CHAPTER 4
FISHERIES MANAGEMENT
Renewable and Nonrenewable Resources
A renewable resource is one that can be replaced as fast as it is exploited. A nonrenewable
resource is one that cannot. Petroleum and metal ore deposits are generally considered to be
nonrenewable, because current rates of human use almost certainly exceed the rate of natural
formation. A fundamental assumption in fisheries management is that a stock of fish is a
renewable resource. If we remove a small number of fish from the population in a given year,
those fish will be replaced the following year by offspring of the remaining adults. We now have
the capability, however, to kill many species of fish (and other land and sea animals) faster than
biological processes can replace them. Without proper management, such resources are
effectively nonrenewable and may become extinct. What is the best way to manage a renewable
resource such as a fishery?
The Concept of Maximum Sustainable Yield
There are many approaches to analyzing the exploitation of fish populations. In Chapter
1 we discussed one of these approaches and showed how it led to the concept of a maximum
sustainable yield. A sustainable yield is a yield that can be achieved year after year. For
example, we could harvest 1,000 tonnes of Peruvian anchovies year after year from the waters
off the coast of Peru without threatening the existence of the anchovy population. Such a harvest
would be a sustainable yield. We could also harvest 2,000 tonnes of anchovies without
threatening the anchovy population. Thus, while 1,000 tonnes of anchovies per year would not
remove the resource faster than it could be replaced by biological processes, such a harvest
would not be the maximum sustainable yield.
There are two theoretical approaches to understanding the concept of maximum
sustainable yield, one associated with the work of Milner Schaefer of the Scripps Institute of
Oceanography (Schaefer, 1954) and the other with the work of Ray Beverton of the Fisheries
Laboratory in Lowestoft, England, and Sidney Holt of the United Nations Food and Agriculture
1
Organization in Rome, Italy (Beverton and Holt, 1957). The so-called Schaefer model is
arguably the easier of the two models to understand, so we will begin with it.
The logic behind the Schaefer model is that the sustainable catch from a fishery will be
related to the fishing effort. Obviously if there is no effort, there will be no catch. However, if
the effort is too great, the stock of fish will eventually become extinct. The sustainable catch is
therefore zero if the effort is zero, and the sustainable catch is also zero if the effort is too great.
It is therefore reasonable to assume that the relationship between sustainable catch and effort
looks qualitatively like Fig. 4.1. On the left side of the diagram, small amounts of effort are
rewarded with a sustainable catch, and increasing the effort increases the sustainable catch.
Eventually, however, the sustainable catch reaches a maximum, and any further increases in
effort actually decrease the sustainable catch, until the stock is eventually driven to extinction.
The left side of the figure is normally associated with the term underfishing and the right side
with the term overfishing. Mathematically speaking, underfishing is associated with a positive
correlation between fishing effort and sustainable catch, and overfishing with a negative
correlation. Determining whether a stock is being underfished or overfished therefore requires
nothing more than making a graph of fishing effort (E) versus sustainable catch (C) and
determining whether the correlation is positive or negative. Unfortunately this is much easier
said than done.
Another method of analysis based on the Schaefer model is to plot catch per unit effort
(C/E) versus catch. The logic behind making such a graph is that the sustainable catch will be
related to the size of the fish stock. If there are no fish, obviously there will be no catch. It is
reasonable to assume that in the presence of a fishery the stock will be smaller than in the
absence of a fishery. Thus a stock equal in size to the virgin stock1 would imply no fishing and
hence no catch. In other words, the sustainable catch will be zero when the stock size is zero,
and the sustainable catch will be zero when the stock is equal in size to the virgin stock. A
modest amount of fishing effort will reduce the stock below the size of the virgin stock and
produce a sustainable catch. Additional effort accompanied by further reductions in the size of
the stock will increase the sustainable catch. However, if the size of the stock is reduced too
much, the sustainable catch will start to decrease, eventually dropping to zero when there are no
more fish. Fisheries biologists then reason that C/E should be a useful proxy for population size.
1
The term virgin stock is used to describe the stock in the absence of a fishery.
2
The logic is that when fish are plentiful, catch per unit effort will be high, and when fish are
scarce, catch per unit effort will be low. This logic is not infallible2, but in many cases it may be
a reasonable assumption. The relationship between C/E and C is therefore expected to look
qualitatively like Fig. 4.2.
Figure 4.1. Theoretical relationship between fishing effort and sustainable fish catch based
on the work of Schaefer (1954).
Fig. 4.2 bears an uncanny resemblance to Fig. 4.1, but there is an important difference
between the two figures. In the case of Fig. 4.2, the left side of the figure is associated with
overfishing and the right side with underfishing. Thus a positive correlation between sustainable
catch and catch per unit effort implies overfishing, and a negative correlation implies
underfishing.
2
For example, if the geographical area occupied by the stock collapses as the size of the stock is reduced,
commercial catch per unit effort may remain high even when the size of the stock has been greatly reduced.
3
Regardless of whether we plot E versus C or C/E versus C, implementation of the
Schaefer model requires information only on sustainable catch and effort, information that
should be obtainable from the fishery. We do not need to know anything about the population
dynamics, ecology, or biology of the fish. We just make graphs of E versus C or C/E versus C
and determine whether the correlations are positive or negative. As we shall see, the real world
is not always so simple.
Fig. 4.2. Theoretical relationship between catch per unit effort and sustainable catch based
on the work of Schaefer (1954)
As noted above, the second approach to fisheries management is associated with the work
of Ray Beverton and Sidney Holt (1957) and is generally referred to as the Beverton-Holt model.
Implementation of the model requires no information on catch and effort but instead requires
knowledge of the population dynamics of the fish stock. We have already been introduced to the
basic concepts of the model in Chapter 1. The result of that analysis is reproduced in Fig. 4.3.
4
Assuming that C/E is a reasonable proxy for the size of the fish stock, Fig. 4.3B and Fig. 4.2 are
directly comparable. In other words, the Schaefer and Beverton-Holt models agree with respect
to their predictions about the relationship between stock size and sustainable fish catch. Both
models assume that in the presence of a fishery the fish stock will become smaller than the size
of the virgin stock. This reduction in stock size is an adjustment that is crucial to the ability of
the stock to withstand the additional mortality imposed by fishing. The Beverton-Holt model
argues that the reduction in stock size creates a differential between gross production (G) and
natural mortality (M). The sustainable fish catch (F) is equal to the difference between G and M,
i.e., F = G – M. Implementation of the Beverton-Holt model requires knowledge of G and M
and how they depend on the size of the adult stock. Thus although the implications of the
Schaefer and Beverton-Holt models are very similar in some respects, the information required
to implement the two models is quite different.
Figure 4.3. Relationship between stock size, population dynamics, and sustainable catch based
on the Beverton-Holt model.
5
The Resource-Limited Population
It is certainly fair to ask why one would expect the G and M curves to behave as depicted in Fig.
4.3A. Let’s consider the M curve first. Obviously fish that are caught cannot also die from
natural causes. From that standpoint alone one would anticipate that M would decrease in the
presence of a fishery. Furthermore, for many adult fish populations, older fish have a greater
chance of dying of natural causes than younger fish. In the presence of a fishery, the chances of
a fish’s reaching old age may be greatly reduced. For example, assume that a certain species of
fish has a life span of ten years and that virtually no fish die of natural causes between the ages
of two and six. Assume that fish are recruited to the fishery3 at two years of age and that about
20% of the adult population is caught each year. The probabilities that a recruit will reach three,
four, five, and six years of age are shown in Table 4.1. There is now only a 41% chance that a
recruit will reach six years of age, and so the natural mortality rate is sure to drop by at least a
factor of 1/0.41 = 2.4 in the presence of the fishery. The actual drop would be even greater,
because the probability that a fish will reach an age of seven to ten is reduced by a factor of three
to six, respectively, in the presence of the fishery. The reduction in M would depend on the
probabilities of natural mortality between the ages of six and ten. Finally, many fish populations
are resource limited. In other words, the availability of food, shelter, and desirable habitat limit
their distribution and biological productivity. In the absence of competitors for these same
resources, when the size of the population is reduced, more resources become available to the
remaining fish. If some fish had previously been in marginal habitats, the population might
contract into the more desirable areas. In any case, a greater availability of resources, including
food and shelter, could certainly reduce the rate of natural mortality.
Gross production G is the sum of two terms, recruitment and growth. As the population
is reduced below the size of the virgin stock, G is not expected to decline as rapidly as M,
particularly if the adults are cannibalistic.4 The same arguments about habitat and resource
availability that apply to natural mortality of the adult stock are pertinent to the growth of the
adult fish and to the growth and survival of juvenile fish prior to their recruitment to the adult
stock. If a decline in the number of adult fish causes the population to abandon marginal
3
Recruitment in the context of fisheries management means that a fish has become large enough to be caught with
whatever gear are being used by the fishermen.
4
As is the case, for example, for the Peruvian anchovy.
6
habitats, and if more resources become available, then it is likely that the remaining fish will
grow more rapidly and that a higher percentage of the juveniles will survive and grow up to
become adults.
Table 4.1. Probability of Survival for a Fish Recruited at Age Two and with an 80% Chance of
Surviving Each Subsequent Year of Life
Age of fish
Probability that fish will reach the given age (%)
2
100
3
80
4
64
5
51
6
41
Practical Problems with Implementation
Although the maximum sustainable yield may seem to be a logically appealing goal of
fisheries management, there are significant problems with both its implementation and its
theoretical underpinnings. For a start, given a real population of fish, how do we decide what the
maximum sustainable yield is? If we use the Beverton-Holt model, we need to know enough
about the dynamics of the population to predict G and M as a function of population size. It is
difficult enough to determine what G and M are under a given set of circumstances, let alone
what G and M may become as the population size changes. Information from controlled
experiments, in which the population size is systematically changed and the population dynamics
given sufficient time to stabilize, is virtually nonexistent. Therefore, in practice, one finds that
application of the Beverton-Holt model to estimate maximum sustainable yield usually involves
a good deal of educated guesswork.
If we do not have adequate information on G and M but instead have data on catch and
effort from the fishery, we can try the Schaefer model. A very practical problem with the
Schaefer model is that because of ongoing fishing the population is virtually never given
sufficient time to come to equilibrium with the fishing pressure. Hence the catch for a given year
usually does not represent the sustainable yield that could be achieved at that population size.
7
Methodologies. Just how do we get the information we need to implement the BevertonHolt and Schaefer models? Let’s consider the Beverton-Holt model first. We need information
on G and M. Before we can calculate those numbers, we will very likely need some way to
determine the size of the stock, and we will need to be able to assign an age to a fish.
For teleost fish5 the most common method of age determination is examination of
otoliths, which are calcareous concretions formed in the fish’s inner ear. The growth increments
are deposited on a daily basis, evidently the result of an endogenous circadian rhythm entrained
by the 24-hour light:dark cycle. Otoliths also form annular rings (annuli) analogous to tree rings,
but the factors that influence their formation are a bit unclear. Examination of otoliths requires a
compound microscope, since the width of the daily increments is usually less than 10 microns.
Correctly interpreting otoliths is by no means trivial. One of the best ways to validate the
methodology is to examine the otoliths of fish grown in captivity, in which case the exact age of
the fish is known.
It is worth pointing out that reading otoliths is by no means the only way to assign an age
to a fish. Scales, bones, and fin rays, in addition to otoliths, have all been used to determine the
age of fish, since they all tend to form annuli similar to tree rings. Virtually every method used
has been subject to some controversy. In the mid 1960s, for example, scientists from several
countries belonging to the International Whaling Commission became concerned about the
accuracy of the methods then being used to determine the age of whales. At a meeting in 1968,
they decided that more accurate estimates could be obtained from ear plug laminations. The new
age determinations, combined with some adjustments in estimates of stock sizes, resulted in a
downward revision of the calculated maximum sustainable yield of whales. This was a very
difficult conclusion for the active whaling nations to accept, and had Norway not decided to drop
out of Antarctic whaling, the problem might not have been resolved (McHugh, 1974).
Determining the number of fish in the stock can be done in a variety of ways, and the
methodologies used reflect the behavioral characteristics of the particular species. Fish such as
salmon and shad that return to freshwater streams to spawn can be conveniently (more-or-less)
counted as they migrate past a census point on a stream. In the eastern tropical Pacific, the size
5
Teleost fish have a skeleton made of true bone. They are to be contrasted with the cartilaginous fish (e.g., sharks,
skates, rays), which have a skeleton made of cartilage.
8
of dolphin populations has been estimated from aerial surveys.6 A convenient but indirect
method of estimating population size is to count the number of fish eggs or larval fish, which can
be sampled by pulling a plankton net through the water. The validity of this method requires that
the number of eggs or larval fish be proportional to the number of adult fish. Acoustic surveys
(sonar) have been used to estimate the abundance of fish that school below the surface. Acoustic
surveys require calibration of two kinds. First, we must know what species of fish we are
looking at. Second, we must know the relationship between the acoustic signal and the number
of fish in the school.
One of the most commonly used methods for estimating stock size is tag-and-release.
The idea is to somehow tag a large number of fish and then release then into the wild. The
validity of the method requires that (1) tagged fish mix uniformly with untagged fish, (2) tagged
fish experience no mortality between their release and the subsequent survey of the stock, (3)
there is no difference in reporting of tagged and untagged fish in subsequent surveys, and (4) no
tags are lost. The technologies available for tagging fish improved dramatically during the
second half of the 20th century, and it became possible to rapidly tag large numbers of fish and
subsequently count the tags. For example, in 1975 Norwegian fisheries biologists internally
tagged about 18,055 Norwegian herring and released them along the west coast of Norway.
During a subsequent survey, they screened about 810,000 fish and recovered a total of 13 tags.
Thus one out of every 810,000/13 = 62,308 fish was tagged. The implication is that the adult
stock consisted of (62,308)(18,055) = 1.1x109 fish.7
If we can assign an age to a fish and estimate the number of fish in the stock, we can
determine the age distribution of the population. If the population is in steady state, we can look
at the age distribution and determine the overall mortality rate for the stock. Figure 4.4 provides
an admittedly simple example of what might be learned from this sort of analysis. From our
estimate of stock size and ability to assign an age to a fish, we have determined the number of
6
Dolphins, being a marine mammal, are not the target of commercial fisheries in the United States. However, their
populations have been impacted by the use of so-called porpoise sets in conjunction with the eastern Pacific
yellowfin tuna fishery. In order to determine the extent of the impact on the dolphins, the National Marine Fisheries
Service has needed accurate estimates of the numbers of dolphins in the area. See Chapter 7.
7
A variation on conventional fish tags is a pop-up tag, which is attached to the exterior of the fish and is
programmed to release from the fish at a certain time after deployment and rise to the surface. The tag then beams
its location and various other information to an orbiting satellite. Such tags can provide valuable information on fish
movement. They are not used to provide information on population numbers.
9
each year class of fish in the adult stock. From this analysis we can see that (1) the fish are
recruited to the stock at age two, (2) the number of recruits is 6,700 fish per year, (3) the lifespan
of the fish is 10 years, and (4) the overall mortality is about 18% per year. If we know the
fishing mortality (obtained from knowledge of fish catch), we can partition the overall mortality
into fishing mortality and natural mortality. Finally, if we know the size of the fish as a function
of its age, we can easily determine growth rates and therefore calculate gross production (i.e.,
growth plus recruitment). Unfortunately, real world data never look as clean or unambiguous as
Fig. 4.4. We will have a chance to examine some real data in later chapters and find out how the
data were used to guide fishery management.
Figure 4.4. Age structure of a hypothetical stock of fish in which recruitment of 6,700 two-year
old fish occurs each year. The mortality rate of the fish is 18% per year. The lifespan of the fish
is 10 years.
10
If recruitment is highly variable from year to year, a snapshot of the age distribution (e.g.,
Fig. 4.4) will probably not be very useful in determining recruitment and mortality rates. In that
case it becomes necessary to follow the abundance of a particular year class over time. The
results from a single year class should look qualitatively like Fig. 4.4. The down side of this
approach is that one must collect data over the lifespan of the fish before the full picture
emerges.
Now let’s consider how to collect catch and effort data for the Schaefer model. Naively
the task seems simple, but there are some potentially serious problems. Let’s consider effort
first. How do we measure fishing effort? There are a great many ways to quantify effort. Let’s
suppose we choose the number of ship-days spent on the fishing grounds. This is fine as long as
the technology the fishermen are using to find and catch the fish does not change. However, if
the gear changes from drift nets to trawl nets, or from trawl nets to purse seines, then ship-days
associated with one type of gear are not comparable to ship-days associated with another type of
gear. There are several ways to try to overcome this problem. We could send out two groups of
fishing boats equipped with different technologies and compare the number of fish caught per
ship-day using the two technologies. Alternatively, instead of relying on the commercial fishing
industry to provide us with catch and effort information, we could conduct scientific surveys
using exactly the same technology year after year. Even if the type of fishing gear used to catch
the fish does not change, there may be significant changes in the technology used to find the fish.
Satellites now provide information on sea surface temperature and chlorophyll concentrations
that, when used by knowledgeable fishermen, can greatly facilitate locating fish. Fish
aggregation devices (FADs) have become a common mechanism for reducing the time spent
looking for fish that tend to be attracted to floating objects. Skipjack tuna fall into this category.
Somehow effort data must be adjusted to allow for changes in the technologies used to find and
catch fish. Making these adjustments is not always straightforward.
Catch data are not always accurately reported, as indicated in Chapter 3. Furthermore,
the catch associated with a particular effort may not be the sustainable catch. The later issue is
not a problem if our intention is to use catch per unit effort as a proxy for stock size, but it
becomes a problem if we are trying to use the correlation between catch and effort to determine
whether we are overfishing or underfishing.
11
Theoretical Problems with the Models
Highly Variable Recruitment. In addition to these practical problems associated with
implementing the Beverton-Holt and Schaefer models, there are some theoretical reasons to
believe that the maximum sustainable yield may not be the wisest goal of fisheries management.
The three theoretical issues most often mentioned are highly variable recruitment, the presence
of competitors, and the catch of sexually immature fish. Variability in recruitment is a
characteristic of many of the world’s commercially important fish stocks, including gadoids
(cod, Pollock, haddock, hake, and their relatives), and clupeids (anchovies, sardines, herring, and
their relatives), which together account for about 1/3 of global capture production. Although
these species appear to time their spawning so as to maximize the probability that their eggs will
survive and grow up to become adults, the fact is that very few do survive.8 Predation on the
eggs and larval fish is undoubtedly a major factor, but some scientists believe that a more
important factor is the availability of food for the larval fish. The hypothesis is that in most
years there is an imperfect match between the peak in the larvae’s need for food and its
availability. This mismatch may be either spatial or temporal. Unfavorable currents may cause
the eggs to drift into an area where the concentration of nutrients is low. In temperate latitudes
there is a burst of growth of microscopic marine algae in the spring. This phytoplankton bloom,
caused by increasing photoperiods and thermal stratification of surface waters, may easily vary
by a week or two from one year to the next as a result of normal fluctuations in the weather.
Many larval fish have only about a day to begin feeding once the nutrition in the egg yolk has
been used. Since their swimming ability is minimal, the concentration of food in the water
during this limited time can have a dramatic influence on survival and growth. A shift of a week
or two in the spring phytoplankton bloom could easily account for large year-to-year variations
in fish survival.
The use of this match/mismatch hypothesis to explain interannual variability in recruitment is
largely the work of David Cushing of the Fisheries Laboratory in Lowestoft, England, and is
illustrated in Fig. 4.4. Not all scientists agree with the details of Cushing’s hypothesis; there is
8
A sexually mature female cod, for example, produces literally hundreds of thousands of eggs each year. If other
than a very small percentage of these survived to become adults, the ocean would be overflowing with cod.
12
some evidence that the most critical phase in the early life of fish is not always when the larvae
begin to feed. However, most scientists agree that critical periods exist in the pre-recruitment
life history of fish and that differences in environmental conditions during those periods largely
account for the inter-annual variability in recruitment. While a moderate variability in
recruitment does not utterly invalidate the concept of a maximum sustainable yield, it does
suggest caution in setting catch limits. For example, a perfectly acceptable catch during years of
Figure 4.4. Illustration of the match/mismatch hypothesis advanced by David Cushing to
account for the highly variable recruitment characteristic of many commercially important fish
stocks. A perfect match requires that the peak in the requirement of the larval fish for food
coincide with the supply of that food. Although Cushing originally formulated his hypothesis in
terms of a temporal match/mismatch, the concept has been extended to include spatial
match/mismatches. The theory assumes that during most years there is a poor overlap between
the two peaks, and recruitment is poor. Occasionally, however, a good overlap occurs, followed
by a spectacular recruitment. Source: Cushing (1982)
13
good recruitment could almost wipe out the stock of fish if recruitment were poor for several
years in a row. In fact, the California sardine fishery was virtually destroyed because of heavy
fishing during 1949 and 1950, when recruitment was quite low.
K and r selection. Closely related to the subject of highly variable recruitment is the
concept of K and r selection of populations of organisms. The use of the terms K and r selection
can be traced to the so-called logistic equation to describe population dynamics. According to
the logistic equation, the rate of change of the number of individuals in the population is
described by the equation
 N
rate of change = rN1  
 K
where N is the number of individuals in the population and r and K are parameters that
characterize the population dynamics. K is generally referred to as the carrying capacity,
because the rate of change is zero when N = K. When N is small compared to K, the rate of
change is approximately equal to rN. Under these conditions, the population grows more-or-less
exponentially. One can therefore envision two extreme situations. In the first case, N remains
small compared to K at all times. The population grows exponentially most of the time but is
occasionally reduced to a very low level by some sort of perturbation, e.g., El Niño. In the
second case, N is comparable to K at all times, and fluctuations in the size of the population are
small.
Figure 4.5 illustrates the difference in the population dynamics of r- and K-selected
populations. The population dynamics are governed by the same logistic equation in both
panels. In Fig. 4.5A the population is reset to a value equal to 10% of the carrying capacity at
regular intervals. The time interval between resets is short enough that the population has time
to rise only to about 50% of the carrying capacity before the next reset. In Fig. 4.5B the
population is reset to a value equal to 90% of the carrying capacity at the same time intervals. In
the case of Fig. 4.5A the population size varies by about a factor of 5 between resets. In Fig.
4.5B the variation in the population size is about 10%.
14
Figure 4.5. Temporal variability of (A) an r-selected population and (B) a K-selected population.
The typical characteristics of r- and K-selected populations are well defined and are
summarized in Table 4.2. It has been argued by two very influential ecologists (MacArthur and
Wilson, 1967) that the life history traits of most species would place them somewhere on a
continuum of r/K selection, with pure r-selection at one end and pure K-selection at the other.
While the concept of r/K selection has drawn some criticism, it has generally proven useful in
explaining how life history traits influence the ability of a species to respond to perturbations,
including fishing. Whales, with few natural enemies, a lifespan of perhaps 50 years, and a
reproductive rate of about one calf every two years per female whale, are an example of K
selection. Clupeids and gadoids lie toward the r-selected end of the continuum.
15
Table 4.2. Characteristics of r-selected and K-selected populations
r-selected
K-selected
Environment
variable and/or unpredictable
constant and/or predictable
Lifespan
short
long
Growth rate
fast
slow
Fecundity
high
low
Natural mortality
high
low
Population dynamics
unstable
stable
Species that experience highly variable recruitment can take out an insurance policy
against unstable population dynamics by having a long life span. For example, if a good
recruitment year comes along only about every four years, a species that becomes sexually
mature at age five and has a lifespan of 21 years can expect to have four good year classes
represented in the adult stock at any time. Now suppose that the fish stock becomes the target of
a rather intense fishery, so intense in fact that the effective lifespan of the fish becomes 10 years
rather than 20. In that case the adult stock is represented by only five years classes at any point
in time. Although a good recruitment year comes along on average every four years, if there is a
series of five or more years without good recruitment, the stock of adult fish will plummet (Fig.
4.5A). Thus an intense fishery can transform a fish stock with a relatively stable adult
population into a stock with highly unstable population dynamics by reducing the lifespan of the
fish, in effect taking away the fish stock’s insurance policy.
Stability. The subject of stability is very important in fisheries management, because the
Schaefer and Beverton-Holt models assume a steady state system. What happens when this
assumption is violated?
To answer this question, let’s examine the relationship between gross production (G =
growth plus recruitment) and total mortality (M + F = natural mortality plus fish catch) as a
function of stock size (Fig. 4.6). In panel A there is no fish catch, and a balance between G and
M occurs at two points, when the stock is zero and when the stock equals the virgin stock. Now
let’s begin to fish at a rate equal to about half the maximum sustainable yield. This moves the
total mortality curve (M + F) upward as shown in panel B. There are again two equilibrium
16
points, one corresponding to a stock size equal to roughly 15% of the virgin stock and the other
to a stock size equal to roughly 85% of the virgin stock. Let’s see if these equilibrium points are
stable.
Figure 4.6. Behavior of total mortality curve (M + F) as fishing effort is increased from (A) zero
to (D) the maximum sustainable yield. With the exception of panel D, there are two possible
equilibrium points for each level of fishing effort.
Let’s consider the equilibrium at 85% of the virgin stock first. If for some reason the
population increases above the equilibrium value, losses (M + F) will exceed gains (G), and the
population will begin to decrease back toward the equilibrium point. If for some reason the
population decreases below the equilibrium value, gains will exceed losses, and the population
will begin to increase back toward the equilibrium point. In other words, the nature of the
population dynamics makes this a stable equilibrium point.
17
Now let’s consider the equilibrium point at 15% of the virgin stock. If for some reason
the population increases above that equilibrium value, gains will exceed losses, and instead of
returning to the same equilibrium point, the population will continue to increase until it arrives at
the equilibrium corresponding to the larger stock size. If for some reason the population
decreases below 15% of the virgin stock, losses will exceed gains, and instead of returning to the
equilibrium point, the stock will continue to decrease until there is nothing left. Clearly the
equilibrium point corresponding to 15% of the virgin stock is unstable.
If we increase the fish catch to about 75% of the maximum sustainable yield, we get the
results shown in panel C. There are again two equilibrium points, corresponding to roughly 25%
and 75% of the virgin stock. The same sort of analysis tells us that the equilibrium at 75% of the
virgin stock is stable, and the equilibrium at 25% of the virgin stock is unstable. Losses exceed
gains when the stock size is greater than 75% of the virgin stock or less than 25% of the virgin
stock. Between 25% and 75% of the virgin stock, gains exceed losses. The population dynamics
will drive the stock toward 75% of the virgin stock if the starting point is anywhere greater than
25% of the virgin stock. However, if the initial stock size is less than 25% of the virgin stock,
the stock will be unable to withstand the fishing pressure and will become extinct.
Now let’s consider panel D, where the fish catch equals the maximum sustainable yield.
In this case there is only one equilibrium point, where the loss curve (M + F) just touches the
gain curve. At any point to the right or left of this equilibrium, losses exceed gains. This is fine
if for some reason the stock increases above the equilibrium value, because the population
dynamics will drive the stock back toward the equilibrium point. However, if for some reason
the stock size decreases, the population dynamics will cause it to continue to decrease, and
eventually there will be no more fish.
The disturbing conclusion is that the equilibrium point corresponding to the maximum
sustainable yield is inherently unstable. Targeting the maximum sustainable yield as a goal of
fisheries management is not a wise policy when dealing with an r-selected fish, whose stock size
may naturally vary a lot from year to year (e.g., Fig. 4.5A). The solution is to accept a
sustainable yield substantially less than the maximum sustainable yield and to target the larger of
the two stock sizes corresponding to that sustainable yield, i.e., manage the fishery at a stable
equilibrium point.
18
The Presence of Competitors. The presence of competitors challenges one of the
underlying assumptions of the maximum sustainable yield concept, namely that more resources
become available as the population is reduced. If there is competition for resources, a selective
fishery could easily shift the balance in favor of the unfished species. Sardines and anchovies
share the same ecological niche, and they are frequently perceived as being in competition. The
record of fish scales deposited and preserved in sediments off the coast of California indicates
that the population of northern anchovies has been stable in the waters of the California Current
over the past two centuries, whereas the California sardine has been abundant only during
periods of climate warming. This suggests that the balance of competition favors the sardine
during times when the offshore waters are unusually warm, though the record of fish scales does
not prove that the two species are in competition. Where competition exists between two
species, it may be advisable to fish both species in order to avoid shifting the balance of
competition in favor of one or the other. Such a policy was followed by the South African
government during the 1960s in an attempt to save the South African pilchard fishery. Scientific
surveys had shown that the ratio of pilchards to anchovies off South Africa had shifted from
about 16:1 during the 1955 fishing season to about 1:10 from 1962 to 1965. The South African
efforts were partially successful, because the sardine fishery remained at a respectable level until
1976. However, despite the best intentions of government officials, the fishery almost
completely collapsed in 1979 (Fig. 4.7). During the 1990s the pilchards began to show signs of
recovering, and in the last few years a balance may have been struck between the pilchards and
anchovies. The combined catch from the two stocks is almost 0.5 Mt, which is certainly a
respectable fishery.
Significant Harvest before First Spawning. If fish are harvested before they have a
chance to reproduce, recruitment can be seriously impacted, and the gross production curve
depicted in Fig. 4.3A may be overly optimistic. Unfortunately, some species of fish do not
become sexually mature until well after the time when they are large enough to be of interest to
commercial fishing.
19
Figure 4.7. Record of South African pilchard and anchovy catches in coastal upwelling system
off the Western Cape coast of South Africa.
In some cases it is possible to lessen the impact on reproduction by carefully selecting the
size and sometimes the sex of the species caught. During the 1970s the International Whaling
Commission imposed restrictions on the size and sex of whales taken by the whaling industry.
Implementing such restrictions was relatively straightforward, because it is possible to estimate
the size of a whale with reasonable accuracy from a boat, and females with calves are easily
identified. In fisheries involving baited hooks it is possible to exclude most small fish from the
catch by choosing large hooks. In drift net fisheries, small fish can be excluded from the catch
by appropriate choice of mesh size. In other words, it may be possible with some species of fish
and some fishing techniques to reduce the impact of fishing on recruitment to an acceptable level
by focusing only on mature fish that have had some time to reproduce. Where it is clear that an
intense fishery is taking sexually immature fish and/or fish that have had a very limited
20
opportunity to reproduce, careful monitoring of recruitment (e.g., by means of egg or larval fish
surveys) can help avert a human-induced population collapse.
Economic Issues
Although subsistence and recreational fishing are motivated by issues not directly related
to free market economics, the profit motive is very much a factor in most commercial fishing.
Figure 4.8 is a reproduction of Fig. 4.1, but with the incremental catch associated with equal
increments of effort depicted by the piecewise linear series of step functions. What is the
message from this figure?
Figure 4.8. Relationship between fishing effort and sustainable catch (dashed line) and
incremental catch associated with incremental fishing effort (solid piecewise linear function).
21
The message from this figure is that as we approach the traditional maximum sustainable
yield, the incremental catch associated with each increment of fishing effort gradually decreases.
Strictly speaking, at the peak of the curve there is no increment in catch associated with an
increment in effort. Given that each increment in fishing effort costs money, it does not make
economic sense to push the catch all the way to the maximum sustainable yield. It is reasonable
to assume that the increment in catch associated with the very first increment in effort will be the
largest catch increment. The increments in catch associated with additional increments in effort
will follow a law of diminishing returns. The first increment in effort will have the highest cost,
because there will be fixed costs (as opposed to variable costs) associated with establishing the
fishery in the first place. How far up the curve it will make economic sense to fish will depend
on the value of the fish and the cost of the incremental effort.
Maximizing Yield per Recruit
There is one other strategy of fisheries management that warrants discussion here,
because we will see an application of it in Chapter 11. The strategy is to harvest fish at an age
that maximizes the yield per recruit. Obviously implementation of this strategy requires that one
be able to harvest fish of a particular age, at least approximately. There are cases where this is
possible. The rationale behind the strategy is apparent from an analysis of the data in Table 4.3.
Table 4.3. Example of effect of natural mortality and growth on yield of a year class
Age
Number of individuals
Weight per individual
Yield per recruit
3
1,000,000
15
15.000
4
900,000
17
15.300
5
810,000
19
15.390
6
729,000
21
15.309
7
656,100
23
15.090
8
590,490
25
14.762
In this example, the fish are recruited at age 3, and natural mortality is assumed to be
10% per year thereafter. The fish gain weight at a constant rate of 2 per year after being
22
recruited. If our goal were to harvest the fish at an age that produced the highest yield per
recruit, we should harvest the fish at age 5 years. If we wait any longer, the increase in the
biomass of the year class due to the continued growth of the surviving fish is more than offset by
the losses from the population associated with natural mortality. Prior to age 5, the opposite is
the case.
A caveat to this strategy is that the actual yield is the product of yield per recruit and the
number of recruits. If the fish do not become sexually mature until age 6, harvesting them at age
5 is not going to maximize anything. Before long there will be no fish left. The strategy of
maximizing the yield per recruit makes sense as long as recruitment is unaffected by the
harvesting strategy. If recruitment is significantly reduced by harvesting at the targeted age, then
it makes sense to allow the fish to grow to an older age and accept a somewhat lower yield per
recruit. In the example cited (Table 4.3), harvesting the fish at age 8 reduces the yield per recruit
by only 4%. If harvesting at age 8 versus age 5 increases recruitment by more than 4%, then it
would be better to harvest at age 8 than age 5.
The Costs and Benefits of a Variable Catch
Up to this point in our discussion we have implicitly taken the attitude that management
targets the same fish catch year after year. There is no a priori reason why this should be the
case. If the stock is in trouble, why don’t we just stop fishing? When the fish are plentiful, why
not just send out more boats and fishermen? While adjusting the fishing effort from year to year
in this way might make sense to a natural scientist, there are some important costs associated
with implementing such a policy, i.e., the policy would probably not make sense to a social
scientist. In a bad year, when the catch must be reduced, people are put out of work, fishing
boats and processing plants are idle, and other sectors of the economy and the food and feeds
industries must pick up the slack. While the fishing boats and processing plants are idle, the
workers must still support their families, and payments must still be made on the loans used to
buy the fishing boats and build the processing plants.
During the 1980s Canadian fishermen caught an average of 465,000 tonnes of Atlantic
cod each year. Since 1994 the catch has averaged 32,000 tonnes. What happened? What
happened is that the stock of cod was being grossly overfished, but the Canadian government and
23
the fishermen stubbornly ignored the warnings from the fisheries biologists. The fishermen were
unwilling to stop fishing because they had no other way to make a living. The government was
reluctant to shut down the fishery because of the impact on the fishermen and other sectors of the
economy. Eventually the government took action, but only after the stock was in very serious
trouble. A partial moratorium on cod fishing was imposed in July of 1992, and 30,000 Canadian
fishermen were put out of work. In January 1994 the moratorium was extended. All Canadian
Atlantic cod fisheries were closed, with the exception of one in southwestern Nova Scotia. As
noted by Kurlansky (1997, p. 186), “Canadian cod was not yet biologically extinct, but it was
commercially extinct – so rare that it could no longer be considered commercially viable.”
Current estimates indicate that it will take perhaps 15 years for the cod stock to recover, because
a healthy population requires some large old spawners (Kurlansky, 1997).
The reaction of the Norwegian government to a similar situation makes an interesting
comparison. The government realized its cod stocks were in trouble and in 1989 severely
restricted the fishery. Many fishermen, fish-plant workers, and boat builders were put out of
business, and the size of the fleet was drastically reduced (Kurlansky, 1997). The unemployment
rate in the northern Finnmark region rose to 23%. Because the government imposed the
restrictions while the stock was still commercially viable (i.e., while there were still some large
spawners left), the stock recovered within a few years. In the 10 years preceding the moratorium
cod landings averaged about 290,000 tonnes. During the period 1989 to 1992 the catch was
158,000 tonnes y-1. From 1993 to 2002 the landings were back up to 300,000 tonnes y-1.
The lesson to be learned from these examples is that adjusting the fishing effort from year
to year to take account of fluctuations in biological productivity is not a simple matter. There are
very significant social and political constraints to this sort of management. A more enlightened
as well as socially and politically feasible approach may be to target a catch perhaps half the
nominal maximum sustainable yield with the expectation that such a catch may well be
sustainable year after year.
How Many Fish Should We Catch?
In Chapter 1 we concluded that the maximum sustainable yield is about 25% of the rate
of gross production of the virgin fish stock. In Chapter 4 we have now seen several reasons why
24
the maximum sustainable yield is probably not a realistic goal for many fisheries. The maximum
sustainable yield is associated with an unstable equilibrium in the population dynamics of the
fish. Since many commercially important species of fish lie toward the r-selected end of the r/K
continuum, from a stability standpoint it would seem reasonable to target a sustainable catch
substantially less than the nominal maximum sustainable yield. Furthermore, from an economic
standpoint there is no reason to target the maximum sustainable yield as a goal of fisheries
management, even if the stock in question is K-selected. Given these considerations, it should
not be surprising to discover that global capture production of finfish has leveled out at about
12% of our estimate of gross production (Chapter 1). Unfortunately we have sometimes had to
learn the hard way that it makes no sense to try to push the catch much beyond this limit (e.g.,
Fig. 4.7). Remember, however, that we are talking about the sustainable catch. If we do not care
whether there are any fish left next year or ten years from now, we could take a different attitude
toward fisheries management. Failure to consider other than short-term goals has sometimes led
to some very unfortunate decisions in fisheries management. As noted by Kurlansky (1997, p.
204), “One of the greatest obstacles to restoring cod stocks off of Newfoundland is an almost
pathological collective denial of what has happened.”
25
References
Beverton, R. J. H., Holt, S. J., 1957. On the dynamics of exploited fish populations. H.M.
Stationery office, London.
Cushing, D. H., 1982. Climate and Fisheries. Academic Press, London.
Kurlansky, M., 1997. Cod: A Biography of the Fish That Changed the World. Walker and
Company, New York.
MacArthur, R. H., Wilson, E. O., 1967. The Theory of Island Biogeography. Princeton
University Press, Princeton.
McHugh, J. L., 1974. The role and history of the international whaling commission. In: Schevill,
W. E. (Ed.), The Whale Problem (pp. 305-335), Harvard University Press, Cambridge.
Schaefer, M. B., 1954. Some aspects of the dynamics of populations important to the
management of the commercial fisheries. Inter-American Tropical Tuna Commission Bulletin 1,
25-56.
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