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Table of Contents
A Basis for Understanding Fishery Management Complexities
Richard G. Dudley °
May 2003
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A Basis for Understanding Fishery Management Complexities !
° Richard G. Dudley
Feb 2003
Abstract
Many fisheries in developed countries are seriously over-harvested in
spite of the efforts of dedicated scientists and management agencies
and a concerned public. Many of these fisheries are well studied —
lack of data is not the primary problem. Complexity with the fisheries
and management systems conspires to defeat seemingly obvious
solutions.
System dynamics modeling may help provide solutions via its
transparent framework for describing and analyzing the complex
decision making systems. In fisheries, such system descriptions often
become enmeshed in the many aspects of fish population dynamics and
fail to adequately describe decision making activities of fishers,
management agencies, and politicians. This paper is an attempt at
providing a simple, but acceptably complex, population model meshed
with both fishery activities and management decision making.
The model is based on the well-known Schaefer biomass dynamic
model but allows for delayed entry of young into the fish stock and for
biomass feedback to rates of addition to the stock due both to growth
and entry of young fish. _ Fishers enter the fishery only if catch rates
are sufficiently high. When catch rates are low remaining fishers
attempt to improve their fishing efficiency. Excessive fishing also can
damage the ecosystem’s ability to support the fish population.
Managers attempt to maintain the fish stock at acceptable biomass
levels, but their efforts are influenced both by lobbying by fishers and
by politicians’ varying support for management.
1. Introduction
Poor resource management is not only a problem of the developing world. Many
marine fisheries in developed countries are seriously over-harvested. Canadian cod
fisheries have not recovered after a completely unexpected collapse (Roy 1996).
Closures in the North Sea have also been implemented (Malakoff and Stone 2002). In
2001, the US government determined that 33% of its commercial fish stocks of
known status were over-fished (National Marine Fisheries Service 2002). Over 80
marine fish species or stocks are vulnerable, threatened, or endangered with extinction
from North American waters (Musick et a/ 2000).
' Prepared for presentation at The 21st International Conference of the System Dynamics Society, July
20 - 24, 2003, New York City.
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
These countries have some of the world’s most sophisticated scientific communities
dedicated to good fisheries management. Members of this community, most members
of the fishing industry, as well as political and governmental entities involved in
fishery decision making, all strive to make good decisions. Yet these decisions have
largely failed to prevent over-fishing. Why?
Is scientific information lacking? Although good data is essential, it is unlikely that
even more data will lead to significantly better decisions. In fact, some of the best
biological and fishery statistical information is associated with those fish stocks (e.g.,
cod) having the most difficulty. In any case, we can’t expect to have perfect
knowledge for all fish stocks on a timely basis. In the USA, sufficient data exist to
determine abundance in only about one third of the 959 identified commercial fish
stocks. In fact, data regarding abundance or fishery status are available for only 40%
of “major stocks” (National Marine Fisheries Service 2002).
A number of authors have examined the causes of fishery management failures.
Some of these have focused on our lack of sufficient knowledge of biological and
climatic mechanisms affecting fish stocks. Others have examined specific failures in
decision making mechanisms, such as the failure to implement needed restrictions on
fishing in a timely manner due to social or economic pressures. A few researchers
have attempted to examine how the complex mixture of biological, social, economic,
and environmental information affect fishery management decision-making processes.
The fishery decision-making system is highly complex including elements of
biological, economic, social, ecological and physical spheres. Elements of each
sphere affect elements of the others causing numerous feedbacks. These feedback
loops remain largely unexamined during the decision making process. Of necessity
the decision process focuses on expected benefits via specific decision pathways.
Inevitably unintended consequences arise from these decisions. As catch rates
decline, for example, the rate of violation of regulations may increase as fishers try to
maximize their ability to pay off debts in a declining industry. Such violations create
unreported catches further decreasing the reliability of fishery data which are the basis
for decisions. Declining catches, and certain fishery restrictions, stimulate more
effective fishing strategies. Such feedbacks conspire to defeat the good intentions of
decision makers.
One overriding influence derives from the lag times needed for economic and
ecological systems to come into equilibrium, if such equilibrium actually exists.
Fishery overcapacity develops before over-fishing becomes apparent. Excessive
fishing capacity is then supported by economic and associated socio-political
concerns. Actions to lower capacity become problematic. If the fishery rebounds
additional overcapacity develops (Hennessey and Healey 2000; Ludwig et al 1993).
Some suggest that the very complexity of the system contributes to its failure. For
example, efforts to make fishery regulations more equitable increases the number of
special regulations for particular user groups, which makes enforcement more
complex and difficult, and further increases non-compliance. As the system becomes
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
more complex uncertainties increase, making desirable outcomes less likely (Healey
and Hennessey 1998).
An increasingly complex decision making environment also increases the likelihood
of litigation. This causes, at best, significant time lags in imposition of regulations. At
worst proposed regulations are reversed causing additional confusion for regulators
and fishers. In the USA in the 1970s and 1980s only one or two court challenges
were made to NMFS rulings annually, but in the late 90s this rose to more than 10
per year reaching over 20 in 2001 (Gade et al 2002).
Uncertainty in fishery data and climatic variables affecting fish stocks is a source of
additional complications for decision makers dealing with fishery systems. While use
of Baysian statistics has improved our ability to understand probable outcomes of
management decisions, the incorporation of uncertainty into the management regime
is still problematic (Charles 1998; Cochrane 1999; Lane and Stephenson 1998).
Lauck (1996) investigated the use of hedging in fishery management, but the
increasing complexity of fishery management systems conspires to limit such options
to address uncertainty. The multiplicity of regulations under complex management
regimes can limit fishers’ options to counteract uncertainty (Hilborn ef a/ 2001). As
uncertainty increases, sustainable management requires significantly lowered
allowable catches (Walters and Pearse 1996), but these may be politically difficult to
implement.
As Gade et al. (2002: xi) state, discussing problems in the USA, “In a real sense, the
fisheries management system is in disarray. Management is increasingly exercised by
the courts through litigation, by Congress through its annual appropriations and
reports, and by constituencies that seek redress through these forums.”
The need to examine fishery systems holistically has been pointed out by several
authors. Walters (1980) highlighted the importance of viewing fisheries as dynamic
systems with interacting biological, political, social and economic components.
Anderson, in his discussion of “bioregunomics”, specifically included lobbying of
fisheries agencies by industry to influence policy, as well as the function of courts as
arbiters, as part of a needed new paradigm for fishery management (Anderson 1984,
1987). Recently Charles structured a book around the concept of fishery systems,
and included in that concept management decisions and the response of fishers to
them (Charles 2001).
It is important to point out that complexity in fishery management exists not only in
its detail, but in its dynamics. Dynamic complexity arises for many reasons
associated with the causal links between components of the system (e.g., see Sterman
2000: 21-22). It is not just that the system is composed of many components, but that
a change in any one component will cause a cycling reaction in the others.
At present fishery management entities are becoming more aware of problems of
complexity in the decision making system and decision makers are extending their
analyses beyond bio-economic issues. There is an opportunity to modify management
approaches to address issues created by the complexity and uncertainty inherent in the
fishery management system. To do this several questions must be answered: How can
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
fishery decision making systems best be analyzed? How can these analyses
sufficiently account for complexity and uncertainty, and still provide meaningful,
sufficiently detailed decision and policy direction? How can the complex
consequences of management decisions be better predicted by inclusion of factors
beyond the realm of fish population biology?
2 The Model ?
There is a need for models that allow us to examine complex fishery issues in a
transparent and understandable manner without becoming overly involved in details
of population dynamics. For this purpose it is also good to have a standardized
starting point for the biological aspects of the model. The Schaefer biomass dynamic
model and its modifications, are well known in fisheries, and are relatively easy to
understand, especially when put into a system dynamics (SD) format. A series of
modifications to the basic model can allow us to examine the effect of various fishery
management policies within a complex framework. Herein I do not wish to focus on
details of fishery biology but rather attempt to provide a starting point for examining
complex interactions between social, political, economic and environmental issues.
System dynamics modeling supplies the needed framework for doing this.
The overall purpose here is to examine the use of the biomass dynamic model as a
basis for modeling the bigger picture of socio-politico-economic interactions.
However, to accomplish this goal, we will first consider some useful modifications to
the original model formulation.
2.1 The basic model
The typical formulation of the Schaefer model (Schaefer M. B. . 1954; 1957) equates
the rate of change of population biomass to inflows of biomass minus biomass
outflows. It is typically presented as follows:
2B _ ye -2)\_ que
dt k
From a system dynamics perspective it is best to write it as:
(8 pp? gee
dt k
Here the rate of change of fish biomass over time is seen to be composed of an inflow,
and two outflows. Increase in population biomass, is a single inflow due both to
growth and to the addition of new fish. It is equal to the biomass fractional growth
rate r times the existing biomass B. Natural decrease in biomass is indicated by —rB
? This section builds on information presented in Dudley, R. G. and Chris S. Soderquist. 1999. A
Simple Example of How System Dynamics Modeling Can Clarify, and Improve Discussion and
Modification, of Model Structure. Presentation to the 129th Annual Meeting of the American Fisheries
Society, Charlotte, North Carolina. August 1999.
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
multiplied by the ratio of B to k, where k is the maximum possible population size.
This causes natural death rate to decline as biomass declines.* The outflow of
population biomass caused by the catch is indicated by the instantaneous fraction of
fish biomass caught by each unit of fishing gear g, times the number of gear units* E,
times the biomass B.
In system dynamics format the model is as illustrated i It is interesting here to
point out the difference in philosophies between the original formulation and the
system dynamics approach. System dynamics modeling emphasizes changes over
time. Also, the system dynamics modeler generally tries to formulate each
component of a model separately, then defines the structure linking components.
Mathematical modelers, on the other hand strive to develop one summary "elegant"
equation that will calculate an answer for a particular set of inputs. Other forms of
modeling are, perhaps, somewhere in between. Presented as a system dynamics
stock and flow diagram the structure of the biomass dynamic model is clear. The
mathematical formulation of each component is also explicitly stated.”
The biomass dynamic model was originally developed to calculate equilibrium yields
under given conditions.° System dynamics models, on the other hand, typically are
used to gain an understanding of system behavior over time. Typical outputs from the
model for a selection of fishing ures illustrate the traditional parabolic curve of
equilibrium catch vs. biomass @ ig. 2).
Importantly, because calculations are carried out numerically, modification to the
system dynamics version of the model is not limited by analytical tractability. The
model structure can be modified to examine increasingly dynamic and complex
situations. Note that there have also been various non-SD approaches to modifying
the model (e.g., see Prager 1994).
2.2 Adjusting the basic model
2.2.1 Providing for recruitment delays
The strength of the biomass dynamic model is its simplicity. It avoids the use of
detailed age structure which in many instances is not needed. However, the standard
model treats additions of biomass to the stock as a single flow with no provision for
separate consideration of increase in stock biomass due to growth and increase due to
recruitment (i.e., addition of new fish to the stock). We may wish to include the
effect of delays in recruitment because young fish often become a part of the fishable
stock only after several years (e.g., at age 4). This delay is particularly important in
the fairly typical situation where large inter-annual variations in recruitment occur,
* Excluding catch, this form of the model is mathematically identical to the classic logistic model of
Verhulst (1838). However, that model considers net growth in numbers (rather than biomass) and
does not explicitly partition growth and mortality. One could argue, for example that losses represent
not only deaths, but lost (potential) growth as well.
* Note that units of fishing gear can be variously defined as boats, nets, hooks, traps, etc.
5 See appendix for model equations.
° An important aspect of the biomass dynamic model is that data needed to determine its parameters are
relatively easy to obtain. Necessary data can be obtained from a fishery, without the need for
determining abundance of fish of different ages.
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
and in heavily fished stocks where “recruits” account for a significant proportion of
the total fish biomass.
Delays in the recruitment of new biomass to a population can be incorporated into the
model without resorting to an age based approach (F Here recruitment is
envisioned as the biomass of fish newly entering the fishery. In this formulation we
largely ignore what actually happens to young fish prior to their entering the fishable
stock, except that large variations in recruitment can occur. That is, the size of the
stock delayed recruitment indicates recruitment expected at a future time. Although
alternate formulations might attempt to accurately model the biomass of young fish as
a fully connected part of the model, additional detail would be needed to account for
rapidly changing growth and mortality rates during early life. Nevertheless, a true
two stock model may be appropriate in some cases.
See comments below about the shape of the relationship between the stock biomass
and amount of recruitment.
2.2.2 Partitioning delayed and non-delayed additions to biomass
components
If we wish to account for delayed recruitment additions to a stock, we should also
account for non-delayed stock increases due to growth of biomass already present.
This can be accomplished by having additions to the stock composed of two
components and by having the fractional growth rate r partitioned into a growth and a
recruitment component (Fi
A question then remains: how much of the addition to a stock is due to recruitment,
and how much is due to growth of biomass already present. This is an important issue
because dynamics of some stocks are dominated by large fluctuations in year-class
size. For the time being we will leave this question unanswered and will assume that
the proportion of additions to biomass due to recruitment is in the range of 30 to 70
percent, with the higher proportions more typical of short-lived fishes. Ata later
point in model development we may wish to examine feedback factors which affect
this proportion. Two components likely to have a feedback effect on this relative
proportion are the fractional rate of increase itself and fishing intensity.
2.2.3 Biomass feedback to additions to biomass
The standard model responds to any decrease in relative biomass, including decreases
due to fishing, by lowering the fractional rate of natural decrease in biomass and thus
the death rate. We must consider, however, that any decrease in stock biomass below
the “virgin” stock size might also cause an increase in growth and reproductive
success — on the additions side of the model. We would expect this because
decreases in population density should improve conditions for growth and
reproduction for remaining fish.
Also, from experience in the real world we know that mean age of biomass in a stock
will decreases with increasing fishing pressure.’ However decreases in stock size in
7 Typically this evidence is manifested as a decrease in average age of individuals in the fish stock. In
fact, the mortality rate is often determined by the slope of a graph of numbers vs age. If the mortality
rate rises the relative abundance of older fishes decreases.
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
the standard biomass dynamic model do not alter mean retention time in the stock.
We know this because, in equilibrium the inflow to the stock must equal the sum of
the outflows. In equilibrium both fractional rate of additions and total death fraction
(death fraction plus catch fraction) are equal to r. Thus at equilibrium mean residence
time in the stock will always equal 1/r which is constant.
A modification to the model which adjusts the growth rate, r, upward as biomass in
the stock decreases seems appropriate. The forms which this feedback might take are
several, but we expect that r will increase somewhat as the stock is diminished and
will decrease somewhat as relative stock size increases. This will also cause average
age of biomass in the stock to drop as we would expect.
One convenient formulation is to allow effect of biomass ratio on r to be 1.0 (r keeps
its original, typical, value) when B/k is 0.5, to have this effect increase linearly by
some small amount (perhaps 10% to 30%) as B/k approaches zero, and to decrease by
a similar amount as B/k approaches 1.0 (Fig. 5). With this formulation, as the stock
biomass decreases effective growth rate will increase, and mean age of biomass in the
stock will decrease. The strength of this effect will undoubtedly vary among
populations.
Combining this feedback from the stock biomass ratio with the partitioning of growth
and reproductive additions to the stock gives us the final formulation for the fish stock
aspects of the model ¢f 6}. Note that in keeping with the concept of the original
model, that the unmodified death rate should equal the growth rate, the basic
fractional death rate should now equal the average growth rate which is a weighted
average of the modified rates for growth additions and recruitment additions.
2.2.4 The effect of stock size on recruitment additions
If we opt to allow separate growth and recruitment additions to biomass as indicated
above, then we need to be concerned with the shape of each of these relationships. In
the standard model additions to biomass is a fixed fraction of current biomass.
However, the relationship of stock size to amount of recruitment has been intensively
studied, and a direct proportional relationship of biomass to recruitment amount is
clearly not realistic. In general a curved relationship with either stable or decreasing
recruitment at high stock biomass levels is typical. It would be reasonable for a
graph of recruitment amount vs. biomass to look like lines B or C in} h
2.2.5 The completed fish stock portion of the model
At this point the model, still without fishery or management components, allows for
both: 1) the partitioning of growth additions and delayed recruitment additions to the
stock and 2) feedback from current biomass ratio to stock additions.
2.3 Adding fishery components
Prior to any attempts at modeling management decisions, development of a model of
an unmanaged fishery seems appropriate. This model, in addition to the simple stock
dynamics shown above, allows for: 1) the entry and exit of vessels from the fishery in
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
response to fishing success, 2) the accelerated improvement of fishing gear when
catch rates drop, and 3) the possibility of fishery damage to the underlying ability of
the ecosystem to support the fish population.
2.3.1 Catch per unit effort determines vessel numbers
Typically vessels® enter a fishery because profits appear attractive. Normally profits
are linked to some acceptable level of catch per unit of fishing effort (referred to as
cpue) which provides sufficient monetary return over and above total costs of fishing
operations. We can assume for our purposes here that some acceptable cpue is the
minimum level of catch that attracts vessels to the fishery. If the actual cpue falls
below this fewer new vessels will be attracted and there will be a net loss of vessels
from the fishery. As cpue rises above this critical level more vessels will be attracted
to the fishery. If cpue falls well below the acceptable level, vessels’ retirement from
the fishery will also be accelerated F
The acceptable cpue level implicitly neOrPOTARES factors related to profitability of
fishing such as cost of operations and investment, and the expected price of the fish
caught. Another model sector could later be added to explicitly examine how these
factors affect acceptable cpue.
The question of capacity utilization is only partially dealt with here. For the most part
the model assumes that vessels are all used at 100 percent capacity if they are
participating in the fishery. However, a test sub-section of the model examines the
effect of recent cpue on capacity utilization. Recent cpue levels (say over a few
weeks) will influence whether a fisher (who is still participating in the fishery) will
put in more or less effort. However, the nature of this relationship is unclear. If cpue
levels are high, additional effort will be made to catch fish while the fish are
abundant. On the other hand if cpue drops somewhat below acceptable levels then
additional efforts might also be made in an attempt to maintain cpue at the acceptable
level. Nevertheless, if cpue drops well below acceptable levels then fishers will
lower the use of their fishing capacity.
2.3.2 Vessels maintain catch rates by increasing efficiency
When catch per unit effort drops below acceptable levels fishers who remain in the
fishery will respond by attempting to improve the efficiency of their fishing gear.
These improvements may be in the form of better application of known technology
(e.g. using their sonar more effectively) or applying recently developed techniques
(e.g. adjusting fishing gear design). We can assume that at any given time some small
amount of improvement, maybe 5% to 20%, to existing gear efficiency is possible.
Importantly, these improvements gradually become absorbed into standard fishing
practice and therefore will permanently increase gear efficiency slightly. Over time
these small changes in gear efficiency will accumulate i
*T have used “fishing vessels” as the unit of fishing gear. However, units of fishing gear could be
defined as number of nets, traps, hooks, etc. Here I use the term ‘vessels’ in this general sense.
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
2.3.3 Fishing decreases carrying capacity
In some fisheries, fishing activity can decrease ecosystem carrying capacity. The
most widely cited example of this phenomenon is the damage which trawling gear
inflicts on the bottom habitat of groundfish. ‘
Presumably damage to carrying capacity is cumulative and is proportional to the
amount of fishing taking place. This idea is incorporated into the model. Here each
effective fishing unit inflicts a small amount of damage on the habitat. This damage in
turn affects the maximum possible biomass which the habitat can support. It can also
be assumed that there is a habitat recovery time of several years, perhaps tens of
years in the case of serious physical damage. Further, we can assume that the rate of
recovery will be slower if habitat damage is extensive Fi
2.4 Adding management strategies
2.4.1 Management attempts to maintain optimum biomass by
adjusting fishing gear numbers
In this paper I have opted to take a fairly simplistic approach to management of the
fishery in which a management entity strives to maintain the fish stock at a fixed
fraction of its un-fished biomass. One typical target value for management would be
at one half the assumed vi i.e. unfished) stock.!° In the model this idea is
captured as indicated ini
Management formulates a revised perception of stock health based on recent stock
assessment information. If the stock estimates are near the desired level the new
perception is neutral: the stock is in reasonable health. If new data indicates that the
stock size is greatly different from the desired size then the new perception of stock
status is revised upward or downward accordingly d g 12). Based on this new
information management’s perception of the fishery is gradually changed.
Management’s perception of the fishery then determines the desired changes in
fishing gear numbers. If the perception of the stock is negative a fractional decrease
in gear numbers will be proposed. If perception of the stock is positive the suggested
fractional change will be positive. These fractional changes become greater the
further management’s perception is from neutral (see: A change in fishing
gear numbers is then proposed to be implemented over some implementation time,
and if management proposals have the force of law, the proposed changes in fishing
gear numbers are fully implemented.
2.4.2 Fishery Conflicts and Political Lobbying
Typically fishery management entities cannot merely dictate changes in fishing effort.
Many social, economic, legal and consequent political issues come into play. Fishers
lobby for more liberal regulations. Environmental groups lobby for more restrictive
° For some interesting examples see the special section in Conservation Biology, Vol. 12, No. 6. Dec.,
1998: Effects of Mobile Fishing Gear on Marine Benthos.
'° Tn theory this is the point where the sustained biomass of the catch is maximum, See the figure
earlier in this paper. However, if there is feedback from biomass ratio to the growth rate as described
in the text, then the stock level where the catch is maximum will be somewhat below 50,000 t.
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
regulations. Both groups may seek political backing for their particular view. If this is
unsuccessful then either group may seek redress in the courts.
In this paper I look only at a simplified version of the first of these scenarios where
fishers and managers will both work to have their own desired adjustment to fishing
gear numbers implemented. In the model this aspect of the fishery is handled in two
ways. Firstly a negotiated vessel entry rate is calculated as a weighted average of the
two desired rates. The weighting is based on the relative strength of management’s
views. Secondly, there is an option of allowing an increasing level of lobbying as
management’s and fisher’s views diverge (Fig. 1+ If the view of the two parties
diverges considerably then, in the model, lobbying can reduce management’s current
effectiveness by up to 50 percent.
The relative strength of management’s views may also be influenced by politics. As
the fishery becomes obviously over-fished in the eyes of politicians, the management
agency will be given strengthened authority. In the model the politicians’ views are
represented by an indicator of the need for stronger management: the relative size of
current fish catches compared to fish catches in the past. Low recent catches
compared to the longer term “historical” catches will result in more influence for the
management entity and its views.
Overall this model, in a general sense, embodies a concept of fishery management
whereby managers view success in terms of stock level, fishers view success in terms
of catch per unit of gear, and politicians view success in terms of catches which
should be at least as good as they were in the past.
3 Model Outcomes
Here we will use the example of a typical fishery for a moderately slow growing
mS a 1
3.1 A fishery with no management
When vessels first enter a new fishery, catch per unit effort is well above the level
necessary to attract additional participants to the fishery. As more fishers enter the
fishery, fish stock biomass starts to drop as does catch per unit effort. Even though
both stock biomass and cpue are dropping, catches continue to rise due to the
continuing influx of new participants to the fishery. Catch per unit effort eventually
drops to unacceptable levels in about year 12 and, with a slight delay, vessel numbers
in the fishery also start to drop. By this time the fish stock is already seriously over-
fished as too many vessels had entered the fishery. Even though participants now
Once cpue rises high enough to attract more fishers the cycle starts again. Because of
the decreased fishing, fish stocks have already started to recover by year 21, and by
year 33 participants are returning to the fishery in increasing numbers. However,
stock biomass never gets the chance to recover to its former size. This is because
" For default settings of these and other model constants see model equations.
10
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
new participants are joining the fishery well before the stock has a chance to recover.
Also fishers have increased their gear efficiency during the period when cpue was
low. The third and subsequent cycles are progressively less productive. Note that
model outcomes are highly dependent on a number of input parameters, some of
which are discussed below.
If we start with an over-fished stock (rather than the virgin stock as above) the results
are similar to the second and subsequent cycles above.
3.2 Managing the fishery
Management in the model, as described above, consists of monitoring the fish stock
and making fractional changes to fishing gear numbers entering the fishery if stock
id 13). ‘Perfect’
feedback effects from fishers’ lobbying or from politicians’ concerned about
maintaining catches. This simple form of management will gradually increase fishing
until stock size drops to the optimal level ( ._ 16}. Ifstarting from an over-fished
state, perfect management overprotects the stock for a fairly long period before it
If, realistically, various forms of lobbying take place, then the situation is different.
Both forms of feedback induce oscillations similar to those in the unmanaged
situation even when the base level of management is 100% effective ¢F }. Here
we see that all these scenarios manage better than the unmanaged situation, with
smaller oscillations having longer periods.
A typical and more realistic situation will have management authority less than
perfect, perhaps at 70%, for example. That is, usually management can be expected
to be successful in implementing 70% of its suggested change to gear numbers. Also
typically, this weakened authority also will be affected by lobbying by fishers and by
varying support from politicians (as described above).
Under this ‘typical’ scenario (Fig 19) the fishery will have substantial fluctuations,
although these are not as sever yhen there is no management. In this example the
mean of the fluctuating fish stock is at a point slightly less than one half of
management’s target stock biomass of 50,000 t.
This example serves to illustrate that using reasonable assumptions it is fairly easy to
recreate a fishery situation that is all too familiar to managers and users of such
resources. Mangers and fishers and politicians all follow “rules of thumb” that seem
reasonable to them but which result in an outcome disliked by all. The question still
remains: how can we improve these systems? That is the subject for much additional
study.
' By perfect here on only mean fully implemented as modeled with management effectiveness at
100%. There are many other possible management scenarios with none actually perfect.
11
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
4 Other Comments
4.1 Random variations in recruitment and its effect on
decision making
Large variations in recruitment to a fishery are very common, and if incoming fish are
a large component of the fish stock, these fluctuations can cause a fairly rapid and
significant change in stock abundance which may last several years. This in turn can
have large effects on catches, cpue and the entry of new fishers. Here a random
uniform pink noise (Sterman 2000) with a mean of zero and standard deviation of | is
added to the recruitment expected at each time step. When starting with a virgin stock
or an over-fished stock this random variation will change the specifics of each model
tun, but will not change the basic patterns created by typical management (e.g.
However, if a fishery is in rough equilibrium, under careful ‘typical’ management,
large variations in recruitment can stimulate a fishery boom or bust and can lead to
4.2 Effects of various parameters
In the above generic examples I have selected parameters which lead to a situation I
believe is typical of many fisheries. Other selections will produce vastly different
outcomes. A brief examination of these differences provides some insight into causes
for different states in a fishery, but a detailed discussion of each of these parameters is
not within the scope of this paper.
Populations with a higher basic growth R rate can sustain heavier fishing pressure.
The stock modeled has a growth rate of 0.2. Faster growing populations (e.g. tuna)
have an R near 0.5, for example, while large sharks and pacific rockfish have R nearer
to 0.1.
The overall catch fraction at any given time is the product of the gear efficiency and
the number of gear units operating. Higher gear efficiency will result in more rapid
over-fishing. Thus the acceptable cpue at which vessels will enter a fishery is also an
important consideration. If this acceptable cpue is low new fishers will continue to
enter the fishery long after the stock has fallen below the optimum biomass. This is
typical of fisheries where fish are of relatively high value (e.g. bluefin tuna) or where
operating costs are relatively low. If acceptable cpue is high then little management is
needed unless excess vessels are forced into the system.
4.3 Other forms of management to be tested
In the above model, decisions of managers have been based only on fish stock size
and its comparison to the standard model’s optimum value of half the virgin stock
size. But actually even this simple implementation of management’s view
incorporates a ‘flaw’ in management’s thinking. As modeled, the current stock size is
compared to the virgin stock size in an un-fished state. As fishing takes place the
actual capacity of the ecosystem decreases so management’s ‘concept’ of 50% of
virgin stock is incorrect. When fished the assumed 50% value is actually above 50%
of current maximum capacity. Interestingly, this ‘confusion’ leads to more
conservative decision making by management. If management somehow received a
12
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
regular update on current maximum stock capacity (e.g. area and quality of suitable
habitat) then more rapid over-fishing might occur because management would
regularly downgrade their estimate of maximum capacity.
There are many other reasonable formulations for management decision making.
Here I have even ignored, for example, the direction of change in the fish stock.
Management would normally make different decisions at a given stock ratio if the
stock were increasing or decreasing.
Also, the management system modeled here relies on management’s knowledge of
recent stock size. A more sophisticated decision making model should incorporate
recommend appropriate fishing levels based on predicted stock sizes and on
inaccuracies in those predictions. In this case one would model the stock assessment
process itself. In fact, this would be one important component of a final version of
the overall modeling venture of examining fishery decision making.
5 Literature Cited
Anderson LG. 1984. Uncertainty in the fishery management process. Marine
Resource Economics 1(1): 77-87.
ooo. . 1987. Expansion of the fisheries management paradigm to include institutional
structure and function. Transactions of the American Fisheries Society 116:
396-404.
Charles AT. 1998. Living with uncertainty in fisheries: analytical methods,
management priorities and the Canadian groundfishery experience. Fisheries
Research 37: 37-50.
. 2001. Sustainable fishery systems. Blackwell Science: Oxford (UK). 370 pp.
Cochrane KL. 1999. Complexity in fisheries and limitations in the increasing
complexity of fisheries management. JCES Journal of Marine Science 56:
917-926.
Gade MA, Garcia TD, Howes JB, Schad TM, Shipman S. 2002. Courts, Congress,
and constituencies: managing fisheries by default, National Academy of
Public Administration
Healey MC, Hennessey T. 1998. The paradox of fairness: the impact of escalating
complexity on fishery management. Marine Policy 22(2): 109-118.
Hennessey T, Healey M. 2000. Ludwig's ratchet and the collapse of New England
groundfish stocks. Coastal Management 28(3): 187-213.
Hilborn R, Maguire JJ, Parma AM, Rosenberg AA. 2001. The precautionary approach
and risk management: can they increase the probability of successes in fishery
management? Canadian Journal of Fisheries and Aquatic Sciences 58(1): 99-
107.
Lane DE, Stephenson RL. 1998. A framework for risk analysis in fisheries decision-
making. ICES Journal of Marine Science 55(1): 1-13.
Ludwig D, Hilborn R, Waters C. 1993. Uncertainty, resource exploitation, and
conservation: lessons from history. Science 260(5104): 36-37.
13
DUDLEY — FISHERY MANAGEMENT COMPLEXITIES
Malakoff D, Stone R. 2002. Fisheries Science: Scientists Recommend Ban on North
Sea Cod. Science 298(5595): 939a-.
Musick JA, Harbin MM, Berkeley SA, Burgess GH, Eklund AM, et al. 2000. Marine,
estuarine, and diadromous fish stocks at risk of extinction in North America
(exclusive of pacific salmonids). Fisheries 25(11): 6-30.
National Marine Fisheries Service. 2002. Annual report to Congress on the status of
US. fisheries 2001, National Marine Fisheries Service, U.S. Dep. Commerce,
NOAA, Natl. Mar. Fish. Serv., Silver Spring, MD
Prager MH. 1994. A suite of extensions to a nonequilibrium surplus-production
model. Fishery Bulletin 92: 374-389.
Roy N. 1996. What went wrong and what can we learn from it? In Fisheries and
uncertainty a precautionary approach to resource management. Gordon DV,
Munro GR (eds). University of Calgary Press: Calgary. 15- 25.
Schaefer MB. 1954. Some aspects of the dynamics of populations important to the
management of commercial marine fisheries. Inter-American Tropical Tuna
Commission Bulletin 1: 27-56.
sence. . 1957. A study of the dynamics of the fishery for yellowfin tuna in the eastern
tropical Pacific Ocean. Inter-American Tropical Tuna Commission Bulletin 2:
245-285.
Sterman JD. 2000. Business dynamics: systems thinking and modeling for a complex
world. Irwin/McGraw-Hill: Boston. 982 pp.
Walters CJ. 1980. Systems principles in fisheries management. In Fisheries
management. Lackey RT, Nielsen RA (eds). Wiley: New York. 167-183.
Walters CJ, Pearse PH. 1996. Stock information requirements for quota management
systems in commercial fisheries. Reviews in Fish Biology and Fisheries 6: 21-
42.
14
Figures for “A Basis for Understanding Fishery Management
Complexities”
Richard G. Dudley
Bae cra
EFFICIENCY Q
catch fraction
INITIAL,
BIOMASS
RATE OF INCREASE R
ratio of current focal death
biomass to fraction
unfished biomass’
BIOMASS OF
UNFISHED <RATE OF INCREASE R>
STOCK K
Figure 1. The standard biomass dynamic model of Schaefer
presented in system dynamics format. Modifications to this model
can form a relatively simple basis for investigating complexities
facing fishery management decision making. Letters at the end of
each component name refer to the equation presented in the text.
15
Effect of Number of Fishing Units on Catch Over
Catch
Figure 2. Time lines of catch at different fixed levels of fishing illustrate the
shape of the relationship between units of fishing gear and eventual
equilibrium catch as produced by the standard model. This curve, shown here
at year 100, has the maximum equilibrium catch at an intermediate level of
effort which also reduces stock size to one half its un-fished size. The time
needed to reach these equilibrium yields can be considerable.
ANTAL
BIOMASS
additions
YEARS PRIOR TO
ENTERING FISH
STOCK
ratio of current normal death,
biomass to unfished fraction
biomass
recnuit
stlis \
\ Yonass oF
Figure 3. This re-formulation will allow for delayed recruitment (addition of
new biomass from reproduction), but ignores additions due to growth.
16
INITIAL,
S z
additions
4
modified +
recruitment
growth
~ gp additions
FRACTION oF
= ADDITIONS FROM
RECRUITMENT
normal death
ec ratio of current fraction
biomass to unfished “
C biomass
a recruit
additions
attr ;
INCREASE R BIOMASS oF
UNFISHED STOCK
YEARS PRIOR TO
ENTERING FISH
STOCK
Figure 4, Partitioning of the rate of increase allows for both growth additions and delayed
recruitment additions but still maintains the basic logic of the standard model.
Example Feedback from Biomass Ratio to Effect on Rates
Or
1 0.0 |
no effect _,
Effect on Growth or Recruitment Rate
0 05 1
Biomass Ratio
Figure 5. In the standard model biomass ratio has no effect on the growth rate. In the
revised model a feedback effect from biomass ratio to growth is proposed. Shown here is a
suggested format for such feedback. Each line represents a particular feedback effect, with a
feedback effect of zero representing no feedback.
17
catch
additions
ef +
growth + «|
modified additions
FRACTION OF é ?
recruitment 3pitions wom —— somata
RECRUITMENT fraction
a. ratio of current
biomass to unfished
" recruit ‘bigs
additions modified rite of g ”
Saass oF
YEARS PRIOR + ifoct of biomass on ee
TOENTERING grate of increase
isi stock oe
INCREASE R ene
' growth rate
modified rte of
modified rate of FEEDBACK EFFECT rec incre:
oe iciaae ON GROWTH R Se ianene
effect of biomass on
recruit rate of ine
FEEDBACK EFFECT
(ON RECRUIT R
Figure 6. Fully modified biomass dynamic model which allows for partitioned additions due
to growth and recruitment and also allows the growth rate of each component to have a
feedback effect from population density.
Result of Feedback to Fractional Rates of Growth or Recruitment
20,000
18,000 + —
16,000
‘standard model
44000 | | 1 BfeedbacktoR=02 | __
= Aq -B feedback to R= 0.3
12,000 ++ —o—BfeedbacktoR=0.5 f--
biomass additions
3
0 20000 40000 60000 80000 100000 120000
Stock Biomass
Figure 7. Results of the feedback to fractional rates of growth or recruitment illustrated in terms
of biomass additions at given stock biomass levels. Maximum stock biomass is 100,000 tons.
Line A might be typical of growth additions to the stock while lines B or C might be more typical
of recruitment additions to a stock.
18
eS eescrsrion
= SMOOTH TIME normally retiring
n from fleet
negotiated vessel
entry rate
RELATIONSHIP OF CPUE,
>
ime) \
actually retirin; |
from fleet . |
+e
effect of cpue
management sub-section
industry's desired
replacement rate
entering fleet
smooth of epue c=. on retirement
a ishing units
7
cPUE cpue
siroeoreim, SMoorTH peri
RATIO TOMS EFFECT ON TIME N ,
VESSELENTRY catch fraction
ACCEPTABLE effect on
cPUE ecosystem 4
sub-section
catch ¢
additions
4 deaths
‘modified gear
efficiency
‘gear improvement sub-section
Figure 8. More vessels tend to enter a fishery when catch per unit effort (cpue) is high. A low cpue will both
discourage vessels from entering, and will encourage remaining fishers to improve gear efficiency. Also
indicated here are links to: 1) management and 2) effects of fishing which degrade the environment’s capacity
to support fish stocks. For simplicity some model components are not shown.
19
aa effect of epue on
AVERAGING improvements
TIME
implemented
improvements
4
10 stock bioma: possible
improvement
modified gear
efficiency
+
new maximum
possible gear
efficiency
recent changes
TIME FOR CHANGES
‘TO BECOME TYPICAL
POTENTIAL GEAR
IMPROVEMENT
FRACTION
changing gear
efficiency
Figure 9. As cpue ratio drops fishers tend to implement strategies that improve the
effectiveness of their gear. These improvements tend to be absorbed into what
becomes normal gear efficiency. At any given time there is a latent potential gear
improvement fraction. Thus, over time gear efficiency tends to increase particularly
when fishing success is poor. For simplicity some model components are not shown.
ecosystem
you capacity ratio
MAXIMUM,
effect on
recovery time
possible a
recovery
effective biomas a ag ay
of unfished stock recovering” rN
capacity
10 stock Biomass sub-section
ECOSYSTEM
LOSS RATE
effective fishin
units capacity
LO ————————
from fishing units sub-se
Figure 10. Fishing activity can degrade the environment’s capacity to support
fish. Once degraded, this environmental capacity takes time to recover. Mean
recovery time will be longer if the ecosystem is severely degraded. For
simplicity some model components are not shown.
20
Po
elfect of differences
RELATIVE STRENGT! on management
OF MANAGEMENTS \# acceptability LOnbyING
VIEWS EFFECTIVENES'
LOOKUP
managements adjustments
after taking into account
expected replacement
f
realized strength of
‘management views
management's proposed y
sdpeshigats t6 gear negotiated vessel replacement rate
numbers entry rate ~~
pf % enter
evecten mas
IMPLEMENTATION j— vessel entry
TIME
units of fishing gear e
PERCEPTION OF STOCK
Vs FISHING GEAR fishing gear sub-section
CHANGE LOOKUP
effect of perception on
pedro
<tatio of current
—_——~ KO biomass to unfished
new perception of biomass
difference in
i stock status perceived siock biomass sub-section
silos pereyten a stock ratio
| has .
q S stock
CHANGE IN
7 PERCEPTION ASSESSMENT
LOOKUP INACCURACIES
change in ‘TIME NEEDED TO
perception ~g—=____ CHANGE
PERCEPTION
Figure 11. Management’s perception of the fish stock status is gradually updated with new data.
Based on its perception, management proposes changes to fishing gear numbers. These proposals are
implemented subject to the relative strength of management’s views. In some cases lobbying will
further weaken the views of management especially if differences between management and fishers are
large. For simplicity some model components are not shown.
Relation of Biomass Ratio to Perception of Stock by Management
Perception value of zero (neural)
‘curs when the biomass half ts
~ expacted maximum value
“ee
Perception of Stock
° 01 02S itis 1
Biomass Ratio
Figure 12. This lookup function describes the effect of biomass ratio on
management’s perception of stock status. Stock status is described in a
range from -10 (heavily overfished) to +10 (unfished). Management
believes that stock is being managed well when the biomass ratio is near
0.5.
21
Effect of Perception of Stock Status on Proposed Fishing Gear Numbers
‘Ata neutal perception no change in
‘gear numbers wil ba proposed
Effect on Fishing Gear Numbers
Perception of Stock Status
Figure 13. This lookup function describes the relationship between
management’s perception of stock status and how management feels it
needs to change current gear numbers.
Differences Between Management and Fishers Affects Lobbying Success
Lobbying Effect on Management's Success
jent's Vessel Entry Programs
ratio of Fishers to Managom
Figure 14. Lobbying can affect the successful implementation of
management's efforts particularly if differences between fisher’s and
management's views are large. This lookup function describes the
relationship between the amount of difference in desires for new vessel
entries into the fishery and the success of lobbying against management
vessel entry proposals.
22
Table 1. Input values for simulation of a fishery.
40,000
100,000
500
400
30.000
75,000
375,
300
catch ¢ = No Management - virgin stock A
Current Fish Biomass B : No Management - virgin tock
pue : No Management - virgin stock A.
Units OF Fishing Gear E: No Management - virgin stock A.
Year
‘u(Year*units)
Year
‘u(Year*units)
Year
‘u(Year*units)
wear
‘u(Year*units)
Year
‘u(Year*units)
Fish Stock
Rate of increase R
Initial biomass:
virgin stock
Over-fished stock
feedback effect on growth
feedback effect on recruitment
fraction of additions due to recruitment
years prior to entering fish stock
Fishery
initial number of units
virgin stock
Over-fished stock
initial gear efficiency
acceptable cpue
average vessel lifespan in fleet
potential gear improvement fraction
ecosystem loss rate
A/year*unit
ton/year*unit
year
dmnl
A/year*unit
No Management Starting with an Un-Fished Stock
---7)7fish biomass
_-- units of fishing gear
catch
catch per unit effort (cpue)
7 75 +80 85 90 95 100
wear
(Year*units)
Figure 15. An unmanaged fishery exhibits typical overshoot and collapse cycles with the peak of each
cycle somewhat smaller than the previous one. Fishers are initially attracted by high cpue, but over
fishing causes the fish stock to collapse. As the stock becomes over-fished enough vessels eventually
leave to allow the stock to recover and the cycle starts over. During periods of poor fishing, fishing
gear is improved in an attempt to maintain cpue. The fish biomass level where sustainable catches will
be highest is slightly below 50,000 tons in this scenario.
23
“Perfect” Management Starting with an Un-Fished Stock
40,000. veer
100000 ¢
S00 tYearunits)
400 nts
Fish biomass
20000 vYear
7500 ¢
375 tYearunits)
300 units
20,000 Year
Snom ¢
250 tearm)
300 une
10,000 wear Units of fishing gear
35,000
125. (Yeaetunts
100 units
catchy.
0 Year =
ot
0 u(Yeaetunits
unis
a a
Year
catch No Management virgin stock A Year
Current Fish Biomass B = No Management - virgin tock A ‘
pue= No Management - virgin stock A u(vear*uits)
Units Of Fishing Gear E No Management - virgin stack A units
Figure 16. Under ‘perfect’ management (as described in the text) management efforts gradually bring
the stock to levels that maximize long term catches.
“Perfect” Management Starting with an Over-Fished Stock
40.000 wear
100.000 &
S00 8(Yearhnis)
400 as
mee Fish biomass.
S75. (Years)
300 is
20.000 vYear
50000 +
4350, tearfunits)
200 sais
10,000 wear
25,000 ¢ i ‘shi
125 (Year‘unis) Units of fishing gear
100 ts
0 eer =
ot eee
0 e(Year*unitsy |) catcl
0 wns
os 30 gS SSS 8S 00
Year
atch : pert management - over fished Year
(Gare Fish Biomass B perct management - oer fed 4
pues pert mangement - over fished eveersnis)
Units Of Fishing Gear perfect management - over fished ws
Figure 17. ‘Perfect’ management starting with an over-fished stock tends to overprotect the
stock somewhat prior to bringing it to the presumed optimum level. Catches progress steadily
toward the optimum level, but reaching this level takes many years.
24
Fish Biomass Under Five Management Scenarios
100,000
perfect management
75,000 catch history effect
g lobbying effect
2
0,000
35,000 lobbying and history effect
no management
°
os 1s 20253035 404550 SSCS CROCS 00
Year
Figure 18. As described in the text, management efforts are effected by lobbying by fishers and also
by changes in politicians’ perceived need for management as reflected in historical catch trends. Here
the fish stock biomass is traced under five management scenarios. In all cases except “no
management” the underlying strength of management (without other effects) is | (i.e. 100 percent).
Typical Management Starting with an Un-fished Stock
biomass
a
40,000
100,000
500
400
units of fishing gear
30,000
75,000
375
300
Year
Year
(Year units)
0
0
0
0
ich : typical management Year
nt Fish Biomass B : typical management
pu mani
Units OF Fishing Ge
vu(Yeartunits)
nt units
E : typical mang
Figure 19. More typical of real management would be a management entity which never has 100%
authority and is subject to variations in both administrative support and lobbying by fishers. Here
management by this typical system (with a normal management authority of 70%) produces significant
cycles in the fishery although again not as severe as an unmanaged situation.
25
Effect of Variability in Recruitment
on Outcome of Typical Management A
100,000
Stock Biomass
50,000
Figure 20. Graph of stock biomass showing results of 15 simulations of ‘typical’ management. With
random variation added to recruitment the system shows significant variability but the overall cyclic
pattern of the fishery remains.
Effect of Variability in Recruitment
on Outcome of Typical Management B
60,000
Stock Biomass
45,000
30,000
15,000
os 0 1 2 28 39 as 40 45 50 55 60 68 70 75 80 85 90 95 100
Year
Figure 21. Four example outcomes from ‘typical’ management with recruitment variation. In this
cases stock size and vessels numbers were in approximate equilibrium at the start of the model.
Without recruit variation (line A) the fish stock remains stable. With variation the stock may remain
near equilibrium (lines B and C) or, if recruitment causes sufficient change in stock size, will start to
oscillate between boom and bust cycles (line D).
26
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