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Abstract: In this paper, major issues to be considered by the FAO Technical Consultation on the Measurement of Fishing Capacity are introduced. Definitions and main approaches to measurement and assessment are reviewed in relation to the requirements of the International Plan of Action for the Management of Fishing Capacity. Conceptual and practical difficulties to be addressed in measuring and assessing capacity, in general as well as in the case of specific fisheries, are also considered.


This document was prepared in order to introduce and review major issues to be considered in the context of the FAO Technical Consultation on the Measurement of Fishing Capacity. It introduces basic definitions and major considerations for the measurement and monitoring of fishing capacity. The ultimate objective of capacity measurement is to provide information for the development of a management strategy that will ensure that fleet capacity is moving in the right direction. In this regard, it is important to estimate the magnitude of the difference between current and target capacity in order to determine the existence of overcapacity (or undercapacity), the severity of the problem and the appropriate steps and path that can be taken to bring capacity in line with the long-term target.

In Section 2, the issue of managing fishing capacity is presented briefly in relation to recent international efforts that led to the adoption of the International Plan of Action for the Management of Fishing Capacity. Related measurement and monitoring aspects were discussed by the Technical Working Group on the Management of Fishing Capacity (TWG) which met in February 1998 in La Jolla (FAO, 1998a). Definitions and main approaches and methods to measure and monitor fishing capacity are presented in Section 3. This section reviews and expands on the main conclusions of the TWG pertaining to the measurement and monitoring of fishing capacity. Specific areas for consideration by the Technical Consultation are presented in Section 4.


The issue of managing fishing capacity has been raised quite recently in reference to growing concern about the spreading phenomenon of excessive fishing inputs and overcapitalization in world fisheries. The issue is essentially one of having too many vessels or excessive harvesting power in a growing number of fisheries. The existence of excessive fishing capacity is largely responsible for the degradation of fishery resources, for the dissipation of food production potential and for significant economic waste. This manifests itself especially in the form of redundant fishing inputs and the overfishing of most valued fish stocks.

Excess fishing capacity affects many domestic fisheries throughout the world and, in an even more pervasive form, many high-seas fisheries. The globalization of the phenomenon is illustrated by the relative stagnation of world marine catches of major species since the late 1980s. Evidence provided by FAO indicates that, in reference to all major marine fisheries, 35 percent are subjected to severe overfishing, 25 percent are fully exploited and 40 percent still offer scope for development. Demersal and other most valued stocks are generally the most affected.

At the global level, overcapitalization in world marine fisheries appears to be a relatively new phenomenon, dating from the late 1980s and following a decade of very intense fleet development. FAO data indicate that nominal fleet size seems to have peaked during the mid-1990s. However, actual fishing capacity may still be increasing due to technological development and the refitting of older vessels.

Essentially, the existence of excess fishing capacity is a result of the widespread tendency to over invest and over fish under open-access conditions. Overcapitalization in world fisheries also came about progressively as a result of broader and related factors, such as the:

The FAO Code of Conduct for Responsible Fisheries recognized that excessive fishing capacity threatens the world's fishery resources and their ability to provide sustainable catches and benefits to fishers and consumers. In Article 6.3, it is recommended that "States should prevent overfishing and excess fishing capacity and should implement management measures to ensure that fishing effort is commensurate with the productive capacity of the fishery resources and their sustainable utilization".

In 1997, the FAO Committee on Fisheries (COFI) recommended that a technical consultation be organized by FAO to clarify issues related to excess fishing capacity and to prepare guidelines. Work undertaken by FAO on this basis (FAO, 1998b) led to the preparation of the FAO International Plan of Action for the Management of Fishing Capacity.

The International Plan of Action was adopted by COFI in February 1999, and further discussed by the FAO Ministerial Meeting on Fisheries in March 1999. The Ministers declared to "attach high priority to the implementation of the International Plan of Action for the Management of Fishing Capacity... and on putting into place within the framework of national plans, measures to achieve a balance between harvesting capacity and available fisheries resources."[2]

The International Plan of Action (IPA) was elaborated within the framework of the Code of Conduct for Responsible Fisheries, as an element of fisheries conservation and sustainable management. The immediate objective of the IPA is for "States and regional fishery organizations, in the framework of their respective competencies and consistent with international law, to achieve worldwide preferably by 2003 but no later than 2005, an efficient, equitable and transparent management of fishing capacity". The IPA further specifies that, inter alia, States and regional fishery organizations, when confronted with an overcapacity problem which undermines the achievement of long-term sustainability outcomes, should endeavour to limit initially at existing level and progressively reduce the fishing capacity applied to affected fisheries. On the other hand, where long-term sustainability outcomes are being achieved, it nevertheless urges States and regional fishery organizations to exercise caution.

The IPA is voluntary, and is based on a number of major principles of the Code of Conduct as well as on complementary principles. These include:

The IPA specifies a number of actions to be taken urgently. Major actions are prescribed in reference to the main section of the document: assessment and monitoring of fishing capacity, the preparation and implementation of national plans, international consideration and immediate actions for major international fisheries requiring urgent attention.

Regarding the assessment and monitoring of fishing capacity, the IPA recommends, inter alia, that States:

In adopting this International Plan of Action in February 1999, COFI further recommended that FAO organize a technical consultation on the measurement of fishing capacity before the end of 1999. This Technical Consultation is the fulfilment of that recommendation, and will serve as a basis for the preparation of technical guidelines that can be used by countries in their preliminary assessment of fishing capacity and for the systematic identification of fisheries requiring urgent attention.


The measurement of fishing capacity is in itself quite complex but has been made even more so by the proliferation and confusion of terms used to address this issue. Some of the confusion stems from the fact that fishing capacity can be addressed either by focusing on productive inputs or on production. Difficulties also arise from the ways the various sciences involved are looking at fishing capacity, its measurement and its assessment in relation to the specifics of fish stocks. It is, therefore, important to clarify some basic concepts.

3.1 Definitions

The following general definitions[3] were considered by the TWG: Fishing capacity is the ability of a vessel or fleet of vessels to catch fish. Fishing capacity (capacity output) can be expressed more specifically as the maximum amount of fish over a period of time (year, season) that can be produced by a fishing fleet if fully utilized, given the biomass and age structure of the fish stock and the present state of the technology.

Capacity utilization can be defined in this context as the ratio of actual output (catch, landings) to some measure of potential output (capacity output) for a given fleet and biomass level. It is essentially a short-run concept.

Fishing capacity can be expressed alternatively in reference to fleet characteristics or as the ability of a fleet to generate fishing effort. In this context, economists prefer to use the related concepts of capital stock (vessels) or capital services (flow of productive services from the capital stock, such as fishing effort) and capital utilization[4]. Aggregate proxies are typically used to measure the capital stock which the fleet represents, e.g. gross registered tonnage or horse power. Capital utilization can be defined as the ratio of actual to desired levels.

The TWG noted several advantages to formulating the definition of fishing capacity in terms of catch: a) it is consistent with economic production theory; (b) it facilitates aggregation between fleets and between the harvesting and processing sectors; (c) it makes it easier to deal with complexities due to fisheries interactions, e.g. when the catch of one fishery is a by-catch of another; (d) it is more appropriate to artisanal fisheries as these fisheries can involve rapid changes in inputs, in the form of numbers of participants rather than capital defined stricto sensu, and (e) it makes it easier to determine optimal capacity for fluctuating stocks.

The TWG found it more relevant to define "target" capacity rather than "optimal" capacity, in deference to the wide diversity of objectives that might be chosen by policy-makers to ensure sustainability of fisheries and meet other needs. Thus, definitions of 'optimal' would be local and specific. The following definition was agreed upon: Target fishing capacity is the maximum amount of fish over a period of time (year, season) that can be produced by a fishing fleet if fully utilized while satisfying fishery management objectives designed to ensure sustainable fisheries. It follows that excess capacity can be expressed by comparing current and target capacity output.

Overcapacity can thus be defined as a situation where capacity output is greater than target output. Overcapitalization will refer on the other hand to a situation where actual capital stock is greater that the optimum capital stock required to produce the target output. The 'optimum' can be defined in a technical manner as the minimum capital stock required, as determined by the production technology, or in an economic manner as the capital stock that will minimize the cost of producing the target output. The two concepts are related and could be equivalent under certain restrictive conditions.

It was suggested by the TWG that target fishing capacity could be better defined in terms of a range rather than a specific quantity or metric. It was suggested that optimal could be specified relative to outer boundaries. According to paragraph 7 of Annex II of the Straddling Stocks Agreement, the minimum standard for a biological reference point should be the fishing mortality rate that generates MSY. The following definition for limit capacity was proposed, in conformity with the direction in which international law is developing: Limit capacity is the maximum amount of fish that can be produced on a sustainable basis by a fully-utilized fleet. Thus, the limit capacity corresponds to MSY. Thus, the capacity which generates a level of fishing effort which puts stock beyond the FMSY limit[5] is an upper bound on optimal or target capacity. A starting point would be to define the maximum fleet size corresponding to this limit fishing mortality rate. Other considerations may be used to determine the lower bound of a range of target capacity (precautionary approach, economic efficiency, social factors, etc.).

Indicators of capacity output, capacity utilization, capital stock and capital utilisation are many. Some are reviewed below. In some cases, and for relatively simple fisheries, one can readily find correspondence between input-based and output-based indicators. Indicators of overcapacity and overcapitalization are fewer as these require explicit reference to the resource constraint and to economic efficiency, at least in terms of cost minimization. Generally, target output capacity to target capital stock will be determined as a rather separate exercise requiring the consideration of resource status (e.g. an estimation of target biomass and MSY) and the consideration of economic factors (e.g. estimation of target capital stock required to catch target output at minimum cost).

3.2 Indicators of capital stocks and capital services

Various proxy variables have been used to monitor fishing capacity (as capital stock) on the basis of fleet size and major vessel attributes. The major difficulty is to identify the combination of attributes that best reflects the productivity of relatively heterogeneous fishing units. An indicator can be developed by weighting key vessel attributes (e.g. length, breadth and power). Other attributes of importance will be gear type and key characteristics, as well as vessel age and embodied technical change.

Accounting for fishing time allows one to monitor capital services. Fishing time can be accounted for as fishing days or days absent from port. Standardization methods need to be used to account for fleet heterogeneity. If nominal fishing effort is expressed as 'standard fishing days', actual effort can be compared to potential effort to derive an indicator of capital utilization for a given fleet. In the presence of regulations on fishing time, capital utilization may be significantly lower than one if the fleet has few alternative uses. Even in the absence of such regulation, capital utilization may also be significantly less than one under specific conditions (adverse price, resource or weather conditions).

An alternative is to monitor capital stock directly in financial terms, e.g. by estimating the market value of all fishing units in a fleet. This would generally imply monitoring investments and disinvestments, while accounting for depreciation.

While the monitoring of these indicators is essential, the assessment of overcapacity and overcapitalization requires a definite linkage to the status of exploitation of the resource and the determination of target capacity and target capital stock.

3.3 Indicators of capacity output and overcapacity

The TWG discussed simple indicators of capacity and overcapacity that can be used with limited data in relation to basic fishery production models. The basic elements of such indicators are the number of vessels in each fleet exploiting a stock, the mean catch rates for each fleet, and the amount of time actually spent fishing by each fleet relative to the maximum possible if there were no constraints on fleet operation. These practical measures of capacity can be expressed in terms of a production-based indicator and a vessel-based indicator. These are easily developed for single stock fisheries.

To appropriately set a long-term target capacity, it is necessary to specify a target stock biomass. However, it is recognized that the long-term target may be difficult to estimate at any point in time, partly because future target capacity will generally be defined on the basis of present-day performance. As the fishing fleet moves along the adjustment path towards a preliminary estimate of a target, accumulation of knowledge and a better indication of changes in technology and other factors may result in continual updating of the ultimate target.

One way to approach the problem is to start with a TAC (either current or a long-term projection). The maximum that a given fleet could potentially catch (capacity output) divided by the target TAC is a measure of excess (or under) capacity. Target fishing capacity can be evaluated in reference to both the current and long-term target biomass.

Potential catch by each fleet under current stock conditions can be estimated as the product of number of vessels and mean catch rate, scaled up to a full-time equivalent based on the ratio of maximum time available to the actual time fished. The potential catch in the fishery is the sum of potential catches by all fleets. This can be compared to the TAC to give an indication of overcapacity by the current fleet. The indicator can be calculated under current stock conditions (TAC and CPUE corresponding to current biomass) and for long-term target conditions (TAC and CPUE corresponding to target biomass). A disadvantage is that it does not account for the 'latency problem', i.e. vessels not currently present in the fleet, which could enter easily when conditions change.

Another measure is based on calculating, using the same information, the minimum number of vessels needed to take the TAC. This approach may be particularly useful when there are several fleets that cannot meaningfully be aggregated into a single measure. The minimum fleet size required to take the entire TAC is calculated for each fleet. These minima can be compared to the actual size of each fleet to provide perspective on overcapacity. If any of the actual fleet size is close or higher than the minimum required, there will be strong evidence of overcapacity. Otherwise, further assessment would require calculating a composite index of boats needed by using a fishery-wide average catch rate. The method can be applied to current and long-term target conditions.

These measures are extremely simple rules of thumb, but should be capable of indicating the presence of overcapacity in current fisheries. The extension of the techniques to fleets fishing multiple stocks was also reviewed by the TWG. In this context, results may be difficult to interpret when there is evidence of overcapacity for some stocks and undercapacity for others.

3.4 Alternative approaches to estimating capacity output

Hold capacity has been applied widely to measure capacity output. It provides a technological limit to maximum production. Applied as such to a fleet over a year or season, it required data on number of vessels, individual hold capacity and maximum number of fishing trips. Although there are many difficulties attached to this method, it may provide an indication of capacity utilisation (ratio of actual catch to technological maximum).

If fishing time is assessed as a key factor, another approach is to estimate capacity output based on current catch rates, but based on the full use of maximum potential effort. In general, capacity output may also be deduced from cross-fishery comparisons at national or international level, e.g. by comparing the maximum output of similar vessels operating in various shrimp or tuna fisheries.

The TWG suggested two other practical alternatives for measuring capacity: peak-to-peak analysis and Data Envelopment Analysis (DEA), both are briefly described in the following paragraphs. Some of the information documents prepared for the Technical Consultation will provide examples on the application of these methods.

The peak-to-peak method defines capacity by estimating the observed relationship between catch and fleet size over time. The approach is called peak-to-peak because the periods of full utilization, called peaks, are used as the primary reference points for the capacity index. The index is fixed to 100 percent for the years for which full utilization is observed. For other periods, the index is expressed as percentages of full utilization with an adjustment for technologically induced changes in productivity. The approach is based on identifying peaks, or periods of full utilization defined as the maximum value of the ratio of output to capital stock (e.g. catch per vessel). In practice, a peak year is often identified on the basis of having a yield per producing unit that is significantly higher than both the preceding and following years. The peak-to-peak method requires data on landings and vessel numbers and some identification of a technological time trend. This approach does provide for a rapid appraisal of the maximum yield of a fleet given the size of the fleet and the potential utilization of inputs. But this is estimated in the absence of resource constraints. Minimum fleet sizes (number of vessels) that correspond to an otherwise-determined target level of capacity can be calculated on this basis.

DEA is a mathematical programming method to determine optimal solutions given a set of constraining relations. The advantages of this method are that it can estimate capacity under constraints including TACs, by-catch, regional and/or size distributions of vessels, restrictions on fishing time, and socio-economic concerns such as minimum employment levels. DEA can be used to identify operating units (i.e. individual vessels or vessel size classes) which could potentially be decommissioned. By rearranging observations in terms of some criterion, such as capacity by region and vessel size class, the desired number of operating units could be determined by adding the capacities of each operating unit until the total reaches the target. DEA readily accommodates multiple outputs (e.g. species, market categories), and multiple types of inputs such as capital and labour). DEA can also determine the maximum potential level of effort and its utilization rate. The analysis accepts virtually all data possibilities, ranging from the most parsimonious (catch levels, number of trips, and vessel numbers) to the most complete (e.g. a full range of cost data). With cost data, DEA can be used to estimate the least-cost (cost minimizing) number of vessels and fleet configuration. It can also measure capacity relative to any desired biomass or TAC. The method is limited by its deterministic specification, but allows for the consideration of an economic definition of capacity.

3.5 Data and monitoring requirements

A minimal requirement would be to establish a system for the collection and regular analysis of the following basic data: estimates of vessel numbers and the main vessel characteristics determining fishing power (e.g. GRT or GT, engine power, length, hold capacity, gear type and dimensions, with the importance of each of these varying depending on the fishery); basic relevant characteristics of fishing operations (e.g. seasonality, number of fisheries in which vessels operate); landings; and at least a qualitative indication of trends in CPUE or other information that can give at least a rough index of MSY.

An advanced system for the monitoring and assessment of capacity will require the collection and analysis of more specific data and information, such as:

3.6 Some unresolved issues on definition and approaches

The TWG identified two major unresolved issues:

This second issue calls to mind the ongoing debate concerning output controls vs. input controls. Although the assessment of overcapacity might be approached from either perspective and independently of the type of control method used, the approach taken is likely to be influenced by the availability of data and thus by the control method used. In countries where TACs are used as control measures, the measurement of overcapacity may be easier to approach on an output basis. On the other hand, many countries (and developing countries in particular), may find it easier to approach measurement in input terms because they rarely use TACs explicitly as output controls, but rely instead on variables that are easier to control (e.g. numbers of vessels, numbers of participants) in relation to indicative long-term TAC figures.

Relating output-based and input-based estimates would generally be difficult except for relatively simple fisheries. Standard fishery production models can be used which relate catch to fishing effort and catchability coefficients (fishing mortality) and biomass. A priori, such models could be of use to relate prevailing or target capacity output to prevailing and target capital services if these are expressed, for example, in terms of potential standard fishing days). A major question will be to assess how the catchability coefficient (q) will change as capacity changes from the current (transient) situation to the long-term target, at least indicatively. A related problem stems from the fact that (biological) limit reference points are frequently defined in terms of fish mortality rates (F). It is interesting to note that stock assessment biologists generally assume q to be constant, which is one reason that they often favour constant fishing mortality strategies, which are assumed to be equivalent to constant fishing effort strategies. Thus, as stock size changes (under a constant F strategy), the optimum fleet capacity would not vary from year to year. On the other hand, many economists consider that fishing effort is not measurable and q is made up of some parts that can be measured and some that are unquantifiable. Further work is thus needed to translate measures of capacity into metrics that can be compared to such reference points.

In a technologically determined approach, capacity output is defined as the maximum output that can be produced, given available fixed inputs and the full utilization of variable inputs, but without any reference to economic aspects. Capacity utilization is thus defined as the ratio of output (catch) to capacity or potential output, the latter being determined in an ad hoc manner in reference to full use, hold capacity, comparison of annual catches under similar conditions, or international comparisons. The calculation of overcapacity further requires one to independently establish a desired target level of catch (short-term and long-term) and to compare it with capacity output. Economics may be considered at this stage in an ad hoc manner by estimating the minimum capital stock required to harvest the target catch (e.g. MSY); by estimating the capital stock required to harvest the target catch at minimum cost or by referring to an independently derived long-term target level of output that accounts for economic efficiency (e.g. by referring to MEY rather than MSY).

A more appropriate economic definition of capacity can however be provided in reference to cost minimization. Capacity output can be defined as the output corresponding to the tangency of short-run and long-run average total cost or alternatively as the output corresponding to the minimum short-run total average cost. Intuitively, this means that capacity output is the level of output for which the vessels in the fleet were designed to operate at lowest average cost. The interest of this definition is that estimates of capacity utilization derived from technological and economic definition can be readily compared. Estimates of overcapacity using the two approaches can also be compared as the ratio of output capacity to short-term and long-term target output.

3.7 Difficulties of application in selected situations

Measurement difficulties are arising from complex situations, such as those created by fluctuation in abundance, both year to year and within a year or season. The latter result in peak load problems, particularly for species that are only available for a short period of the year (or only available in a certain high-priced form such as fish roe for a short period of the year). Proposed definitions may need to be adjusted to deal adequately with such peak load problems. Year to year fluctuations lead to difficulties in the determination of target levels for catch and capital stock. It may be appropriate to consider in this case an acceptable level of potential over or under capacity. Estimates of overcapacity may also be confounded by age-structure effects (e.g. both yield per recruit and price aspects).

Measurement methods should account for the fact that fishing units are multiple-input productive units, generally composed of a vessel, gear, technology and skills. In some cases, the number and type of fishing vessels may be a good indicator of the amount of fishing capacity. In other cases, the capacity of similar fishing units may vary broadly in relation to gear use (e.g. multiple gear), to technology, skills or labour intensity (e.g. artisanal boat used in shifts by different crews). For major and complex fleets, an analysis of the influence of major input characteristics needs to be conducted so as to identify determining factors of production.

Special problems associated with small-scale fisheries also require detailed examination, whether they constitute recreational fisheries or artisanal commercial or subsistence fisheries. There are indeed difficulties associated with the collection of data as well as with input-based or output-based measurements of capacity in such fisheries (e.g. the flexibility with which crafts involved can accommodate additional labour and shift from fishery to fishery). Difficulties also arise with regard to establishing target output and input levels, especially in geographic areas where small-scale fishing constitutes an activity of last resort.

Fleet mobility constitutes one of the main difficulties encountered in measuring capacity and assessing overcapacity. Fleet mobility may relate to geographic mobility and/or the ability of vessels to redirect effort from one target stock to another in the same area. Thus capacity needs to be considered on a fleet basis as well as a species or stock basis, with further consideration being given to the relevant geographic perspective (local, national, regional or global perspective according to fisheries). The key question is where to draw the line and, if starting from a stock perspective, how to define "latent capacity". This question relates directly to the need to define fisheries as management units that are relevant to the management of fishing capacity.

Fisheries can be defined as interacting stocks and fleets. One can define a fishery with primary reference to stock. For stock-based fisheries, the main difficulty in measuring capacity will be to account for latent fleet or fishing effort. Fisheries can also be defined more broadly with primary reference to fleet characteristics. A fleet-based fishery will generally be specified in reference to gear, vessel size, area and species group, e.g. inshore trawling for demersal fish in specific area. A fleet-based definition allows one to deal more easily with the problem of latent capacity but makes it more difficult to determine target catch levels as fisheries may involve a large number of stocks. The monitoring and measurement of capacity needs to be approached from both perspectives in the context of an appropriate set of related stock-based and fleet-based fisheries (management units). Accounting for mobility would imply a multi-tiered approach by which capacity and overcapacity are measured at various levels in reference to a broader multispecies/ecosystem/industry context. One can start alternatively from the broadest (ecosystem or major fleet) or more restrictive perspective (a stock). In any case allowance will have to be made for major fleet-stock interactions in the disaggregation or aggregation process.

A major problem with the monitoring of fishing capacity is that stocks and fleets are generally monitored quite separately. Typically, one will have numerous data on specific stocks and their exploitation on the one hand, and on vessel characteristics (physical and sometimes economic) on the other hand. The important missing link is information on fleet-stock interactions in time and space. The monitoring and study of fleet deployment in time, space and across stocks is a priority and the only way to properly define relevant fleet-based management units.

Finally, there is a need to establish a link between harvesting and processing capacity. Such a link may be established more easily if fisheries used as management units correspond to a rather specific processed product (e.g. in the case of a major small pelagic fisheries and related fishmeal plants or in the case of species-specific fleet and processing sectors as observed for shrimp, lobsters or crabs in some countries). Otherwise, a relevant link can only be established at a fairly aggregated level.


The Technical Consultation was invited to examine the matter of measuring fishing capacity, with due consideration being given, inter alia, to the following considerations:


FAO. 1998a. Report of the Technical Working Group on the Management of Fishing Capacity. La Jolla, United States, 15-18 April 1998. FAO Fisheries Report No. 586. Rome, FAO.

FAO. 1998b. Report of the Consultation on the Management of Fishing Capacity, Shark Fisheries and Incidental Catch of Seabirds in Longline Fisheries, Rome 26-30 October 1998. FAO Fisheries Report No. 593. Rome, FAO.

Kirkley, J. E. & Squire, D. 1999. Measuring Capacity and Capacity Utilization in Fisheries. In: Gréboval, D (Ed). Managing Fishing Capacity: Selected Papers on Underlying Concepts and Issues. FAO Fisheries Technical Paper No 386. pp. 75-200. Rome, FAO.

[1] Fishery Policy and Planning Division, FAO, Viale Terme di Caracalla 00100 Rome, Italy. Email:
[2] The Rome Declaration on the Implementation of the Code of Conduct for Responsible Fisheries, adopted by the FAO Ministerial Meeting on Fisheries, Rome, 10-11 March 1999
[3] All definitions discussed in this section may be referred to as “technologically determined”, with capacity utilization being necessarily less or equal to 100 percent.
[4] For further details, see Kirkley and Squire (1999).
[5] That is, the level of fishing mortality that produces the maximum sustainable yield.

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