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Yield-per-recruit analysis for black drum, Pogonias cromis, along the East Coast of the United States and management strategies for Chesapeake Bay.

Abstract--Black drum, Pogonias cromis, along the U.S. East Coast is subject to commercial and recreational harvest. However, prior to this study no modeling had been undertaken to examine the potential for overfishing Overfishing occurs when fishing activities reduce fish stocks below an acceptable level. This can occur in any body of water from a pond to the oceans. More precise biological and bioeconomic terms define 'acceptable level'.  in the Chesapeake Bay Chesapeake Bay, inlet of the Atlantic Ocean, c.200 mi (320 km) long, from 3 to 30 mi (4.8–48 km) wide, and 3,237 sq mi (8,384 sq km), separating the Delmarva Peninsula from mainland Maryland. and Virginia.  region. We present evidence from yield-per-recruit models that growth overfishing of black drum The black drum (Pogonias cromis) is a saltwater fish similar to its cousin, the red drum. It is the only species in the genus Pogonias. Though most specimens are generally found in the 5-30lb range, the black drum is well known as the largest of all the drum  is unlikely under current fishing practices in this region. Particular attention was given to fishing practices in the Chesapeake Bay region where old, large fish predominate in the commercial and recreational catches (mean age=26 years; mean total length=108.4 cm; mean weight 22.1 kg). Yield-per-recruit model results showed that growth overfishing was unlikely in the Chesapeake Bay region under all but the lowest estimates of natural mortality (M=0.02-0.04). Such extreme low values of M predict potential life spans of 200 years and were dismissed as improbable--the oldest age recorded for this species is 59 years. Additionally, biomass-per-recruit model results indicated a 42-59% decrease to current biomass from the unfished stock. The apparent age-specific migration of this stock argues for protection of young fish that have dominated the catch in Northeast Florida. Modeling indicated that growth overfishing could result from heavy fishing on these young ages and would all but eliminate this resource of the northern fishery.

Black drum (Pogonias cromis; family Sciaenidae) range in U.S. waters primarily from Massachusetts Massachusetts (măsəch`sĭts), most populous of the New England states of the NE United States.  to Florida along the East Coast and, in the Gulf of Mexico Noun 1. Gulf of Mexico - an arm of the Atlantic to the south of the United States and to the east of Mexico
Golfo de Mexico

Atlantic, Atlantic Ocean - the 2nd largest ocean; separates North and South America on the west from Europe and Africa on the east
, from the west coast of Florida along the northern Gulf to Texas. They form at least three populations, at least two in the Gulf of Mexico (Gold et al., 1995) and one along the U.S. East Coast (Gold and Richardson, 1998; Gold(1)). This population structure is seen as "isolation by distance" (Gold and Richardson, 1998). East Coast black drum undertake long-range migrations with a general pattern of movement to the north and inshore in·shore  
adv. & adj.
1. Close to a shore.

2. Toward or coming toward a shore.


in or on the water, but close to the shore:
 in spring, and south and offshore in the fall (Richards Rich·ards , Dickinson Woodruff 1895-1973.

American physician. He shared a 1956 Nobel Prize for developing cardiac catheterization.
, 1973; Murphy and Taylor, 1989; Jones and Wells, 1998). These seasonal migrations are age-specific and influence exploitation patterns differently along the coast. Although the East Coast stock shows a maximum age of 59 years, which indicates low total annual mortality of 8-11% (Jones and Wells, 1998), a greater proportion of old fish are found north of Cape Hatteras Noun 1. Cape Hatteras - a promontory on Hatteras Island off the Atlantic coast of North Carolina; "frequent storms drive ships to their destruction on Cape Hatteras" , and the potential exists for different age-specific mortalities along the range. Along the East Coast, fisheries fisheries. From earliest times and in practically all countries, fisheries have been of industrial and commercial importance. In the large N Atlantic fishing grounds off Newfoundland and Labrador, for example, European and North American fishing fleets have long  for black drum predominantly pre·dom·i·nant  
1. Having greatest ascendancy, importance, influence, authority, or force. See Synonyms at dominant.

 target small, young fish in the south (Music and Pafford, 1984; Murphy and Muller Mul·ler , Hermann Joseph 1890-1967.

American geneticist. He won a 1946 Nobel Prize for the study of the hereditary effect of x-rays on genes.

Mül·ler , Johannes Peter 1801-1858.
(2) and Wenner(3)) and large, old fish in the north (Jones and Wells, 1998). Although small fish are targeted in the south, large fish are present and are caught occasionally in the recreational fisheries there. In contrast, small fish are rarely present north of Cape Hatteras besides young of the year fish that leave the bays after their first summer. Hence, little fishing mortality occurs to young fish in the northern part of the range.

Compared with other exploited sciaenids, black drum do not support large recreational or commercial fisheries. Along the East Coast between 1979 and 1994, commercial catches averaged only 99,510 kg yearly (218,923 pounds)(2,4,5,6,7,8) Virginia Virginia, state, United States
Virginia, state of the south-central United States. It is bordered by the Atlantic Ocean (E), North Carolina and Tennessee (S), Kentucky and West Virginia (W), and Maryland and the District of Columbia (N and NE).
 and Florida have the greatest average annual landings (averaging 37,000 and 26,000 kg respectively), whereas New Jersey, Delaware Delaware, state, United States
Delaware (dĕl`əwâr, –wər), one of the Middle Atlantic states of the United States, the country's second smallest state (after Rhode Island).
, Maryland Maryland (mâr`ələnd), one of the Middle Atlantic states of the United States. It is bounded by Delaware and the Atlantic Ocean (E), the District of Columbia (S), Virginia and West Virginia (S, W), and Pennsylvania (N). , North Carolina North Carolina, state in the SE United States. It is bordered by the Atlantic Ocean (E), South Carolina and Georgia (S), Tennessee (W), and Virginia (N). Facts and Figures

Area, 52,586 sq mi (136,198 sq km). Pop.
, South Carolina South Carolina, state of the SE United States. It is bordered by North Carolina (N), the Atlantic Ocean (SE), and Georgia (SW). Facts and Figures

Area, 31,055 sq mi (80,432 sq km). Pop. (2000) 4,012,012, a 15.
, and Georgia Georgia, country, Asia
Georgia (jôr`jə), Georgian Sakartvelo, Rus. Gruziya, officially Republic of Georgia, republic (2005 est. pop. 4,677,000), c.26,900 sq mi (69,700 sq km), in W Transcaucasia.
 have average landings of less than 18,000 kg. In contrast, between 1981 and 1994 recreational landings averaged 315,000 kg (693,000 pounds)(2,9) annually, 300% higher than the commercial catch. Recreational landings north of Cape Hatteras vary from 0.4% to 78% of the annual East Coast recreational catch, reflecting variations in abundance Abundance
See also Fertility.


horn horn of Zeus’s nurse-goat which became a cornucopia. [Gk. Myth.: Walsh Classical, 19]


conical receptacle which symbolizes abundance. [Rom. Myth.
 of older fish and in their seasonal migration patterns.

With its location at the northern end of the range, Chesapeake Bay fisheries target black drum that are primarily old (26 yr), and large (108.4 cm; 22.1 kg) during a short season; most of the catches occur from April to June (Jones and Wells, 1998). Large fish enter the Bay in April and are caught by the commercial fishery with 33-cm stretch mesh Refers to an interconnect architecture that cross- connects several devices. See mesh network, wireless mesh network and switch fabric.

(character) mesh - The INTERCAL name for hash.
 anchored and drifted gill gill, in weights and measures
gill, in weights and measures: see English units of measurement.
 nets. Historically, the commercial market is local, and fillets and roe are a spring treat for residents of the eastern shore of Virginia The Eastern Shore of Virginia is on the Atlantic Coast of the Commonwealth of Virginia. The region is part of the Delmarva Peninsula and is separated from the rest of Virginia by the Chesapeake Bay.  and Maryland during April and May (Jones et al., 1990). Because of this limited market that becomes saturated saturated /sat·u·rat·ed/ (sach´ah-rat?ed)
1. denoting a chemical compound that has only single bonds and no double or triple bonds between atoms.

2. unable to hold in solution any more of a given substance.
, the price drops in late spring and commercial fishermen turn from black drum to pursue more profitable fishes. The recreational fishery usually begins and ends a month later than the commercial fishery, from May to June, and anglers target large trophy fish with hook and line. Although the recreational season is short, it occurs before more popular fish enter the Bay, and the fishery supports local business at that time. Thus, the black drum fishery is important to the economies of two of the poorest counties in Virginia The Commonwealth of Virginia is divided into 95 counties and 39 independent cities, which are considered county-equivalents for census purposes. Note that the map in this article, taken from the official United States Census Bureau site, includes Clifton Forge as an independent city. , which are located on the eastern shore (Jones et al., 1990).

In the mid-Atlantic region, the lack of accurate catch and effort data from the commercial and recreational black drum fisheries makes it difficult to evaluate whether the long-term Long-term

Three or more years. In the context of accounting, more than 1 year.


1. Of or relating to a gain or loss in the value of a security that has been held over a specific length of time. Compare short-term.
 fluctuations in population abundance and the current decline in abundance of citation-size fish result from natural patterns of dominant year classes or from excess exploitation and subsequent population decline. Reports of catch and effort in the commercial fishery have been based, generally, on voluntary reporting. Likewise, the difficulty in sampling this short-season and charter-based recreational fishery has led to estimates of catch and effort that are characterized char·ac·ter·ize  
tr.v. character·ized, character·iz·ing, character·iz·es
1. To describe the qualities or peculiarities of: characterized the warden as ruthless.

 by extremely broad confidence limits. Even so, in response to the concerns of Virginia's recreational anglers to supposed population decline, commercial harvest quotas were imposed on these fisheries in 1992 in the absence of any stock assessment (Commonwealth of Virginia, 1992, VMRC VMRC Virginia Marine Resources Commission
VMRC Valley Mountain Regional Center (Stockton, California)
VMRC Virtual Machine Remote Client (Microsoft)
VMRC Virtual Machine Remote Control
 regulation 4 VAC (Volts Alternating Current) See volt and AC.  20-320-10 et seq et seq. (et seek) n. abbreviation for the Latin phrase et sequentes meaning "and the following." It is commonly used by lawyers to include numbered lists, pages or sections after the first number is stated, as in "the rules of the road are found in Vehicle Code .).

Yield-per-recruit models can provide the benchmarks for assessing growth overfishing (Gulland, 1983; King, 1995). Specifically, yield-per-recruit modeling provides reference points to theoretically maximize yield from a cohort cohort /co·hort/ (ko´hort)
1. in epidemiology, a group of individuals sharing a common characteristic and observed over time in the group.

 ([F.sub.MAX]), or increase the number of trophy-size fish in the population. Because [F.sub.MAX] frequently results in unsustainable harvests, an ad hoc For this purpose. Meaning "to this" in Latin, it refers to dealing with special situations as they occur rather than functions that are repeated on a regular basis. See ad hoc query and ad hoc mode.  benchmark ([F.sub.0.1]) is calculated to provide more conservative harvest recommendations. However as important as this modeling is to science-based management, no published application of yield-per-recuit models exists for black drum from the Chesapeake Bay region. In our study we used data from Chesapeake Bay (Jones and Wells, 1998) and Florida (Murphy and Taylor, 1989) to evaluate the effect of fishing mortality and age at first capture on yield-per-recruit models of these fish, especially for management in the Bay. Although more accurate stock assessments result when catch-age or age-structured models such as ADAPT are used, the absence of a time series of aged-catch data precludes their use for this fishery. Until such data become available, the results of yield-per-recruit models can be used now to determine whether regulations such as size limits, catch quotas, and effort limitations, which are already in effect, are necessary to manage this fishery.

Materials and methods

Yield-per-recruit analysis

The Beverton-Holt yield-per-recruit model (Beverton and Holt holt  
n. Archaic
A wood or grove; a copse.

[Middle English, from Old English.]


the lair of an otter [from
, 1957) was used to calculate yield-per-recruit curves following the formula

(1) [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression.  NOT REPRODUCIBLE re·pro·duce  
v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es
1. To produce a counterpart, image, or copy of.

2. Biology To generate (offspring) by sexual or asexual means.
 IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ]

where Y/R = yield-per-recruit in weight (kg);

F = instantaneous in·stan·ta·ne·ous  
1. Occurring or completed without perceptible delay: Relief was instantaneous.

 fishing mortality coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.


M = instantaneous natural mortality coefficient;

[U.sub.n] = summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument)  parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  ([U.sub.0]=1, [U.sub.1]=-3, [U.sub.2]=3, [U.sub.3=-1);

[t.sub.c] = mean age (years) at first capture;

[t.sub.r] = mean age (years) at recruitment to the fishing area; and

[W.sub.[Infinity infinity, in mathematics, that which is not finite. A sequence of numbers, a1, a2, a3, … , is said to "approach infinity" if the numbers eventually become arbitrarily large, i.e. ]] = asymptotic weight;

[t.sub.0] = hypothetical Hypothetical is an adjective, meaning of or pertaining to a hypothesis. See:
  • Hypothesis
  • Hypothetical
  • Hypothetical (album)
 age the fish would be zero length; and

K = the Brody growth coefficient.

Computations were performed by using a modification of the computer program B-H3 available in the Basic Fisheries Science Programs package (Saila et al., 1988). Parameters used in these simulations are summarized in Table 1. The first two parameters, [t.sub.0] and K, are derived from the von Bertalanffy growth equation for black drum (Jones and Wells, 1998):

(2) [l.sub.t] = 117.3(1 - [e.sup.-0.105(t+2.3)]).
Table 1
Parameter estimates or range of values used in yield-per-recruit
and biomass simulations for black drum, Pogonias cromis, on the
east coast of the U.S. Data taken from Jones and Wells (1998)
for the Chesapeake Bay and Murphy and Taylor (1989).

Parameter            Chesapeake Bay   NE Florida   Method

[t.sub.c]               5-25 yr                    age composition
                                                   of catches

[t.sub.r]                  5 yr            1 yr    life history

[t.sub.0]               -2.3 yr         -1.3 yr    growth curve

K                      0.105 yr        0.124 yr    growth curve

[L.sub.[infinity]]     117.3 cm        117.2 cm    growth curve

[W.sub.[infinity]]      27.5 kg         25.5 kg    converted from

Z                     0.08-0.12                    catch curves and

M                     0.00-0.12                    longevity

[Beta]                     3.11                    length-weight

Because fish aged 1-5 were not available in Chesapeake Bay, our estimate of K (0.105) was smaller than that obtained by Murphy and Taylor, (K=0.124; 1989) for black drum sampled from the northeast coast of Florida. Hence, we also used estimates of K from the northeast coast of Florida in our modeling to ensure that results would reflect the available scientific data from the U.S. East Coast. For both areas, asymptotic mean weight, [W.sub.[infinity]], was converted from an allometric al·lom·e·try  
The study of the change in proportion of various parts of an organism as a consequence of growth.

 weight-length relationship (b=3.11; Jones and Wells, 1998). This slight deviation DEVIATION, insurance, contracts. A voluntary departure, without necessity, or any reasonable cause, from the regular and usual course of the voyage insured.
 from isometric isometric /iso·met·ric/ (-met´rik) maintaining, or pertaining to, the same measure of length; of equal dimensions.

 growth (b=3.0) may result in a small overestimation o·ver·es·ti·mate  
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.

2. To esteem too greatly.
 of yield (less than 7%) which Ricker (1975) dismissed as inconsequential in·con·se·quen·tial  
1. Lacking importance.

2. Not following from premises or evidence; illogical.

A triviality.
 to further calculations. Because we focused on the relative yields that result from varying [t.sub.0] and F at different levels of M, differences in yield should be even less than this absolute level (Barbieri et al., 1997).

Age of recruitment to the fishing area, [t.sub.r], was unknown for this fishery and was set to age 1 for the Florida fishery and age 5 for the Chesapeake Bay fishery, a year less than the youngest adult black drum caught in the Bay during our three-year study. Fisheries-based data included Z, F, M, and [t.sub.c]. Estimates of the instantaneous total mortality, Z, for fully recruited black drum were obtained from catch-curve analysis and maximum age procedures, and ranged from 0.08 to 0.12 (Murphy and Taylor, 1989; Jones and Wells, 1998). Although we had direct estimates of total mortality, Z, we lacked independent estimates of instantaneous fishing mortality, F, and instantaneous natural mortality, M. However, the estimate of Z allowed us to estimate current levels of fishing mortality, [F.sub.CUR(i)], for different values of M, as

(3) [F.sub.CUR(i)] = Z - [M.sub.i],

where [M.sub.i] = 0.02-0.12.

We estimated the most probable value of M by extrapolating to maximum age estimates realistic for an unfished fishery. This range of M was lower than that predicted with a multiple regression Multiple regression

The estimated relationship between a dependent variable and more than one explanatory variable.
 developed by Pauly (1980; M=0.16-0.30). Using our lower estimate of M, we made our modeling more sensitive to potential growth overfishing; therefore management strategies would be conservative.

Ricker yield model

Ricker's yield model is used to simulate simulate - simulation  the potential for growth overfishing over the life of a cohort by measuring available biomass at age under various levels of F (King, 1995). Mortality and growth are opposing effects that result in a maximum biomass during the lifetime at the age of maximum biomass, [t.sub.CRITICAL]. The model equation is from Saila et al. (1988):


where [Y.sub.e] = estimated lifetime equilibrium equilibrium, state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body.  yield referenced to an arbitrary recruitment biomass of 1000 g;

[B.sub.i] = biomass at age;

[F.sub.i] = instantaneous fishing mortality at age;

[Z.sub.i] = total mortality at age;

[G.sub.i] = growth in weight-at-age; and

[t.sub.i] = age where [t.sub.i] is calculated from the age of first capture, [t.sub.c], to the last fishable age, [t.sub.L].

When calculated at F=0, the model produces estimates of equilibrium yield for the unfished stock. Computations were performed by using the computer program Ricker modified from the Basic Fisheries Science Programs package (Saila et al., 1988).

Parameter values used in simulations are summarized in Table 1. Estimates of growth parameters [B.sub.i], and [G.sub.i] for Chesapeake Bay and Florida black drum were obtained from Jones and Wells (1998) and Murphy and Taylor (1989). Because of the long life of black drum, we grouped parameters into 5-year intervals to increase computation Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking.  efficiency. Simulations used six values of M (0.02, 0.04, 0.06, 0.08, 0.10, and 0.12) and six levels of F (0.0, 0.02, 0.04, 0.06, 0.08, and 0.10). This model is not used to calculate optimum yield as is the Beverton-Holt yield-per-recruit model. By integrating the area under the curves, reduction in stock biomass at a given level of F can be compared with biomass of the unfished stock, thus demonstrating the loss of trophy-size fish that are prized in recreational fisheries.

Simulations were done to model two scenarios of fishing mortality and their effect on biomass: 1) uniform low F over the life span, and 2) very high F in the first 5-year interval and uniform low F over the remaining lifetime. In the first scenario the chosen level of F was partitioned par·ti·tion  
a. The act or process of dividing something into parts.

b. The state of being so divided.

 equally over 12 age intervals. (Because we lacked age-specific estimates of F, the most straightforward approach was to equally partition A reserved part of disk or memory that is set aside for some purpose. On a PC, new hard disks must be partitioned before they can be formatted for the operating system, and the Fdisk utility is used for this task.  F across age intervals.) In the second scenario fish in the first 5-year interval were given an F=2.0 and thereafter experienced the chosen level of F partitioned equally over the remaining 11 age intervals. Hence, in the second scenario the lifetime Z was greater than 2.0. The second scenario was chosen to model extremely severe F on young fish that could be experienced from both directed fisheries and bycatch where young fish predominate.

Cohort biomass and harvesting time

The maximum possible yield for a year class occurs at the age ([t.sub.CRITICAL]) when the biomass of the cohort is at its maximum in the absence of fishing. For comparison with the Beverton-Holt and Ricker yield-per-recruit modeling results, we estimated [t.sub.CRITICAL] for black drum following Quinn and Deriso (1999) with the following equation:

(5) [t.sub.CRITICAL] = [t.sub.0] + 1/K ln(1 + [Beta]/m),

where m = M/K,

[Beta] = the length-weight allometry al·lom·e·try
The study of the change in proportion of various parts of an organism as a consequence of growth.


measurement of the changes in shape of an animal relative to increases in its size.
 coefficient, and [t.sub.0], K, and M are defined as in Equation 1.

Parameter estimates or the range of values used in calculations are listed in Table 1. Age at maximum biomass can be compared to mean age in the catch to indicate whether further juvenesence is possible.

To calculate the proportion of potential growth span ([P.sub.g]) remaining when black drum enter the exploited phase of life (Beverton and Holt, 1957), we used the quantity (Beverton, 1963):

(6) [P.sub.g] = (1 - [l.sub.c]/[L.sub.[Infinity]]),

where [L.sub.[Infinity]] the asymptotic length, was obtained from Jones and Wells (1998); and [l.sub.c], the average length at first capture, was obtained by converting [t.sub.c] to length with the von Bertalanffy growth curve reported for black drum in Chesapeake Bay (Jones and Wells, 1998) and Florida (Murphy and Taylor, 1989). Both parameters are based on total length in cm.


Modeling with parameters from Chesapeake Bay

Yield-per-recruit curves on F showed that the yield of black drum in Chesapeake Bay could be maximized by decreasing [t.sub.c] to 10-15 yr over most of the range of M (0.06-0.12) and F used in our simulations (Fig. 1; Table 2). The gains in yield-per-recruit could be substantial. For example, at the estimated current levels of fishing mortality for black drum in Chesapeake Bay ([F.sub.CUR]=0.04-0.06), yields could be increased 58% at M=0.06 and 89% at M-0.08 by decreasing current [t.sub.c] from 25 yr to 15 yr.

Table 2
Estimates of [F.sub.0.1] and [F.sub.MAX] compared to [F.sub.CUR]
from Beverton-Holt yield-per-recruit modeling for various levels
of K, M, and [t.sub.c]. The symbol (***) indicates that [F.sub.Max]
occurs at the highest values of F. [F.sub.CUR(i)] was calculated
from the upper-bound estimate of Z (as [F.sub.CUR(i))]=Z-[M.sub.i])
and represents the upper-bound estimate of current F.

K        M     [t.sub.c]   [F.sub.0.1]   [F.sub.Max]   [F.sub.CUR]

0.105   0.02       5          0.03          0.06          0.10
                  10          0.05          0.09
                  15          0.06          0.17
                  20          0.07          0.40
                  25          0.09          (***)
        0.04       5          0.06          0.08          0.08
                  10          0.07          0.17
                  15          0.09          0.51
                  20          0.10          (***)
                  25          0.12          (***)
        0.06       5          0.07          0.13          0.06
                  10          0.09          0.31
                  15          0.11          (***)
                  20          0.13          (***)
                  25          0.15          (***)
        0.08       5          0.09          0.17          0.04
                  10          0.12          0.61
                  15          0.15          (***)
                  20          0.17          (***)
                  25          0.19          (***)
        0.10       5          0.11          0.23          0.02
                  10          0.15          1.51
                  15          0.19          (***)
                  20          0.22          (***)
                  25          0.25          (***)
        0.12       5          0.13          0.30          0.00
                  10          0.19          (***)
                  15          0.23          (***)
                  20          0.27          (***)
                  25          0.31          (***)
0.124   0.02       5          0.05          0.07          0.10
                  10          0.06          0.11
                  15          0.07          0.23
                  20          0.08          (***)
                  25          0.09          (***)
        0.04       5          0.06          0.10          0.08
                  10          0.07          0.24
                  15          0.09          1.38
                  20          0.12          (***)
                  25          0.12          (***)
        0.06       5          0.08          0.15          0.06
                  10          0.10          0.47
                  15          0.13          (***)
                  20          0.14          (***)
                  25          0.14          (***)
        0.08       5          0.09          0.21          0.04
                  10          0.14          1.11
                  15          0.17          (***)
                  20          0.19          (***)
                  25          0.20          (***)
        0.10       5          0.12          0.28          0.02
                  10          0.18          (***)
                  15          0.20          (***)
                  20          0.23          (***)
                  25          0.27          (***)
        0.12       5          0.14          0.39          0.00
                  10          0.20          (***)
                  15          0.25          (***)
                  20          0.29          (***)
                  25          0.30          (***)

Yield-per-recruit curves showed marked peaks only at the lowest levels of M (0.02; 0.04) when [t.sub.c] [is less than or equal to] 10-15 or at higher levels of M when [t.sub.c] [is less than or equal to] 10 (Fig. 1). Otherwise, curves were asymptotic or rising, and [F.sub.MAX] was reached only at the highest fishing mortalities ([F.sub.MAX] [is greater than] 2.0; Table 2). When M was 0.02, curves peaked for [t.sub.c] up to 20 yr, resulting in [F.sub.MAX] (0.4. However, because an M of 0.02 predicts a maximum age of over 200 yr in an unexploited stock and because there is no indication of such longevity longevity (lŏnjĕv`ĭtē), term denoting the length or duration of the life of an animal or plant, often used to indicate an unusually long life.  in black drum, we rejected this scenario as improbable. When M was 0.04, curves peaked for [t.sub.c] [is less than or equal to] 15, for ages constituting less than five percent of the catch and well below the mean age (25 y) in the catch in the Chesapeake Bay fishery. At higher values of M when [t.sub.c] [is greater than or equal to] 10, curves were asymptotic or rising and [F.sub.MAX] occurred only at the highest levels of F. Although yields increased continuously with F for M [is greater than] 0.04, increases in yield beyond F=0.1-0.3 were very small.

For M [is greater than or equal to] 0.06 and [t.sub.c] [is greater than or equal to] 5, estimates of [F.sub.CUR] were below the levels giving maximum potential yield-per-recruit ([F.sub.MAX]) and [F.sub.0.1] (Fig. 1; Table 2). For M=0.06, [F.sub.CUR] equals 0.06 at most and [F.sub.0.1] equals 0.07, indicating that, although below the maximum potential yield-per-recruit, estimated current levels of harvest are only slightly below this more conservative benchmark of F. When M [is greater than] 0.06, [F.sub.0.1] is greater than 0.08 and always above [F.sub.CUR], indicating that current levels of harvest are below this conservative benchmark. In contrast, if M [is less than or equal to] 0.04 and [t.sub.c] [is less than or equal to] 10, [F.sub.0.1] is higher than [F.sub.CUR] (Table 2) indicating that there is some justification for decreasing F. However, as mentioned previously, we believe these levels of M [is less than or equal to] 0.04 to be unrealistically low for this species.

Curves of biomass on age showed that biomass decreased with increases in M or F (Table 3). Lifetime cohort biomass of an unfished stock decreased by 85% from M=0.02 to M=0.12. Within a given M, increased F resulted in decreased lifetime cohort biomass. For example, when the most credible combinations of M and [F.sub.CUR] were modeled (M=0.06, [F.sub.CUR]=0.06; M=0.08, [F.sub.CUR] = 0.04), biomass declined 59% and 42%, respectively, from that of the unfished stock (Fig. 2).

Table 3
Lifetime cohort biomass (g) from the Ricker biomass model (Saila
et al. 1988) under M=0.02-0.12, and uniform F=0-0.12. Integration
was by rectangular approximation. Simulations were based on an
arbitrary starting biomass of 1000 g.


M         0        0.02     0.04     0.06

0.02   180,730   107,915   70,195   49,170
0.04   107,915    70,195   49,170   36,595
0.06    70,195    49,170   36,595   28,595
0.08    49,170    36,595   28,595   23,210
0.10    36,595    28,595   23,210   19,420
0.12    28,595    23,210   19,420   16,675


M       0.08     0.1      0.12

0.02   36,595   28,595   23,210
0.04   28,595   23,210   19,420
0.06   23,210   19,420   16,675
0.08   19,420   16,675   14,600
0.10   16,675   14,600   13,040
0.12   14,600   13,040   11,750

Similar patterns were shown when we modeled heavy fishing in the first 5 years (F=2.0), and uniform low mortality was evident thereafter. Curves of biomass on age showed a much larger decrease in biomass with increasing M and F (Fig. 3; Table 4). Maximum biomass at minimum fishing mortality (F=0.02; M=0.02-0.12) was 81-67% less than seen without heavy early mortality. For example, under the most likely combinations of M and [F.sub.CUR] for the Chesapeake Bay fishery, biomass was reduced approximately 82-87% (M=0.06 [F.sub.CUR]=0.06; M=0.08 [F.sub.CUR]=0.04).

Table 4
Lifetime cohort biomass (g) from the Ricker biomass model (Saila
et al. 1988) under M=0.02-0.12, and F=2.0 over the first 5 years
and low uniform F=0-0.12 thereafter. Integration was by rectangular
approximation. Simulations were based on an arbitrary starting
biomass of 1000g.


M         0       0.02     0.04     0.06     0.08     0.10    0.12

0.02   180,730   20,395   15,785   13,075   11,390   10,270   9495
0.04   107,915   14,750   12,305   10,775     9760     9055   8560
0.06    70,195   11,610   10,225     9315     8675     8225   7875
0.08    49,170     9730     8895     8325     7910     7600   7370
0.10    36,595     8525     8000     7630     7360     7145   6990
0.12    28,595     7730     7380     7130     6940     6785   6660

Values of [t.sub.CRITICAL] estimated by using different values of M were relatively high for black drum in Chesapeake Bay. Increasing M resulted in a decrease in [t.sub.CRITICAL] from 25 yr at M=0.02 to 10 yr at M=0.12. This finding indicates that, for the range of M considered in our study, maximum theoretical cohort biomass, in the absence of fishing, is achieved before black drum reach age 25. This occurs at the lowest value of M, approximately the mean age of capture in Chesapeake Bay. For the most likely combinations of M and F (M=0.06 [F.sub.CUR]=0.06; M=0.08 [F.sub.CUR]=0.04), [t.sub.CRITICAL] declined from 13(M=0.08)-15(M=0.06) yr in the unfished stock to 10 yr in the fished stock. In this example, [t.sub.CRITICAL] is below the mean age of capture in the Bay, 26 yr, and potential yield is lost to natural mortality.

Estimated values of [P.sub.g] were also low for black drum caught in Chesapeake Bay. For [L.sub.[Infinity]]=117 cm, and the current estimated [l.sub.c] (110 cm, corresponding to [t.sub.c]=25), [P.sub.g]=0.06, i.e. on average, only 6% of their potential growth still remains when black drum in Chesapeake Bay enter the exploited phase at age 25. For alternative values of [t.sub.c] equal to 5, 10, 15, 20, and 30 years, values of [P.sub.g] are 0.46, 0.27, 0.16, 0.09, and 0.03, respectively.

Modeling with K=0.124

Yield modeling was also done to encompass an alternative estimate of growth based on the Brody coefficient (K) determined from the northeast Florida fishery (Murphy and Taylor, 1989). Because Chesapeake Bay region catches did not include fish aged 1-5, the estimate of K (0.105; Jones and Wells, 1998) differed slightly from that estimated for northeast Florida (K=0.124) which did include these ages. The values for [L.sub.[infinity]] were virtually identical from both studies Model results based on this faster growth rate produced similarly shaped yield-per-recruit curves but with slightly higher yields and benchmark values (Fig. 4). At the most probable values of M (0.06; 0.08), yield-per-recruit curves peaked only at [t.sub.c] [is less than or equal to] 10 yr. Otherwise, curves were asymptotic or rising. [F.sub.MAX] at [t.sub.c]=5 yr was 0.15 for M=0.06 and 0.21 for M=0.08 (Table 2), greater than our estimate of Z and [F.sub.CUR]. At [t.sub.c] [is greater than] 10, [F.sub.MAX] occurred at the highest levels of F. At the most probable levels of M, [F.sub.0.1] was greater than [F.sub.CUR] (Table 2). Hence under either [F.sub.MAX] or [F.sub.0.1] and larger K, [F.sub.CUR] was still below that needed to obtain maximum yields from the fishery in Chesapeake Bay.


Similarly, model results from this faster growth (K=0.124) and broader levels of M (0.02-0.12) showed that [F.sub.CUR] is below [F.sub.MAX] and [F.sub.0.1] for Bay region fisheries except for M [is less than or equal to] 0.04. Yield values were slightly higher than for K=0.105 for all levels of M (Fig. 4; Table 2), and the benchmarks, [F.sub.MAX] and [F.sub.0.1], fell at higher values of F. Hence, the reasoning that was used to discount growth overfishing previously can also be used here. When M=0.02-0.04, yield-per-recruit curves peaked at [t.sub.c]=5-15 yr and were asymptotic or rising at older ages. Both scenarios indicated that growth overfishing is possible but improbable because of the unlikely maximum ages that such low values of M imply and because curves peaked at values of [t.sub.c] lower than those experienced in this fishery. At higher levels of M (0.10; 0.12), growth overfishing was even less likely than at slower growth levels. Yield-per-recruit curves peaked only at [t.sub.c]=5 and for F [is greater than] 0.28. Likewise, this [t.sub.c] was too young for the fishery, and Z and [F.sub.CUR] were considerably smaller than the lowest values of [F.sub.MAX] or [F.sub.0.1]. Hence, even when the full range of M and faster growth were considered, growth overfishing was not likely for the Chesapeake Bay region fishery.

Overall, yield-per-recruit curves showed that a sixfold sixfold

1. having six times as many or as much

2. composed of six parts


by six times as many or as much

Adj. 1.
 increase in M resulted in a 50% decrease in yield for both growth rates Growth Rates

The compounded annualized rate of growth of a company's revenues, earnings, dividends, or other figures.

Remember, historically high growth rates don't always mean a high rate of growth looking into the future.
 (Figs. 1 and 4). As M increased, yield-per-recruit decreased. For a given M, yield-per-recruit increased to a maximum at an intermediate level of [t.sub.c]. Increases in yield slowed from 5-15 yr and decreased from maxima thereafter at older ages. In only one case (M=0.02 and K=0.105), yield-per-recruit increased with increased [t.sub.c] up to 20 yr. In all other cases, yield decreased for [t.sub.c] [is greater than] 20 yr, indicating that, beyond 20 yr, biomass was lost to natural mortality.


Our results indicate that yield-per-recruit for black drum in the Chesapeake Bay region is below its maximum for all but the lowest values of M used in our simulations. For M [is greater than or equal to] 0.04, current fishing mortality was below [F.sub.MAX]. Only when M=0.02 and [t.sub.c] [is less than] 15 does the upper bound of [F.sub.CUR] fall above [F.sub.MAX]. We discounted this case of extreme low M because of the unusually long lifetime that it predicts--some 200 years. Yield-per-recruit and economic efficiency could be maximized for black drum in Chesapeake Bay by decreasing [t.sub.c] to 5 years along with higher rates of fishing mortality. However, this may not be the most viable management option for this species for several reasons. First, because the relation between yield-per-recruit and F is essentially asymptotic, harvesting black drum in the Bay at or near [F.sub.MAX] would require a huge increase in fishing effort, making harvest of this species economically inefficient, especially with the current low demand for these fish. Besides, benchmarks such as [F.sub.MAX] are no longer thought to provide a sustainable measure of long-term maximum yield from a fishery. Second, the current [t.sub.c] may refect re·fect  
tr.v. re·fect·ed, re·fect·ing, re·fects Archaic
To refresh with food and drink.

[Latin reficere, refect-, to refresh : re-, re-
 the mean age of migrating adults that are recruited to the fishery. If so, decreasing [t.sub.c] may not be possible because young fish may not undertake migration along the coast, and a decrease in mesh size may result in failure of the net to "gill" the larger fish, with the result that catches would be diminished di·min·ish  
v. di·min·ished, di·min·ish·ing, di·min·ish·es
a. To make smaller or less or to cause to appear so.


Large reductions in biomass, especially of older fish, were shown in biomass modeling. Biomass decreases 42-59% under the most likely values of mortality (M=0.08, [F.sub.CUR]=0.04; M=0.06, [F.sub.CUR]=0.06, respectively) more than that of the unfished stock. Reductions in biomass (up to 87%) are exacerbated when heavy fishing mortality is concentrated on young fish. Concurrent with these reductions in biomass, is a rapid and dramatic loss of older fish from the stock. This juvenescence ju·ve·nes·cent  
Becoming young or youthful.

[Latin iuvensc
 occurs quickly--[t.sub.CRITICAL] is reduced from 15 in the unexploited stock to 10 at F=0.02 for M=0.06, and from 13 to 10 at M=0.08. At greater F, the decrease in [t.sub.CRITICAL] is even greater and the abundance of older fish diminishes further.

Altogether these modeling results show no indication of growth overfishing in the Chesapeake Bay region where old fish are predominantly targeted. Moreover, it is difficult to growth overfish o·ver·fish  
v. o·ver·fished, o·ver·fish·ing, o·ver·fish·es
To fish (a body of water) to such a degree as to upset the ecological balance or cause depletion of living creatures.

 a stock when fishing concentrates on capturing primarily older, larger fish. For example, black drum have already obtained 58% of their lifetime growth in length, and 22% of their lifetime weight when they first recruit to the Chesapeake Bay region at age six (Jones and Wells, 1998). By their mean age of capture in this region, they have obtained 90% of their lifetime growth in length and 51% in weight. Exploited cohorts have already surpassed their maximum growth by the time they enter the Bay region, and thereafter, natural mortality predominates. Cohort biomass has already declined from its optimum by the age fish enter the exploited stock in the Bay region.

Although these modeling results show no indication of growth overfishing in Chesapeake Bay, they do indicate that black drum are vulnerable when heavy fishing is directed to young fish in the southern portion of their range along the U.S. East Coast. We chose a high level of F in the first five years of life to dramatically illustrate the effect of targeted fishing on small fish and the potential effects of bycatch from other fisheries. These simulations clearly indicate the importance of limiting fishing mortality in regions where young fish occur. Prior to 1989, black drum landed in the Florida east coast commercial fisheries averaged 320 mm (Murphy and Muller(2)), and 80% of the catch was 4 yr or younger (Murphy and Taylor, 1989), raising the potential of growth overfishing at that time. Capture at this young age also raises concern for recruitment over-fishing, which our modeling does not address, especially when fish are targeted before they can reach sexual maturity (age 5). The potential for recruitment overfishing is minimal in areas, such as Chesapeake Bay, where the fishery targets older fish that have reproduced for many years before capture. Moreover, recent bans on gillnetting in Florida and other regulations on black drum fishing since 1989 should preclude pre·clude  
tr.v. pre·clud·ed, pre·clud·ing, pre·cludes
1. To make impossible, as by action taken in advance; prevent. See Synonyms at prevent.

 recruitment overfishing and help preserve the stock.

Models are typically used in management to regulate fishing mortality in order to obtain sustainable harvests from a stock. These regulations have historically resulted in harvests with large biomass that are valued in commercial fisheries. In contrast, recreational anglers are not as interested in obtaining maximum biomass as they are in catching fewer, but larger fish. Moreover, increased production of larger fish occurs when fishing mortality is below [F.sub.MAX] and when recruitment is high. Hence, in the black drum fishery, which is targeted by both commercial and recreational fishermen, management objectives are at cross purposes. The commercial fishery benefits when yields are maximized to the detriment Any loss or harm to a person or property; relinquishment of a legal right, benefit, or something of value.

Detriment is most frequently applied to contract formation, since it is an essential element of consideration, which is a prerequisite of a legally enforceable contract.
 of survival and growth for the trophy-size fish desired by recreational anglers. In the Chesapeake Bay region, fishing mortality is low and supports the objectives of managing the recreational fishery. However, the most influential fishing mortality is on young fish and is not under the control of the Bay region management agencies, but is controlled by states farther south.

The long-range migrations of the East Coast black drum stock argue for a coast-wide management strategy. Through our modeling, we have shown that fishing practices in the Bay region have little impact on the production of harvestable biomass and that mortality on young fish drives eventual production available to the Chesapeake Bay region black drum fishery. The supply of fish to the Bay region depends on mortality during the first ten years of life, years when these fish are found off the coasts of the South Atlantic states The South Atlantic United States form one of the nine divisions within the United States that are recognized by the United States Census Bureau.

This division includes nine states — Delaware, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, West
. Hence, management practices by states south of Cape Hatteras will determine the supply of fish to this coast-wide stock.


We would like to thank Barbara McClellan for her assistance with modeling and graphics, and Douglas Vaughan and Michael Murphy Michael Murphy may refer to:
  • Michael Murphy (actor), an American actor
  • Michael Murphy (politician), a New Jersey lobbyist, former Prosecutor and candidate for Governor
  • Michael Murphy (author), a New age author and a co-founder of the Esalen Institute
 for their review of and suggestions for improving this manuscript manuscript, a handwritten work as distinguished from printing. The oldest manuscripts, those found in Egyptian tombs, were written on papyrus; the earliest dates from c.3500 B.C. . This research was funded by a Wallop/Breaux Program Grant for Sport Fish Restoration from the U.S. Fish and Wildlife Service through the Virginia Marine Resource Commission, Project F-88-R3 to C. Jones and Mark E. Chittenden Jr.

(1) Gold, J. R. 1995. Personal commun. Center for Biosystematics bi·o·sys·tem·at·ics  
n. (used with a sing. verb)
The statistical analysis of data obtained from genetic, biochemical, and other observational studies to assess the taxonomic relationships of organisms or populations, especially within an
 and Biodiversity biodiversity: see biological diversity.

Quantity of plant and animal species found in a given environment. Sometimes habitat diversity (the variety of places where organisms live) and genetic diversity (the variety of traits expressed
, Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX 77843.

(2) Murphy, M.D., and R. G. Muller. 1995. A stock assessment of black drum, Pogonias cromis, in Florida. Unpubl. manuscript, 20 p. Department of Environmental Protection, Florida Marine Research Institute, St. Petersburg, FL, 33701-5095.

(3) Wenner, C. 1995. Personal commun. South Carolina Department of Natural Resources The South Carolina Department of Natural Resources is a South Carolina state agency charged with regulating hunting, fishing, boating, duck stamp orders, state parks and the conservation efforts of the South Carolina state government. , P.O. Box 12559, Charleston, SC 29422.

(4) Virginia Marine Resources Commission. 1993. Mimeo: Virginia black drum landings by gear type 1973-1993. Virginia Marine Resources Commission, 2600 Washington Ave, Newport News Newport News, independent city (1990 pop. 170,045), SE Va., on the Virginia peninsula, at the mouth of the James River, off Hampton Roads, near Norfolk; inc. 1896. , VA, 23607.

(5) North Carolina Division of Marine Fisheries. 1980-94. Mimeos: North Carolina landings reports (1979-1993). North Carolina Division of Marine Fisheries, Morehead City, NC, 28557-0769.

(6) Werner, C. 1996. Personal written commun. Preliminary South Carolina landings reported to the Fisheries Statistics Program 1979-1995. South Carolina Department of Natural Resources, P.O. Box 12559, Fisheries Statistics Program, Charleston, SC, 29422-2559.

(7) Pafford,J. 1995. Fisheries Statistics Project: Georgia black drum landings 1972-94. Georgia Department of Natural Resources The Georgia Department of Natural Resources is an administrative agency of the U.S. state of Georgia. The agency is charged with the responsibility of regulating hunting, fishing, boating, and non-game plants and animals. The agency is headed by a commissioner. , Coastal Resources Division, One Conservation Way, Brunswick, GA 31523-8600.

(8) Sutherland Sutherland or Sutherlandshire, former county, N Scotland. Under the Local Government Act of 1973, Sutherland became (1975) part of the new Highland region (now a council area). , D. 1995. 1979-94 Black drum commercial landings for Atlantic Coast states. Fisheries Statistics Division, National Marine Fisheries Service The U.S. National Marine Fisheries Service (NMFS) is a United States federal agency. A division of the National Oceanic and Atmospheric Administration (NOAA) and the Department of Commerce, NMFS is responsible for the stewardship and management of the nation's living marine , 1315 East West Highway, Silver Spring, MD 20910.

(9) Fisheries Statistics Division and Economics Division. 1996. Personal commun. Fisheries Statistics Div. and Economics Div., National Marine Fisheries Service, 1315 East West Highway, Silver Spring, MD 20910.

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A small silvery food fish (Micropogonias undulatus) common in Atlantic waters south of Massachusetts.

Noun 1.
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Atlantic croaker

croaker - any of several fishes that make a croaking noise

genus Micropogonias, Micropogonias - croakers
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 Bight bight, broad bend or curve in a coastline, forming a large open bay. The New York bight, for example, is the curve in the coast described by the southern shore of Long Island and the eastern shore of New Jersey. The term bight may also refer to the bay so formed. . Fish. Bull. 95:637-645.

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1. the process of becoming mature.

2. attainment of emotional and intellectual maturity.

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Any of various widely distributed soft-finned fishes of the family Clupeidae, which includes the herrings, menhadens, and sardines.

Of, relating to, or belonging to the family Clupeidae.
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Gold, J. R., and L. R. Richardson. 1998. Mitochondrial DNA Mitochondrial DNA (mtDNA) is the DNA located in organelles called mitochondria. Most other DNA present in eukaryotic organisms is found in the cell nucleus. Nuclear and mitochondrial DNA are thought to be of separate evolutionary origin, with the mtDNA being derived from the  diversification Diversification

A risk management technique that mixes a wide variety of investments within a portfolio. It is designed to minimize the impact of any one security on overall portfolio performance.

Diversification is possibly the greatest way to reduce the risk.
 and population structure in fishes from the Gulf of Mexico and Western Atlantic. J. Heredity heredity, transmission from generation to generation through the process of reproduction in plants and animals of factors which cause the offspring to resemble their parents. That like begets like has been a maxim since ancient times.  89:404-414.

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  • John C. Wiley, American ambassador
  • John D. Wiley, Chancellor of the University of Wisconsin-Madison
  • John M. Wiley (1846–1912), U.S.
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New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
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American psychiatrist who cofounded the first psychotherapy clinic in the United States (1908).
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Cynthia M. Jones Brian K. Wells Old Dominion University “ODU” redirects here. For other uses, see ODU (disambiguation).

The university was recently named one of the best colleges in the Southeast by The Princeton Review.
 Department of Biological Sciences Norfolk, Virginia Norfolk is an independent city in the Commonwealth of Virginia, in the United States of America. With a population of 234,403 as of the 2000 census, Norfolk is Virginia's second-largest incorporated city.  23529-0456 E-mail address See Internet address.

e-mail address - electronic mail address
 (for C. M. Jones):
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Geographic Code:1USA
Date:Apr 1, 2001
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