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UMASS/AMHERST

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Insight into the Methodology and Logic Behind

National Marine Fisheries Service

Fish Stock Assessments

f mj

How Did You Guys Come Up With Those Numbers,

Anyway?

Commonwealth of Massachusetts
Edward J. King, Governor

Executive Office of Environmental Affairs
John A. Bewick, Secretary

Insight into the Methodology and Logic Behind

National Marine Fisheries Service

Fish Stock Assessments

How Did You Guys Come Up With Those Numbers,

Anyway?

Written by:
David E. Pierce

Senior Marine Fisheries Biologist
Massachusetts Division of Marine Fisheries
AOO Cambridge Street
Boston, MA 02202
DMF: (617) 727-3193

Patricia E. Hughes

Marine Fisheries Biologist

Massachusetts Coastal Zone Management

Office

100 Cambridge Street

Boston, MA 02202

CZM: (617) 727-9530

The printing of this publication was funded by the Office of Coastal Zone Management, National Oceanic and Atmospheric
Administration, U.S. Department of Commerce under a program implementation grant to the Commonwealth of Massachusetts.

EDWARD J. KING
GOVERNOR

THE Commonwealth of Massachusetts

EXECUTIVE DEPARTMENT
STATE HOUSE • BOSTON 02133

January 25, 1979

Dear Reader,

I am pleased to present the members of the public this paper
which describes the way in which fisheries scientists estimate the
health and size of the fish stocks in the waters off New England.
This biological information is used by the New England Fisheries
Management Council in developing fisheries management plans.
Some fishermen and others have expressed concern about the way
the 200 mile fisheries conservation law has been implemented.
This publication seeks to answer some of these questions. It was
developed jointly by staff in the Division of Marine Fisheries and
the state's Coastal Zone Management Office, both within the
Executive Office of Environmental Affairs headed by Secretary
John A. Bewick.

Commercial fishing is one of the Commonwealth's oldest industries
and today contributes some one-half billion dollars annually to
our economy. This administration looks forward to an expanded and
more productive commercial f ishj,«g~~Nidustry in the years to come.

rely.

x^iyuil/

EDWARD J. KING
Governor

INTRODUCTION

The National Marine Fisheries Service provides
the various Regional Fishery Management Councils
with stock assessments that are used to help deter-
mine that portion of the fish stock which may be
harvested (optimum yield), given certain manage-
ment objectives. In order for management to be
effective, these assessments must be acceptable to
those being regulated; otherwise, management
measures implemented by the Councils are doomed
to failure.

Unfortunately, during 1977 many New England
fishermen felt that some groundfish assessments
made by the Northeast Fisheries Center (NMFS)
appeared to contradict their observations made
during actual fishing operations. As a result, opti-
mum yields, which at that time were based by the
New England Council primarily on scientists' esti-
mates of catches required to maintain or increase
stock sizes in later years, met with a great deal of
skepticism. Fishermen commonly asked "How did
you guys come up with those numbers anyway?"
Questions such as this and criticisms resulted, in
part from a lack of understanding of what
information scientists used to perform their
assessments and how it was gathered, what
assessments' results actually indicated, and what
the role of assessments was in the setting of
optimum yields by the New England Council.

Since the need for assessments and the Councils'
dependencies on them are here to stay, it is extremely
important that all concerned individuals become
familiar with the assessment process, else the same
questions and confusion will arise year after year.
For example, as part of a fish stock assessment, the
following basic information is needed: past and
present age composition of the stock; number of
young fish which eventually enter a fishery (recruit-
ment); weight of the stock; growth rates; deaths due
to fishing; and deaths due to factors other than fish-
ing. This information is collected from two main
sources: NMFS bottom trawl surveys and fishermen
in the form of commercial and recreational catches
and/or landings.

Our intent is for this paper to be readable and
understandable by fishermen, administrators and
Council members. However, we don't pretend to
believe that everything will be made clear and all
questions laid to rest. Some sections must be read
carefully and deliberately. We feel the scientific
language has been kept at a minimum and that fre-
quent, specific examples, particularly in the stock
assessment section (appendix), which is very difficult
to make understandable to laymen, illustrate certain
important points.

The material presented attempts to guide the
reader through the methodology and logic behind the
surveys and to relate the information obtained from
commercial and recreational catches and landings. A
simplified example is given to illustrate how all this
information is used to produce a fish stock assess-
ment; more detailed information is given in the
appendix. A list of definitions of important, com-
monly heard, scientific terms is also presented (itali-
cized terms in the text are defined in the glossary).

If nothing else, we hope that one point is made
clear. Scientists use commercial and recreational
catches and landings (when available and reliable) to
perform fish stock assessments. Accurate informa-
tion gathered from commercial and recreational
catches and landings, whether it be from logbooks,
dealer weighout slips, etc., is at least as important as
the results from the bottom trawl surveys. They com-
plement one another. Quantities, locations, and age-
length data of catches (not just landings) and records
of fishing effort (number and duration of tows) are
indispensable for accurate assessments which give a
true reflection of the status of the stocks.

We welcome all questions. If we have failed to
cover specific points of interest or if further explana-
tions of material covered are needed, please let us
know by caUing either 617-727-3193 (DMF) or 617-
727-9530 (CZM), or by writing to either one of us at
the addresses shown on the title page.

RESEARCH VESSEL
BOTTOM TRAWL SURVEY

Purposes

1) To obtain annual estimates of the relative
abundance of major finfish species in terms of both
number and weight {biomass).

2) To determine long term changes or trends in rela-
tive abundance and species composition of the entire
groundfish community, not just a few species such as
cod, haddock and yellowtail flounder.

3) To describe fish distribution on a very broad scale
in relation to bottom features, geography and envi-
ronmental factors such as temperature.

4) To gather information on age and species compo-
sition, growth and maturity changes, mortality, food
habits, stock identification, future recruitment and
other biological as well as environmental data.

Survey Areas

1) Historically, surveys have ranged from 15-200
fathoms from Cape Hatteras to Nova Scotia (75,000
square nautical miles). Currently, surveys extend
from approximately 4-200 fathoms and reach south-
ward to Cape Fear, North Carolina.

2) There are five depth zones (in fathoms): approxi-
mately 4-14 (referred to as the inshore zone); 15-30;
31-60; 61-100; greater than 100. Each zone is divided
into separate sampling areas which are called strata.
From Cape Hatteras to Nova Scotia (15-200
fathoms) 65 strata have been established based
primarily on geography (latitude) and depths. These
strata may be combined to represent the Middle
Atlantic, southern New England, Georges Bank, and
Gulf of Maine regions (Figure 1). The inshore zone
from Cape Hatteras to Nova Scotia is divided into 74
strata; an additional 15 strata extend southward to
Cape Fear. These strata have also been established
based on geography and depths; the locations of
major estuaries (for example, Chesapeake Bay) and
coastal configurations have influenced the number
and size of each stratum.

3) Until recently, inshore tows (less than 15
fathoms) were made occasionally. Now, inshore
tows are regular features of the surveys, especially
those performed in the Mid-Atlantic. Inshore tows
are stressed in recently begun summer surveys since
fish tend to move inshore during the warmer summer
months, particularly in the Mid-Atlantic region. The
number of inshore tows during the summer in the
more northern regions, for example, the Gulf of
Maine, is more limited due to the nature of the
bottom and great abundance of fixed gear.

Stations (Tow Locations)

1) Time considerations limit the number of stations
(tow locations) per season to 250-300. A predeter-
mined number of stations within each stratum is sel-
ected at random before each cruise. The procedure
for determining the numbers and locations of tows
per stratum is essentially as follows:

For the offshore zones (15-200 fathoms):

a) The number of tows in a given stratum is pre-
determined and roughly proportional to the area of
each stratum. In other words, the larger the stratum,
the greater the number of tows.

b) The smallest number of stations in a stratum is
two; this is typical of narrow strata along the shelf
edge in the Mid- Atlantic.

c) Each of the 65 strata (15-200 fathoms) is sub-
divided into rectangles of standard size (5 minutes
latitude by 10 minutes longitude).

d) Each rectangle is further subdivided into 10
smaller rectangles (2 Vi minutes latitude by 2 minutes
longitude). Every stratum, therefore, is subdivided
into a large number of IVi by 2 minutes rectangles
which are then numbered consecutively starting
with 001.

e) For each stratum, numbers are randomly chosen
(from a table of random numbers — statistically
accepted practice) until the predetermined number of
stations is obtained. Tow locations correspond to the
numbered IVi by 2 minutes rectangles selected. A
constraint is that only one tow can be selected for
each 5 by 10 minutes rectangle in a stratum. This
ensures that all possible tow locations in a given area
have an equal chance of being chosen during any one
cruise (randomization).

f) An entire stratum often cannot be subdivided into
equal 5 by 10 minutes rectangles due to the irregular
boundary of that stratum. Therefore, in this case,
irregular shaped blocks are formed with the area of
each block equalling that of a 5 by 10 minutes
rectangle.

For the inshore zone (less than 15 fathoms):

a) Each strata is divided into 2 Vi minutes latitude by
2 minutes longitude rectangles. Since the inshore
strata are smaller than those offshore, there is no
initial subdivision to 5 by 10 minutes rectangles.

b) Each 2 Vi by 2 minutes rectangle per strata is
numbered. For each stratum, numbers are randomly
chosen until a predetermined amount per stratum is
obtained. The only constraint is that no adjacent rec-
tangles may be selected.

After tow locations are selected, a cruise route is
established; the route ignores stratum boundaries
and attempts to minimize steaming time. Extra sta-
tions are added in the route to fill gaps in large areas
which lack stations selected by the above methods
(no more than 6 are added per survey).

During the survey, tow locations may be moved
or omitted if the original location is found to be near
a charted obstruction or the haul leads to net
damage. Alternate tows are made nearby in the same
stratum and depth. Every effort is made to tow on
original locations.

2) Average sampling intensity from Cape Hatteras
northward (15-200 fathoms) represents roughly one
trawl haul every 300 square miles (includes non-
trawlable areas).

3) It is not always possible to finish an entire survey
because of weather, vessel breakdowns, etc.; how-
ever, key regions (southern New England, Georges
Bank, and the Gulf of Maine) receive top priority
and are always covered on each survey.

In 1977, during the autumn bottom trawl survey
(September 26 - December 5), 100 tows were made on
Georges Bank -South Channel; 64 tows in the Gulf
of Maine; 63 tows in the southern New England
region (27 additional tows inside 15 fathoms); and 59
tows in the Mid-Atlantic region (48 additional tows
inside 15 fathoms) (Figure 2).

Time of Surveys

1) Autumn (since 1963); spring (since 1968); summer
(since 1977).

2) Approximately 10 weeks to cover Cape Hatteras
to Nova Scotia during each survey.

3) 24 hours a day during each survey.

In 1977, surveys were performed from March 19 -
May 14, July 27 - August 13, and September 26 -
Decembers.

Vessels and Gear

1) Research vessels Albatross IV (187 foot stern
trawler; in use since 1963) and the Delaware II (155
foot stern trawler; infrequent in past years but re-
cently being used more often) are of equal fish-
ing power. Foreign vessels are also used in joint,
cooperative surveys, but these survey data are only
used to supplement U.S. survey results.

2) Fall and summer surveys use the #36 Yankee
trawl while the spring surveys use the high opening, 2
seam #41 Yankee trawl (since 1973).

3) #36 Yankee and #41 Yankee trawls are 5 inch
mesh throughout except for a 4!/2 inch mesh cod end
with a 1/2 inch mesh liner in the cod end and upper
belly; both are fished with rollers, thus tows on
rough bottom are possible.

#36

Effective headrope height 10-12'
Effective wingspreads 32-36'

Footrope 80'

Legs 5 fathom

Doors 1 ,200 lbs. BMV oval

#41

14-16'

34-37'

100'

10 fathom

1,500 lbs. BMV oval

4) 16 inch diameter, 5 inch wide, hard rubber rollers
with 6-7 inch long, 1/2 inch diameter rubber spacers
along the footrope.

5) 36 floats of 8 inch diameter; aluminum, deep sea
type.

Tows

1) Thirty minute tows are made at each station at an
average speed of 3.5 knots. The speed through the
water has previously been indicated by an electro-
magnetic log; however, a Doppler Speed Log is now
in use. A Doppler provides an immediate record of
vessel velocity and a cumulative readout of dis-
tance traveled over the bottom.

2) Tows are made with enough wire to obtain a
scope of 3:1 except in water greater than 150 fathoms
where a 2V2 :1 scope is used.

3) Tow direction is on heading toward the next sta-
tion on the route except when wind and sea states are
unfavorable. Tows are made along depth contours to
maintain constant depth.

Limitations

1) The exact number and weight of each species in a
given area (absolute abundance) is impossible to
determine. The sampling reflects increases or
decreases in the relative abundance of fish stocks and
is therefore a useful measure of change in absolute
abundance.

2) With a series of annual surveys, scientists can test
for significant trends in relative abundance with
time; that is, whether there is a decline or an increase
in relative abundance over a period of years. Because
fish are not uniformly distributed, a great many tows
are required to detect small yearly changes in stock
size, in some regions as many as 350-500 tows. This
sample size is not possible due to time, vessel and
personnel limitations. Current abundance indices
(stratified mean catches per tow) are only precise
enough to detect major changes in stock size between
years. Generally, it takes several years before major
changes in stock size occur.

Management policy has a great deal of influence
on whether or not the lack of high precision is a limi-
tation. If managers decide that it is only necessary to
detect when large changes (for example, 50^o and
greater) in relative abundance have occurred, then
the survey's lack of high precision is not a limitation.
However, if the detection of small yearly changes
(for example, 5-10%) in relative abundance is
required, the lack of high precision presents a
problem.

3) While a number of inshore areas (less than 15
fathoms) from Cape Cod to Cape Hatteras have
been sampled during the spring and fall bottom
trawl surveys (since 1972) and more so during the
summer surveys, the coverage of inshore areas,
particularly in the New England region, is less
intensive than that of offshore areas (greater than 15
fathoms). In addition, rocky bottoms (for example,
rock piles) are not surveyed due to the likelihood of
hang ups and "rimracks." Consequently, measures
of relative abundance and distribution of some
inshore species and young-of-the-year of some
inshore and offshore species may not be truly
representative.

To increase the coverage of the New England in-
shore areas, the State of Massachusetts Division of
Marine Fisheries has begun spring and fall bottom
trawl surveys with a contracted commercial fishing
vessel. This involves approximately 90-100 20 minute
tows per survey within Massachusetts territorial
waters from the New Hampshire to Rhode Island
borders. Spring and fall 1978 surveys have been com-
pleted. The State of Maine Department of Marine
Resources also intends to perform similar survey
work off its shores; none has been completed as yet.

4) Tow locations are randomly selected and are
therefore widespread. The survey design is limited
when there is a need to assess the relative abundance
of a particular species and that species' seasonal
movements are local and primarily restricted to spe-
cific areas. However, unchanged habits and distribu-
tions between seasons in different years are excep-
tional rather than common.

It should be noted that recently the Northeast
Fisheries Center has begun to ask for fishermen's
suggestions as to where additional survey effort
should be placed. The Center has modified and
intends to continue to modify its surveys' patterns of
tows to comply with some of the suggestions.

the same but fish distribution changes in response to
some factor (perhaps temperature) so that fish
become more aggregated or concentrated, commer-
cial catch results will suggest false increases in rela-
tive abundance, and vice versa. This same reason
appHes for not performing research vessel surveys
only in areas where catches are expected to be great-
est. However, if habits and distribution of a fish
stock do remain unchanged between years, commer-
cial catches alone may give satisfactory estimates of
changes in relative abundance of the stock with time.
This is possible provided gear efficiency does not
change with time and the Northeast Center is pro-
vided with accurate catch and effort records by area
and is able to perform sufficient port sampling.

3) Over the years, fishing power of commercial ves-
sels has changed due to technological improvements,
etc., while the research vessels' fishing powers have
not varied. Consistent use of particular trawl nets
and 30 minute hauls has resulted in a standardized
fishing method.

4) Small mesh liners enable retention of young-of-
the-year and juvenile fish of many species. This
enables estimates of the number of fish which will
enter a fishery in future years {year-class strengths
and recruitment).

5) Fish distribution and seasonal movements as
influenced by the environment can be investigated.

6) Estimates of abundance of '*non-traditional"
species are possible.

7) Regulations (for example, catch limitations) en-
courage or make necessary high discard rates, false
reporting, and even smuggling; therefore, reliable
estimates of total removals from the stock by area,
and records of commercial landings and effort
become difficult to obtain. Greater reliance on
bottom trawl survey results becomes necessary.

Reasons for the Need of Bottom IVawI Surveys

1) Since commercial fishing strategies vary accord-
ing to market conditions and prices, commercial
landings reflect only those species and sizes suitable
or desirable for market in a given port at a particular
season. In contrast, entire catches (all species and
sizes) of research vessels' hauls are examined and
recorded.

2) Since commercial vessels generally fish where
catches are expected to be greatest, fishing patterns
vary according to fish availability which may be
related more to fish aggregation than relative abun-
dance. If in different years stock abundance remains

COMMERCIAL STATISTICS

Personnel

1) 18 Offices: MAINE — Eastport, Rockland, Port-
land; MASSACHUSETTS — Gloucester, Boston,
Plymouth (covers Harwich to Westport), Province-
town (covers Chatham), Woods Hole, New Bedford;
RHODE ISLAND — Newport (covers Connecticut),
Point Judith; NEW YORK — Greenport, Patchoque;
NEW JERSEY — Cape May, Tom's River; MARY-
LAND — Easton; VIRGINIA — Franklin City,
Hampton.

2) Staff: Total of 31 permanent employees (17 port
samplers and 14 supervisory and administrative per-
sonnel); New England has 10 port samplers and 6
supervisory and administrative personnel (Newport
has one person with both responsibilities), plus 5 co-
op students who work in the port sampling section.

Sources of Information

1) Dealer weighout slips: provide information on
pounds and ex-vessel prices of fish species landed;
catches are generally recorded by vessel and on a trip
basis.

2) Vessel captain interviews: provide information on
pounds of fish caught ("hail") by species, area
fished and gear type, time, number and duration of
tows or sets, and estimates of catch of each species
discarded.

3) Logbooks: provide information similar to that
obtained from vessel captain interviews. Weights of
catch by species are estimates.

4) Commercial catch samples: dockside sampHng to
determine length and age compositions of the land-
ings, growth rates, and length/weight relationships
of different species.

5) Sea sampUng: on board collection of information
on length and age composition of catch and amount
of discards by species.

Coverage

1) Weighout slips: 95% of New England landings
are assumed by NMFS to be reflected in the monthly
collections from dealers; weighout information is
collected in Maine, Massachusetts, Rhode Island,
and New Jersey. Landings in the other states (New
Hampshire, Connecticut, and in the Mid- Atlantic)
are collected monthly (total landings by species, no
breakdown by vessel or trips), but will be incor-
porated into the system in the near future.

2) Interviews: 50-60% coverage of greater than one
day vessel trips; 10-15% coverage of day trip vessels.
Percent coverage of total weight landed is greater
than coverage for individual trips.

In 1977, 3,500 greater than one day vessel trips
were interviewed out of a total of 7,000 trips made.
Out of 41,000 day trips made, 6,150 trips were
interviewed.

3) Logbooks: currently required for headboats and
groundfish vessels greater than 100 gross registered
tons (GRT); logbooks will soon be mandatory for all
groundfish vessels.

4) Commercial catch samples: daily sampling by
area; for a given species catches from a selected com-
bination of sub-areas of statistical areas are sampled
— see Figure 3. Catch samples are obtained through-
out the year for 29 species; two illustrations are:

Yellowtail flounder — since this species is landed
and sorted by count (number per 125 pound box),
each different count is sampled for length and age;
attempts are made to obtain one length sample (100)
fish) and age sample (50 fish) per count, sampUng
area, and quarter of the year.

Cod and haddock — attempts are made to obtain
5 length samples (50-100 fish each) and 5 age samples
(15-20 fish each) per market category, month and
sampling area.

There are also sampling requirements by regional
area and by port.

Problems

1) Weighout slips are not collected in every port due
to a lack of personnel.

2) In some instances, consignment shipping of catch
makes impossible a record of first landing location.

3) Extent of discard is difficult to evaluate since
fishermen are asked to estimate the amount of
discard by species, and are often reluctant or unable
to provide the information.

4) Gaps in coverage exist even for species of major
commercial importance due to a lack of funds and
personnel and an insufficient amount of port
sampling by area, gear type, etc.

5) Participation and cooperation in the logbook pro-
gram is not complete, and the accuracy of the infor-
mation is questionable. The greater the accuracy of

logbooks, as well as weighout slips, etc., the greater
the ability of the NMFS assessments to depict the
true nature and status of different fisheries and fish
stocks.

6) Some transactions are never recorded; for
example, purchases by restaurants.

7) Extent of coverage in sea sampling program is
limited due to personnel, funding and some insur-
ance coverage problems.

8) False reporting occurs to "get around" regula-
tions. For example, reporting yellowtail from W69
when caught in E69 waters; reporting one species as
another (cod as pollock); reporting catch from inside
territorial waters when actually taken outside in the
Fishery Conservation Zone (FCZ).

RECREATIONAL STATISTICS

In 1960, 1965, and 1970, door to door household
interviews were conducted during the National
Survey on Fishing and Hunting. Information was
provided, on a regional basis, on number of anglers
and number and weight by species of fish caught. In
1974, NMFS conducted a Northeast region telephone
survey which collected the same information as the
previous surveys. Since 1974, a number of smaller
surveys, principally in the mid-Atlantic region, have
been done to collect information for specific species.
In the fall of 1978 an extensive intercept and phone
survey of recreational catch was begun.

The weight by species caught is used by Northeast
Fisheries Center scientists in their stock assessments.

A SIMPLIHED EXAMPLE OF
ONE METHOD USED TO DETERMINE
STOCK ABUNDANCE AND EFFECTS OF
DIFFERENT LEVELS OF CATCH

1) Total Catch — Commercial landings (weight) by
the U.S., Canada, and other countries are obtained.
Recreational catch (angler, charter/headboat) is
estimated from Marine Angler Surveys. Discards are
estimated from logbook records, fishermen inter-
views, and fishermen scuttlebutt.

2) Total Length Composition — Length frequency
information is obtained from commercial and
recreational samples and from foreign catches. This
information is appHed to catch from specific areas to
estimate length frequency of total catch from those
areas.

3) Total Catch Age Composition — Age/length
relationships or "keys" are estabhshed from
commercial and/or research vessel survey catches.

**Keys" are then applied to commercial length
frequencies to estimate age composition. The
resulting age frequency is then increased by propor-
tionately distributing recreational catches within the
frequency.

4) Stock Size in Past Years — With determination of
catch age composition over a period of years, and an
estimation of natural mortality dind. fishing mortality
in the most recent year, techniques are available to
determine past stock sizes and fishing mortality over
time. A Virtual Population Analysis (VPA) is one
such method used to determine past stock sizes and
fishing mortahties of different year-classes at each
age. The total stock weight in metric tons can be
obtained by applying commercial weight at age
information determined from biological sampling to
numbers at age calculated from, for example,

the VPA.

5) Current and Future Stock Size — Techniques are
available which can be used to evaluate current stock
size and to predict future trends in stock size under
various assumptions of recruitment and discard. To
illustrate how research vessel survey results are used
to predict future prospects for fisheries, the
following example is given:

It may be possible to set up a relationship to
determine the size of a year class which has yet to
enter a fishery but is catchable in the research vessel
trawl survey if the following holds true: poor catches
in the research trawl survey of a series of past year-
classes correspond to poor abundance of the same
year-classes when they are commercially and recrea-
tionally exploited, and high catches in the trawl
survey of a series of past year-classes correspond to
high abundance when those year-classes enter the
fishery. Therefore, if the relationship can be
established and a particular survey results in good
catches of a year-class, then it is possible to predict
that abundance of older ages of that year-class will
also be good. Hence prospects for the future of the
fishery will be promising.

6) Effects of Future Catch — A group of options of
future catch and resultant stock size are calculated
and presented to the Fishery Management Councils.
The setting of optimum yields or total allowable
catches is done by the Councils after consideration
of the options with regard to Council objectives.

Other types of assessments exist to determine the
status of fish stocks. The type depends on the kinds
and amounts of reliable information which is avail-
able to the scientist and the objectives of
management which are set independently of the
scientist. This dicates whether an assessment can be
sophisticated or relatively simple and not complex.

APPENDIX

A DETAILED EXAMPLE OF ONE METHOD
OF STOCK ASSESSMENT

1) Landings (weight) by the U.S., Canada, and other
countries plus estimates of recreational catch (angler,
charter/headboat) and discards are obtained. The
recreational catch and discards, unlike commercial
landings, are difficult to determine (at times, com-
mercial landing data are not always satisfactory for
many species); therefore, stock assessments may be
performed under different assumptions of total
recreational catch and percentage of discards.
Marine angler surveys are sources of estimates of
recreational catch while percentage of discards are
available from logbook records, fishermen inter-
views, sea sampling and fishermen scuttlebutt.

2) Length frequency information for a particular
species is obtained from U.S. commercial and recrea-
tional samples and from foreign catches of that
species if an allocation exists. This information is
applied, depending on the amounts of data available,
to monthly, quarterly, half-year, or annual catch
from specific areas to estimate length frequency of
the total catch from those areas. When possible,
length frequency information is appHed to catch by
harvesting sector (for example, by gill netters, long-
liners, otter trawlers, etc.). As an illustration, the
following procedure might be used:

a) From a number of vessels, samples of a particular
species (of each market category if separated) are
taken by measuring the lengths of fish in one or more
boxes, baskets, etc., per vessel. The weight of each
sample can be determined after-the-fact by previ-
ously estimated length/weight relationships. In other
words, by knowing the number of fish and each of
their lengths in the samples, the weights for each fish
can be estimated to determine the total weight of the
samples.

b) Results of all sampled landings of a species caught
from specific areas are added together to give sample
length frequency and weight by area for a given time
period, such as a month.

c) By knowing the total landings and the areas fished
during that period, the length frequency of sampled
landings can be expanded to estimate the length fre-
quency of total landings by area for all vessels. The
eventual outcome is a length frequency by area for
an entire year.

For example, suppose during May a cod length
distribution is obtained from samples
(approximately 1000 fish) of 10 vessels that fished in
South Channel (Statistical area 521 — see Figure 3).
It is determined from a length/weight relationship
that the total weight of the samples is 5,000 lbs. It is
also known from weighout slips, logbooks, inter-
views, etc., that a total of 200,000 lbs. was landed
from the South Channel in May by vessels from
various ports. The total weight is 40 times the
amount of the sampled weight (200,000 ^ 5,000);
thus the length frequency determined from the
samples is multiplied by 40 to obtain an estimate of
the length composition of landings in all ports of cod
caught in the South Channel during May.

3) Age/length relationships or **keys" are estab-
lished from commercial samples when enough data
are available; otherwise, they are determined from
spring and fall bottom trawl surveys. "Keys" are
then applied, in some cases by calendar quarter, to
commercial length frequencies. This provides an
estimate of total commercial landings age composi-
tion (by number, not weight). The resulting age fre-
quency is then increased by proportionately dis-
tributing recreational catches within the frequency.
The following is a representation of how an estimate
of age composition (over a selected length range)
might be obtained by application of an age/length
key to final results of step 2 (total length
composition).

Length

category

500
500
500

Age as determined from

scale and/or otolith

examination

Total number of

fish by length

category estimated

in step 2
(thousands of fish)

2 3 4

400 80 20
65 375 60
30 110 250

110

1500
2600
4500

Estimate of total

age composition

(thousands of fish)

1200

240

338

1950

312

270

990

2250

990

1808 3180 2622 990

To explain further, from scale and/or otolith
(earbone samples taken from 500 fish which ranged
from 14-16 inches, 400 are found to be age 2, 80 age
3, 20 age 4, and none age 5. In other words, 80% are
age 2 (400/500), 16% age 3, 4% age 4, and 0% age 5.
These percentages are appHed to the total number of
fish in the same size range or category determined in
step 2. Thus, if 1,500,000 fish from 14-16 inches
comprise the commercial landings, then 1,200,000 are
age 2 (0.80 x 1,500,000), etc. The number of fish of
each age over all lengths is obtained by addition; for
example, from 14-22 inches there are 1,808,000 age 2
fish (1,200,000 + 338,000 + 270,000), etc. The length
categories can be varied and are normally recorded
in metric units (millimeters or centimeters).

4) A Virtual Population Analysis (VPA) is
performed to estimate past stock sizes in numbers of
fish and fishing mortalities of different year-classes
at each age. For any one calendar year, the sizes of
the various year-classes are added to obtain an
estimate of total stock size in that year. For example,
total stock size of a particular species in 1976 might
be estimated by adding the following: age 1 of the
1975 year-class; age 2 of the 1974 year-class; age 3 of
the 1973 year-class, etc.

This method requires an estimate of natural
mortality (M), total catch (C) of each age of differ-
ent year-classes estimated from step 3 and an
estimate of fishing mortality (F) for the oldest age
taken in the fishery. This information is used in the
relationships:

c =

F+M

(1)

(F+M)(e-<^*^')

P(1^-,F.M,)

(2)

explanations of how the values are obtained, as well
as the logic behind some of the equations, are given
in this paper.

175,000 = N

0.55

(0.55 + 0.20)

(1-e

(0 55 + 0.20)1

(1)

N - 452,000

To determine the number of 6 year old fish alive
at the beginning of 1975 (again the 1969 year class),
the value of fishing mortahty of that age during 1975
must first be determined by equation (2). N repre-
sents the number of 7 year old fish aUve at the
beginning of 1976 which was just calculated. C now
represents the number of 6 year old fish caught in
1975 (estimated in step 3). If 477,000 6 year old fish
were caught in 1975, then equation (2) takes the
following form:

452,000 _(F + 0.20)(e-<^*''^'")

477,000

F(l-e

F = 0.664

(2)

F is determined by trial and error; a computer is
utilized to perform the calculations. F is the only
unknown in the above equation and is calculated to
be 0.664.

The catch equation is again utilized but with F
equal to 0.664 in place of 0.55. Since in 1975, 477,000
6 year old fish were caught, the number of 6 year olds
alive at the beginning of 1975 is calculated to be
1,073,000.

477,000 = N

0.664

e is a mathematical constant and always equals 2.718

The manner of assessment cannot be given
proper treatment without mathematical expressions.

The first relationship is called the catch equation.
It simply means that total catch (C) in a year of any
age of a particular year-class is equal to the number
of fish of that age (N) at the beginning of the year
multiplied by the percentage of those fish caught that
year. By knowing C, F, and M, N can be calculated.
For example, if from step 3 it had been estimated
that in 1976, 175,000 age 7 fish (1969 year-class)
were caught, fishing mortality in 1976 was 0.55, and
natural mortality equalled 0.20, then the number of
7 year old fish alive at the beginning of 1976 would
have been 452,000. The ways to calculate F and M
are too diverse to discuss in this paper, thus no

(0.664 + 0.20)

(1-e

(0.664 + O 20)

) (1)

N = 1,073,000

Equation (2) is again used to calculate the next F
value, the catch equation to determine the number of
5 year old fish alive at the beginning of 1974, and so
on until the past history of the year class is deter-
mined. This procedure is followed for each year-
class in the fishery and as stated previously, for any
one calendar year, the sizes of the various year-
classes are added to obtain an estimate of total stock
size in that year.

5) Average weights at the beginning of the year of
fish at the various ages are applied to stock size at
each age (numbers) calculated from the VPA as in
step 4 to obtain stock weights at the beginning of
each year. The following gives an illustration of the
procedure used to calculate stock size in a particular
year (for example, 1976) for a particular species:

Average

Number of fish of

weight

each age calculated

Year-

(lbs. per

from step 4

Total

weight of each

Class

Age

fish)

(thousands of fish)

age (th

ousandsof lbs.)

1975

34,000

17,000

1974

l'/2

25,500

38,250

1973

13,800

41,400

1972

5'/2

7,650

42,075

1971

3,550

28,400

1970

1,600

19,200
186,325 pounds or
84,539 metric tons

To explain, assume that in 1976 it is estimated
from the VPA (step 4) that 34,000,000 one year old
fish are present. At an average weight of Vi pound
per fish, the total weight of one year old fish is
17,000,000 pounds (34,000,000 x Vi). At an average
weight of 1 !/2 pounds per fish the total weight of two
year old fish is 38,250,000 pounds. This procedure is
performed for each age and the results added to
estimate the total weight of the stock (84,539 metric
tons) in 1976 for ages 1-6.

6) At the completion of step 5, the histories of stock
sizes in past years are known. The next step involves
an estimate of present stock size, then a projection
into the future. The following procedure with the
assumption that 1977 is the current year might be
used to estimate the above information.

An estimation of abundance of each age group
(different year-classes) present in the stock during
1977 must be made. First, a relationship is deter-
mined between annual estimates of abundance
obtained from the VPA of young ages (for example,
ages 1-3, which in this case are considered not yet
catchable or are partially catchable by fishing
vessels) and past autumn bottom trawl survey
average catch per tow of those same ages. The data
used to establish this relationship might be as

follows:

Age 1 abundance

from VPA Average catch per

Year (thousands of fish) tow 1 year olds

1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973

25,765

15.2

17,151

13.4

22,600

6.2

15,000

5.1

22,759

22.3

35,454

18.5

27,000

26.2

30,562

26.4

40,150

45.7

36,572

33.0

39,532

49.9

The data can be illustrated graphically as:
50,000 r

GO
<

£
o
.t-i

40,000 -

30,000 -

20,000

10,000 -

Average catch per tow
1 year olds

If a line (straight or curved) can be fit statistically
through these points, a predictive relationship can be
determined. In other words, if an estimate of relative
abundance of age 1 fish (average catch per tow) from
a bottom trawl survey is obtained, by referring to the
graph, an approximate value of the corresponding
abundance of one year old fish (numbers) can be
determined. If in 1977 the autumn bottom trawl
survey resulted in an average catch of 20.0 one year
old fish, then an estimate of one year old fish from
the graph would have been approximately 27,000 at
the beginning of 1977 (point A).

A similar procedure is followed for the rest of the
not yet catchable or partially catchable ages to
determine their abundance at the beginning of 1977.
In this example, the abundance of age groups 2 and 3
must also be calculated.

Once these values are obtained, they are inserted
in equation (3) to estimate size of year classes
during the coming year.

N. = NoC

-(F + M)

(3)

This relationship simply means that size of an age
group of a particular year-class at the beginning of
the current year (No) multiplied by percent survival
(g-(f + M )^ equals the size of that year-class at the
beginning of next year (Ni). If, for example, the 1977
abundance of one year old fish was 27,000,000 and
survival of these fish was determined to be 78%
during 1977, then 1978 abundance of these same fish
at age 2 would be 21 ,060,000.

N, = 27,000,000 X 0.78 = 21 ,060,000

(3)

This procedure is followed until 1978 abundance
of ages 3 and 4 are calculated. Age 1 abundance in
1978 can be estimated, in some instances, by a
relationship between past survey catch per tow of
young-of-the-year fish (age 0) and resulting one year
old fish a year later (from the VPA).

Secondly, 1977 abundance is calculated for those
ages (for example, ages 4 and older) which are fully
catchable by fishing vessels. By knowing catch and
having an estimate of fishing mortality of age 4 fish
in 1977, the abundance of 4 year old fish at the
beginning of 1977 can be determined from equation
(1) as shown in step 4. Once this abundance is ob-
tained, it is inserted into equation (3) to calculate the
number of 5 year-old fish at the beginning of 1978.
And to continue, by knowing catch and fishing
mortahty of age 5 fish in 1977, the abundance of 5
year-old fish at the beginning of 1977 can be
determined from equation (1). Once this abundance
is obtained, it is inserted into equation (3) to
calculate the number of 6 year old fish at the
beginning of 1978. This procedure is followed in
step-wise fashion until the abundance of the oldest
age at the beginning of 1978 is determined.

Values of 1977 fishing mortality of the young,
not fully catchable ages (needed to calculate the
above) are determined by procedures similar to those
in step 4. Fishing mortality in 1977 for the fully
catchable ages is obtained in another way, however.
Annual fishing effort indices are determined by
dividing total catches of fully catchable age groups
(age 4 and older) by the autumn survey catch per tow
of these same age groups. A relationship is then set
up between these effort indices and average values of
fishing mortahty for the fully catchable ages
obtained from the VPA (step 4). The data used to
establish this relationship might be as follows:

Autumn

The data can be illustrated graphically as:

average

Catch

Fishing

catch

thousands

Effort

Average

Year

per tow

5.5

of fish
10,549

Index
1918

1963

0.66

1964

10.1

12,670

1254

0.40

1965

7.6

10,600

1395

0.62

1966

8.0

9,750

1219

0.48

1967

15.7

17,987

1146

0.42

1968

20.0

20,576

1029

0.44

1969

22.5

19,490

866

0.32

1970

30.0

26,757

892

0.38

1971

18.9

19,711

1043

0.24

1972

6.8

11,000

1618

0.62

1973

15.0

18,971

1265

0.62

800 1000 1200 1400 1600 1800 2000

Fishing Effort Index
Age 4 and older

For example, if in 1963 the autumn average catch
per tow was 5.5 fish and catch was 10,549 (thousands
of fish), then the fishing effort index would be 1918
(10,549/5.5). This value plus the average fishing
mortahty during 1963 represent one point on the
graph (point B). If a line can be fit statistically to all
the points, a predictive relationship can be
determined. In other words, if a fishing effort index
can be obtained, an approximate value of the
average fishing mortality can be estimated by
referring to the graph. If in 1977 the autumn average
catch per tow of 4 year fish and older was 13.5 and
1977 catch was 17,500 (thousands of fish), the fishing
effort index would have been 1350 (17,500/13.5).
From the graph, the corresponding average value of
fishing mortahty would be approximately 0.5 (point
C).

The above procedure is only used when fishing
effort cannot be accurately obtained from the
fisheries themselves. When reliable commercial
catch/effort data are available, catch can be divided
by catch per unit effort to determine fishing effort.
Attempts can then be made to establish a relation-
ship between that effort and average fishing
mortality.

7) From step 6 numbers of fish of each age in the
stock at the beginning of 1978 is determined. To
convert numbers of fish to total weight of the stock,
the number of fish at each age is multiplied by the
average weight of fish at the corresponding age and
the results are added together. The procedure used is
identical to the example shown in step 5.

8) The final step involves calculations of a group of
options of catch and resultant stock size which
managers, in this case the New England Council, can
consider. By using procedures similar to those found
in steps 6 and 7, the impacts of various amounts of
catch on stock size at the beginning of next year can
be presented. It then becomes the manager's respon-
sibility to determine which catch/stock size option
should be selected. For example, catches to maintain
the same stock size or perhaps result in a 10%
increase in stock size from 1978 to 1979 could be
selected. Managers might decide to let the stock size
decrease but not let it fall below some certain level,
for example, the smallest stock size that has resulted
in the production of strong year-classes in the past,
and then set the allowable catch accordingly.
Whatever the case may be, the choice to be made is
outside the responsibility of the assessment scientists.
One of their roles is to determine the impacts of
potential management actions; that is, the effects of
total stock removals, not to determine strategy.

The above example of a stock assessment is one
of the more demanding types in terms of the
amounts of information needed for its performance.
Many years of commercial catches/landings records
and annual samples of age and length composition
are required. It is a sophisticated analysis which is
neither simple to perform nor to understand by a
layman. This is why we stated in our introduction
that patient reading of this section is necessary.

The aforementioned type of assessment has been
performed for the cod stock of Georges
Bank/southern New England and a similar one has
been done for haddock. Other types of assessments,
such as the one used for yellowtail flounder, rely
more heavily on the results of bottom trawl surveys.
The type utilized depends on the kinds and amounts
of reliable information which is available to the
scientist.

Grosslein, M.D. 1971. Some observations on accuracy of
abundance indices derived from research vessel surveys. Int.
Comm. Northwest, Atl. Fish. Redbook 1971 (III):249-266.

Gulland, J. A. 1966. Manual of sampling and statistical methods
for fisheries biology: Part 1. Sampling methods. (FAO) Food
Agric. Organ., United Nations.

Pennington, M.R. and M.D. Grosslein. 1978. Accuracy of
abundance indices based on stratified random trawl surveys. Int.
Comm. Northwest Atl. Fish. Res. Doc. 78/VI/77. 42 p.

Sissenwine, M.P., B.E. Brown, and J. Brennan-Hoskins. 1978.
Brief history and state of the arts of fish production models and
some applications to fisheries off the northeastern United States.
To be published in "Report of the Climatology and Fisheries
Workshop," March 1978, University of Rhode Island.

PERSONAL COMMUNICATIONS

Mr. Thomas Azarowitz, NMFS Fishery Biologist

Ms. Patricia Gerrior, NMFS Fishery Reporting Specialist

Mr. Ronnee L. Schultz, NMFS Fisheries Management Supervisor

ACKNOWLEDGEMENTS

Scientists of the Northeast Fisheries Center: Drs. Stephen H.
Clark, Frederic M. Serchuk, Michael P. Sissenwine, Bradford E.
Brown, Marvin D. Grosslein, and Emory D. Anderson offered
many excellent and valuable comments, suggestions, and
criticisms during reviews of two drafts of our manuscript. We
greatly appreciate their input. We acknowledge the contributions
of Messrs. Arnold B. Howe and H. Arnold Carr of the Massa-
chusetts Division of Marine Fisheries; their reviews and sugges-
tions were very beneficial. Dr. Guy Marchesseault, a New
England Fishery Management Council biologist, also provided
helpful advice.

REFERENCES

Anderson, E.D. 1978. An Explanation of Virtual Population
Analysis. NEFC, Woods Hole, Mass., Lab. Ref. No. 78-09, 5 p.

Clark, S.H. and B.E. Brown. 1977. Changes in biomass of fin-
fishes and squids from the Gulf of Maine to Cape Hatteras,
1963-74, as determined from research vessel survey data. Fishery
Bulletin. 75(1): 1-21.

Clark, S.H. and P.W. Wood. 1978. Sea sampling program of the
Northeast Fisheries Center, Woods Hole, Mass. NEFC, Woods
Hole, Mass., Lab. Ref. No. 78-31, 18 p.

Grosslein, M.D. 1969. Groundfish survey methods. NEFC,
Woods Hole, Mass., Lab. Ref. No. 69-2, 34 p.

Grosslein, M.D. 1969. Groundfish survey program of BCF,
Woods Hole, Commercial Fisheries Review. 31(8-9):22-35.

GLOSSARY

Abundance Index Information obtained from
samples or observations and used as a measure of the
weight or number of fish which make up a stock.

Biomass Measure of the quantity, usually by weight
in pounds or metric tons (2,205 pounds = 1 metric
ton), of a stock at a given time.

Fishing Mortality Deaths in a fish stock caused by
fishing.

Fishing Power The catch which a particular gear or
vessel takes from a given density of fish during a
certain time interval. For example, larger vessels
(horsepower) have a greater ability to catch more
fish, thus the greater their fishing power. Also, im-
provements in a vessel or gear, such as fish finders,
Loran, etc., can increase fishing power.

Growth Overfishing The level of fishing which
destroys small fish before their yield in weight due to
growth is maximized.

Length Frequency An arrangement of recorded
lengths which indicates the number of times each
length or length interval occurs. For example, 10
measurements of lengths are taken in the following
order: 10, 12, 12, 14, 12, 15, 15, 19, 12, and 10. A
length frequency would be:

Length

Occurrence

Interval

Occurrence

10-12

13-15

0 or 16-18

19-21

Maximum Sustainable Yield (MSY) The largest long
term average catch or yield that can be taken yearly
from a stock under existing environmental condi-
tions; often used as a management goal.

Natural Mortality Deaths in a fish stock caused by
predation, pollution, senility, etc., but not fishing.

Optimum Yield (OY) The yield from a fishery which
provides the greatest overall benefit to the nation
with particular reference to food production and
recreational opportunities; it is based on MSY as
modified by economic, social or ecological factors.

Precision and Accuracy Precision is the closeness to
each other of repeated measurements of the same
quantity or object, while accuracy is closeness of a
measured or computed value to its true value.

As an illustration, suppose regulations state that
fishermen can only land 5,000 lbs. of cod per trip. A
fisherman makes 10 trips with the intent to not
exceed the 5,000 lbs. limit. Before landing each trip,
he estimates that his total catch for each was
approximately 5,000 lbs. However, after landing
each trip, weigh-in's at a dealer showed that every
catch was just about 5,500 lbs. The fisherman's
estimates of his catch were, therefore, precise but not
accurate.

Two fictional series of research vessel tows were
made in a single stratum. The first series resulted in
catches of 61, 55, 60, 64, 63 and 59 pounds. The
second resulted in 10,20,45,60, 110 and 115
pounds. Both resulted in mean catches per tow of 65
lbs. The first series of tows is a very precise estimate
of abundance while the estimate of the second series
is very imprecise. The range of values about the
average in the first series (55-64) is much narrower
than that of the second (19-115); therefore,
confidence in the first average as an estimate of
relative abundance is much greater than confidence
in the second average. Nothing can be stated about
the accuracy of either of the series of tows in provid-
ing estimates of true abundance. The degree of
accuracy is affected by fish behavior, gear perform-
ance, and a possible mismatch between the timing
and area of surveys in relation to fish movements
and distribution.

Recruitment This term is used two ways. (1) Number
of young produced from a given stock each year, or
(2) addition of new fish to the catchable portion of a
stock brought about by growth or migration of
smaller fish; the catchable portion is influenced by
the mesh size in use and fish distribution.

Recruitment Overfishing A decline in recruitment
due to fishing pressure; that is, the parent or
spawning stock is reduced to a level at which the
potential number of young, which will eventually
enter the fishery, is severely reduced. This is gen-
erally considered to be more serious than growth
overfishing.

Relative Abundance An estimate of actual or
absolute abundance; usually stated as some kind of
index; for example, as bottom trawl survey stratified
mean catch per tow.

Sample A proportion or a segment of a fish stock
which is removed for study, and is assumed to be
representative of the whole. The greater the effort, in
terms of both numbers and magnitude of the
samples, the greater the confidence that the
information obtained is a true reflection of the status
of a stock (level of abundance in terms of numbers
or weight, age composition, etc.)

Standardization The procedure of maintaining
methods and equipment as constant as possible.
Without standardization one cannot determine
whether measurements of yearly differences in rela-
tive abundance are caused by actual fluctuations in
stock abundance or by differences in the measure-
ment procedure used.

The lack of standardization is one reason why
surveys using different commercial fishing vessels in
different years do not produce comparable informa-
tion. For example, if two vessels of different horse-
power are used in separate years, the results can't be
compared, unless vessel mensuration experiments are
performed. This would involve a comparison of the
two vessels' catches to determine the influence of
their fishing power on the size of the catch, and a
determination of a correction factor.

Stratum

#Tows

Sq.

Nautical

Miles

Average
Catch

Per Tow
(lbs.)

1
2
3
4

5
5
5
5

20
40
15
10
15

30
40
10

area
egion)

20x30= 600
40x40=1600
15x10= 150
lOx 5= 50
15x15= 225

100 (total
of the r

2625 total

Stratified Mean Catch Per Tow = 26.25 pounds (2625 ^ 100)

as opposed to a simple mean or average of
(30 + 40 + 10 + 5 + 15) H- 5 = 20 pounds

Yield Per Recruit The expected yield in weight from
an individual fish over its life in the fishery. The
yield is influenced by its age at entry to the fishable
stock and by mortality rates. The maximum yield per
recruit which can be obtained is often used as a man-
agement goal.

Year-Class Fish of a given species spawned or
hatched in a given year; a three-year old fish caught
in 1978 would be a member of the 1975 year-class.

Stock A part of a fish population usually with a par-
ticular migration pattern, specific spawning grounds,
and subject to a distinct fishery. A fish stock may be
treated as a total or a spawning stock. Total stock
refers to both juveniles and adults, either in numbers
or by weight, while spawning stock refers to the
numbers or weight of individuals which are old
enough to reproduce.

Stratified Mean (Average) Catch Per Tow For

separate species of fish, each average catch per tow
— determined from a series of tows — in each
geographic stratum of a region is multiplied by that
area (square nautical miles) of the stratum in which
the tows were made. All of the individual products
are added together and the total is divided by the
sum of the entire area of the region. The final result
is the stratified mean catch per tow; this is used as an
index of relative abundance. For example, a scientist
wishes to calculate the stratified mean catch per tow
of cod in a region (perhaps Georges Bank) that
measures 100 square nautical miles. The region has
been divided into 5 strata on the basis of depth. In
each strata, 5 tows are made and the average catch of
cod calculated.

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Fig. 3

Fisheries Statistical Areas

and Northeast Regional Branch of Statistics

Office Locations

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