. W

u..;:

Wi

Z

600 0

_lII

~u1

400

«w

z>

~o

200 g

1.0001..----------------------------.....,1.000

Cf) __ Landings

z ___ Effort

0 800 Ia:

IW 600

0

0

0

.... 400

Cf)

C)

z

0 200

z

«

..J

0

FISHING YEARS

Figure 2

Gulf menhaden landings and nominal fishing effort tor fishing years, 1946-R5,

2
100

fz 80 Age

w

!f ()

a:

w

0.. 60

W

>

f-

« 40

...J

::::>

::::>

() 20

0 65 67 69 71 73 75 77 79 81 83 85

FISHING YEAR

Figure 3

Contribution in percent of total numbers of gulf menhaden landed by age group, 1964-85.

(Nicholson and Schaaf 1978), estimates of fish older than age-4 in

the landings were assumed to be unreliable. Therefore, fish older

than age-4 were pooled with age-4 fish. Estimates of the annual

instantaneous fishing mortality rate (F;) for age-2 fish were derived

separately for each year class primarily from comparing catches of

age-2 and age-3 fish,

models are used to investigate the equilibrium (sustainable) yields

from the gulf menhaden stock when different levels of fishing

mortality (F -multiples) are applied, based on two Ricker models

(number of recruits on number of spawners and number of recruits

on spawners as eggs) and on the assumption of random recruitment. Estimates of MSY are obtained from the population simulation model and compared with those estimates from the surplus

production models. The results of the models are used to evaluate

the impact of the fishery on the gulf menhaden stock. F; = (In C; - In C;+I) - M, (I)

Virtual Population Analyses _

Estimates of initial population sizes and fishing mortality rates by

age are obtained from virtual population analysis (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 independent of catch-per-uniteffort (CPUE). Backward sequential computations (oldest to

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

same estimates, while forward calculations tend to diverge unless

the true starting value was used.

A major component of the input data for this analysis is catch in

numbers-at-age. The calendar year was divided into four periods

(or quarters) of approximately equal duration as described in Nelson and Ahrenholz (1986), with the first quarter beginning on I

January. The catches in numbers-at-age were summarized by quarter from weekly estimates by sampling methods outlined by

Nicholson (1978) and reviewed in Chester (1984). The annual

instantaneous natural mortality rate (M) was obtained from an

analysis of mark-recapture data (Ahrenholz 1981). This estimate

(I.I per year or 0.275 per quarter) was assumed constant for all

ages (>0.5) and years.

Because of uncertainties in aging, especially with older fish

3

where C is the annual catch in numbers-at-age (i or i +I). Following Nelson and Ahrenholz (1986), initial starting values of F for

the oldest age group landed in a year class were adjusted by trial

and error until the sum of the quarterly F's for age-2 fish was

virtually equal to the annual estimate of F2 obtained from Eq. (I)

(Table 3). Since an extremely low value of F2 was obtained for the

1972 year class, and a negative value of F2 was obtained for the

1979 year class, a convergence criterion based on F for age-3 fish

was used instead. Since no age-4 fish were landed from the 1972

year class, an average of F for age-3 fish from the 1971 and 1973

year classes was used. Furthermore, no age-2 fish were available

in the landings data for the 1960 and 1961 year classes (sampling

began in 1964), and no age-3 fish were available in the landing data

for the 1960 year class. The mean F for age-3 fish for year classes

1964 through 1979 was used for estimating F for age-3 fish in the

1961 year class, and the mean F for age-4 fish for year classes 1964

through 1979 was used for estimating F for age-4 fish in the 1960

year class.

The distribution of numbers-at-age in the population as estimated from the VPA for years 1964-80 on 1 January (beginning of

the first quarter, Table 4) closely parallel the distribution of

numbers-at-age in the landings (Table 2) for the same years. Recruits at age-Ion I January ranged from 8.3 billion fish in 1966

to 41.8 billion fish in 1982, with the three highest recruitment

years for the study period (1964-80) being the 1978, 1981, and
Size-at-Age and Growth Analyses _

a<0.OO5x 109.

bTypographic error found 'in original NMFS data set and corrected in 1984.

cCorrection made in tonnage for one vessel since analysis of Nelson and

Ahrenholz (986).

Estimates of growth in length and weight are needed for estimating

fishing yield, both from yield-per-recruit and pbpulation simulation analyses. Growth in length also is used to assess a densitydependent growth hypothesis and to reconstruct the spawners in

terms of equivalent egg production for use in obtaining spawnerrecruit relationships. Fork length (L[, in mm) is estimated from age

(t, in yr) on the basis of the von Bertalanffy (1938) growth function,

well represented in the fishery for only three years, this time span

appears adequate.

Short-term impacts of the fishery on the stock can be assessed

by considering the exploitation rate (u) which is the fraction of the

remaining stock removed by the fishery during some preset period

of time (usually I year). Average exploitation rates (1964-83) were

approximately 27% for age-I fish and about 55% for age-2 and

age-3 fish (Fig. 5). Annual natural mortality losses averaged about

54% for age-l fish and 38% for age-2 and age-3 fish, although, in

the absence of fishing, annual natural mortality losses would be

about 67% for all ages. A general decline over time is noted both

in the age-specific and population exploitation rates with fishing

year. Population exploitation rate has declined from an average of

44% in the 1960's to 25% in the 1980's (Fig. 5). This decline, in

part, represents the large increase in recruits to age-I and population size compared with relatively smaller increases in landings.

L[ = L (2) inl(1 - exp(- K(t - to))),

Table 2

Estimated landings of gulf menhaden in numbers-at-age (0-4+), total numbers landed (ages 0-4+), total landings by weight and nominal fishing effort

(vessel-ton-weeks) for the fishing years, 1964-85.

Nominal

Landings in numbers-at-age (109) Total fishing

Fishing landings effort

year 0 2 3 4+ Total (103 mt) (1000 vtw)

1964 3.33 1.50 0.12 4.95 409.4 272.9

1965 0.04 5.03 1.08 0.08 6.23 463.1 335.6

1966 0.03 3.31 0.87 0.03 4.24 359.1 381.3

1967 002 4.27 0.34 0.01 0.0 4.64 317.3 404.7

1968 0.07 3.48 1.00 0.04 4.58 373.5 382.3

1969 0.02 6.07 1.29 0.03 0.0 7.41 523.7 411.0

1970 0.05 3.28 2.28 0.04 0.0 5.65 548.1 400.0

1971 0.02 5.76 1.96 0.18 7.92 728.2 472.9

1972 0.02 3.05 1.73 0.09 4.89 501.7 447.5

1973 0.05 3.03 1.11 0.10 4.29 486.1 426.2

1974 3.85 1.47 0.06 0.0 5.38 587.4b 485.5

1975 0.11 2.44 1.50 0.46 4.51 542.6 538.0c

1976 0.0 4.59 1.37 0.20 0.0 6.17 561.2 575.8

1977 0.0 466 1.33 0.11 6.11 447.1 532.7

1978 0.0 6.79 2.74 0.05 9.59 820.0 574.3

1979 0.0 4.70 2.88 0.34 7.92 777.9 533.9

1980 0.07 3.41 3.26 0.44 0.05 7.22 701.3 627.6

1981 0.0 5.75 1.42 0.33 0.03 7.54 552.6 623.0

1982 0.0 5.15 3.30 0.50 0.06 9.01 853.9 653.8

1983 0.0 4.69 3.81 038 0.03 8.90 923.5 655.8

1984 0.0 775 2.88 0.44 0.05 11.12 982.8 645.9

1985 0.0 8.13 2.72 0.28 0.02 11.15 881.1 560.6

Table 1

Number of gulf menhaden reduction plants by port and total, number of

purse-seine vessels, and number of fish sampled for age and size for fIShing

years, 1964-85.

Ports No. No. /'<'0.

Fishing reduction reduction fish

year A MP E 0 MC IC C SP plants vessels sarrpled

1964 0 3 2 2 1 0 2 I 11 78 12.457

1965 0 3 2 3 I 1 2 I 13 87 15,819

1966 I 3 2 2 I I 2 I 13 92 13,016

1967 0 3 2 2 I I 3 I 13 85 14,519

1968 I 3 2 2: 1 I 3 I 14 78 16,499

1969 I 3 2 I I I 3 I 13 75 15,281

1970 0 3 2 2 I I 3 I 13 76 10,560

1971 0 3 2 2 I 1 3 I 13 85 7,859

1972 0 3 2 I 1 1 3 0 II 75 10.030

1973 0 2 2 I I I 3 0 10 66 8,958

1974 0 2 2 I I 1 3 0 10 71 10,120

1975 0 3 2 I I I 3 0 II 78 9,529

1976 0 3 2 I I I 3 0 11 82 13,586

1977 0 3 2 I I I 3 0 11 80 14,918

1978 0 3 2 I I I 3 0 11 80 12,985

1979 0 3 2 I I I 3 0 II 78 11,620

1980 0 3 2 I I I 3 0 11 79 9,961

1981 0 3 2 I I I 3 0 II 80 10,408

1982 0 3 2 I I I 3 0 II 82 10,709

1983 0 3 2 J I I 3 0 11 81 14,840

1984 0 3 2 I I 1 3 0 II 81 16,000

1985 0 2 I I 0 1 2 0 7 73 13,240

A = Appalachicola, FL: Fish Meal Co. (1966, 1'168-69).

MP = Moss Point, MS: Seacoast Products Co. (1964-72, 1975-84), Standard

Products Co. (1964-85), Zapata Haynie, Inc. (1964-85).

E = Empire, LA: Empire Menhaden Co. (1964-85), Petrou Fisheries, Inc.

(1964-84).

0= Dulac, LA: Dulac Menhaden Fisheries (1964- I968, 1970

-71), Fish Meal and Oil Co. (1964-65), Zapata Haynie, Inc. (1965-85).

MC = Morgan City, LA: Seacoast Products Co. (1964-84).

IC = Intracoastal City, LA: Seacoast Products Co. (1965-84), Zapata Haynie,

Inc. (1985).

C = Cameron, LA: Louisiana Menhaden Co. (1964-85), Seacoast Products

Co. (1964-84), Zapata Haynie, Inc. (1967-85).

SP = Sabine Pass, TX: Texas Menhaden Co. (1964-71).

1982 fishing years (1977, 1980, and 1981 year classes) (Fig. 4).

Since recruits to age-I are a major portion of the population. the

general trend in increasing recruitment to age-l since 1964 is also

reflected in increasing population size (age-I and older fish).

Age-specific estimates of instantaneous fishing mortality rates

(F) indicate that age-l fish are not completely recruited to the

fishery (F values for age-I fish are considerably less than F values

for age-2 and age-3 fish), while age-2 fish generally are fully

recruited (Table 5). However, age-2 fish in 1974 (1972 year clas~)

do not appear to be fully recruited (compare F2 in 1974 with F3 in

1975), nor do age-2 fish in 1981 (1979 year class; compare F2 in

1981 with F3 in 1982). The general conclusion drawn here compares closely with that of Ahrenholz (1981) based on tagged fish.

Since the estimated F values were forced to converge towards a

preset F2, the estimates of F3 and F4 are, in effect, obtained from

forward computations, so that an estimate of F4 tends to diverge

from its "true" value_ This tendency is especially evident in the

variability present in estimates of F4 . However, errors in population estimates of age-4 fish will have little effect on the following

analyses because of their small contribution to the total adult population (Table 4). Furthermore, Ulltang (1977) noted that when F

is high, convergence is rapid. Hence, even though a year class is

4
Table 3

Estimated convergent F, age of convergent F, and ages used in virtual population analysis (VPA) for gulf menhaden

by year classes, 1960-82.

Year Convergent Age 01 VPA

class F' convergence ages

1960 2.899b 4 4

1961 1.693c 3 3-4

1962 1.825 2 2-4

1963 2.362 2 1-3

1964 3.098 2 0-4

1965 1.099 2 0-3

1966 2.354 2 0-3

1967 2.474 2 0-4

1968 1.429 2 0-4

1969 1.995 2 0-4

1970 I.757 2 0-3

1971 1.830 2 0-4

1972 3.562d 3 0-3

1973 0.895 2 0-4

1974 1.422 2 0-4

1975 2.J30 2 0-4

1976 0.996 2 1-4

1977 0.787 2 1-4

1978 1.193 2 1-4

1979 1.953 3 1-4

1980 1.055 2 0-4

1981 1.062 2 1-4

1982 1.220 2 1-3

'Convergenl F calculated from:

F = In(c;) - In(c;+I) - M,

where i = age of convergence and M is the

inslantaneous natural mortality rale (1. II

yr).

bConvergent F for 1960 year class was

obtained from the mean F for age-4 fish for

year classes, 1964-79.

cConvergent F for 1961 year class was

obtained from the mean F for age-3 fish for

year classes. 1964-79.

dConvergent F calculated from the mean

F for 1971 and 1973 year classes.

where L;nj, K, and to are parameters to be estimated. The computer

program BGe3 (Abramson 1971) was used to obtain parameter

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

algorithm (Vaughan and Kanciruk 1982). Weight (W" in g) is then

estimated from the weight-length relationship expressed in the

linear form of the power function,

Table 4

Estimated number of spawners (by age on I January and total) that produced the year class, estimated egg production from the spawning stock, and

estimated numbers of recruits at age-O.S and -I for gulf menhaden by year

classes, 1964-84.

Spawners Recruits (106)

Numbers,at-age (106)

Year Eggs

class 2 4 Total (10 12) Age-0.5 Age-I

1964 2,992.7 240.5 7.5 3,240.7 38.6 23,159.4 13,357.7

1965 1,950.7 160.5 14.7 2,125.9 24.4 14,372.3 8.261.8

1966 1.525.0 61.2 81 1,594.3 16.1 22,909.7 13,199.6

1967 877.0 25.1 1.2 903.3 10.3 24,081.1 13,876.7

1968 1,921.0 97.3 1.2 2,019.5 22.4 46,799.3 26,943.2

1969 2,493.3 61.1 8.5 2,562.9 31.6 30,294.4 17,462.4

1970 5,292.2 82.2 3.5 5,377.9 55.6 36,925.8 21,271.8

1971 3,801.5 422.1 6.8 4,230.4 54.4 21,713.2 12,512.1

1972 3,670.5 172.1 39.6 3,882.2 45.5 35,879.7 20,688.2

1973 2,384.1 210.9 6.0 2,601.0 32.9 36,819.9 21,210.9

1974 5,009.1 127.5. 7.5 5,144.1 74.2 24,192.2 13,955.6

1975 4,765.0 821.3 6.8 5,593.1 88.1 28,400.5 16,305.9

1976 3,132.2 661.3 7.8 3,801.3 58.9 54,129.7 31.230.1

1977 2,634.6 251.5 98.7 2,984.8 39.4 69,001.8 39,810.6

1978 7,592.8 129.2 20.4 7,742.4 80.6 58,612.0 33,816.2

1979 9,195.2 933.6 14.3 10,143.1 125.2 40,114.8 23,144.2

1980 8,287.1 1,389.6 110.4 9,787.1 125.2 65,029.0 37,461.3

1981 5,442.9 847.7 208.0 6,498.6 69.2 72,429.8 41,788.4

1982 8,997.3 971.1 95.4 10,063.8 103.8 53,745.6 31,008.5

1983 10,786.1 1,043.0 45.9 1,1875.0 143.3 NE NE

1984 7,345.9 1,241.2 1188 8,705.9 107.8 NE NE

In W, = a + b In L

" (3)

where a and b are estimated parameters. Annual weight-length

regressions based on Eq. (3) were calculated coastwide for each

fishing year, 1964-85 (Table 6). The statistic, r 2, ranged from 0.92

to 0.98 for the annual coastwide weight-length regressions.

Weighted averages of the estimated parameters were calculated by

pooling fishing years 1964-85 and 1978-85 (Table 6). Weighting

factors were catch in numbers by year (Table 2).

Mean fork length-at-age was calculated by quarter and aligned

by year class so that the resultant growth curves represent the

growth of a year class (or cohort) through its life span, rather than

across several year classes during a single fishing year. Von Bertalanffy growth equation parameters were estimated for each year

5
60

-I/)

c:

0

=

.0 50

C/)

ex:

w 40 Population m Total (1+)

::J

Z

z 30

w

N

C/)

z 20

0

....

«

....J 10 ::J

a.

0

a.

1964

FISHING YEAR

Figure 4

Population total (age-I and older gulf menhaden) and recruits to age-Ion 1 January for each fishIng year, 1964-83.

FISHING YEAR

Table 6

Weight-length regression parameters for gulf menhaden by fishing

year, 1964-85 (In W=ln a +b

In L).

Fishing

year In a b r 2

1964 -12.601 3.346 0.94

1965 -12.468 3.326 0.97

1966 -11.459 3.131 0.95

1967 -11.263 3.083 0.94

1968 -11.622 3.158 0.95

1969 -11.365 3.106 0.95

1970 -11.921 3.216 0.95

1971 -12.192 3.269 0.95

1972 -11.726 3.174 0.94

1973 -11.663 3.181 0.94

1974 - 10.785 2.994 0.92

1975 -11.562 3.\44 0.96

1976 -10.795 2.989 0.95

1977 -11.382 3.098 0.97

1978 -12.052 3.239 0.96

1979 -12.238 3.268 0.97

1980 - 13.045 3.427 0.92

1981 -11.682 3.166 0.96

1982 -12.657 3.358 0.95

1983 -12.256 3.280. 0.96

1984 -11.906 3.125 0.98

1985 -11.531 3.131 0.97

Weighted means

1978-85 -12.131 3.253

1964-85 -11.878 3.205

U.J 0.6 I-

<C

Z II:

0 z 0.4 0 <C I- ...J <C ::::> I- Q. <5 0.2 0

Q. ...J

Q.

X

UJ

0.0

0.8 U.J I"'~ • Age-3 I- , .;, - II <C /.1 \ \ f"\ "l\' i' 'I (,) II: .- 'I I . " I u::: 0.6 " ., . \' I ~..:~. \ / \ , \ z .. AI -. , ., rl,. /. u 0 " \. ,~ / ,'\, /' \" UJ \ " \. I \ I .' / Q. \ 'V '\/ /-......... C/) <C \......'. '.; . \ / I I- 0.4

U.J <5 Age-1 • Age-2 (!) ...J

<C Q.

x

UJ 0.2

0.0 85

Figure 5

Annual estimates for gulf menhaden of (upper) population exploitation rates and

(lower) age-specific exploitation rates (ages 1 through 3).

6
241.8------------------

..

200

237B-----------------

Lt=241.8(1-e-O.

430(t+O.773) )

01--------------1

100

200

100

J:

C)

Z

W

...J

ex:

o

lJ..

E

E

'"'

Table 7

Estimated von Bertalanffy growth

parameters for gulf menhaden obtained

from mean quarterly lengths for year

classes, 1960-82. For use in yield-perrecruit analyses, nol for general use.

Year

class n Litif K to

1960 2 220.5 0.413 -4.307

1961 4 23,986.4 0.001 -4.759

1962 7 7,628.5 0.003 -5.470

1963 8 279.2 0.260 -1.514

1964 10 419.3 0.116 -2.254

1965 II 423.1 0.135 -1.729

1966 10 469.1 0.102 -2.027

1967 II 241.2 0.504 -0.486

1968 12 293.4 0.208 -1.957

1969 II 351.4 0.164 -2.102

1970 10 298.8 0.264 -1.170

1971 10 62,949.2 0.001 -3.124

1972 10 249.8 0.512 -0.497

1973 12 279.4 0.339 -1.026

1974 13 237.3 0.573 -0.394

1975 17 244.1 0.384 -1.135

1976 13 242.1 0.437 -0.613

1977 12 240.7 0.423 -0.925

1978 12 248.5 0.333 -1.457

1979 14 329.3 0.157 -2.203

1980 14 240.2 0.457 -0.425

1981 12 227.9 0.577 -0.373

1982 9 2543 0.354 -1.054

Lt=237.6(1-e-O.493(l+O.385) )

O~_+_----:!:-_+_----:~_-J

o

class from 1964 through 1982 (Table 7). Lengths and corresponding weights for ages 0.50 to 5.00 (in increments of 0.25) were

calculated for Eqs. (2) and (3) for used in the yield-per-recruit and

population simulation models. Weighted averages across fishing

years of the mean lengths-at-age were calculated for 1964-85 (Fig.

6, upper) and 1978-85 (Fig. 6, lower) mean conditions. Length-atage for the 1964-85 mean conditions uniformly exceeds that for the

1978-85 mean conditions. However, the difference between the

two growth curves decreases from 11.4 mm at age 1 to 0.5 mm at

age 4.

The sizes of age-0.50 and age-0.75 gulf menhaden were found

by Nelson and Ahrenholz (1986) to be biased upwards. Therefore.

lengths at these ages were deleted when fitting the von Bertalanffy

growth equation to mean coastwide lengths-at-age for use in estimating egg production from spawners (Table 8). No difference is

noted between Tables 7 and 8 for year classes when no age-O fish

were landed (1960-63,1976-79 and 1981-85). Large values of Linf

and correspondingly low values of K occur when curvature in the

data is not pronounced, leading to estimation problems (Vaughan

and Kanciruk 1982). However, interpolation of lengths and corresponding weights within the range of ages used in estimating the

parameters are valid for use in yield-per-recruit (Table 7) and

spawner-recruit (Table 8) analyses.

Estimates of annual mean weight-at-age for gulf menhaden in

purse-seine catches were calculated to determine any trends in

yield-per-recruit that could be expected in the fishery (Fig. 7). No

specific trends in mean weight are noted, other than an apparent

peak between 1973 and 1975 for age-I through -3 fish.

AGE (years)

Figure 6

Von Benalanffy growth curves estimated from mean length at age data for gulf

menhaden based on (upper) 1964-85 fishing years, and (lower) 1978-85 fishing years.

Two aspects of density dependence are considered in this report.

The first is concerned with the hypothesis that when stock size is

large, the resultant competition among young-of-the year (age-a)

fish will result in slower growth than when stock size is small. It

is believed that if this mechanism occurs, it will express itself in

the mean length-at-age for the second quarter (April - June) when

fishing begins, especially for age-l gulf menhaden. Reish et al.

(1985) demonstrated density dependence in Atlantic menhaden for

the mean length of age-l fish, but not for older fish. Our results for

gulf menhaden were not significant when mean length-at-age (ages

1-3) were regressed against recruits to age-I. The latter aspect of

density dependence refers to the relationship between spawning

stock size and subsequent recruitment and is discussed in the section "Spawner-Recruit Relationships."

7
FISHING YEAR

0l-;:;6\;-5----:6;;1:9=----::7'!';.3;----:::7'==7--~8~1--8,.L5~

150

2

tJ:

(!)

jjj

100

z

«

w Age-1

50

Table 8

Estimated von Bertatanffy growth

parameters for gulf menhaden obtained

from quarterly mean lengths for year

classes, 1960-82. Estimates obtained

when mean lengths from age-O deleted

from analysis, for use in estimating egg

production from spawners.

Year

class n Lin! K to

1960 2 220.5 0.413 -4.307

1961 4 23,986.4 0.001 -4.759

1962 7 7.628.5 0.003 -5.470

1963 8 279.2 0.260 -1.514

1964 8 3170 0.216 -1.333

1965 9 26.741.1 0.001 -3.558

1966 9 15,778.1 0.002 -3.319

1967 10 252.4 0.397 -0.881

1968 10 238.3 0.457 -0.568

1969 10 27,504.7 0.001 -5051

1970 9 2,578.6 0.012 -3.667

1971 9 48,839.3 0001 -3.417

1972 9 275.0 0.341 -1.104

1973 10 296.6 0.270 -1.437

1974 12 246.9 0431 -0.933

1975 15 239.9 0441 -0.800

1976 13 242.1 0437 -0613

1977 12 240.7 0.423 -0.925

1978 12 248.5 0.333 -1.457

1979 14 329.3 0.157 -2.203

1980 12 238.5 0.462 -0469

1981 12 227.9 0.577 -0373

1982 9 254.3 0.354 -1.054

Figure 7

Mean annual weight of purse-seine landed gulf menhaden, ages I, 2, and 3, for

fishing years 1964-85.

Yield-per-Recruit Analyses _

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 Rieker-type yield-per-recruit

model to accommodate a multiple-area fishery. As described in

Nelson and Ahrenholz (1986), yield is summed by time intervals

such that individual lengths, weights, and estimates of natrual and

fishing mortality can be inserted for each quarter. Two MAREA

runs were made in which the data (Table 9) were developed based

on mean conditions for 1964-85 and 1978-85. The age-at-entry

into the fishery was 0.5 years, the age when gulf menhaden first

appear in the landings. Fishing occurs primarily during the second

and third quarters (April-September) on age-I and age-2 fish

(Table 9). Various multiples of the average fishing mortality (Fmultiples) at each age were used to simulate increased or decreased

fishing mortality (see example for 1978-85 mean conditions,

Fig. 8). It is clear from this example, as well as for the 1964-85

mean conditions. that increasing the age-at-entry into the fishery

beyond 1.5 years of age generally decreases the yield-per-recruit.

No gain is realized when increasing age-at-entry from 0.5 to 1.5

years for F -multiple = 1.0. This results from the very high natural

mortality rate (M = I.I/year) and the typical growth parameter

(K = 00493/year for this example). Yield-per-recruit can only be

increased by increasing the F -multiple, but this is not recommended due to a concern for the long-term stability of the stock

through possible recruitment overfishing. Figure 8 appears different from Nelson and Ahrenholz (1986) because age-at-entry is

plotted in different increments over different ranges of values. The

step-like appearance to the isopleth diagram in Nelson and Ahrenholz (1986) results from fishing primarily during two quarters and

plotting in increments of 0.25 years for the age-at-entry.

Additional MAREA runs were made for each fishing year from

1964 through 1983 (Table 10). Yield-per-recruit estimates are presented for these individual fishing years, and for 1964-85 and for

1978-85 mean conditions, for two levels of age-at-entry (0.5 and

1.25 years), and three levels of the F -multiple (004, 1.0, and 1.6).

Annual yield-per-recruit varies from 6.87 g from the 1982 fishing

year to 19.26 g from the 1977 fishing year (Fig. 9, left). Yield-perrecruit based on 1964-85 mean conditions was 15.84 g, while for

mean conditions during the most recent year-classes (1978-85) it

was 12.17 g. An inverse relationship is shown between annual

yield-per-recruit and population size at the start of the fishing year

(Fig. 9. right). This relationship results from the lag in landings

behind the rapid increase in recruitment during the late' 1970's. It

is not suggested that there is a density-dependent relationship for

yield-per-recruit.

8
Table 9 20.0 Input area of quarterly length, weight, and instantaneous

fishing mortality rate by age for 1978-85 and 1964-85 mean

conditions. 'a 15.0 I1978-85 mean conditions 1964-85 mean conditions ::>

a:

u Fork Fork W 20.0

Age length Weight length Weight a:

a: (yr) (mm) (g) F (mm) (g) F w

ll. 15.0 0 0.50 84.0 9.6 0.ססOO 101.9 18.9 0.0007 ...J

0.75 10l.8 18.3 0.0002 116.1 28.8 0.0004 >- 1.00 117.6 29.3 0.ססOO 128.9 40.3 0.0001 0.0

1.25 131.5 42.1 0.0771 140.4 53.0 0.1468 'j-?

1.50 143.8 56.3 0.2020 150.8 66.5 0.3503 "'Q 'j-t:;>

1.75 154.7 71.4 0.0444 160.1 80.6 00325 5.0

~, .;.., 0.0002 94.8 168.4 OOסס0. 86.9 164.3 200

2.25 172.8 102.4 0.2722 175.9 109.0 0.3864 ~1- ,t:;> 2.50 180.3 117.6 0.5639 182.6 122.9 1.0080 ~}- 0.0

2.75 186.9 132.3 0.1149 188.6 136.4 0.1352 fj. O~O.O 0.5 1.0 1.5 2.0 l\l~ 3.00 192.8 146.3 0.ססOO 1940 149.3 0.0002 "'1l'..J

325 198.0 159.5 0.4122 198.9 161.7 0.4302 F-MULT1PLE

3.50 202.6 171.8 0.6500 203.3 173.3 1.0380

3.75 206.7 183.3 0.1124 207.2 184.3 0.1969

4.00 210.2 193.8 0.0000 210.7 194.5 0.0000 Figure 8

4.25 213.4 203.5 0.4733 213.9 204.1 0.2155 Overall yield-per-recruit isopleth for gulf menhaden under 1978-85 mean conditions

4.50 216.2 212.3 2.7370 216.7 212.9 1.4580 of growth and multiples of fishing mortality by 3-month interval (F -multiple = 1.0). 4.75 218.7 220.4 2.0760 219.3 221.0 1.1390

5.00 220.9 227.6 221.6 228.5

Surplus Production Models _

Surplus production models are typically used to obtain estimates of

maximum sustainable yield from yield and fishing effort data

(Vaughan et al. 1984). When using these models, yield is assumed

to be proportional to population abundance and fishing effort proportional to fishing mortality. Theoretically, plotting catch against

effort should give a dome-shaped curve, which is not the case for

gulf menhaden data, although the points might lie along the ascending limb of such a curve (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.,

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

for gulf menhaden, As noted in Nelson and Ahrenholz (1986), 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 cIupeid fishes, which are

more susceptible to fishing effort than non-schooling species [see

discussion of "dynamic aggregation process" in Clark and Mangel

(1979)]. The concern here is that severe stock depletion could

occur before it was indicated by an analysis of yield and CPUE

data.

To demonstrate that the population catchability coefficient, q,

for gulf menhaden is not constant but dependent upon the population size, it was estimated by solving Eg. (4) for q (=FIE) for each

fishing year from 1964 through 1983 (Fig. II) and compared with

the population size for the same fishing year (Fig. 12). To calculate

the population (all ages combined) instantaneous fishing mortality

rate (F), it was first necessary to compute the population exploitaTable 10

Estimates of yield-per-recruit (g) for gulf menhaden for each

fishing year from 1964 through 1983, and for two sets of

mean conditions (1978-85 and 1964-85 fishing years).

Age-at-entry (yr) F-multiple Population

Fishing sizea

year 0.5 125 0.4 1.0 1.6 (106)

1964 17.16 1715 11.79 17.16 19.42 II ,315.6

1965 18.01 17.99 13.22 18.01 19.65 11,761.0

1966 18.60 18.58 14.06 18.60 20.29 7,479.8

1967 17.01 17.01 11.15 17.01 19.33 10,707.6

1968 1733 17.31 12.50 17.33 19.29 12,074.3

1969 10.41 10.39 5.83 10.41 13.37 22,411.9

1970 15.32 15.30 9.56 15.32 1805 17,348.7

1971 17.52 17.50 12.43 17.52 1950 19,359.2

1972 15.68 15.68 11.10 15.68 17.35 12,444.5

1973 15.12 15.10 10.18 15.12 17.55 17,686.7

1974 16.33 16.33 9.58 16.33 19.79 20,018.5

1975 1653 16.47 10.93 16.53 19.20 14,848.7

1976 18.59 18.59 11.88 18.59 21.14 15,272.9

1977 19.26 19.26 1320 19.26 21.39 25,988.6

1978 1398 13.98 8.32 13.98 16.78 36,120.0

1979 1336 13.36 8.32 13.36 16.22 33,390.1

1980 15.43 15.43 9.28 15.43 1831 25,013.7

1981 10.21 10.21 5.83 10.21 12.43 33,390.7

1982 6.87 6.87 3.92 6.87 9.22 39,385.5

1983 13.57 13.57 8.49 13.57 16.09 32,573.0

Mean conditions

1978-85 12.17 12.17 7.88 12.17 14.20 33,312.2

1964-85 15.84 15.83 10.64 15.84 18.06 20,929.5

'Population size based on ages'" I on 4 April.

9

F = q E, (4)
40

YR =20.35-0.24 P

r

2 =0.53

POPULATION SIZE (April 4)

(billions)

o

25

20 ......

Cl ....,

lS

a: 15 ()

UJ

a:

a:

UJ

Q. 10

Cl

...J

UJ

>= 5

0

1964

FISHING YEAR

Figure 9

Annual estimates of yield per recruit for gulf menhaden plotled against (left) fishing year, and (right) population size

(age-I and older fish).

Figure 10

Gulf menhaden landings plotled against nominal fishing effort for the 1946-85

fishing years. Solid curves represent range in landings depending on fishing effort.

NOMINAL FISHING EFFORT

(1000 vessel-Ion-weeks)

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

ages 1-4) with the population size (for all ages 1-4) on 4 April for

that year (Table 11). The population F is then calculated iteratively

from the equation:

(7)

(5)

E'=Eq/qa' (6)

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

F = u (F + M)/(l - exp(- (F + M»),

where E' is a unit of "effective" fishing effort (Fig. 13). Note that

while nominal effort has increased rapidly, effective fishing effort

has declined since 1966.

The computer program PRODFIT (Fox 1975), which accounts

for non-equilibrium conditions, is used to estimate parameters for

different surplus production models depending on the value of m

in the following equation:

where u and M (= I .1Iyear) are known. Estimates of q range

between 6.9 x 1O-7/year'vessel-ton-week in 1982 when the population size was 39.4 billion (age-I and older fish) and 43.5 x 10- 7/

year·vessel-ton-week in 1965 and 1966 when the population sizes

were 11.8 and 7.5 billion, respectively (Table II). As noted in

Nelson and Ahrenholz (1986), there is a pronounced inverse relationship between the catchability coefficient and population size

(Fig. 13). Furthermore, the historical trend that they noted continues to be evident with the addition of seven more years of data;

i.e., there appears to be a functional curve. With generally increasing population size since 1964, the catchability coefficient has

declined to a level in 1982 that is one-sixth that of 1965-66.

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

I used the 1964 value of q (qa) and adjusted nominal effort (E) so

that q is constant (qa); i.e.,

300 400 500 600 :'00

1000

900

800

700

c;;

c

E 600 .g

Qj

E

0 500 0

0

.:;

en

C) 400 z

is

z

<{

-'

10
0.005 50 M

I -l

0 it:

Q.

x 0.004 40

« II 0- f \ Z

1-- " f \ 0 I , , \

Z I \ I \ ,.... W I , I

<3 0.003 , , I

30 1\1 I \ I G>,.... u:: I I Population I \ I OJ en u.. I " Size « c: W I .......

0 II W

<.> 0.002 I, 20 N :0

Ci5 ....... >- I

I

I- Z :::i 0 iii

0.001 --,« 10 « I -l

<.> q ::>

I- Q.

« 0

<.> 0.0 Q.

FISHING YEAR

Figure 11

Catchabilily coefficient (q) and population size (age-I and older) for gulf menhaden plotted against fishing year, 1964-83.

Cl

..... 5.0

'0

X

C" 4.0 .....

l- In q=3.73-1.11 In P,

z

w 3.0 r 2 :O.80

U

l.L.

l.L.

W 68. 0 2.0 .72 U

>-

I-

::::i 1.0 iii 83 .79 .78 82 « . ::c 81

u

I-

« 0.00

u 10 20 30 40

POPULATION SIZE (Age ~1) ON APRIL 4 (billions)

Figure 12

Catchability coefficient (q) plotted against population size (age-! and older) of gulf menhaden. Also shown is

linearized regression of In q against In P (solid curve).

11
Table 11

Estimated population size (ages 1-4) on 4 April, numbers landed (ages 1-4),

population exploitation rate (u), population instantaneous fishing mortality

rate (F, yr-I ), catchability coefficient (q, yr-I vessel·ton·weeks-I ), and

effective fishing etTort (E', vessel-ton-weeks) for gulf menhaden by fishing

year, 1964·85.

Population Numbers Population

Fishing size landed

year (109) (109) u F q(lO-6) E' (103)

1964 11.32 4.95 0.437 1.071 3.92 272.9

1965 11.76 6.19 0.526 1.459 4.35 371.8

1966 7.48 4.21 0.563 1.658 4.35 422.5

1967 10.71 4.62 0.431 1.048 2.59 267.1

1968 12.07 4.51 0.374 0.850 2.22 216.7

1969 22.41 7.39 0.330 0.716 1.74 :82.4

1970 17.35 5.60 0.323 0.695 1.74 177.2

1971 19.36 7.90 0.408 0.965 2.04 245.9

1972 12.44 4.87 0.392 0.910 2.03 231.9

1973 17.69 424 0.240 0.477 1.12 121.6

1974 20.02 5.38 0.269 0.549 1.13 140.0

1975 14.85 4.40 0.296 0.620 1.15 158.1

1976 15.27 6.17 0.404 0.951 1.65 242.4

1977 25.99 6.11 0.235 0.465 0.87 118.5

1978 36.12 9.59 0.265 0.539 0.84 137.4

1979 33.39 7.92 0.237 0.470 0.88 119.7

1980 25.01 7.15 0.286 0.593 0.95 151.2

1981 33.39 7.54 0.226 0.444 0.71 113.1

19H2 39.39 9.01 0.229 0.451 0.69 114.9

1983 32.57 9.80 0.273 0.559 0.85 142.6

1984 11.12

1985 11.15

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, and when m is forced

equal to 1.0, the Gompertz 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 non-equilibrium 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 (1946-85).

Estimates of MSY based on 1946-85 fishing years range from

621.1 KMT when m is estimated freely (m = 0.99; PellaTomlinson model) to 696.4 KMT when m is forced equal to 2.0

(Schaefer model) (Fig. 14). The scatter evident in Figure 14 illustrates why little confidence is placed in this approach to estimating

MSY. More confidence is placed in population simulation models,

which are discussed later.

1000r----------------,

900

800

FISHING EFFORT (1000 vessel-ton-weeks)

\

I

\

\

I

\

\

\

\

I

I

I

I

I

I

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\

\

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..

/"-......,

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I \

\

\

,

,

,

,

I

I

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I

I

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\

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..

144.3 228.8

700 ~696.4

oL--1:-:9~6:::"7;---=1;-;:9;.1:;7;-;1;--'1n9l:;7;;5-'-:19;t7~9;:;--:1;-;:9'f;8;::3.---J

100

..--.

l/l

c: -+621.1 0 600 I

- It

U 1

700 .-= .1

- 1 Q) 1 , -. E 500 I , I • ,"'-' , 0 Nominal Effort , I 600 : , 0 , , 0 I

I, I, "

, ... I \ I \ I , ..... I

/ \/ \1 rn 400 I

500 " C) I

,

, Z I

,

, B I , Z , , I

I " «

400 300 I ...I I

I

I

I . 300 I . 200 I . I . I . I • 200 I

100 I

I

o

o

o

en

..l<

<ll

<ll

I

C

o

I

<ll

en'"

<ll

>

I0:

o

U.

u.

W

(!)

z

:c

en

u.

FISHING YEAR

Figure 13

Nominal and effective fishing effort for gulf menhaden plotted against fishing

year, 1964-1985.

Figure 14

Catch of gulf menhaden plotted against effective fishing effort for 1946-85 fishing

years. The solid curve is the Pella-Tomlinson generalized production model, and the

dashed line is the parabolic (Schaefer) production model.

12
Spawner-Recruit Relationships _

With MSY estimates ranging between 620 and 700 KMT, one

would expect that recent levels of landings could not be maintained. However, these high levels of landings are occurring with

relatively low fishing mortality (i.e., 25% mean exploitation rate

in the 1980's compared with 44% mean exploitation rate in the

1960's; Table II) and declining effective fishing effort. The decline in exploitation rate (and effective fishing effort) appears to be

the result of increased population size due to recent high recruitment (Table 4). 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.

where EGGS equals numbers of eggs produced per female, and L

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

quarter (Table 12) was calculated from the von Berta1anffy growth

curves given in Table 8. The expected egg production per female

of a given age was calculated using Eg. (8) and the lengths given

in Table 12. Assuming a 50:50 sex ratio, multiplying one-half

population numbers at age (Table 4) by the expected egg production per female-at-age gives the potential egg production per

individual-at-age (Table 12). Summing across ages for the same

fishing year gives the numbers of spawners as potential eggs

(Table 4).

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

between 903.3 x 106 in 1967 and 11,875.0 x 106 fish in 1983.

Spawners as potential eggs on I January ranged between

10.3 x 109 eggs in 1967 and 143.3 x 109 eggs in 1983. Low to

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 that there are sufficient spawners to

produce subsequent recruits to the population and to preserve the

quality of the habitat utilized by pre-recruit juveniles. If there is a

quantifiable relationship between spawners and recruits, then management can be designed to maximize the landings or some other

objective based on this relationship. Such a relationship was examined for gulf menhaden using the Ricker (1954) model. The Ricker

model was selected over the Beverton and Holt (1957) model based

on arguments by Nelson and Ahrenholz (1986) favoring a domeshaped spawner-recruit relationship. The primary biological argument for the Ricker model is that adult filter-feeding menhaden are

known to ingest their own eggs.

Estimation of the number of recruits to age-0.5 and to age-I has

been described in the VPA section (Table 4). Estimation of spawners follows the description given in Nelson and Ahrenholz (1986).

The number of mature spawners for each year on I January is given

by age (Table 4), where spawning peaks in December and January

and all fish mature by the end of their second year (Lewis and

Roithmayr 1981). The total number of spawners for each recruitment year (I January) is given by the sum from age 2.00 through

age 4.00 (Table 4).

Potential egg production has also been estimated as an index of

spawners. Estimates of egg production as a function of fish length

were obtained from the equation (Lewis and Roithmayr 1981):

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

Table 12

Estimated mean fork length and potential egg production at age on 1 January (2-4 yr) for gulf menhaden by

fishing year, 1964-84.

Age-specific egg

Lengths (mm) production (10 12)

Fishing

year 2 4 2 4

1964 169.9 188.3 213.4 34.30 4.11 0.21

1965 167.3 192.3 212.5 21.06 2.97 0.40

1966 162.6 192.9 214.7 14.74 1.15 0.23

1967 168.6 192.6 212.7 9.76 0.47 0.03

1968 166.4 198.8 216.7 20.31 2.05 0.04

1969 172.1 197.5 229.0 30.04 1.26 0.31

1970 164.7 198.4 228.6 53.77 1.72 0.13

1971 172.8 191.7 216.1 46.53 7.73 0.20

1972 168.8 197.2 208.8 41.02 3.52 1.01

1973 171.5 197.4 221.6 28.34 4.32 0.19

1974 179.5 203.1 225.7 71.05 2.92 0.26

1975 179.5 207.1 234.7 67.59 20.28 0.27

1976 177.2 207.2 226.7 42.26 16.36 0.27

1977 170.0 201.6 228.4 30.26 5.60 3.56

1978 164.9 194.9 217.4 77.51 2.52 0.61

1979 170.8 192.2 211.0 107.57 17.26 0.38

1980 170.0 194.9 209.9 95.20 27.12 2.87

1981 158.8 192.2 210.7 48.01 15.67 5.49

1982 162.3 183.6 208.2 86.35 15.03 2.41

1983 169.9 190.5 204.7 123.62 18.63 1.08

1984 167.9 195.3 208.2 80.42 24.42 2.99

moderate spawning stock size was the rule from 1964 to 1977, and

medium to high spawning stock size from 1978 to 1984. High

recruitment in 1977, 1980, and 1981 year classes resulted in large

spawning stocks in 1979, 1982, and 1983 (as age-2 fish). Since

1964, the proportion of age-2 spawners to the spawning stock has

been fairly consistent, ranging between 82% and 98% in numbers

and between 69% and 97% as eggs (Fig. 15). Since the mid1970's, the contribution of age-2 spawners to the spawning stock

has averaged about 88% in numbers and about 80% as eggs.

Parameters of the Ricker model were estimated by nonlinear

regression from the equation:

where R equals recruits (numbers at age 0.5 or age 1), S equals

spawners (number of adults or potential eggs), and a and bare

parameters to be estimated. Four regressions were calculated from

the data presented in Table 4 (Table 13). In all cases parameter

estimates for both a and b were significantly greater than zero,

indicating a significant relationship.

As illustrated in Figure 16 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 appreciable extent upon the size of the spawning

stock which produced them, and hence can be used in population

simulation projections to investigate sustainable yield for a variety

of F -multiples and to determine MSY.

Ricker models obtained in these analyses suggest that maximum

equilibrium stock size (age-2 and older fish on 1 January) could be

between 19 and 24 billion fish (Table 13). However, stock size for

maximum recruitment (about 30 billion age-I fish) would occur at

In(EGGS) = -9.8719 + 3.8775 In L, (8)

13
100,-----------------------------.

z

O~-050

(IJf- a:(/)

f-C)

Zz 0- OZ

f-~ z<X:

UJO- o(/)

rcO

UJf0-

80

60

40

20

__ Numbers

____ Eggs

I' I ,

/ ' , / "- / ' I "

-.. I

' .........t

FISHING YEAR

Figure 15

Contribution of age-2 spawners (%) to total spawning stock (Numbers) and to total egg production (Eggs) of gulf menhaden, 1964-84.

50,---------------------,

_79

-82

_80

R= 9.46S exp(-0.12S)

R,S in billions

Pseudo-r 2 =0.14

-78

_81

40 _77

30 ~29.9 -76

-68

20

_73 -72 -70

69- -75

-64

- -74

71

.....

I

UJ

C)

<X:

o

f-

(/)

f5

rc

o

UJ

rc

,.....,

(/)

C

:0

......

SPAWNERS IN NUMBERS (billions)

Figure 16

Numbers of gulf menhaden recruits (R) plotted against numbers of spawners (5) for year classes, 1964-82. Curve

represents the fitted Ricker function.

14
Population Simulation Models _

Table 13

Estimates of Ricker spawner-recruit parameters, maximum

equilibrium stock size (S,), stock size for maximum recruitment

(Sm) and maximum recruitment (Rm ) for models regressing

number of recruits (age-O.5 on 4 July or age-Ion 1 January) on

numbers of spawners (ages 2-4) and on potential egg production

from spawners for 1964-82 year classes of gulf menbaden.

15

A .

ii 'I !\

i \ 'I 1\ iii. I '

i i._ I \ i \ i \ L---1.i _.L ~-~-_-- ---------j---i-

<:.1 \ '\ I \ . \

V Ii';' !

\.\. \i\ A II

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VI! Vl/\iil

V V V

1000

(j)

c 900 .E

0

.;:

Q;

E 800 0

0

0

Cl 700 oJ

w

>=

600

500

a

1978-85). For each of these six conditions (3 x 2), population

simulations or projections were run for a series of F-multiples

ranging from 0.2 to 3.0. The projections were for at least 50 years

(e.g., a 25-year projection is shown in Figure 17), and produced

estimates of population-size-at-age, and yield to the fishery for

each year. For most runs involving either of the Ricker spawnerrecruit relationships, only a few years of the simulation were required for equilibrium (sustainable) conditions to be attained. Obviously, no such equilibrium conditions are attainable from the

random recruitment model. Table 14 presents the equilibrium conditions obtained from F-multiples ranging from 0.2 to 2.0 for the

Ricker model with spawners in numbers and using 1964-85 mean

conditions. F-multiples greater than 2.0 would ultimately lead to

a population crash. Estimates of MSY for the 1964-85 mean conditions range from 803 KMT (F -multiple of 1.0, spawners as eggs)

to 825 KMT (F -multiple of 1.0, spawners in numbers), while

estimates of MSY for the 1978-85 mean conditions range from 705

KMT (F-multiple of 1.5, spawners as eggs) to 713 KMT

(F -multiple of 1.5, spawners in numbers) (Table 14).

Two features become evident after comparing the equilibrium

yields between 1964-85 and 1978-85 mean conditions for the two

Ricker models (spawners in numbers, Fig. 18). First, the 1964-85

mean conditions have a higher MSY than do the 1978-85 mean

conditions; secondly, the 1978-85 mean conditions appear less

susceptible to population collapse than do the 1964-85 mean conditions at higher values of the F-multiple. The higher MSY estimate, obtained for the 1964-85 mean conditions compared with the

1978-85 mean conditions, is probably due to the higher mean

weight of individuals landed during the full 1964-85 period compared with the recent 1978-85 period (Fig. 7). The lower MSY

estimate is obtained in spite of higher recruitment levels since

1978. The apparent decrease in susceptibility to population collapse is based on lower exploitation rates (Fig. 5), a shift to higher

F for MSY (Fig. 18), and results from the higher recruitment levels

since 1978. Fifty-year mean yield can be compared between two

PROJECTION YEAR

Figure 17

Population projections for 25 years with F -multiple = 1.0 under 1978-85 mean conditions for gulf menhaden. Three superimposed curves are for Ricker model with

spawners in numbers (solid line), Ricker model with spawners as eggs (dashed line),

and random recruitment model (dot-dashed line).

8.58 51.86

8.59 29.91

90,909.09 49.77

90,909.09 28.69

b(SE) s,

Spawners as numbers (109)

a(SE)

Spawners as eggs (10 12)

1.49(0.35) 0.011(0.003)

0.86(0.20) 0.011(0.003)

Age-0.5 16.42(3.65) 0.117(0.034) 24.02

Age-1.0 9.46(2.11) 0.116(0.034) 19.31

Recruits

Age-0.5

Age-1.0

Estimating maximum sustainable yield, based on biological characteristics of the population, is more preferable than estimates

based on yield and fishing effort (surplus production models discussed earlier in this report). Walters (1969) developed a simulation model (computer program POPSIM), which allows the inclusion of estimates of growth in weight, a spawner-recruit

relationship, and natural and fishing mortality rates. Estimation of

weight-at-age was discussed in the section "Size at Age And

Growth Analyses." In addition to the two estimated Ricker

spawner-recruit models described in the previous section (based on

recruits to age-I), a third spawner-recruit relationship was developed on the basis of the uniform probability density function for

the range in observed recruitment to age-Ion I January during the

period 1964-82 (8.3 to 41.8 billion fish) (Table 4). Fishing mortality can be different for each age class, but must be constant between seasons for which F is greater than zero. Because of between-season limitation on fishing mortality rates in the Walters

(1969) model, no fishing is assumed to occur before age-I, and

fishing on age 1-4 fish is assumed to occur only during the second

and third quarters (April-September). These limitations are not

thought to have any significant effect on the model results, since

few age-O fish have been caught since the mid-1970's and the

fishing season is restricted by law to the period from mid-April to

mid-October. Natural mortality (M) is assumed equal to 1.1Iyear

(67% per year) as in previous analyses.

Numerous POPS1M runs were made for three spawner-recruit

relationships (spawners in numbers, spawners as eggs, and random

recruitment) and for two sets of mean conditions (1964-85 and

about 9 billion spawners (Table 13). Since 1978, stock size has

averaged 9.3 billion fish and recruits to age-l have averaged 33.4

billion (Table 4). Although the spawner-recruit relationships are

marginal, recent mean conditions appear to indicate that recruitment is at or near maximum. However, environmental conditions

appear to be more important in regulating recruitment, so greater

(or lesser) recruitment values may occur. It is not suggested that

maximizing stock size (19-24 billion fish) is necessarily an attainable goal for management given the marginal nature of the

spawner-recruit relationship. Some of the gains in landings already

may be evident in the recent high landings that have come from

high recruitment and population size since 1978.

15
Mean Conditions

__ 1964-85

____ 1978-85

--,"-"-'\

'\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

803.3

//

,-

/

/

/

I

I

/

/

I

I

I

I

I

I

I

I

I

J

J

I

I

I

J

f

I

I

I

I

O~-----::~_.......l.._---::~ --::J

0.0 3.0

F-MULTIPLE

Figure 18

&juilibrium (or sustainable) yield curves from gulf menhaden population simulation

model using Ricker spawner-recruit relation with spawners in numbers. Two superimposed curves are for 1964-85 mean conditions (solid line) and for 1978-85 mean

conditions (dashed line).

704.8

825.1

803.3

712.6

Spawners as numbers:

1.5 0.0 0.547 1427 1.760 7.927 1363.2 34.0

Spawners as eggs:

1.5 0.0 0.547 1427 1.760 7.927 1355.3 338

1964-85 mean conditions

Spawners as numbers:

1.0 0.0 0.543 1.531 1.666 2.815 1709.2 33.9

Spawners as eggs:

1.1 00 0.598 1.648 1.833 3.097 16662 33.5

Table 14

Annual age-specific fishing mortality rates for gulf menhaden expressed as multiples of the average fishing mortality rate at age, actual fishing mortality rates

at age used in the population simulation model, population size in biomass and

numbers and sustainable yield based on Ricker spawner-recruit relationship

between numbers of recruits at age-I and spawners as numbers (agl:S 2-4) for

1964·85 mean conditions. Additional maximum sustainable yield (MSY) estimates obtained for 1978-85 mean conditions and for spawner-recruit curves VI

based on spawners as eggs. c:

.8

Population .g 600 Actual F at age Sustainable a;

F- Biomass No. yield E

multiple 0 2 3 4 (103 mt) (109) (103 mt) 0

0

0

0.0 0.0 0.000 0.000 0.000 0.000 2596.8 40.2 0.0 ......

0.2 0.0 0.109 0.306 0.333 0.563 2394.1 40.1 366.0 0

...J

04 0.0 0.217 0.613 0.667 1.126 2221.1 39.5 5MO.2 W 400

0.6 0.0 0.326 0.919 1.000 1.689 2056.8 38.3 710.6 >=

0.8 0.0 0435 1.225 1.333 2.252 1890.7 364 780.8 ::J

1.0 0.0 0.543 1.531 1.666 2.815 1709.2 33.9 803.3 a:

1.2 0.0 0.652 1.838 2.000 3.378 1504.9 30.6 780.7 III

::::i

14 0.0 0.761 2.144 2.333 3941 1271.7 264 7135 :5

1.6 0.0 0.869 2450 2.666 4.504 997.3 21.1 5973 0 200 1.8 0.0 0.978 2.756 3.000 5.067 677.2 14.5 428.2 W

2.0 0.0 1.807 3.063 3.333 5.630 295.8 64 196.2

MSY for Ricker spawner-recruit relations

1978-85 mean conditions

of the spawner-recruit relationships (Ricker model with spawners

in numbers and random recruitment) for the 1978-85 mean conditions (Fig. 19). If recruitment is random and independent of stock

size, a population crash is unlikely. However, the curve for the

random recruitment model appears to be approaching an asymptotic value for 50 year mean yield as the F -multiple increases. The

yearly average for the asymptotic MSY from the random recruitment model is about 750-800 KMT for 1978-85 mean conditions

(Fig. 19).

The MSY estimates from the population simulation approach

(705-825 KMT) are generally higher than those obtained from the

surplus production models (620-700 KMT). I expect that estimates

of MSY from the population simulation model would be more

realistic than those obtained from the surplus production models

which are based solely on catch and effort data.

Management Implications _

Thc gulf menhaden fishery is conducted within the territorial sea

and offshore of five coastal states (Florida to Texas). All states

voted in favor of a cooperative management plan under the Gulf

States Marine Fisheries Commission (GSMFC) in 1977 (Christmas

and Etzold 1977). This plan was revised and adopted in 1983

(Christmas et al. 1983). Since management authority is vested in

the individual states, some regulations are area-specific on a state

or county basis, but other regulations, such as length of fishing

season (mid-April through mid-October), are common to all states.

No state controls or limits the catch or fishing effort of vessels.

Both landings and fishing effort have increased dramatically

since 1946 (Fig. 2), with high record landings during the 1984

fishing season (982.8 KMT) and record high nominal fishing effort

during the 1983 fishing season (655,800 vessel-ton-weeks). Although an earlier stock assessment revealed that levels of stock

biomass were sufficient to produce historicaf landings (Nelson and

Ahrenholz 1986), a new analysis was deemed necessary to determine if more recent high harvests are due to (a) an increase in

effective fishing effort and availability of the stock, or (b) an

increase in stock size due to exceptionally large year classes in

recent years. Given either of the above conditions, it is unlikely

that the fishery can sustain these high levels of harvest indefinitely;

16
800r----------- --,

Acknowledgments _

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

Southeast Fisheries Center, Beaufort Laboratory, who were involved in the many aspects of the menhaden program, especially

Eldon J. Levi, Ethel A. Hall, and Joseph W. Smith. I am grateful

to Charles W. Krouse for his assistance in preparing the computerized data sets for analysis and for other programming help. I would

also like to thank Dean W. Ahrenholz for getting me started on

several of the computer library programs used in these analyses,

my wife Nancy for loading many of the tables and figures on our

home microcomputer, and Herbert R. Gordy for final drafting of

the figures. I thank Dean W. Ahrenholz, Joseph W. Smith, James

R. Waters, Charles S. Manooch, John V. Merriner, and two

anonymous reviewers for reviewing this manuscript.

for MSY is probably more indicative of the average landings that

could have been removed from the gulf menhaden stock during the

period from which data were obtained (1964-85 fishing years),

given the limitations in adjusting the fishing effort (restricted to

1964-83 fishing years, Table II) used in surplus production models and the firmer biological basis for the population simulation

approach. The concern is that recent landings greater than historical estimates of MSY (greater than 850 KMT since 1982, Table 2)

may be too high. However, these analyses are always retrospective

and have an inherent time lag in them which prevents a direct

assessment of the period since 1982.

Estimates of MSY from surplus production models continue the

upward trend noted in Nelson and Ahrenholz (1986). Chapoton

(1972) obtained an estimate of MSY of 430 KMT for the 1946-70

period, Schaaf (1975) obtained an estimate of 478 KMT for the

1946-72 period, and Nelson and Ahrenholz (1986) obtained estimates ranging from 540 to 640 KMT for the 1946-79 period. The

primary biological concern raised by stock assessment scientists is

that the nature of the descending limb can only be determined

accurately if landings exceed the current MSY for several years. If

the descending limb were steep, this could put the stock at risk.

The Pella-Tomlinson model from catch and effective effort data

has a flat descending limb (m =0.99, Fig. 14), while the PellaTomlinson model from catch and population F data has a steep

slope (m =2.78).

The gulf menhaden is shorter lived than the Atlantic menhaden

(higher natural mortality), which can result in rapid year-to-year

changes in fishable stock. Although increasing the number of year

classes in the fishable stock is neither biologically practical nor

suggested, caution is advised relative to the high F's found and the

dependency of the fishery upon very few age groups. Expansion of

this fishery by effort or area is not recommended.

In summary, the gulf menhaden fishery is currently fully exploited and biologically appears reasonably stable in view of the

age composition, life span, and effects of environmental factors.

Annual production, fishing effort, and fleet size appear reasonably

balanced. Although recent short-term harvests in excess of MSY

do not appear detrimental to the stock, long-term harvesting above

MSY cannot be maintained given our current understanding of the

resource and uncertainties in our estimates of MSY.

3.0

---- .....-----

2.0

1.5

F-MULTIPLE

1.0

__ Ricker Spawner- Recruit with

Spawners in Numbers

___ Random Recruitment

/

/ /

/'

/'

/ / /

/

/

/

/

I

I

/

/

/

/

/

/

I

I

I

I

I

I

I

I

I

I

1

~718.1

c 400 ...J

LlJ

...J

<::::>

z

z

<

z

<

LlJ

Cil .8 600

.g

Qi

E

8

o

....,

Figure 19

Fifty year mean yield for 1978-85 mean conditions from gulf menhaden population

simulation model. Two superimposed curves are for Ricker model with spawners in

numbers (solid line) and random recruitment model (dashed line).

landings eventually will be reduced. If condition (a) is prevalent,

stock damage may occur and harvests would drop below levels that

would occur if condition (b) is prevalent where no stock damage

is expected to occur.

Recruitment to age-I (on I January) has varied between 8.3 and

41.8 billion fish (Table 4), with many of the greater values occurring since 1977. Greater values for population size and spawners

(Table 4) and smaller values for exploitation rate (Table II) have

resulted. Therefore, effective fishing effort has actually declined

since the 1960's (Fig. 13). The implication is that the increased

landings since 1978 are the result of exceptionally good recruitment (i.e., year classes) and not the result of greater fishing effort.

Increased availability of gulf menhaden to the fishery does not

seem likely, given the loss of reduction plants at the geographic

extremes (Table I) and area and seasonal closures that have been

implemented (Christmas et at. 1983).

Although recruitment has been high since the late 1970's, it

depends largely upon environmental conditions that are beyond the

control of management (as evidenced by the unexplained scatter in

Figure 16). To the extent that recruitment does depend upon the

spawning stock, the dependency rests primarily on age-2 spawners. The concern to management is that several poor environmental

years leading to several poor recruitment years could put the gulf

menhaden population at risk. Thus, there is need for frequent

monitoring and evaluation of the gulf menhaden stock.

Estimates of MSY data range from 620 to 700 KMT based on

surplus production models (landings and fishing effort data from

1946-85 fishing years), and from 705 to 825 KMT based on population simulation models (using Ricker spawner-recruit relationships based on 1964-82 year classes). The latter range of estimates

17
Citations _

ABRAMSON, N. J.

1971. Computer programs for fish stock assessment. FAO Fish. T~ch. Pap.

101:1-154.

AHRENHOLZ, D. W.

1981. Recruitment and exploitation of gulf menhaden (Brevoortia patronus).

Fish. Bull., U.S. 79:325-335.

BEVERTON, R. J. H., and S. J. HOLT.

1957. On the dynamics of exploited fish populations. Fish. Invest. Ser. II Mar.

Fish. G.B. Minist. Agric. Fish. Food 19:533 p.

CHAPOTON, R. B.

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