Fisheries Stock Assessment - A Guide to - Andrew B. Cooper
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A Guide to
Fisheries Stock Assessment
From Data to Recommendations
Andrew B. Cooper
Department of Natural Resources
University of New Hampshire
Fish are born, they grow, they reproduce and they die – whether from natural causes or from fishing.That’s it. Modelers just use complicated (or not so complicated) math to iron out the details.
A Guide to
Fisheries Stock Assessment
From Data to Recommendations
Andrew B. Cooper
Department of Natural Resources
University of New Hampshire
Edited and designed by Kirsten Weir This publication was supported by the National Sea Grant
NH Sea Grant College Program College Program of the US Department of Commerce’s
Kingman Farm, University of New Hampshire National Oceanic and Atmospheric Administration under
Durham, NH 03824 NOAA grant #NA16RG1035. The views expressed herein do
603.749.1565 not necessarily reflect the views of any of those organizations.
www.seagrant.unh.edu
Acknowledgements Funding for this publication was provided by New Hampshire Sea Grant (NHSG) and the Northeast Consortium (NEC). Thanks go to Ann Bucklin, Brian Doyle and Jonathan Pennock of NHSG and to Troy Hartley of NEC for guidance, support and patience and to Kirsten Weir of NHSG for edit- ing, graphics and layout. Thanks for reviews, comments and suggestions go to Kenneth Beal, retired assistant director of state, federal & constituent programs, National Marine Fisheries Service; Steve Cadrin, director of the NOAA/UMass Cooperative Marine Education and Research Program; David Goethel, commercial fisherman, Hampton, NH; Vincenzo Russo, commercial fisherman, Gloucester, MA; Domenic Sanfilippo, commercial fisherman, Gloucester, MA; Andy Rosenberg, UNH professor of natural resources; Lorelei Stevens, associate editor of Commercial Fisheries News; and Steve Adams, Rollie Barnaby, Pingguo He, Ken LaValley and Mark Wiley, all of NHSG. Photo credits: front cover, Pingguo He; back cover, Kirsten Weir.
Contents
1 Stock Assessments: An Introduction. . . . . . . . . . . . . . . . . . . . . . . 5 5 Applying Stock Assessment Models to Data. . . . . . . . . . . . . . . . 29
2 What Types of Data are Available? . . . . . . . . . . . . . . . . . . . . . . . . 7 Indices of Abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Fishery-Dependent Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Catch-per-Unit Effort . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Landing Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Estimates of Actual Stock Size . . . . . . . . . . . . . . . . . . . . . 31
Portside Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Index-Only Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Onboard Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Fitting Models to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Log Books and Vessel Trip Reports. . . . . . . . . . . . . . . . . . . 8 Frequentist versus Bayesian Approaches. . . . . . . . . . . . . . 32
Telephone Surveys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Biomass Dynamics Models – Theory. . . . . . . . . . . . . . . . 34
Fishery-Independent Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Biomass Dynamics Models – Targets and thresholds . . . . 34
3 Biological Reference Points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Age-Structured Models – Theory. . . . . . . . . . . . . . . . . . . 35
Targets versus Thresholds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Age-Structured Models – Targets and thresholds . . . . . . . 37
Determining Thresholds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Estimating Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6 Making Recommendations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Population Dynamics Models: Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
The Underpinnings of Stock Assessment Models. . . . . . . . . . 21
The Basic Population Dynamics Model. . . . . . . . . . . . . . . . . . . 21
Adding Complexity: Mortality . . . . . . . . . . . . . . . . . . . . . . . . . 22
Adding Complexity: Age Structure. . . . . . . . . . . . . . . . . . . . . . 23
Adding Complexity: Stock-Recruitment Functions. . . . . . . . . . 26
Adding Complexity: Weight and Biomass. . . . . . . . . . . . . . . . . 28Stock Assessments:
An Introduction
Fishery managers have a range of goals. They be as large as the Atlantic Ocean or as small as
strive to maintain healthy fish populations and a single river. A fish stock, on the other hand,
a healthy fishing industry while still preserving is defined as much by management concerns
vital recreational communities. To achieve their – such as jurisdictional boundaries or harvesting
goals, managers rely on a collection of tools, location – as by biology. For example, alewives
1 including quotas, size limits, gear restrictions,
season timing and area closures. But how do
decision makers determine which combinations
of tools will best accomplish their objectives?
from the Taylor River are considered a separate
population from those in the Lamprey River,
but both are part of the Gulf of Maine alewife
stock.
To choose the best approach to managing a fish
stock, managers must equip themselves with as
much information as possible. A stock assessment provides
A stock assessment provides decision mak-
ers with much of the information necessary to decision makers with the
make reasoned choices. A fishery stock assess- information necessary to
ment describes the past and current status of a
fish stock. How big is the stock? Is it growing make reasoned choices.
in size or shrinking? A stock assessment also at-
tempts to make predictions about how the stock
will respond to current and future management Within a fish stock or population, a co-
options. Will a slight increase in fishing pressure hort is a group of fish all born in the same
have a negative effect on the stock next year? year. Within the Gulf of Maine cod stock, all
Ten years from now? In the end, the manager of the cod born in 2004 belong to one cohort
must decide how to interpret the information and those born in 2005 comprise a second
from the stock assessment and determine which cohort. Stock assessments often track a cohort
options are best overall. over time. Short-term increases or decreases in
A complete stock assessment contains a vast the size of a particular stock can sometimes be
array of information on both the fish popula- explained by the existence of an exceptionally
tion and the fishery itself. A fish population is large or small cohort.
a group of individual fish of a single interbreed- A stock assessment describes a range of
ing species located in a given area, which could life history characteristics for a species, such as
information (derived from other studies) about This publication is not designed to be an
age, growth, natural mortality, sexual maturity all-inclusive description of data and methods Recommended Reading
and reproduction; the geographical boundaries used for stock assessments. Rather, the goal of
of the population and the stock; critical envi- this document is to provide an overview of how Our goal is to provide readers with
ronmental factors affecting the stock; feeding stock assessment scientists and managers turn a basic understanding of the stock
habits; and habitat preferences. Drawing on the data into recommendations. We assume readers assessment process. For readers
knowledge of both fishermen and scientists, have some working knowledge of the fisheries looking for more detailed and technical
stock assessments give qualitative and quantita- management process, but no modeling or statis- descriptions of stock assessment models
tive descriptions of the fishery for a species, past tics background is necessary. and their role in fisheries management, we
and present. Final stock assessment reports also We’ll discuss the range of data that might recommend the following publications.
contain all of the raw data used in the assess- be available to scientists and the types of in-
ment and a description of the methods used to formation a stock assessment provides. We’ll
collect that data. then describe the range of population dynam-
The mathematical and statistical techniques ics models (from the simple to the complex) Quantitative Fisheries Stock
used to perform a stock assessment are referred that can underlie the assessment model. Finally, Assessment: Choice, Dynamics,
to as the assessment model. Scientists compare we will discuss how stock assessment scientists and Uncertainty, by Ray Hilborn
different assumptions within a given assessment merge data and models to determine the status and Carl J. Walters. Published by
model and may also examine a variety of differ- of the stock and generate recommendations. A Champan and Hall, 1992.
ent assessment models. Ultimately, stock assess- glossary in the back of this publication defines
ment scientists will estimate the current status the technical terms associated with stock Quantitative Fish Dynamics,
of the stock relative to management targets and assessment science. by Terrance J. Quinn and Richard
predict the future status of the stock given a B. Deriso. Published by Oxford
range of management options. They will also University Press, 1999.
describe the most likely outcomes of those op-
tions and the uncertainty around those out- Fisheries Stock Assessment User’s
comes. Manual, edited by Jeffery C. Burst
and Laura G. Skrobe. Published
as Special Report No. 69 by the
Atlantic States Marine Fisheries
Commission, 2000.
What Types of Data
are Available?
Data used in stock assessments can be catego- distribution of the catch, but such informa-
rized as either fishery-dependent or fishery- tion is rarely precise enough to be used directly
independent. Fishery-dependent data are in a stock assessment. Other forms of data are
derived from the fishing process itself and are required to sort out these landing records into
collected through such avenues as self-reporting, specific size or age distributions.
2
onboard observers, portside surveys, telephone
surveys or vessel-monitoring systems. Portside Sampling
Fishery-independent data are derived from
activities that do not involve the commercial or Some portion of both recreational and commer-
recreational harvest of fish, such as trawl, acous- cial catch is sampled on the docks for size and
tic, video and side-scan sonar research surveys age by government scientists known as portside
and some tagging experiments. Stock assess- observers or port agents. When the observers
ments generally require data on catch, relative are sampling from recreational fishermen, the
abundance and the life history of the species in survey is called a creel survey. In sampling both
question. Both fishery-dependent and fishery- recreational and commercial catch, the size of
independent data can help fulfill these needs. a fish is measured on site. Determining a fish’s
age, however, requires taking biological samples
to be evaluated in a lab. Scientists can determine
Fishery-Dependent Data a fish’s age by counting the growth rings in a
scale or an otolith (ear bone), much like
Landing Records counting the rings of a tree.
Because a fish’s age must be determined in
The most common sources of fishery-dependent a lab, many more length samples are taken than
data are landings records and port samples. age samples. Scientists then estimate the length
Landing records, which result directly from the frequency, or the total number of landed fish in
sale of caught fish, provide information only on each length class. These estimates are calculated
landed catch. The data is often in the form of for each type of fishing gear separately, as each
total weight and rarely in total numbers of fish. gear may have its own length-frequency
When the market for a given species has distribution.
multiple size categories, the landing records For example, if 80 percent of the fish
can give some coarse information on the size sampled from a gill net fall within a given size
range, it is assumed that 80 percent of the total Bycatch are the fish caught during the fish- tables, scientists can then estimate the number
number of fish landed by that gill net fall within ing process that were not specifically targeted for of discards in each age class.
this size range. But gill nets with larger or harvest. Not all bycatch is discarded. Some by- In the absence of onboard observers, sci-
smaller mesh sizes would have their own length- catch is landed and recorded by landing records entists are forced to make assumptions about
frequency distributions. If length-sampling or portside observers. Bycatch that are thrown how many fish are discarded. They often set the
data is sparse, though, scientists may not have back (because they were the wrong size, sex or amount of discards equal to some proportion
enough information to reliably estimate the species, or because trip limits or quotas were of the landed catch, based on previous research.
length distribution. met) are called discards. All discards are a form Scientists also refer to previous research to
of bycatch. Only a portion of the discarded estimate the discard mortality (the rate at which
bycatch will survive the catch and discard- the discarded fish die.)
ing process, which means that the estimate of
landed catch will underestimate, sometimes Log Books and Vessel Trip Reports
quite severely, the total amount of fishing-
related mortality. In some commercial fisheries, either as a
Usually only a portion of the vessels in a requirement or as an organized voluntary effort,
fishery carry onboard observers. To generate a fishermen keep their own records, called log
fleet-wide estimate of discards, scientists assume books or vessel trip reports, which they pass on
By taking both size and age samples from a that the unobserved vessels behave in the same to government officials. Data from landing re-
number of individual fish, scientists can deter- fashion as the observed vessels. Scientists often cords and onboard observers are generally con-
mine how to estimate the age of a fish based on calculate the length-frequency distribution of sidered more reliable than log books in terms
its length. Fisheries scientists use these estimates the discards, which allows them to estimate of estimating landed total weight and numbers.
to develop a length-age table, or length-age the number of fish discarded for each length Nevertheless, the log books can be incredibly
key. This table allows a stock assessment scientist class for the entire fleet. Drawing on length-age valuable for determining the spatial distribution
to convert the length distribution of the landed and amount of effort in the fishery. In some
catch (which is based on many, many samples) fisheries, boats also use electronic devices that
into an age distribution of the landed catch. Any fish caught automatically record the location of a
vessel, called vessel monitoring systems.
Onboard Observers
that were not specifically
targeted for harvest are
To gain a broader understanding of the ways Telephone Surveys
in which commercial fishermen interact with a
called bycatch. Bycatch that
range of species, government personnel known are thrown back are known The primary method for collecting data on
as onboard observers sometimes accompany recreational fisheries is through a telephone
fishing vessels. Observers are trained to sample
as discards. survey conducted as part of the National Marine
catch for size, and sometimes age, and to esti- Fisheries Service’s Marine Recreational Fishery
mate bycatch and discards. Statistics Survey (MRFSS). Scientists use this
survey to estimate the number of recreational herring survey), or even a specific age-class of a Results from tagging, mark-and-recapture
fishing trips that target a specific species and specific species (such as beach seine surveys for and other studies typically fall under the cat-
those that merely encounter a specific species, young-of-the-year bluefish). egory of fishery-independent data. Such studies
even if that species isn’t targeted. may estimate the movement or migration rates
Each fish encountered during a trip falls between stocks, the natural mortality rate of the
into one of three categories: caught and sampled Survey data provide an fish, the reproductive output of the fish, growth
by portside observers (labeled type A fish), index of fish abundance as rates, maturity schedules (the percent of individ-
caught but not sampled by portside observers uals mature at each age), and hooking or discard
(type B1 fish), or caught but thrown back (type well as information about mortality rates. All of this information enhances
B2 fish). An estimated percentage of type B2 size, age and maturity of stock assessment models.
fish is assumed to die as a result of the catch-
and-release process, based on information from the fish in the stock.
other studies.
For the purposes of stock assessment, the Regardless of the target or the gear, main-
total mortality associated with the recreational taining standard survey practices over time is
fishery equals all the fish caught and sampled crucial. Changes in mesh size, soak times and
by portside observers, all the fish caught and tow length or speed can all impact the compara-
not sampled, and an estimated portion of the bility of a survey over time. Whenever new gear
fish that were thrown back. Scientists take the or sampling methods are adopted, they should
survey data and estimate the number of fish be calibrated so that results can be directly com-
caught in each length class by applying the pared to results from the old gear or method. By
length-frequency data from portside sampling to sampling across the potential range of the fish,
the estimated total number of fish caught. rather than just its current range, the survey can
detect shifts in distribution, including range
Fishery-Independent Data contraction or expansion.
The survey data provide an index of fish
The vast majority of fishery-independent data abundance, typically the number of fish caught
comes from research surveys conducted by the per unit of effort (such as the number of fish per
federal or state governments. Scientists take tow). Surveys can also provide information on
samples throughout the potential range of the the size and age distributions of the stock, esti-
target fish using standardized sampling gear in- mates of the percentage of fish mature at each
cluding trawls, seines, hydroacoustics and video. age, and size-age relationships (similar to those
These surveys can target a group of several derived from portside or onboard observation
species (such as the Northeast Fisheries Science of the catch). By sampling stomach contents,
Center bottom trawl survey), a single species survey scientists can even determine a species’
(such as the Northeast Fisheries Science Center diet.
10
Biological
Reference Points
Through stock assessments, scientists attempt to rate is equivalent to the fishing mortality rate.
estimate the amount of fish in a stock and the Biological reference points based on fishing
rate of fishing mortality. They do so with regard mortality help managers keep the withdrawal
to a stock’s biological reference points. A rate at a level that will ensure the long-term
biological reference point is a concrete number, production or stability of the stock.
3
a value for, say, stock size or fishing mortality. A The concept of maximum sustainable yield
stock assessment produces a series of estimates (MSY) serves as the foundation for most biolog-
for stock size and fishing mortality over time. ical reference points. The maximum sustainable
Biological reference points serve as a way to yield is typically thought of as the largest
judge those estimates based on knowledge and average catch that can be continuously taken
assumptions about the species’ growth, repro- from a stock under existing environmental
duction and mortality. conditions. That is, maximum sustainable yield
Biological reference points give decision is the greatest number of fish that can be caught
makers guidance in determining whether popu- each year without impacting the long-term
lations are too small or fishing pressure is too productivity of the stock.
great. They help provide targets for how large Stock assessment scientists and decision
the population or how intense the fishing makers use the letter B to denote biomass, the
pressure should be. total weight of the fish in a given stock. Oc-
Why do we care about the fishing mortal- casionally, rather than total biomass, scientists
ity rate? In its simplest form, the fishing mor- will refer to the spawning stock biomass (SSB),
tality rate is the rate at which fish are removed the total weight of the reproductively mature
from the stock by harvesting. Think of a fish individuals in the stock. The term BMSY is used
stock as money in an interest-bearing bank ac- to indicate the stock size that can produce the
count. If the interest is five percent per year, the maximum sustainable yield. The term SSBMSY
bank account balance will grow as long as you indicates the size of the reproductive mature
withdraw less than five percent per year. If you portion of the stock that will produce the
withdraw more than five percent per year, the maximum sustainable yield. Similarly, the letter
bank principal will decrease. If you do that con- F denotes the fishing mortality rate, while FMSY
sistently, you’ll eventually empty the account. indicates the fishing mortality rate at the level
The interest rate in this example is equiva- that would maintain the maximum sustainable
lent to the stock’s growth rate. The withdrawal yield for a stock at BMSY.
11Fisheries scientists aim to determine a stock’s biological and socioeconomic factors. This is to withdraw more money than your account
optimum yield, the amount of catch that will where optimum yield comes into play. Should is earning through interest, you’ve crossed a
provide the greatest overall long-term benefit the population target be BMSY or something threshold. When a fishery crosses a threshold,
to society. The optimum yield must take into larger than BMSY? Should the target fishing mor- the stock is being depleted too quickly and ac-
account the biology inherent in maximum tality rate be FMSY or something lower? Should tions must be taken to correct the situation.
sustainable yield, as well as economics and the the target fishing mortality rate be managed Two of the key questions that a stock as-
attitudes of the public towards risk and envi- to provide for a relatively constant catch? Or sessment aims to address are whether overfish-
ronmental protection. The optimum yield can should it allow for a relatively constant effort, ing is occurring and whether the stock is in an
never be greater than maximum sustainable within an acceptable range of fishing mortality overfished state. Although they sound similar,
yield. In some cases scientists may set optimum rates? they are actually two distinct concepts. Over-
yield equal to maximum sustainable yield, but fishing occurs when the fishing mortality rate
they often set it at a value less than maximum exceeds a specific threshold. The stock is being
sustainable yield. Targets are stock size and depleted too quickly, but the stock size may still
In theory, if the environment is constant fishing mortality levels be fairly large. Conversely, a stock is determined
a fishery should be able to produce an average to be overfished when stock size falls below a
catch equal to maximum sustainable yield for that managers aim to specific threshold, either in terms of numbers or
eternity. By environment we mean everything achieve and maintain. biomass of fish.
from water temperature and habitat composi- A stock may fall into any of four categories
tion to predator and prey abundance – Thresholds are levels they with regard to overfishing and being in an
anything that affects the birth, growth or death wish to avoid. overfished state. (See Overfished or Overfish-
rates of a fish. That’s a pretty tall order. ing? page 13.) In 2004, for example, the fishing
The environment is anything but constant mortality rate for Georges Bank Atlantic cod
and the ability of fisheries managers to control Deviations from the targets may or may was determined to be greater than the fishing
harvest from year to year can, in some situa- not result in changes in policy. Control rules, mortality threshold. The same year, the spawn-
tions, be quite shaky. Despite this, the concept designed by scientists but chosen by managers, ing stock biomass for Georges Bank Atlantic
of maximum sustainable yield serves as the un- guide the ways in which the fishing mortality cod fell well below the spawning stock biomass
derpinning for many of the biological reference rates are adjusted over time based on the status threshold. In other words, overfishing was
points that are evaluated in a stock assessment. of the stock. occurring and the stock was overfished.
While targets are levels that managers aim
Targets versus Thresholds for, thresholds are levels they aim to avoid.
Thresholds are also referred to as limits, es-
Biological reference points provide quantitative pecially in the realm of international fisheries
values for targets and thresholds. Targets are policy. A threshold is often defined as a specific
values for stock size and fishing mortality rate fishing mortality rate or stock size that is some
that a manager aims to achieve and maintain. fraction of BMSY. Consider again the bank ac-
Targets are determined by a combination of count example described earlier. If you begin
12If a stock is overfished, or if overfishing
Overfished or Overfishing? is occurring, managers are required by law to
put measures in place to correct the situation.
Stock assessments attempt, in part, to determine whether overfishing is occurring and whether While the stock assessment produces estimates
a stock is in an overfished state. While the two concepts are obviously related, they are not of the fishing mortality rate and stock size, the
identical. Overfishing occurs when the fishing mortality rate (F) is greater than the fishing choice of thresholds is dictated by government
mortality threshold (Fthreshold). A stock is overfished when the stock size (B) falls below the policy. In the case of federally managed species,
stock size threshold (Bthreshold). Fish stocks fall into one of four categories based on these the policies are known as the National Stan-
principles. dard Guidelines. These policies have evolved
over time and have involved a fair bit of debate
between scientists.
Determining Thresholds
B < Bthreshold B Bthreshold
In order to manage a stock, decision makers
must define a stock size threshold (Bthreshold),
also called a minimum stock size threshold.
F Fthreshold Stock is overfished Stock is not overfished As discussed previously, the stock size that
& but can produce the maximum sustainable yield is
Overfishing is occuring Overfishing is occuring known as BMSY. The stock size threshold can be
defined in one of two ways, both of which are
relative to BMSY. The stock size threshold may be
F < Fthreshold Stock is overfished Stock is not overfished defined simply as a percentage of BMSY – typical-
but & ly half (but never less than half ) of BMSY. Alter-
Overfishing is not Overfishing is not natively, the stock size threshold can be defined
occuring occuring as the smallest stock size that could grow to BMSY
in 10 years if the fishing mortality rate was as
low as possible (which might not be zero, de-
pending on fishermen’s ability to avoid bycatch).
Current law requires the stock size threshold to
be set equal to the larger of these estimates.
Determining the fishing mortality thresh-
old (Fthreshold), or maximum fishing mortality
threshold, is a much more complicated mat-
ter than determining the stock size threshold.
Because managers attempt to keep the stock at
13or above BMSY, the fishing mortality threshold by catching all fish at exactly that age, when it to maximize its potential yield per recruit.
should be less than the fishing mortality that the percentage of fish dying of natural causes In other words, mortality rates are outpacing
would produce BMSY – that is, less than FMSY. equaled the percent weight gained by the fish. growth rates in terms of the overall weight or
Given that the estimate for natural mortal- For example, if 10 percent of a cohort of biomass of the stock.
ity (M) is an upper limit for FMSY, the fishing equally sized fish will die due to natural causes
mortality threshold for many fish stocks should between now and next fishing season, but the
also be less than the natural mortality rate. How cohort will increase in weight by 15 percent
much less is a function of the reproductive ca- during that same time period, then this co-
pacity of the stock. hort will still be five percent larger, in terms of
A variety of methods exist to estimate fish- weight, next year. Ignoring changes in price and
ing mortality thresholds. Some fishing mortal- the value of a dollar today versus a dollar tomor-
ity thresholds are based on “yield-per-recruit” row, one would be better off waiting to fish the
analyses, where yield is the expected weight of cohort next year.
fish caught by the fishery and recruits are fish at The yield per recruit (the total weight of fish To combat the anti-conservative nature
the youngest age entering the fishery. Yield-per- caught divided by the number of fish from that of Fmax, researchers developed an alternative
recruit analyses are performed in the last stages cohort that originally entered the stock) would measure based on yield-per-recruit analyses
of the stock assessment and will be discussed in increase over the year, and fishermen would called F0.1. (See Calculating Fishing Mortality
greater detail later. get a higher yield by waiting. But if the cohort Thresholds, page 15.) This analysis is based on
Yield per recruit depends on the growth would only increase in weight by 10 percent, the amount of fishing effort, described in terms
rates of individual fish, natural mortality and a fisherman would get the same yield this year, of “units of fishing effort.” In a recreational
fishing mortality. In the simplest sense, if it in terms of weight, as he or she would the next fishery, a single “unit of fishing effort” could be
was possible to catch fish of just one optimal year. If the cohort only increased in weight defined as one fisherman fishing for one day.
age, one would maximize the yield per recruit by eight percent, it would have a smaller total In a trap fishery, it might be defined based on
weight next year and one would be better off a trap of standard size soaking for one day. For
harvesting the fish this year. trawl fisheries, defining one “unit of fishing
The fishing mortality rate that achieves a effort” would involve factors such as vessel size,
maximum yield per recruit is called Fmax. How- net size and the like.
ever, Fmax is often greater than FMSY and can lead Imagine that we add one standardized “unit
to unsustainable harvest levels and an anti- of fishing effort” to a stock that has been in an
conservative fishing mortality threshold. Much unfished state and maintain that effort over
of this is due to the fact that Fmax does not take time. The outcome of this increase in one unit
the reproductive viability of the remaining stock of fishing effort is a specific fishing mortality
into account. When the fishing mortality rate rate and a specific yield per recruit. Adding a
does exceed Fmax, it’s called growth overfishing. second unit of effort (a second fisherman fishing
When growth overfishing occurs, the stock for one day, for example) will increase the fish-
is being harvested at a rate that does not allow ing mortality and the fishery’s yield per recruit,
14Calculating Fishing Mortality Thresholds
Some fishing mortality thresholds are based on “yield-per-recruit” analyses, where yield is the weight of fish caught by the fishery and recruits
are fish at the youngest age entering the fishery. In the real world, fishing at a level equal to Fmax (the maximum yield per recruit) can lead to
unsustainable harvest levels. Instead, researchers developed F0.1, a more conservative measure based on yield-per-recruit analyses. This analysis is
based on “units of fishing effort.”
If fishermen apply a single “unit of fishing effort” to a previously unfished stock, the outcome will be a specific yield per recruit. With each
additional increase in units of fishing effort, yield per recruit will increase – but it will do so by a smaller and smaller margin. Eventually, increasing
fishing effort will actually lead to decreasing the yield per recruit, when fishing mortality is greater than Fmax. In other words, increasing fishing
pressure will increase yield, up to a point. Beyond that point, though, increasing fishing pressure will result in harvesting more fish than the number
of young fish entering the fishery. Past this point (Fmax), yield per recruit will decrease. Using F0.1 as a threshold results in a fishing mortality rate that
is lower than Fmax, and it has proven to be relatively conservative.
10% of the increase in
yield per recruit associated
Maximum yield with first unit of effort
per recruit
Yield per Recruit
Increase in yield F0.1 Fmax
per recruit associated
with first unit of effort
}
Fishing mortality Fishing Mortality
caused by first
unit of effort
15but the amount of that increase will be less than of reproductively mature fish per recruit in the new recruits 50 percent of the time, given the
the increase from zero effort to one unit of absence of fishing. Fishing mortality thresholds observed recruitment history. In other words, if
effort. (in the form of F%) equal the fishing mortality future recruitment is similar to past recruitment,
With each additional increase in fishing rate that reduces the spawning stock per recruit fishing at a rate equal to Fmed will remove less
effort, the yield per recruit will increase by a to a given percentage in the absence of fishing. spawning stock biomass than the new recruits
smaller and smaller margin. Eventually, increas- will contribute 50 percent of the time, but will
ing effort, and therefore fishing mortality, will remove more biomass than the new recruits will
not increase the overall yield per recruit and
Spawning stock is the contribute 50 percent of the time.
will even lead to decreasing the yield per recruit, amount, in numbers or The value Flow is the fishing mortality rate
when fishing mortality is greater than Fmax. This that will result in the spawning stock replacing
is called decreasing marginal rates of return, as
in weight, of the itself, given historical levels of recruitment, 90
each additional unit of effort produces smaller reproductively mature percent of the time. (That is, fishing will remove
and smaller increases in yield per recruit. less biomass than new recruits will contribute
The value of F0.1 equals the fishing mortality
individuals in a stock. 90 percent of the time.) The value Fhigh lies on
rate when the increase in yield per recruit from the opposite end of the spectrum. Fhigh is the
adding a single unit of effort is only 10 percent For example, F40% is the fishing mortality fishing mortality rate that will result in the
of the increase achieved by going from zero to rate that reduces the spawning stock per recruit spawning stock biomass replacing itself only 10
one unit of effort. The value of 10 percent was to 40 percent of that which would exist in the percent of the time. One way to remember these
chosen somewhat arbitrarily based on simula- absence of fishing. A fishing mortality threshold is that Flow has a low probability of stock decline
tion models developed by scientists. But using set to F40% is relatively common. whereas Fhigh has a high probability of stock
F0.1 as a threshold results in a fishing mortality On rare occasions, the stock size threshold decline.
rate that is lower than Fmax, and it has proven to itself, rather than the fishing mortality thresh- Again, a stock assessment will produce esti-
be relatively conservative. old, is based on a percentage of the maximum mates for these threshold values, but the choice
Another set of potential fishing mortality spawning potential. For example, the stock of which threshold is appropriate is often based
thresholds is based on spawning-stock-per- would be considered overfished if the spawning- on predetermined policies. The risk of stock
recruit analyses, where spawning stock is the stock-per-recruit value was below some thresh- collapse is one of the aspects incorporated into
amount, in numbers or in weight, of reproduc- old percentage of maximum spawning potential.
tively mature individuals in the stock. As with A final set of potential fishing mortality
yield-per-recruit analyses, these analyses are thresholds combines the spawning stock per re-
performed in the last stages of a stock cruit and the assumed relationship between this
assessment. year’s spawning stock biomass and the number
As fishing pressure increases, the biomass of of recruits expected for next year.
reproductively mature fish created by recruits Without going into the mathematical details
entering the stock decreases. Essentially, the of how these are created, Fmed (sometimes called
more you catch the fewer survive. The maxi- Frep) is the fishing mortality rate that will allow
mum spawning potential (MSP) is the biomass the spawning stock biomass to replace itself with
16these policies. Short-lived, highly reproductive
Terms at a Glance species may be able to sustain a higher fishing
mortality threshold and lower stock size thresh-
old than a long-lived species with a low repro-
F.....................fishing mortality rate ductive rate.
More uncertainty will exist in estimates
B.....................stock size, in terms of biomass for fishing mortality threshold and stock size
threshold for species with poor data. This great-
FMSY...............fishing mortality rate at the level that would produce maximum er uncertainty will increase the chance that the
sustainable yield from a stock that has a size of BMSY estimates are too high or low, thus increasing
the chances of setting policies that may actually
BMSY...............stock size that can produce maximum sustainable yield when it is fished lead to a stock collapse. In such data-poor
at a level equal to FMSY situations, scientists may choose a more conser-
vative measure of fishing mortality threshold or
Bthreshold.........stock size threshold, the threshold below which a stock is overfished stock size threshold than they might otherwise.
Fthreshold . .......fishing mortality threshold, the fishing mortality rate that causes a stock Uncertainty
to fall below its stock size threshold
Through stock assessments, scientists aim to
Fmax................fishing mortality rate that achieves maximum yield per recruit determine a numerical value for parameters
such as stock size and fishing mortality rate.
F0.1..................the fishing mortality rate when the increase in yield per recruit from adding That value is called a point estimate. Discus-
a single unit of effort is only 10 percent of the increase achieved by going from
sions of stock assessments can give the impres-
zero to one units of effort
sion that when an assessment model produces a
F%. ..................fishing mortality rate that reduces the spawning stock per recruit to a given point estimate (for, say, the current stock size),
percentage of the maximum spawning potential, in the absence of fishing the modeler has strong confidence that the
particular value is the “true” state of the stock.
In reality, point estimates are simply the most
likely values. In fact, a wide range of values and
alternative models may exist. Those other values
or models may explain the data just as well.
In order to make sense of the range of
possible values, assessment models produce an
estimate of the uncertainty about these values.
Often, uncertainty is simply stated as a range
within which the true value may lie. That range
17is called a confidence interval or confidence
bound. Comparing Uncertainty
The wider the confidence interval, the more
uncertainty exists about where the true value The two curves in this graph have the same estimated value, or point estimate, for the
lies. For example, a stock assessment might stock size (the peak of the curve). However, the two estimates have very different levels of
determine that the current year’s biomass equals uncertainty. The steeper curve has a high probability that the point estimate is the true value,
100,000 metric tons (the point estimate) with and the range of possible values is tighter. In the flatter curve, there is a lower probability that
a 95 percent confidence interval of 80,000- the point estimate is the true value.
120,000 metric tons. In other words, the most
likely value for biomass is 100,000 metric tons,
but we can be 95 percent sure that the true
estimate lies somewhere between 80,000 and Point Estimate
120,000 metric tons.
Another approach to estimating uncertainty
produces values, called posterior distributions,
that actually estimate the relative probability of Less Uncertainty
a value being the true value. These distributions
Relative Probability
are defined by the relative height of the curve.
Wide or flat posterior distributions indicate
greater uncertainties than do narrow or steep
distributions. (See Comparing Uncertainty,
Greater Uncertainty
right.)
Uncertainty has many sources. Different
models allow these uncertainties to affect the
outputs in different ways. There is a fine line
when dealing with uncertainty. Ignoring too
many uncertainties will lead to decision mak-
Estimated Stock Size
ers putting too much confidence in the output
and possibly making poor management choices.
On the other hand, incorporating all the uncer-
tainties will likely lead to outputs that are too
muddled to give managers useful information.
Uncertainty often exists in the informa-
tion being input into a stock assessment model.
What is the true natural mortality rate? Are
catches fully accounted for or might some be
18missing? Are there errors in the way a fish’s age case, fishing both stocks at the same level has
Uncertainty and or weight is estimated based on its length? Are a greater likelihood of causing problems in the
fish migrating into or out of the stock? Other stock with greater uncertainty, because it’s more
Biomass uncertainties arise from the choice of stock as- likely that this stock is already close to or even
sessment model. Is there a relationship between below its biomass threshold. Formally incorpo-
Here again is the graph illustrated in
stock size and recruitment? Does a fish’s vulnera- rating this uncertainty to predict the results of
Comparing Uncertainty on the previous
bility to the fishing gear change each year? Does management actions is called risk assessment.
page. In this case, a biomass threshold is
natural mortality vary from year to year? As with stock assessments, the goal of a risk
also illustrated. Only a small portion of
the steeper curve lies to the left of the
No model can fit the data perfectly because assessment is not to provide a single solution
biomass threshold; the probability is low no model can possibly capture the true com- to stock management, but rather to provide
that the true stock size falls below this plexity of the system. The goal is to capture the decision makers with the information necessary
threshold. A larger portion of the flatter general trends as accurately as possible. Some to effectively compare the various choices. Such
curve lies to the left of the biomass statistical or estimation uncertainty is inevitable. risk assessments are often included within a
threshold, indicating a higher probability A number of point estimate values may be stock assessment to predict a stock’s response to
that the true stock size is actually below equally defendable from a statistical standpoint, different levels of fishing pressure.
the biomass threshold. due to the nature of the data and the complexity While a stock assessment cannot remove or
of the models. incorporate all uncertainty, it should explain
Estimating uncertainty allows decision mak- how uncertainty is incorporated and why it may
ers to get a handle on how accurate the point be ignored. It should also test the sensitivity of
Biomass Threshold
values may be, and allows them to choose their the model to any assumptions that were made.
actions appropriately. For example, consider
two distinct cod stocks with the same biomass
Relative Probability
Less Uncertainty
threshold. (See Uncertainty and Biomass, left.)
The stocks share the same point estimate
Greater Uncertainty
for the current size of the stock, but have very
different levels of uncertainty. We are much
less certain about the true status of the stock
with greater uncertainty. A stock with greater
Estimated Stock Size
uncertainty has much more of its curve to the
left of the biomass threshold than the stock with
less uncertainty. In other words, there is larger
probability that the true stock size is below the
biomass threshold for the stock with the greater
uncertainty.
Would you manage these two stocks in
an identical manner? Probably not. In this
1920
Population
Dynamics Models:
The Underpinnings
of Stock The Basic Population
Assessment Dynamics Model Calculating
Models Next Year’s Population
Nearly all the stock assessment models used
in fisheries today are based on some kind of The most basic way to predict the size of
4
population dynamics model, although they each next year’s fish stock is with this formula:
look at the population dynamics model from
a different angle. The goal of this section is to The number of fish alive this year (N1)
shed some light on exactly what these popula- – those that die this year (D1)
tion dynamics models are designed to do, and + those that are born this year (R1)
how they may be made more complex. The ways
in which these population dynamics models = the number alive next year (N2)
are applied to stock assessment models will be
discussed in later sections. This is written mathematically as
Simply put, fish are born, they grow, they (N2 = N1 – D1 + R1 ).
reproduce and they die, whether from natural
causes or from fishing. That’s it. Modelers just
use complicated (or not so complicated) math
to iron out the details of these processes. We’ll
start this section by taking a look at the basic Population Population
population dynamics model. Then we’ll examine This Year
(N1)
Next Year
(N2)
the ways in which scientists can make the model
more complex. Recruits Deaths
How many individuals will exist in a fish (R1) (D1)
stock next year? The number of fish alive at the
beginning of next year will equal the number
alive this year, minus those that die, plus the
number of recruits entering the stock. (See
Calculating Next Year’s Population, right.)
Rather than looking at the hard number of
fish that die this year, modelers generally assume
21that some percentage of the fish will die. If they Because the growth rate is given as a per- as a single parameter and doesn’t try to model
have estimates of the initial population size and centage, it does not depend on the abundance, the birth and death processes separately. Differ-
the percentages of fish that will die and recruits or density, of individuals. The growth rate is ent models describe the specific ways in which
that will survive, they can calculate the popula- therefore categorized as density-independent. the growth rate changes with increasing stock
tion size for each year in the future. The density-independent growth rate is also size. Each of those models will have different
This initial formula assumes that a fixed called the intrinsic growth rate. The stock will implications for the values of maximum sustain-
number of fish are born and survive to be grow or shrink at the same rate, regardless of the able yield.
counted each year. But it may be more accu- size of the stock. These dynamics may apply to The basic population dynamics model dis-
rate to assume that each reproductively mature stocks at small abundance levels or over short cussed in this section is the infrastructure upon
fish produces, on average, a fixed number of periods of time. However, the intrinsic growth which most stock assessment models are built.
offspring that survive to be counted. This is rate model doesn’t provide very realistic dynam- More complex equations are often added to the
known as net fecundity. While fecundity can be ics for longer-term modeling, let alone projec- basic model to improve its accuracy, but the
defined as the number of offspring produced by tions of future conditions. general principles remain the same.
an individual, net fecundity is the number of A more realistic model assumes that there Stock assessment modelers essentially try to
recruits (offspring that survive to be counted or is some limit to the size of the stock. At some estimate values for mortality rate, the number
caught) produced by an individual. point, due to habitat limitations, the availability of recruits, and the initial population size, such
of prey, or the presence of predators, a stock that the predicted population size follows what-
will reach an upper limit. This limit is called the ever trends exist in the data.
The upper limit for the size carrying capacity. Unlike density-independent
models, density-dependent models assume that
of a stock is known as its the growth rate for a stock is directly related to
carrying capacity. how close the stock is to reaching its carrying
capacity.
At very small stock sizes, the growth rate
If the net fecundity rate is greater than the is unaffected by density-dependent forces and
mortality rate, the stock will grow larger over is equal to the intrinsic growth rate. As the
time. If net fecundity equals mortality, the stock stock moves closer to its carrying capacity, the
will remain at a constant level. But if the net fe- mortality rate will increase or the net fecundity
cundity falls below the mortality rate, the stock rate will decrease. The result is a decrease in the
Adding Complexity:
will eventually shrink to zero. The relationship growth rate.
between the net fecundity rate and the mortal- For most fisheries, it is assumed that den- Mortality
ity rate is called the growth rate for the stock. If sity dependence appears most prominently
the mortality rate is 20 percent per year and the as a change in the net fecundity rate. This is Rather than thinking of mortality as just an
net fecundity rate is 25 percent, the stock will discussed more specifically in the stock-recruit- annual percentage, stock assessment modelers
increase at a rate of five percent; the growth rate ment section on page 26. The basic population focus instead on the instantaneous mortality
is equal to five percent. dynamics model treats the intrinsic growth rate rate. Natural mortality is, in theory, occurring
22constantly throughout the year. Essentially, a ing the population into age classes. In an age-
Instantaneous Mortality small portion of the population is dying each structured model, separate mortality rates exist
day, each hour, each minute, each second. The for each age class, and the number of recruits
Rates instantaneous mortality is the rate at which the is only relevant to the first age class. (See Age
population is shrinking in each one of these tiny Structure, page 24.)
The total instantaneous mortality rate
periods of time. Rather than build a model out to some
(Z) equals the instantaneous natural
For mathematical purposes, the instanta- maximum age (and thus assume all fish die after
mortality rate (M) plus the instantaneous
fishing mortality rate (F). If scientists have
neous mortality rate (Z) is converted into an they reach that age), modelers often include
estimates for M and F, they can calculate annual survival rate. The table in Instantaneous what they call a plus group. The plus group
both annual mortality and annual survival Mortality Rates (left) shows the relationship be- contains all fish of a certain age and older. For
using a table such as the one below. tween survival rate values and the instantaneous example, a species may be separated into classes
mortality rate. such as age-0, age-1, age-2 and age-3+. In this
Of course, not all mortality is due to fish- case, to calculate the size of next year’s plus
Total Inst. Annual Annual
ing. The instantaneous mortality rate is actually group (3+), modelers multiply the number of
Mortality Survival Mortality the combination of the instantaneous natural this year’s age-3+ individuals by the survival
Rate (Z) Rate Rate mortality rate (M) and the instantaneous fishing rate for that class, then add to that the number
mortality rate (F). When scientists and man- of age-2 individuals expected to survive to next
0.0 100 % 0.0 % agers talk about mortality in a management year.
0.1 90.5 % 9.5 %
context (that is, fishing mortality rate thresholds Scientists typically define a plus group
and targets), the instantaneous fishing mortality based on their ability to predict age from length
0.2 81.9 % 18.1 %
rate (F) is the rate to which they are referring. (which can become more difficult with older
0.3 74.1 % 25.9 % The table at left can also be used to convert M fish whose length may not be changing much
0.4 67.0 % 33.0 % and F to annual mortality rates. For example, over time), or based on the age above which
0.5 60.7 % 39.3 % an F of 0.2 means that 18.1 percent of the stock very few individuals appear in the data set.
0.6 54.9 % 45.1 % dies due to fishing. As was the case when we were looking at
0.7 49.7 % 50.3 % just the basic population dynamics model, the
0.8 44.9 % 55.1 % Adding Complexity: mortality rate in age-structured models is typi-
0.9 40.7 % 59.3 % cally transformed into instantaneous mortality
Age Structure
1.0 36.8 % 63.2 %
rates. Both fishing mortality rates and natural
mortality rates may be different for differ-
1.5 22.3 % 77.7 % The basic population dynamics model assumes
ent ages. Fish of a certain size (or age) may be
2.0 13.5 % 86.5 % that mortality, both natural and fishing-related,
more susceptible to a particular fishing gear, for
2.5 8.2 % 91.8 % affects all fish equally. In reality, of course, fish
example, or they may be more vulnerable to
3.0 5.0 % 95.0 % of different ages experience different rates of
predators.
mortality. When appropriate data, such as valid
The pattern of instantaneous fishing mortal-
length-age keys, are available, modelers often
ity rates across ages is called the partial recruit-
add complexity to the basic model by separat-
23ment pattern. When the older age classes have
Age Structure the highest instantaneous fishing mortality rates
and these rates are relatively constant across
This diagram illustrates an age-structured population dynamics model, with a plus-group that these older age classes, the partial recruitment
starts at age 3. The plus group contains all fish age 3 and older. pattern is referred to as “flat-topped.” When the
intermediate age classes have the highest instan-
taneous fishing mortality rates and these rates
decrease for younger and older fish, the partial
recruitment pattern is referred to as “dome-
Age 0 Age 1 Age 2 Age 3+ shaped.” (See Partial Recruitment, page 25.)
When different instantaneous fishing
Recruits 1-year 2-year 3-year mortality rates are calculated for each age, stock
Year 1 year 1 olds olds olds & up assessment models will occasionally use what is
called the separability assumption. Modelers
assume that the instantaneous fishing mortality
rate for a specific age class in a specific year can
be separated into two parts: gear selectivity and
Recruits 1-year 2-year 3-year
instantaneous fishing mortality rate for the fully
Year 2 year 2 olds olds olds & up selected age classes.
Gear selectivity is the probability that a
fish of a certain age or size will be captured by a
given gear. The term “fully selected” implies that
100 percent of the fish that encounter a given
gear are caught by that gear.
Recruits 1-year 2-year 3-year
Year 3 year 3 olds olds olds & up Fully selected age classes have a selectivity
value of 1.0, meaning that when fish of that age
encounters the gear (whether it be a net, hook,
pot, etc.), it will be caught 100 percent of the
time and will experience 100 percent of the fully
selected instantaneous fishing mortality.
If an age class has a selectivity of 0.25, a fish
of that age that encounters the gear will only be
caught 25 percent of the time, and that age class
would experience only 25 percent of the fully
selected instantaneous fishing mortality. When
multiple fisheries target a single stock, each
24fishery has its own selectivity pattern, which will
Partial Recruitment lead to each fishery having different age-specific
instantaneous fishing mortality rates.
“Flat-topped” partial-recruitment patterns occur when the older age classes have the highest The term L50 is occasionally used to denote
instantaneous fishing mortality rates and the rates are relatively constant across the older age the length at which a fish has a 50 percent prob-
classes. “Dome-shaped” partial-recruitment patterns occur when the intermediate age classes ability of being retained by the gear if it en-
have the highest instantaneous fishing mortality rates and the rates decrease for ages above counters the gear. This should not be confused
and below the intermediate ages. with the L50 that refers to the length at maturity
discussed later.
Flat-Topped Partial Recruitment
In order to actually use an age-structured
model, scientists must be able to separate the
fishery-dependent and fishery-independent data
0.25
into age classes. This exercise can be undertaken
Instantaneous Fishing Mortality
0.2 as a separate analysis, external to the basic stock
assessment model, or it can be incorporated
0.15
directly into the stock assessment model.
0.1 When incorporating age structure exter-
nally, scientists generally rely on the length-age
keys mentioned previously. When both age
0.05
0 and length data are taken from the same fish,
0 2 4 6 8 10 12 14 16
scientists can estimate what percentage of fish
Age
of a given length fall into each age class. Imag-
ine a species in which 10 percent of nine-inch
Dome-Shaped Partial Recruitment individuals are age one, 70 percent are age two
and 20 percent are age three. If a fishery caught
0.25 1,000 fish that were nine inches long, we would
classify 100 of them as age one, 700 as age two,
Instantaneous Fishing Mortality
0.2
and 200 as age three.
0.15 This catch-at-age data is incorporated as
a direct input into the basic stock assessment
0.1
model. Performing this analysis outside of the
0.05
basic stock assessment model typically ignores
the uncertainty inherent in the process, howev-
0
0 2 4 6 8 10 12 14 16
er. Therefore, incorporating age structure exter-
Age nally often overestimates the degree of certainty
in the results.
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