NOAA Technical Report NMFS 149 April 2000

U.S. Department of Commerce

Population Characteristics of 

Gulf Menhaden, Brevoortia patronus

Douglas S. Vaughan

Joseph W. Smith

Michael H. Prager
U.S. Department of Commerce

Seattle, Washington

NOAA Technical Report NMFS 149

A Technical Report of the Fishery Bulletin

Population Characteristics of 

Gulf Menhaden, Brevoortia patronus

Douglas S. Vaughan

Joseph W. Smith

Michael H. Prager

April 2000
iii

Contents

Introduction 1

Virtual Population Analysis 4

Size at Age and Growth Analyses 6

Biological Reference Points for Mortality 7

Spawner-Recruit Relationships 10

Surplus Production Models 12

Juvenile Abundance Indices and Environmental Factors 14

Management Implications 17

Acknowledgments 18

Literature Cited 18
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 (Nelson and 

Ahrenholz, 1986; Christmas et al., 1988). Adult menhaden 

are fi lter feeders (feeding primarily on phytoplankton) 

and, in turn, support predatory food fi shes. Gulf menhaden form large surface schools, appearing in nearshore 

Gulf waters from about April to November. Although no 

extensive coastwide migrations are known to occur, there 

is evidence that older fi sh move toward the Mississippi 

River delta (Ahrenholz, 1981). Spawning peaks during 

December and January in offshore waters (Lewis and 

Roithmayr, 1981). Eggs hatch at sea and ocean currents 

carry the larvae to estuaries where they develop into juveniles (Christmas et al., 1988). Juveniles migrate offshore 

1

Population Characteristics of Gulf Menhaden, Brevoortia patronus

DOUGLAS S. VAUGHAN, JOSEPH W. SMITH, and MICHAEL H. PRAGER

Beaufort Laboratory

Southeast Fisheries Science Center

National Marine Fisheries Service, NOAA

101 Pivers Island Road

Beaufort, North Carolina 28516-9722

ABSTRACT

The status of the Gulf menhaden, Brevoortia patronus, fi shery was assessed with purse-seine 

landings data from 1946 to 1997 and port sampling data from 1964 to 1997. These data were 

analyzed to determine growth rates, biological reference points for fi shing mortality from yield 

per recruit and maximum spawning potential analyses, spawner-recruit relationships, and maximum sustainable yield (MSY). The separable virtual population approach was used for the 

period 1976–97 (augmented by earlier analyses for 1964–75) to obtain point estimates of stock 

size, recruits to age 1, spawning stock size, and fi shing mortality rates. Exploitation rates for 

age-1 fi sh ranged between 11% and 45%, for age-2 fi sh between 32% and 72%, and for age-3 

fi sh between 32% and 76%. Biological reference points from yield per recruit (F0.1: 1.5–2.5/yr) 

and spawning potential ratio (F20: 1.3–1.9/yr and F30: 0.8–1.2/yr) were obtained for comparison 

with recent estimates of F (0.6–0.8/yr). Recent spawning stock estimates (as biomass or eggs) 

are above the long-term average, while recent recruits to age 1 are comparable to the long-term 

average. Parameters from Ricker-type spawner-recruit relations were estimated, although considerable unexplained variability remained. Recent survival to age-1 recruitment has generally 

been below that expected based on the Ricker spawner-recruit relation. Estimates of long-term 

MSY from PRODFIT and ASPIC estimation of production model ranged between 717,000 t and 

753,000 t, respectively. Declines in landings between 1988 and 1992 raised concerns about the 

status of the Gulf menhaden stock. Landings have fl uctuated without trend since 1992, averaging about 571,000 t. However, Gulf menhaden are short lived and highly fecund. Thus, variation 

in recruitment to age 1, largely mediated by environmental conditions, infl uences fi shing success over the next two years (as age-1 and age-2 fi sh). Comparisons of recent estimates of fi shing 

mortality to biological reference points do not suggest overfi shing.

during winter and move back to coastal waters the following spring as age-1 adults.

Gulf menhaden are subject to an extensive purseseine fi shery in the northern Gulf of Mexico from 

mid-April through 1 November as regulated by interstate compact (Leard et al., 1995). Since 1964, NOAA’s 

National Marine Fisheries Service has maintained a sampling program for Gulf menhaden. Participation in the 

Gulf menhaden fi shery, in terms of numbers of fi shing 

companies, plants, and purse-seine vessels, has fallen 

dramatically since the 1970s. During the study period 

the number of active reduction plants where menhaden 

are processed for meal and oil has varied between 5 and 

14, with 5 plants active in 1997 (Table 1). The number 

of purse-seine vessels has varied between 51 and 92, 

with 52 vessels active during the 1997 fi shing season. 

The declines were primarily due to corporate consolida-
2 NOAA Technical Report NMFS 149

Table 1

Number of Gulf menhaden (Brevoortia patronus) reduction plants by port and total, number of purse-seine vessels, and number 

of fi sh sampled for age and size for fi shing years, 1964–97.

 Ports1 No. No. No.

Fishing reduction reduction fi sh

year A MP E D MC IC C SP plants vessels sampled

1964 0 3 2 2 1 0 2 1 11 78 12,457

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

1966 1 3 2 2 1 1 3 1 13 92 13,016

1967 0 3 2 2 1 1 3 1 13 85 14,519

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

1969 1 3 2 1 1 1 3 1 13 75 15,281

1970 0 3 2 2 1 1 3 1 13 76 10,560

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

1972 0 3 2 1 1 1 3 0 11 75 10,030

1973 0 2 2 1 1 1 3 0 10 66 8,958

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

1975 0 3 2 1 1 1 3 0 11 78 9,529

1976 0 3 2 1 1 1 3 0 11 82 13,586

1977 0 3 2 1 1 1 3 0 11 80 14,918

1978 0 3 2 1 1 1 3 0 11 80 12,985

1979 0 3 2 1 1 1 3 0 11 78 11,620

1980 0 3 2 1 1 1 3 0 11 79 9,961

1981 0 3 2 1 1 1 3 0 11 80 10,408

1982 0 3 2 1 1 1 3 0 11 82 10,709

1983 0 3 2 1 1 1 3 0 11 81 14,840

1984 0 3 2 1 1 1 3 0 11 81 16,001

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

1986 0 2 2 1 0 1 2 0 8 72 16,530

1987 0 2 2 1 0 1 2 0 8 75 16,530

1988 0 2 2 1 0 1 2 0 8 73 12,410

1989 0 2 2 1 1 1 2 0 9 77 13,970

1990 0 2 2 1 1 1 2 0 9 75 11,670

1991 0 1 2 1 1 1 1 0 7 58 11,690

1992 0 1 1 1 1 1 1 0 6 51 15,590

1993 0 1 1 1 1 1 1 0 6 52 15,730

1994 0 1 1 1 1 1 1 0 6 55 16,820

1995 0 1 1 1 1 1 1 0 6 52 14,520

1996 0 1 1 0 1 1 1 0 5 51 13,550

1997 0 1 1 0 1 1 1 0 5 52 10,950

1 A = Appalachicola, FL: Fish Meal Co. (1966, 1968–69); MP = Moss Point, MS: Seacoast Products Co. (1964–72, 1975–84), AMPRO Fisheries, 

Inc. (formerly Standard Products (1964–90), Zapata Haynie, Inc. (1964–92); E = Empire, LA: Empire Menhaden Co. (1964–91), Daybrook 

Fisheries (formerly Petrou Fisheries, Inc. (1964–92); D = Dulac, LA: Dulac Menhaden Fisheries (1964–68, 1970–71), Fish Meal and Oil Co. 

(1964–65), Zapata Haynie, Inc. (1965–92); MC = Morgan City, LA: Seacoast Products Co. (1965–84), Gulf Protein (1989–92); IC = Intracoastal 

City, LA: Seacoast Products Co. (1965–84), Zapata Haynie, Inc. (1985–92); C = Cameron, LA: Louisiana Menhaden Co. (1964–90), Seacoast 

Products Co. (1964–84), Zapata Haynie, Inc. (1967–92); SP =Sabine Pass, TX: Texas Menhaden Co. (1964–71).

tion. Major acquisitions of competitor fi sh companies 

occurred in 1984, 1992, and late 1997. Ports of landing 

such as Cameron, Empire, and Moss Point, which historically supported multiple plants owned by several 

companies, eventually harbored only a single plant per 

port. By early 1998, a single company dominated the 

fi shery and owned four of fi ve plants in the northern 

Gulf of Mexico. Counter to the demise of menhaden 

plants in recent years, has been the relative stability of 

fl eet. Despite the fall in absolute numbers of plants, surviving plants have tended to increase processing capacity, and thus maintain a relatively stable fl eet of about 

50 vessels since 1992. Annual landings and nominal 

fi shing effort data in vessel-ton-weeks (vtw), available 
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 3

Figure 1

Landings and nominal fi shing effort by the Gulf menhaden (Brevoortia patronus) reduction fi shery, 1946–97.

Figure 2

Percent of numbers for ages 1–3+ [fi gure shows 3+] estimated from landings by the Gulf menhaden (Brevoortia 

patronus) reduction fi shery, 1964–97.

since 1946, show an upward trend in landings from 

1946 through 1984 when landings peaked at 982,800 t 

(Fig. 1). Nominal effort peaked the previous year (1983) 

at 655,800 vessel-ton-weeks. Landings and nominal effort 

then declined to 421,400 t and 408,000 vessel-tonweeks in 1992, respectively. Between 1984 and 1992, 

the number of reduction plants declined from 11 to 6 

and the number of purse-seine vessels from 81 to 51. 

Since 1992, landings have varied between 463,900 and 

761,600 t, while effort has varied between 417,000 and 

472,000 vessel-ton-weeks without apparent trend.

Detailed information on daily vessel landings and fi sh 

sampled for length, weight, and age (from scales) is 

available from 1964 to the present. This information 

is used to estimate the number of fi sh landed at age, 

1964–97 (Table 2). A new computer program for estimating catch at age was developed during 1996–97 and 

re-estimation of catch in numbers at age based on this 

program was done for 1985–97. The fi shery depends 

primarily on age-1 (comprising 35–92% of the landings) and age-2 fi sh (7–62%) (Fig. 2). The remaining 

ages (age-0, -3, and -4+) generally contribute insignifi -

cantly to the landings (<1% to 13%), although age-3 

contributed 10% in 1975. Age-2 menhaden comprised 

over 50% of the landings in 1986, 1995, and 1996.

Vaughan et al. (1996) last analyzed coast-wide Gulf 

menhaden data for the 1964–92 fi shing years. At that 

time, landings had been declining for almost a decade 

since the record high in 1984. The purpose of this 

paper is to reevaluate the status of the Gulf menhaden 

stock using fi ve additional fi shing years (through 1997 

fi shing year). The analyses that follow parallel to some 

extent those presented in Nelson and Ahrenholz (1986), 

Vaughan (1987), and Vaughan et al. (1996) with modifi cations as described. Estimates of population numbers 

and fi shing mortality rates by age are obtained from virtual population analysis (VPA), specifi cally by separable 

VPA for the period 1976–97. The Murphy VPA results 

for 1964–75 from Vaughan et al. (1996) are used in 

population models. For each fi shing year, length at age 

is estimated by fi tting the von Bertalanffy growth curve 

to obtain parameter estimates; weight at age is obtained 

by relating weight to length. Biological reference levels 

of fi shing mortality are obtained from yield per recruit 

and spawning stock biomass per recruit approaches. 

Spawning stock biomass is compared with subsequent 

recruitment to age 1, from which Ricker spawner-recruit 

model parameters are estimated. Effective fi shing effort 

is obtained by adjusting nominal effort for estimated 

variability in the catchability coeffi cient, from which 

parameters and biological reference values from surplus 

production models are estimated (with annual landings 

data using PRODFIT [Fox, 1975] and ASPIC [Prager, 

1995]). Recruitment estimates are compared to juvenile 

abundance data recently made available from Louisiana 

and Texas, and to several environmental factors. The 

results from these models are used to evaluate the Gulf 

menhaden stock status.
4 NOAA Technical Report NMFS 149

Table 2

Estimated landings of Gulf menhaden (Brevoortia patronus) in numbers at age (0–4+), total numbers landed (ages 0–4+), total 

landings by weight, and nominal fi shing effort (vessel-ton weeks) for the fi shing years, 1964–97. New method of estimation of 

catch at age used for 1985–97.

 Landings in nos. at age (109) landings Total Nominal

Fishing landings fi shing

year 0 1 2 3 4+ Total (1000 t) effort1

1964 0.0 3.33 1.50 0.12 0.0 4.95 409.4 272.9

1965 0.04 5.03 1.08 0.08 0.0 6.23 463.1 335.6

1966 0.03 3.31 0.87 0.03 0.0 4.24 359.1 381.3

1967 0.02 4.27 0.34 0.01 0.0 4.64 317.3 404.7

1968 0.07 3.48 1.00 0.04 0.0 4.58 373.5 382.3

1969 0.02 6.08 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 0.0 7.92 728.2 472.9

1972 0.02 3.05 1.73 0.09 0.0 4.89 501.7 447.5

1973 0.05 3.03 1.11 0.10 0.0 4.29 486.1 426.2

1974 0.0 3.85 1.47 0.06 0.0 5.38 587.4 485.5

1975 0.11 2.44 1.50 0.46 0.0 4.51 542.6 538.0

1976 0.0 4.59 1.37 0.20 0.0 6.17 561.2 575.8

1977 0.0 4.66 1.33 0.11 0.01 6.11 447.1 532.7

1978 0.0 6.79 2.74 0.05 0.01 9.59 820.0 574.3

1979 0.0 4.70 2.88 0.34 0.01 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 0.38 0.03 8.90 923.5 655.8

1984 0.0 7.75 2.88 0.44 0.05 11.12 982.8 645.9

1985 0.0 8.68 2.50 0.23 0.04 11.45 881.1 560.6

1986 0.0 4.28 4.89 0.17 0.03 9.37 822.1 606.5

1987 0.0 6.70 3.98 0.43 0.01 11.12 894.2 604.2

1988 0.0 5.34 2.58 0.15 0.02 8.09 623.7 594.1

1989 0.0 5.55 1.62 0.07 0.00 7.24 569.6 555.3

1990 0.0 3.89 1.79 0.14 0.01 5.83 528.3 563.1

1991 0.0 2.22 2.34 0.22 0.03 4.80 544.3 472.3

1992 0.0 2.19 1.51 0.20 0.03 3.92 421.4 408.0

1993 0.0 3.49 1.53 0.19 0.02 5.24 539.2 455.2

1994 0.0 3.63 3.20 0.44 0.05 7.32 761.6 472.0

1995 0.0 1.37 2.42 0.10 0.00 3.90 463.9 417.0

1996 0.0 1.78 2.51 0.25 0.02 4.57 479.4 451.7

1997 0.0 3.24 2.40 0.28 0.04 5.95 611.2 430.2

1 Units are 1,000 vessel-ton weeks.

Virtual Population Analyses

The results from two methods of virtual population analysis (VPA) are used in this assessment. The fi rst method, 

that of Murphy (1965), is described in Vaughan (1987) 

and is used for 1964–75. The second method, that of 

Doubleday (1976), is referred to as “separable” VPA and 

is applied to more recent years, 1976–97; it assumes that 

age- and year-specifi c estimates of F can be partitioned 

into the product of an age component (partial recruitment) and a year component. We used the computer program (SVPA.EXE) as modifi ed by Clay (1990) from Pope 

and Shepherd (1982). This method was applied to the 

catch-in-numbers-at-age matrix (or catch matrix) based on 

annual ages (not quarterly ages as in the Murphy VPA).

Because Vaughan et al. (1996) demonstrated that the 

two VPA approaches (Murphy VPA and separable VPA) 

gave similar results for the period 1976–92, the latter 

approach was used for updating the period 1993–97. 

Additional separable VPA runs were made to explore the 
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 5

Figure 4

Comparison of (a) unweighted mean F, and (b) recruits 

to age 1 estimated using separable virtual population analysis on old and new methods for estimating catch at age 

of Gulf menhaden (Brevoortia patronus) applied to overlapping years, 1985–94.

plausibility of the separable assumption for the period 

1976–97. Inspection of the approximate coeffi cient of 

variation (CV) and sum of squared deviations (SSQ) 

(output produced by SVPA.EXE program), when plotted against initial year of data appearing in the catch 

matrix (Fig. 3), suggested that the separable assumption 

continued to be reasonable when extending the catch 

matrix (1976–92) to 1997. See Vaughan et al. (1996) for 

discussion of possible causes for this discontinuity in CV 

and SSQ.

A new method for estimating catch-in-numbers at age 

was developed which uses a more statistically-rigorous 

approach to fi lling missing port/week combinations 

for which sampling was unavailable. A general linear 

model (GLM) approach was used to estimate catch-innumbers at age for each port and week combination 

throughout the fi shing year based on season (quarterly) 

and NMFS area (east and west of Mississippi River) using 

length, weight, and age structure information, rather 

than ad hoc approaches previously used. Sensitivity of 

VPA output to the change in catch-at-age estimation procedure (which overlaps for 1985–94) was explored. Only 

small differences are noted in estimates of weighted 

mean F (ages 1–4 with M=1.1/yr) and recruitment to 

age 1 (except 1993 and 1994) (Fig. 4a, b).

An estimate for natural mortality (M) of 1.1/yr was 

used in previous assessments (Nelson and Ahrenholz, 

1986; Vaughan, 1987; Vaughan et al., 1996). As noted in 

Vaughan et al. (1996), estimates of M based on tagging 

studies range from 0.7 to 1.6/yr. Life history approaches 

provide estimates of M that range from 0.9 to 1.1/yr 

Figure 3

Coeffi cient of variation (CV) of catch data and sum 

of squared (SSQ) deviations of log catch ratios plotted 

against increasing starting year of the Gulf menhaden 

(Brevoortia patronus) catch matrix used in the separable 

VPA approach. Starting year varies between 1964 and 

1994 and fi nal year in the catch matrix for all computations is 1997.

based on Pauly (1979) using mean temperature and 

von Bertalanffy growth parameters, and 0.7 to 1.1/yr 

based on Hoenig (1983) using maximum age. As noted 

in Vaughan et al. (1996), life history approaches for 

estimating M do not refl ect additional mortality due to 

other sources (e.g., losses to a small bait fi shery or as 

bycatch in other fi sheries). Hence, most analyses that 

follow assume M = 1.1/yr, although sensitivity runs are 

made with M = 0.8, 0.9, and 1.0/yr.

For comparison with and as a continuation of Vaughan 

et al. (1996), exploitation rates u [proportion removed 

annually]:

 u = F(1–e –Z)/Z, (1)

where Z is the total instantaneous mortality rate (M+F ) 

for ages 1, 2, and 3, and ages 1–4 combined are plotted 
6 NOAA Technical Report NMFS 149

against year based on the Murphy VPA (from Vaughan 

et al., 1996) for 1964–75 and separable VPA for 1976–97 

(Fig. 5). Exploitation rates for each age and ages 1–4 combined generally have declined since 1964. Exploitation 

rates for age-1 fi sh ranged between 11% in 1995 and 45% 

in 1966; ranges for age-2 fi sh were between 32% in 1995 

and 72% in 1966; and for age-3 fi sh were between 32% 

in 1995 and 76% in 1975. Overall exploitation rates (ages 

1–4) ranged between 16% in 1995 and 52% in 1966.

To investigate sensitivity of fi shing mortality estimates 

(F ) to assumed values of natural mortality, additional 

estimates of fi shing mortality were made using the separable VPA with lower estimates of M (0.8, 0.9, and 

1.0/yr). Estimates of annual weighted mean F are compared between estimates of M for 0.8, 0.9, 1.0, and 

1.1/yr from SVPA on the catch matrix (Fig. 6a). As M

is decreased, consistently higher estimates of annual 

weighted mean F are obtained. Although differences 

are small, they are signifi cant, especially if the present 

value of M is a gross overestimate (<<0.8 compared to 

1.1/yr). During the period 1976–97, weighted (by catch 

in numbers) mean fi shing mortality (ages 1–4) from 

the separable VPA (with M = 1.1/yr) ranged between 

0.16/yr in 1995 and 0.42/yr in 1988.

Recruitment to age 1 was generally high and variable 

between 1976 and 1988, but has been lower and less 

variable since then (Fig. 7a). Because age-1 menhaden 

form a large component of the population size, the total 

population (ages 1–4) shows a similar pattern. On average, recruitment to age 1 was highest during the 1980s, 

with 41.1 billion recruits to age 1 in 1985.

Retrospective analyses also were conducted to determine uncertainty in recent VPA output estimates, al -

Figure 5

Gulf menhaden (Brevoortia patronus) exploitation rates (u) for 

ages 1, 2, 3, and ages 1–4 combined obtained from separable 

VPA approach (M = 1.1/yr), 1964–97.

though the analyses were not as detailed as those presented for Atlantic menhaden in Cadrin and Vaughan 

(1997). Retrospective analyses were run with separable 

VPA by parallel runs deleting the most recent year (initial year was always 1976). Terminal F value was obtained 

from a catch curve analysis on the cohort that was age 

4 in the fi nal year. Although the retrospective error in 

F (Fig. 6b) and recruits to age 1 (Fig. 7b) were occasionally large, the error is generally without bias as was 

found for Atlantic menhaden. Typical of retrospective 

error with large total mortality, this error tends to disappear after a few years. Hence, retrospective error is largest for the most recent 2–3 years of the analyses.

Size at Age and Growth Analyses

Interpolated lengths and weights of Gulf menhaden at 

age are needed for estimating optimum fi shing yield and 

spawning stock biomass. Estimates of annual mean weightat-age for Gulf menhaden in the purse-seine catches were 

calculated to determine any trends in yield-per-recruit that 

could be expected in the fi shery. No specifi c upward or 

downward trends in mean weight-at-age are noted (Fig. 8).

Weight (W, in g) is estimated from the weight-length 

relationship expressed in the linear form of the power 

function,

 ln W = ln a + b ln L, (2)

where L is fork length (mm), and ln a and b are parameters estimated by linear regression for each fi shing year 

(Table 3). A correction factor (σ2/2), where σ2 is the variance, based on the mean squared error (MSE) was 

used when retransforming from ln W to W based 

on properties of the lognormal distribution (Beauchamp and Olson, 1973).

Fork length (L, in mm) can be estimated from 

age (t, in yr) on the basis of the von Bertalanffy 

(1938) growth equation,

L L Kt t t = − −− ∞ ( ) 1 exp ( ) , ( ) 0 (3)

where L∞, K, and t

0 are parameters that in this 

case were estimated by nonlinear regression (PROC 

NLIN, MARQUARDT OPTION, SAS Institute Inc., 

1987). The maximum length (L∞) is approached 

asymptotically, at a rate described by parameter K, 

with t

0 shifting the curve to the left or right. Annual 

estimates are based on all individual fi sh weighted 

by the inverse of numbers of fi sh in sample at age. 

This is done to improve convergence and correct 

for parameter bias and poor precision resulting 

from too few older fi sh compared to large numbers of young fi sh, as noted in Vaughan and Kan-
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 7

Figure 6

Mean fi shing mortality (F ) over ages 1–4 for Gulf menhaden (Brevoortia patronus) from separable VPA compared by 

(a) natural mortality (0.8, 0.9, 1.0, and 1.1/yr), 1976–97, 

and (b) retrospective comparison with decreasing maximum year in catch matrix (M =1.1/yr).

Figure 7

Recruits to age-1 Gulf menhaden (Brevoortia patronus)

compared by (a) natural mortality (0.8, 0.9, 1.0, and 

1.1/yr), 1976–97, and (b) retrospective comparison with 

decreasing maximum year in catch matrix.

ciruk (1982) (Table 4). Converged estimates of L∞ ranged 

from 216 mm to 745 mm in fork length, with a median 

value of 241 mm and an interquartile range (middle 

50%) between 232 and 278 mm. Converged estimates of 

K ranged from 0.06 to 0.84/yr, with a median value of 

0.41 and interquartile range between 0.29 and 0.51/yr. 

One should note that because of the typically high correlations among the parameters, ranges in estimates of L∞

and K can give an exaggerated impression of their variability. Biologically extreme values of parameters are still 

useful for interpolating size at age within the range of 

ages available for the statistical fi t. It is not appropriate to 

extrapolate sizes at ages beyond those used in the fi tting 

process.

Biological Reference Points 

for Fishing Mortality

Two modeling approaches are used in estimating biological reference points based on fi shing mortality rates, to 

assess whether recent estimated rates are too high. Reference points from the fi rst modeling approach (yieldper-recruit analysis) have been used for several decades, 
8 NOAA Technical Report NMFS 149

Figure 8

Gulf menhaden (Brevoortia patronus) mean weight at age, 

1964–97.

Table 3

Weight-length regression parameters (and standard 

errors) for Gulf menhaden (Brevoortia patronus) by fi shing year, 1964–97 (ln W = ln a + b ln L). Sample size (n) 

and mean squared error (MSE) also given.

Fishing

year n ln a b r2 MSE

1964 12,377 –12.7 (0.04) 3.4 (0.007) 0.94 0.009

1965 15,673 –12.5 (0.03) 3.3 (0.005) 0.96 0.009

1966 12,681 –11.6 (0.03) 3.2 (0.006) 0.95 0.007

1967 14,401 –11.3 (0.03) 3.1 (0.006) 0.94 0.008

1968 15,829 –11.7 (0.03) 3.2 (0.006) 0.95 0.008

1969 15,044 –11.4 (0.03) 3.1 (0.006) 0.95 0.009

1970 10,531 –12.0 (0.04) 3.2 (0.008) 0.95 0.006

1971 7,848 –12.2 (0.04) 3.3 (0.009) 0.95 0.008

1972 9,975 –11.8 (0.04) 3.2 (0.008) 0.94 0.008

1973 8,954 –11.7 (0.05) 3.2 (0.009) 0.94 0.008

1974 10,085 –10.8 (0.04) 3.0 (0.009) 0.92 0.010

1975 9,528 –11.6 (0.03) 3.1 (0.007) 0.96 0.008

1976 13,532 –10.8 (0.03) 3.0 (0.006) 0.95 0.008

1977 14,910 –11.4 (0.02) 3.1 (0.005) 0.97 0.006

1978 12,983 –12.1 (0.03) 3.2 (0.006) 0.96 0.006

1979 11,618 –12.2 (0.03) 3.3 (0.005) 0.97 0.005

1980 9,948 –13.0 (0.05) 3.4 (0.010) 0.92 0.023

1981 10,405 –11.7 (0.03) 3.2 (0.006) 0.96 0.010

1982 10,678 –12.7 (0.04) 3.4 (0.007) 0.95 0.011

1983 14,837 –12.3 (0.03) 3.3 (0.005) 0.96 0.008

1984 15,955 –11.9 (0.03) 3.2 (0.005) 0.96 0.007

1985 13,227 –11.5 (0.03) 3.1 (0.006) 0.95 0.007

1986 16,495 –11.8 (0.02) 3.2 (0.005) 0.97 0.006

1987 16,458 –11.7 (0.03) 3.2 (0.005) 0.96 0.006

1988 12,403 –11.4 (0.04) 3.1 (0.008) 0.93 0.011

1989 13,951 –11.8 (0.03) 3.2 (0.007) 0.95 0.007

1990 11,500 –11.7 (0.04) 3.2 (0.007) 0.95 0.012

1991 11,637 –12.2 (0.04) 3.3 (0.009) 0.93 0.008

1992 15,231 –10.4 (0.03) 2.9 (0.006) 0.94 0.009

1993 15,348 –11.3 (0.04) 3.1 (0.007) 0.93 0.012

1994 16,785 –11.0 (0.03) 3.0 (0.006) 0.95 0.007

1995 14,275 –12.0 (0.04) 3.2 (0.007) 0.94 0.008

1996 12,784 –12.6 (0.05) 3.3 (0.010) 0.90 0.017

1997 10,583 –11.7 (0.03) 3.2 (0.006) 0.96 0.005

while those from the second modeling approach (spawning-stock-biomass-per-recruit) have been used recently by 

the fi shery management councils and commissions. Mean 

values for growth parameters are used in these modeling 

approaches to refl ect average conditions over a specifi ed 

time period (e.g., decadal means for both weight-length 

relationships in Table 3 and length-age relationships in 

Table 4).

Yield-per-Recruit Analysis

The trade off between decreasing numbers of fi sh and 

increasing biomass per average individual fi sh forms the 

conceptual basis for yield-per-recruit analysis. The Ricker 

(1975; eq. 10.4) formulation was used for estimating yield 

per recruit [this was the basis for MAREA used in previous Gulf menhaden stock assessments (Nelson and Ahrenholz, 1986; Vaughan, 1987)]. Data required includes 

age-specifi c estimates of fi shing mortality (from VPA) and 

weight (relationships given in Tables 3 and 4). Yield per 

recruit for Gulf menhaden was estimated from fi shing 

estimates for 1976–97 (Fig. 9).

Two important biological reference points are typically obtained from this approach: Fmax and F0.1. Fmax

represents the level of fi shing mortality which maximizes yield per recruit, while the latter represents the 

level of fi shing mortality where the slope of the increasing yield per recruit curve is 10% of the slope at the 

origin (Sissenwine and Shepherd, 1987). F0.1 was developed because it is more conservative (precautionary) 

than the former, so as to protect against possible recruitment overfi shing. Estimates of Fmax were not obtained 

for the Gulf menhaden data because yield per recruit 

continues to rise with increasing F (>4.0/yr). Estimate 

of F0.1 ranged between 1.4 and 2.5/yr, increasing with 

increasing M (Table 5).

Annual (fi shing year) estimates of yield per recruit 

(M = 1.1/yr) since 1976 ranged between 9 and 31 g 

with values generally lower since 1980 (Fig. 9). Yield 

per recruit declined from an average of 26 g in the late 

1970s to 13 g during the 1980s and 1990s. A value of 13 

g was estimated for the 1997 fi shing year.
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 9

Figure 9

Yield per recruit for Gulf menhaden (Brevoortia patronus) 

compared by natural mortality (0.8, 0.9, 1.0, and 1.1/yr), 

1976–97.

Table 4

Estimated von Bertalanffy growth parameters (and asymptotic standard errors) for Gulf menhaden (Brevoortia 

patronus) for fi shing years, 1964–97.

Year n L∞ K t0

1964 12,261 242.7 (0.81) 0.39 (0.005) –0.97 (0.017)

1965 15,185 400.8 (7.18) 0.13 (0.004) –1.81 (0.032)

1966 12,429 278.1 (1.44) 0.29 (0.004) –1.14 (0.018)

1967 14,065 235.0 (0.80) 0.53 (0.005) –0.50 (0.009)

1968 15,271 281.0 (1.24) 0.32 (0.004) –0.79 (0.014)

1969 14,764 473.5 (19.6) 0.10 (0.007) –2.15 (0.049)

1970 10,402 233.4 (0.97) 0.51 (0.008) –0.55 (0.014)

1971 7,654 246.2 (0.88) 0.41 (0.006) –0.85 (0.017)

1972 9,886 223.7 (0.41) 0.65 (0.006) –0.34 (0.009)

1973 8,953 283.7 (1.93) 0.30 (0.006) –1.19 (0.026)

1974 10,086 226.0 (0.36) 0.82 (0.006) +0.02 (0.005)

1975 9,527 745.0 (37.9) 0.06 (0.004) –2.28 (0.043)

1976 13,389 411.4 (19.7) 0.15 (0.013) –1.63 (0.093)

1977 14,897 389.2 (7.28) 0.15 (0.006) –1.52 (0.046)

1978 12,944 397.6 (12.2) 0.12 (0.007) –2.34 (0.084)

1979 11,121 231.3 (0.48) 0.51 (0.008) –0.61 (0.028)

1980 9,883 232.1 (0.45) 0.61 (0.006) –0.04 (0.009)

1981 10,273 241.0 (0.67) 0.41 (0.007) –0.67 (0.032)

1982 10,341 263.3 (0.99) 0.29 (0.005) –1.29 (0.037)

1983 14,523 245.9 (0.75) 0.40 (0.006) –0.85 (0.031)

1984 15,936 241.9 (0.52) 0.44 (0.005) –0.54 (0.021)

1985 13,225 233.7 (0.65) 0.51 (0.008) –0.37 (0.022)

1986 16,494 227.7 (0.43) 0.54 (0.006) –0.18 (0.018)

1987 16,458 262.9 (2.23) 0.27 (0.007) –1.47 (0.049)

1988 12,402 224.0 (0.78) 0.51 (0.010) –0.41 (0.029)

1989 13,950 241.1 (1.17) 0.37 (0.008) –0.94 (0.035)

1990 11,456 234.4 (0.43) 0.44 (0.006) –0.67 (0.026)

1991 11,378 234.4 (0.73) 0.42 (0.008) –1.06 (0.043)

1992 14,214 235.0 (0.43) 0.44 (0.006) –0.87 (0.029)

1993 14,578 246.8 (0.53) 0.34 (0.003) –1.36 (0.017)

1994 16,062 235.6 (0.44) 0.48 (0.006) –0.61 (0.022)

1995 13,489 237.6 (0.64) 0.42 (0.007) –0.94 (0.032)

1996 11,883 215.6 (0.23) 0.84 (0.012) –0.16 (0.020)

1997 9,879 225.9 (0.40) 0.56 (0.008) –0.43 (0.025)

Table 5

Biological reference points from yield-per-recruit (Y/R) 

and spawning potential ratio (static SPR) analyses based 

on different virtual population analyses (M = 0.8, 0.9, 

1.0, and 1.1/yr) for Gulf menhaden (Brevoortia patronus). 

The mean fi shing mortality rate (ages 1–4) for the 1990s 

and 1997 are given for comparison. Decadal (i.e., 1990s) 

means for growth parameters (weight-length and von 

Bertalanffy growth function) were used in developing 

the biological reference points below.

Biological Natural mortality, M

reference

point 0.8 0.9 1.0 1.1

Mean F for 1990s 0.83 0.77 0.69 0.63

Mean F for 1997 0.77 0.70 0.63 0.57

Y/R: F0.1 1.4 1.8 2.1 2.5

Static SPR (biomass):

F20 1.9 2.1 2.3 2.4

F30 1.2 1.4 1.5 1.6

Static SPR (eggs):

F20 1.3 1.5 1.7 1.9

F30 0.8 0.9 1.0 1.2

Spawning Potential Ratio

Gabriel et al. (1989) refer to the percent maximum spawning potential (%MSP) as the ratio of spawning stock biomass per recruit with and without fi shing mortality. This is 

equivalent to static SPR (Gulf of Mexico SPR Management 

Strategy Committee, 1996). Hence, the equilibrium spawning stock for an estimated level of fi shing mortality is compared to a maximum potential spawning stock for which 

no fi shing had occurred (ignoring adjustments to population parameters through compensatory mechanisms).

Static SPR was calculated in two ways. The fi rst method, 

described by Gabriel et al. (1989), accumulates mature 

female spawning stock biomass per recruit across all ages 

within a fi shing year. The second method, described 

by Prager et al. (1987), accumulates the corresponding 

number of eggs produced by the mature female biomass, 

using the fecundity relationship for Gulf menhaden of 
10 NOAA Technical Report NMFS 149

Lewis and Roithmayr (1981). A knife-edged maturation 

schedule of 0% for ages 0 and 1 and 100% for ages 2 

and older was used for Gulf menhaden (Nelson and 

Ahrenholz, 1986).

Spawning stock biomass is calculated annually from 

the number of adults (ages 2 through 4 on 1 January) 

times the weight at age calculated from the weightlength (Table 3) and length-age (Table 4) relationships 

and divided by 2 (assuming a 1:1 sex ratio).

Potential egg production was also estimated as an 

index of spawners. Estimates of egg production as a 

Figure 10

Spawning potential ratio (static SPR) for Gulf menhaden 

(Brevoortia patronus) compared by natural mortality (0.8, 

0.9, 1.0, and 1.1/yr) based on (a) female biomass and (b) 

egg production, 1976–97.

function of fi sh length were obtained from the equation (Lewis and Roithmayr, 1981):

 ln (EGGS) = –9.872 + 3.877 ln L, (4)

where EGGS equals total numbers of eggs produced per 

female, L equals estimated fork length (mm), n = 70, sy.x = 

0.375 (root mean squared error), and r2 = 0.65. Expected 

egg production per female of a given age was calculated 

using Eq. (4) and lengths from Table 4, with retransformation correction. Assuming a 1:1 sex ratio, spawning 

stock as potential eggs (PE) is calculated by

PE N = ∑ i i

1

2 EGGS , (5)

where EGGSi

 is egg production per female at age i, and Ni

is population numbers at age i (ages 2–4 on January 1).

Values of static SPR below 20 or 30 are typically considered evidence of recruitment overfi shing for many 

Exclusive Economic Zone species (Mace and Sissenwine, 1993). Levels of fi shing mortality (with M = 1.1/yr) 

that produce 20 or 30% SPR are summarized in Table 

5. Estimates of fi shing mortality from additional runs of 

the separable VPA using lower estimates of natural mortality (M = 0.8, 0.9, and 1.0/yr) were used to estimate 

the same biological reference points.

Annual estimates of static SPR ranged between 20 and 

50% with values generally higher since the late 1970s 

(Fig. 10). Static SPR (female biomass) varied among an 

average of 49% during the late 1970s, 48% during the 

1980s, and 57% during the 1990s (Fig. 10a). A value of 

59% was estimated for the 1997 fi shing year. A similar 

pattern of static SPR was obtained based on egg production, but with lower values (Fig. 10b). These estimates 

of static SPR varied among a mean of 37% for the late 

1970s, 38% for the 1980s, and 49% for the 1990s. A 

value of 51% was estimated for 1997.

Spawner-Recruit Relationships

An important question in population dynamics and in fi sheries management concerns the degree of dependency 

between spawning stock and the number of subsequent 

recruits to the stock. If there is no such dependency (except 

in the extreme; e.g., no spawners implies no recruits), 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 suffi cient spawners to produce subsequent recruits to the population and to preserve the quality 

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

is a quantifi able relationship between spawning stock and 

recruits, then management can be designed to maximize 
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 11

the landings or some other objective based on this relationship. To investigate the relationship between spawners 

and recruits, the Ricker (1954) model was used [see arguments by Nelson and Ahrenholz (1986) for a dome-shaped 

spawner-recruit relationship]. 

Estimation of recruits to age 1 was described in the 

VPA section (Fig. 7) and spawning stock biomass indices 

in the SPR section. Since 1964, egg production by age-2 

spawners has contributed generally greater than 80% to 

the total spawning egg production (Fig. 11). Note the 

decreasing trend in dependence on fi rst year spawners 

(averaging over 90% in the 1960s to about 82% in the 

1990s based on egg production).

Spawning biomass based on mature female biomass 

was on average highest during the 1980s when it averaged 321,900 t, and lowest during the 1960s when it 

averaged 98,200 t (Fig. 12). Intermediate values were 

obtained during the 1970s and 1990s when spawning 

stock biomass averaged 251,200 t and 282,200 t, respectively. A similar pattern was obtained from the index of 

egg production instead of mature female biomass.

Parameters of the Ricker model were estimated by non -

Figure 11

Percent contribution of age 2 Gulf menhaden (Brevoortia 

patronus) based on mature female biomass and egg production, 1964–97.

Figure 12

Indices of spawning stock biomass for Gulf menhaden (Brevoortia patronus) based on mature female biomass and egg production.

linear regression (SAS Institute Inc., 1987) 

from the equation:

R = αS e –βS, (6)

where R equals recruits to age 1, S equals 

spawners (female biomass or potential egg 

production previous year), and α and β are 

parameters to be estimated.

Parameter estimates for Gulf menhaden, 

with spawning stock biomass estimated in 

1000 t and recruits to age 1 in millions, 

resulted in α = 201.6 (standard error = 

39.1) and β = 0.00308 (standard error = 

0.00066). According to Ricker (1975), maximum recruitment occurs at α/βe (or 24.1 billion recruits to age 1) and the spawning stock 

biomass that will produce maximal recruitment is given by 1/β (or 324,700 t).

The fi t of the Ricker model to the data 

is poor (Fig. 13), and considerable variability, possibly due to environmental conditions 

(Goodyear and Christensen, 1984) or measurement error, remains unexplained. Nonetheless, the density-dependence parameter of the Ricker 

function is signifi cant (H0: β > 0; α=0.05), suggesting 

that the number of future recruits depends nonlinearly 

on the size of the spawning stock that produced them. 

The simple model that recruitment is equal to its longterm mean fi ts the data better than the Ricker model; 

however, the constant-recruitment model is inconsistent 

with biological theory and not useful for management. 

The sizable unexplained variability (Fig. 13) suggests 

that the Ricker model is of limited use in precisely predicting future recruitment in this stock.

Survival from spawning biomass to recruitment to age 

1 can be indexed for 1964–97 by:

S0 = R1/SSB (7)

where R1 is recruits to age 1 and SSB is spawning stock biomass for the previous year. The pattern of survival generally 
12 NOAA Technical Report NMFS 149

Figure 13

Spawner-recruit relation for Gulf menhaden (Brevoortia patronus), 

1964–97. Number indicates year of spawning.

varies between 0.05 and 0.15 with two large peaks during 

1966–69 and 1976–78. (Fig. 14a). Relative survival (Sr) was 

calculated by dividing observed survival by predicted survival (Se ; based on Ricker spawner-recruit curve) and rescaling to 0 by subtracting 1 (Sr

 = 0 at S0 = Se); that is,

Sr = (S0/Se)–1 (8)

Estimates of relative survival suggest that better than 

expected survival occurred from 1966–69, 1973, 1976–78, 

1980–82, 1984, and most recently in 1986 (Fig. 14b). 

Poorer than expected survival is particularly noted in 

1964–65, 1971, 1974–75, 1990–91, and possibly 1994–95. 

Since recruitment success greatly affects fi shing success, it 

is not surprising that high landings were common during 

the 1980s when better than expected relative survival 

occurred and lower during the 1990s when poorer than 

expected relative survival occurred.

The most recent estimate of spawning stock biomass 

is 292,100 t (in 1997); this is 32,600 t below the estimate 

of spawning stock biomass from the Ricker equation 

which gives maximum recruitment. Mean recruitment 

during the 1980s (27.2 billion) exceeded the maximum 

predicted by the Ricker curve by 3.1 billion recruits to 

age 1. During that time (1980s), spawning stock biomass averaged 321,900 t (or only 2,800 t less than the 

“optimal” spawning stock biomass). However, because 

of the large unexplained error remaining from fi tting 

the Ricker curve, the predicted value of 23.9 billion 

recruits from 292,100 t of spawners has a very large confi dence interval (approximate 95% confi dence interval 

is between 15.9 and 34.7 billion recruits to age 1).

Surplus-Production Models

Surplus-production models (Schaefer, 1954, 1957; Pella, 

1967; Fox, 1970; Prager, 1994) use data on removals 

from the stock and relative abundance through time to 

obtain estimates of maximum sustainable yield (MSY) 

and related benchmarks. In fi tting production models, 

it is common to use the reported landings to represent 

removals, under the assumption that landings are a constant fraction of total removals. To index population 

abundance, the most commonly used measure is catch 

per unit effort (CPUE), under the assumption (used frequently in fi sheries modeling) that CPUE is proportional 

to abundance. 

Under the theory of production models, sustainable 

yield can be represented by a dome-shaped function of 

abundance; if stock abundance is in equilibrium, plotting observed landings against effort also gives a domeshaped curve. Such a curve does not represent the Gulf 

menhaden data well; this may indicate lack of equilibrium, or the data may lie along the ascending limb of 

such a curve (Fig. 15).

When using CPUE as an index of abundance, fi shing effort rate (E) is assumed proportional to instantaneous fi shing mortality rate (F). Specifi cally, 

the catchability coeffi cient (q) is assumed to 

be constant in the following equation:

F = qE, (9)

where the unit of fi shing effort, E, for Gulf 

menhaden is defi ned as vessel-ton-weeks. As 

noted in Nelson and Ahrenholz (1986), unadjusted fi shing effort (nominal effort) is not 

a reliable index of fi shing mortality rate for 

menhaden. The diffi culty in directly obtaining a reliable unit of fi shing effort results 

from the schooling nature of clupeid fi shes, 

which at small population sizes are relatively 

more susceptible to fi shing effort [see discussion of “dynamic aggregation process” in Clark 

and Mangel (1979)]. The resulting concern is 

that severe stock depletion could occur before 

being detectable from an analysis of landings 

and nominal CPUE data.

To determine whether the catchability coeffi cient, q, for Gulf menhaden is constant or 

dependent upon population size, it was estimated by solving Eq. (9) for q(= F/E) for each 

fi shing year since 1964 and compared with 
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 13

Figure 14

Indices of (a) observed and (b) relative survival for Gulf 

menhaden (Brevoortia patronus) based on recruits to age 1 

divided by spawning stock biomass, 1964–96. Relative survival adjusted by expected survival from Ricker spawnerrecruit relationship.

Figure 15

Gulf menhaden (Brevoortia patronus) landings plotted 

against nominal fi shing effort (vessel-ton-weeks), 1946–97.

the population biomass (ages 1–4) for the same fi shing 

year (Fig. 16; F and population biomass estimates were 

from VPAs for ages 1–4). As noted in Nelson and Ahrenholz (1986), there is a pronounced inverse relationship between the catchability coeffi cient and population 

biomass.

A measure of fi shing effort proportional to fi shing 

mortality rate F is referred to as “effective effort.” To 

adjust nominal fi shing effort to account for variations 

in q, the 1964 value of q(qa) was used to adjust nominal 

effort (E) so that E' is proportional to F ; i.e.,

E' = Eqt /qa , (10)

where E' is a unit of effective fi shing effort and qt is the 

catchability coeffi cient in that year, normalized to the catchability coeffi cient in 1964 (Fig. 17). Note that while nominal effort was increasing from 1964 through the mid-1980s, 

effective effort remained low. A CPUE index derived from 

effective effort is frequently referred to as adjusted CPUE.

Two varieties of production model were fi t to data on 

Gulf menhaden. The computer program PRODFIT (Fox, 

1975), which attempts to account for nonequilibrium conditions through a smoothing process, was used to estimate 

parameters (and MSY) for the Pella-Tomlinson generalized production model (Pella and Tomlinson, 1969):

U = (A + BE')1/(m –1) (11)

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

parameters to be estimated. In using PRODFIT, reported 

landings and effective effort, as estimated above, were 

used, and two ages were assumed to contribute to the 

landings (Fig. 2). Parameter estimates and associated 

square root of the variability index (Fox, 1975) were estimated using landings and effective effort for 1964–97: A

= 2.14 (1.26), B = –0.0031 (0.0035), m = 1.33 (0.90), MSY 

= 717,200 t (32,000 t), and f

MSY = 171,400 vtw (20,600 

vtw) (Fig. 18). Although effort in 1997 was 430,200 vtw, 

it was only 118,000 vtw in terms of 1964 equivalent units 

of effort. Estimated f

MSY has only been exceeded once 
14 NOAA Technical Report NMFS 149

Figure 16

Catchability coeffi cient (q) versus estimated population abundance 

for Gulf menhaden (Brevoortia patronus), 1964–97. Number indicates 

year.

Figure 17

Gulf menhaden (Brevoortia patronus) nominal and effective fi shing effort from reduction fl eet, 1964–97. Nominal 

fi shing effort only is shown for 1946–63.

during the 1990s (in 1994), four times during 

the 1980s, six times during the 1970s, and 

exceeded in all years from 1964–69.

The second production modeling approach 

was the non-equilibrium production model 

described by Prager (1994) and implemented 

in the ASPIC computer program (Prager, 

1995). The models described were fi t to the 

observed landings data and the effective CPUE 

data derived in Eq. (10), above.

The model used (Prager, 1994) is an extension of the logistic Schaefer (1954, 1957) 

model and uses a fi tting procedure similar to 

that developed by Pella (1967) and later used 

by Pella and Tomlinson (1969) in their GENPROD computer program. The model makes 

no equilibrium assumption, but rather represents the population as a dynamic quantity of 

biomass subject to removals (fi shing) and net 

biological production (the surplus of growth 

and recruitment over natural mortality). In 

fi tting, an observation-error estimator is used, 

conditioned on yield and assuming lognormal error in the adjusted CPUE index, which 

is mathematically equivalent to assuming lognormal error in E'.

The ASPIC run for Gulf menhaden, which used the 

estimated effective effort series for 1964–97, estimated 

MSY = 752,700 t and f

MSY = 196,900 vtw (and f0.1 = 

177,200 vtw). R2 for this model was 0.542. A plot of 

annual fi shing mortality rate relative to that fi shing mortality rate producing MSY is shown in Fig. 19a; while 

a plot of population biomass relative that population 

biomass producing MSY is shown in Fig. 19b. If relative 

biomass (B/BMSY) is below 1, the stock is depressed 

(whether from natural phenomena or overfi shing) and 

cannot provide MSY; if the relative F (F/FMSY) is above 1, 

the rate of fi shing mortality is above that which can provide MSY, and if continued through time will result in a 

stock size below BMSY. In the 1960s and late 1980s, relative F was signifi cantly above 1, while relative biomass 

was signifi cantly below 1 only in the 1960s. In recent 

years, relative F was signifi cantly below 1, while relative 

biomass was signifi cantly above 1.

Both methods of surplus production modeling agree 

as to when the stock was in good condition and the 

fi shing rates were in acceptable ranges. Also, both estimated MSY and FMSY are at about the same levels.

Juvenile Abundance Indices and 

Environmental Factors

Attempts have been made to relate estimates of juvenile 

abundance to subsequent year class strength of menhaden. For example, Ahrenholz et al. (1989) were unable 

to relate Gulf menhaden juvenile abundance from a gulfwide surface-trawl survey conducted by the NMFS Beaufort Laboratory to VPA estimates of recruits to age 1 

during 1971–78. However, for this assessment two juvenile 

Gulf menhaden data sets were investigated as potential 

indices of year class strength (i.e, recruitment): trawl data 
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 15

Figure 19

Plots of (a) relative fi shing mortality (F/FMSY) and (b) relative biomass (B/BMSY) from ASPIC production model for 

Gulf menhaden (Brevoortia patronus), 1964–97.

Figure 18

Generalized surplus production model (PRODFIT) for 

Gulf menhaden (Brevoortia patronus) using reduction landings and effective fi shing effort, 1964–97.

from Louisiana and bag seine data from Texas. In addition, several environmental factors were investigated that 

may contribute to recruitment success; these included 

Mississippi River fl ow, indices of El Niño (e.g., NINO 3.4 

Anomaly), North Atlantic sea surface temperature (SST), 

and North Atlantic Oscillation (NAO). These juvenile 

indices and environmental variables are compared to VPA 

estimated recruitment to age 0 (approximately 6 months 

of age). Recruits to age 0 for a given year are equal to 

recruits to age 1 for the following year times e0.55. Estimates for recruits to age 1 are from the VPA using the 

catch matrix with ages 1–4 and years 1976–97 (providing 

estimates of age 0 recruits for 1975–96). All time series 

in this section are normalized by subtracting the series 

mean and dividing by the series standard deviation, prior 

to any statistical comparison.

Louisiana Trawl Juvenile Abundance Index

Juvenile abundance data for Gulf menhaden were 

obtained from otter trawl samples collected by Louisiana 

Department of Wildlife and Fisheries (LDWF) from 1966 

through 1997. As described in Guillory (1993): “Samples 

were taken weekly or biweekly throughout the year at 

selected stations across the coast. The otter trawl measured 4.9 meters (m) in length with 19.1 mm bar mesh 

wings and 6.4 mm bar mesh tail. Samples consisted of tenminute tows at speeds of approximately three knots.”

Sampling locations, or Coastal Study Areas (CSA), 

from east to west are as follows: 1) Lake Borgne/Pon chartrain, 2) Breton Sound, 3) Barataria Bay, 4) Timbalier/

Terrebonne Bay, 5) Caillou Lake/Lake Mechant, 6) Vermilion Bay, and 7) Calcasieu Lake. Coastal areas 1B4 

(deleting CSA 3 - Barataria Bay) and 5B7 were combined into two groups, respectively. Based on availability 

of young menhaden, we used data from March through 

August.

Three types of juvenile abundance indices were computed by two area groups and coastwide for Gulf menhaden: presence/absence, catch per effort (CPE), and 

retransformed General Linear Model (GLM). The GLM 

was based on ln(count+1) as the dependent variable 

with year, season (nested in year), area, and station 

(nested in area) as class variables. This model was run 

outputting least squares mean (SAS Institute Inc., 1987) 

by year as index of juvenile abundance. Coastwide esti-
16 NOAA Technical Report NMFS 149

mates of the three index types are compared to the estimate of recruits to age 0 (six months of age) (Fig. 20a).

Correlations between the two Louisiana area groups 

using the three indices from each area group were 

mostly non-signifi cant (P<0.057 for group 1 CPE vs 

group 2 retransformed GLM). Both groups were correlated with the coastwide indices. The CPE index from 

area group 2 (western CSAs) and coastwide showed 

strong correlation with recruits to age 0 (r = 0.65 and 

0.56, respectively, both signifi cantly different from 0).

Texas Bag Seine Juvenile Abundance Index

Juvenile abundance data for Gulf menhaden were obtained 

from bag seine samples collected by Texas Parks and Wildlife Department in nine coastal bays from 1978 through 

Figure 20

Comparison of normalized half-year-old Gulf menhaden 

(Brevoortia patronus) recruits (R0) with normalized juvenile abundance indices calculated from presence-absence 

(P/A), catch per unit effort (CPE), and general linear 

model (GLM) from (a) Louisiana trawl data and (b) Texas 

bag seine data.

1997. Bag seines are “18.3 m long, 1.8 m deep with 1.3-cm 

stretched nylon multifi lament mesh in the 1.8 m wide central bag with remaining webbing 1.9-cm stretched mesh”

(Dailey et al., 1991). Details on sampling frequency and 

procedures for bag seines are given in Dailey et al. (1991; 

p. 2). Each sample covered about 0.03 h per tow of surface area. Additional environmental information was collected prior to each bag seine sample (water temperature, 

surface salinity, dissolved oxygen, and turbidity).

The major sampling areas from east to west are as follows: 1) Sabine Lake, 2) Galveston Bay, 3) East Matagor -

da Bay, 4) Matagorda Bay, 5) San Antonio Bay, 6) Aransas Bay, 7) Corpus Christi Bay, 8) Upper Laguna Madre 

Bay, and 9) Lower Laguna Madre Bay. The analyses that 

follow emphasize the four eastern most areas for March 

through September, with sampling commencing in East 

Matagorda Bay in February 1983 and in Sabine Lake in 

January 1986.

As with the Louisiana trawl data, three types of juvenile abundance indices were computed by area and 

for the northern group for Gulf menhaden: presence/

absence, CPE, and retransformed GLM. The GLM was 

based on ln(count+1) as the dependent variable with 

year, season (nested in year), area, and station (nested 

in area) as class variables. This model was run outputting LSMEANS by year as index of juvenile abundance. 

Coastwide estimates of the three index types are compared to the estimate of recruits to age 0 (six months of 

age) (Fig. 20b).

Using the three indices from each area group, some 

signifi cant correlations among the western Louisiana 

area group and the eastern Texas group were found. 

Greatest signifi cance was shown with the western Louisiana group (P<0.045 for P/A and P<0.010 for CPE). The 

P/A and retransformed GLM indices for the eastern 

Texas group showed strongest correlation with recruits 

to age 0 (r = 0.57 and 0.52, respectively, both signifi cantly 

different from 0).

Environmental Relationships

Several environmental variables are briefl y investigated in 

this section as they may relate to Gulf menhaden recruitment success or failure. Changes in weather patterns and 

introduction of pollutants can have signifi cant effects on 

Gulf menhaden survival. Patterns in survival to recruitment have been investigated relative to spawning stock 

earlier in this report. Govoni (1997) has demonstrated an 

inverse relationship between changes in Mississippi River 

fl ow with changes in Gulf menhaden recruitment to age 

0. We have updated the data used by Govoni through 

1997. We continue to note a signifi cant inverse relationship (r = –0.46, P < 0.008) between 1-yr change in river 

fl ow with 1-yr change in recruitment success (Fig. 21). 
Vaughan et al.: Population Characteristics of Gulf Menhaden, Brevoortia patronus 17

Figure 21

Normalized difference in combined average monthly 

discharge rates of the Mississippi and Atchafalya rivers 

(m3/S) and normalized differences in the number of half 

year old Gulf menhaden (Brevoortia patronus) recruits (R0) 

(r=–0.46, P<0.008) (updated for 1991–97 from Govoni, 

1997).

That is, if river fl ow declines from one year to the next then 

recruits to age 0 are likely to increase (and vice versa).

Because river fl ow is greatly affected by weather patterns such as El Niño (i.e., NINO 3.4 anomaly), North 

Atlantic sea surface temperature (SST), and the North 

Atlantic Oscillation (NAO), intercorrelations among 

these variables and Gulf menhaden recruits to age 

0 were investigated. El Niño refers to a warming pattern in the eastern equatorial Pacifi c (Cane, 1983). 

SST index values and anomalies (i.e., NINO 3.4 from 

NOAA Climate Prediction Center (NCEP))1 were available monthly from 1950–97. An index of North Atlantic SST (5–20 N, 60–30 W) was available monthly for 

1950–97 from this same web site. The NAO index, which 

refers to sea-level pressure changes based on the normalized pressures between Lisbon, Portugal, and Stykkisholmur, Iceland, was obtained from Hurrell2. Winter 

indices (December–March) based on the NAO have 

been related to long-term variations in climate (Hurrell, 1995, 1996; Hurrell and van Loon, 1997). Normalized indices were correlated among themselves and with 

normalized Gulf menhaden recruits to age 0.

Mississippi River fl ow correlated well with the North 

Atlantic SST and NAO (P<0.006 and P<0.020, respectively), but not with NINO 3.4 anomaly (P<0.90). NINO 

3.4 anomaly correlated weakly with North Atlantic SST 

1 Web site URL: http://nic.fb4.noaa.gov/data/cddb/

2 Hurrell, J. W. 1998. National Center for Atmospheric Research, P.O. 

Box 3000, Boulder, CO 80307. Personal commun.

(P<0.09), and North Atlantic SST correlated well with 

NAO (P<0.005). But none of these indices showed any 

signifi cant correlation with Gulf menhaden recruits to 

age 0. One-year differences (lagged) in these indices 

showed signifi cant correlations among Mississippi River 

fl ow, North Atlantic SST and NAO, with only differences 

in river fl ow correlating with differences in recruits to 

age 0 as noted above (P<0.008).

Management Implications

The Gulf menhaden fi shery is conducted within the territorial sea and offshore of fi ve coastal states (Florida to 

Texas). All states, except Florida, enacted the cooperative 

management plan under the Gulf States Marine Fisheries Commission (GSMFC) in 1977 (Christmas and Etzold, 

1977). The plan was revised in 1983, 1988, and 1995 

(Christmas et al., 1983, 1988; Leard et al., 1995), and was 

revised again during 2000. Because management authority is vested in the individual states, some regulations are 

area-specifi c on a state or county basis, but other regulations, such as length of fi shing season (mid-April through 

1 November), are common to all states, except Florida. 

The extension of the fi shing season through 1 November 

(previously mid-October) was adopted by the GSMFC at 

their March 1993 annual meeting. No state controls or 

limits the catch or fi shing effort of vessels.

Landings and nominal effort were quite high during 

the 1980s, but have declined precipitously during the 

late 1980s and early 1990s. Landings peaked in 1984 

with 982,800 t, while nominal fi shing effort peaked 

in 1983 with 655,800 vessel-ton-weeks. Most recently 

(1997), landings were 611,200 t with 430,200 vesselton-weeks. Landings between 1982 and 1987 were very 

high, exceeding estimates of long-term MSY, but were 

supported by generally high recruitment to age 1. More 

recent landings (421,400 to 761,600 t) are comparable to, 

or somewhat below, recent estimates of MSY (717,000 to 

753,000 t based on the PRODFIT and ASPIC estimates of 

surplus production). Vaughan (1987) noted an upward 

trend in historical estimates of MSY, which was no longer 

maintained in this or the previous assessment.

Relative survival index suggests that recent estimates of 

recruits to age 1 are below what would be expected based 

on the Ricker spawner-recruit relationship between 

spawning stock biomass and recruits to age 1. This relatively poor survival should be viewed in the context that 

while spawning stock biomass was generally rising from 

1989 to 1997 (161,000 t to 292,100 t), recruits to age 1 

have fl uctuated without apparent trend (13 to 23 billion 

during the 1990s).

Recent estimates of fi shing mortality (for M = 1.1/yr) 

compare favorably with the different estimates of biological reference points. Recent estimates of F (ages 
18 NOAA Technical Report NMFS 149

1–4) are below F0.1 for the range of natural mortality 

(M) considered in this assessment. For the preferred 

natural mortality value of 1.1/yr (based on tagging), 

mean of the estimates of F (ages 1–4) is 0.6/yr. This 

value compares favorably with F0.1 of 2.5/yr, F20 between 

1.9 and 2.4/yr, and F30 between 1.2 and 1.6/yr. When 

lower estimates of natural mortality (M) are assumed, 

then the estimated biological reference points decrease 

while estimates of fi shing mortality increase. For M

of 0.8/yr, recent estimates of F (mean of 0.8/yr for 

1990–97) are below estimates of F0.1 (1.4/yr), F20 (1.3–

1.9/yr), and F30 (0.8–1.2/yr). Only the biological reference point for F30 based on egg production is about 

equal to the mean F for the 1990s. The retrospective 

pattern observed in current-year estimates of F indicates 

that it takes several years of observation for estimates 

of F to be known with good precision, which implies 

that management actions based on recruitment would 

be made under considerable uncertainty.

Recent estimates of relative F (F/FMSY) and relative 

biomass (B/BMSY) from the ASPIC fi ts to the Schaefer 

surplus production models suggest that recent fi shing 

mortality is low and biomass is high relative to FMSY and 

BMSY, respectively.

Our original intent had been to use juvenile abundance indices obtained from Louisiana and Texas to 

calibrate the Gulf menhaden VPA. Unfortunately, unstable results were obtained from FADAPT (Restrepo, 

1996), while the limited number of ages precluded use 

of XSA (Darby and Flatman, 1994) or ICA (Patterson 

and Melvin, 1995). Further exploration of calibration 

approaches is needed.

In summary, Gulf menhaden have higher natural mortality and are shorter lived than Atlantic menhaden, and 

as a result there are rapid annual changes in the Gulf 

menhaden fi shable stock. The Gulf menhaden fi shery 

is currently fully exploited and the population appears 

reasonably stable in view of the age composition, life 

span, and effects of environmental factors. Annual production, fi shing effort, and fl eet size appear reasonably 

balanced and risk of overfi shing low with 1997–98 fl eet 

size and recent mean recruitment. Given the variability 

in the data and model estimates, recent landings below 

long-term MSY (and well below high landings of the mid1980s) suggest that the stock appears reasonably stable.

Acknowledgments

The authors wish to acknowledge the many past and present employees of the Southeast Fisheries Science Center, 

Beaufort Laboratory, who were involved in the many 

aspects of the menhaden data collection program, especially Ethel Hall, Eldon Levi, and Dean Ahrenholz. We also 

wish to thank Vince Guillory (Louisiana Dept. of Fish and 

Wildlife) and George Lewis and Jerry Mambretti (Texas 

Parks and Wildlife Dept.) for providing Gulf menhaden 

juvenile data from Louisiana trawl and Texas bag seine surveys, respectively. We also thank Jeff Govoni for his guidance in updating river fl ow data from the U.S. Corps of 

Engineers, and the U.S. Corps of Engineers for providing 

river fl ow data. We thank Dean Ahrenholz, James Waters, 

and John Merriner for reviewing the manuscript.

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