by Andrew A. Rosenberg
National Marine Fisheries Service
Gloucester, MA, USA
and Victor R. Restrepo
University of Miami
Cooperative Unit for Fisheries Education and Research
Miami, FL, USA
Precautionary management reference points are those intended to prevent recruitment overfishing, even if a direct link between spawning stock size and subsequent recruitment cannot be established statistically. In order to be precautionary, the appropriate null hypothesis is that the stock does not compensate for reduced abundance by increasing productivity. There are many limit reference points that can be used to prevent recruitment overfishing. However, it is unlikely that a single limit reference point can provide protection for the resource under all foreseeable circumstances and, thus, it is useful to define harvest control laws which combine several thresholds. A precautionary management strategy should contain, in addition to limit reference points, a priori decision rules on the acceptable probability (risk) that recruitment overfishing will take place, given the target harvest and the estimated stock status. The choice for a particular definition of risk should be tied to uncertainty and precautionary management dictates that more uncertain situations require more conservative measures.
The precautionary approach to fishery management, as described by Garcia (1994) seeks to protect fishery resources from fishing practices which might put their long-term viability in jeopardy. In order to take appropriate precaution, fishing activities may need to be controlled even before there is clear scientific evidence that current practices can not be sustained by the resource. In order to develop fishery control policies, biological reference points are needed for measuring current resource status and the projected effects of fishing.
Biological reference points (BRP) have long been used in fishery management as benchmarks for the development of management strategies. The most widely cited such benchmark is maximum sustainable yield, often thought of as a default management objective from a biological perspective (Hilborn and Walters 1992). Biological reference points really are not objectives in and of themselves, however, but quantitative indicators of variables such as fishing mortality rate, yield or stock biomass by which the current state of the fishery can be judged. For example, if the objective is to obtain the largest possible yield on an ongoing basis from a resource, comparing the time stream of catches to the estimated level of MSY and its uncertainty may indicate if the objective is being achieved over time. Alternatively, a management strategy to approach the objective may be based on estimates of MSY and its uncertainty as well as on other aspects of the dynamics of the resource and the fishery. In the first instance, the reference point, MSY, is used retrospectively to evaluate past performance. In the latter example, it is used prospectively for the development of future management tactics. These two usages of biological references points are needed for both developing and developed fisheries.
There are a very wide variety of reference points available as bechmarks for different management objectives. For most fisheries, more than one reference point is needed to outline the overall management strategy. FAO (1993) describes most of the commonly applied reference points and that summary will not be repeated here. Exceeding a reference can, in one way or another, be classified as overfishing. However, overfishing can take a number of forms; for example, target overfishing, growth overfishing, recruitment overfishing, and economic overfishing. While the first type of overfishing is associated with a target, growth and recruitment overfishing are generally associated with thresholds or limit reference points (FAO 1993), and economic overfishing may be expressed in terms of either targets or limits, depending on the definition used. The difference is that while fishing activity is expected to fluctuate about targets, limits should generally not be crossed. Strictly, target overfishing could be said to occur whenever the target is overshot; however, small deviations would not generally be considered serious until and unless a consistent bias became apparent. Conversely, even a single violation of a limit reference point may indicate the need for immediate action to reduce fishing mortality.
For the development and evaluation of precautionary management strategies, limit reference points for biological conservation are the most important, to set the constraints within which the management strategy must operate. In particular, to maintain a sustainable resource recruitment overfishing must be protected against, and precautionary management would seek prevent recruitment declines due to overharvesting even if the scientific evidence of the impact of fishing is weak and a causal link has not been established. Fishing effects on recruitment may be related to such factors as habitat loss, disturbance of egg beds or harvesting of prerecruits, but the major factor in most fisheries is the relationship between the spawners or the eggs they produce and the recruitment of young fish to the fishable or spawning population. The relationship between spawning stock or other factors and recruitment may be weak in many cases, but must exist in the limit as the number of spawners is reduced to very low levels. In a study of empirical stock-recruitment data sets from around the world, Myers and Barrowman (1994) found that lower stock sizes were generally associated with lower recruitment levels. In order to be precautionary, the appropriate null hypothesis is that spawning biomass or egg production is linearly related to subsequent recruitment (Fogarty et al. 1992). That is, that the population does not compensate for increasing mortality or reduced abundance of adults by increasing productivity. Unfortunately, the lack of a clear relationship between spawning stock and recruitment has led some fishery managers (and scientists !) to conclude that the appropriate null hypothesis is a line with slope 0. Such a null hypothesis can result in continued harvesting until a major decline in recruitment is observed at low biomass, the antithesis of precaution.
The need to define recruitment overfishing reference points has been largely neglected until recent times, as the number and diversity of fisheries that are considered overfished continues to increase. Even now, far fewer BRP's have been developed to identify recruitment overfishing than to identify growth overfishing, and their generality is often questioned. Once F0.1 was invented (Gulland and Boerema 1973), fisheries scientists often advocated the use of F0.1 as a target and Fmax as a limit. Other early limit reference points included minimum spawning biomass levels based on observed stock collapses, and 20% of the unfished stock biomass (20% B0; e.g., Beddington and Cooke 1983). Alternative indicators of poor stock condition that have long been advocated are truncated age distributions, small or decreasing mean size in landings, and a markedly declining survey index, but these have rarely been articulated into measurable, unambiguous quantities.
Within the last 10 years, an important new class of reference points associated with recruitment overfishing have been developed based on percentiles of survival ratios estimated from stock and recruitment observations. This work began with Shepherd (1982), who showed how a standard spawner per recruit (SPR) analysis could be combined with stock and recruitment observations to generate reference fishing mortality rates. The relationship between the two types of information is straightforward (Gabriel et al. 1989; Mace and Sissenwine 1993); for any constant F, there is a corresponding SPR level that can be inverted and used as the slope of a straight line through the origin of the stock and recruitment data. Points along the line represent the average survival ratio (R/S) required to support that particular constant F. Percentiles of observed survival ratios can therefore be used to define threshold and target levels of F, which can then be translated back to the SPR scale (see Gabriel et al. 1989 for the computational details).
Two percentiles that have been advocated as reference points for overfishing thresholds are the 90th percentile (denoted Fhigh; Shepherd 1982) and the median (denoted Fmed; Sissenwine and Shepherd 1987). Both are intended as indicators of recruitment overfishing. The tangent through the origin of a stock and recruitment relationship corresponds to Fextinction. Fhigh may overestimate the tangent, since the highest survival ratios may just reflect anomalously favorable environmental conditions, not the ability of the population to sustain fishing under average environmental conditions. On the other hand, Fmed may underestimate the slope if the data exhibit compensation (concavity). It is more correct to use Fmed as an estimate of Frep (F-replacement), the fishing mortality rate corresponding to the observed average survival ratio. Thus, Frep is the fishing mortality rate that, on average, allows for replacement of successive generations over the observed range of stock and recruitment data. Frep is a valid approximation of the slope at the origin in the case where the observations are restricted to low stock size, or where there is little compensation in the relationship. However, Frep may forego potential yield if the stock has a recent history of light exploitation, and Fmed may underestimate Frep if the distribution of recruitment is highly skewed.
Mace and Sissenwine (1993) surveyed 91 well-studied European and North American fish stocks with sufficient data to construct stock-recruitment plots and conduct yield per recruit and spawning per recruit analyses to obtain estimates of reference points such as F0.1, Fmax, Fmed and associated levels of %SPR. They estimated the median ratio of Fmed/Fmax at 1.3 and the median of Fmed/F0.1 at 2.3. The average %SPR corresponding to F0.1 was 38%, the average %SPR corresponding to Fmax was 21%, and the average %SPR corresponding to Fmed was 19%. Mace and Sissenwine advocated use of 20% SPR as a recruitment overfishing threshold for stocks believed to have average resilience and 30% SPR for little-known stocks. That study complements earlier theoretical and empirical work by Goodyear (1977, 1980, 1989, 1993), Gabriel et al. (1989) and Clark (1991) that has resulted in SPR becoming the most common basis for recruitment overfishing reference points in U.S. fishery management plans (Rosenberg et al. 1993). The choice of reference level is usually based on theoretical considerations and analogy with other stocks, such that most definitions use either 20% SPR and 30% SPR as the recruitment overfishing reference point.
There have also been developments in the use of stock and recruitment observations to define biomass reference points. Despite the fact that theoretical stock-recruitment curves (e.g., Ricker 1954, Beverton and Holt 1957, Shepherd 1982) have been widely used for decades, there are no generally accepted methods for calculating biomass thresholds from the parameters. Some methods require that the data be fitted by theoretical relationships, whereas others are based on the observations themselves (non-parametric methods). The latter includes subjective, visual approaches that may be able to identify critical biomass levels below which recruitment appears to begin to decline rapidly. The main problem with subjective methods is that they do not always give consistent answers, and are often biased by the status quo.
Serebryakov (1991) and Shepherd (1991) suggested an objective, non-parametric method for estimating a threshold biomass. They defined the threshold by the intersection of the upper 90th percentile of the observed survival ratio and the upper 90th percentile of the recruitment observations. This intersection approximates the minimum stock size within the range of the observations that, based on the data, can be expected to be capable of producing a good year class when environmental conditions are favorable for survival. Unfortunately, although this method generally performs well based on several different types of evaluation criteria, it is extremely sensitive to the range of the data observed (Myers et al. 1994), with the threshold tending to get revised downward as a stock is fished down and new S-R observations are added.
A more common method of specifying biomass thresholds is to express them as a percentage of the unfished, virgin biomass (%B0), most often using 20% B0 as a default. However, it may be difficult to estimate B0 for stocks that have been fished down substantially from virgin levels. In some cases, it may be reasonable to define virgin biomass as the point where the F=0 replacement line intersects a fitted S-R relationship, or the average or median observed recruitment. This method of estimation is likely to be less valid for stocks far below the virgin state, particularly if the observations cover only the recent history of the fishery. Indeed, Myers et al. (1994) found that the point of intersection often occurs well outside the range of observations, at stock sizes where density-dependent effects may well differ from those in operation during the period of observations.
Ideally, threshold levels of biomass should be based on the associated level of recruitment relative to some reference level. Although some definitions of biomass thresholds refer to recruitment levels, the association is often somewhat vague. For example, the Advisory Committee on Fishery Management of the International Council for the Exploration of the Sea has adopted the process of specifying the minimum biologically acceptable level (MBAL) of biomass, defined as the biomass level below which the probability of poor recruitment increases as spawning biomass declines further. In practice, there are no set standards for calculating MBAL levels, and “poor” recruitment has not been defined explicitly.
Few BRP's have been expressed in terms of recruitment, per se. One possibility that has recently been suggested by Mace (1993) is to define a threshold biomass which corresponds to the point on the SRR where expected recruitment is 50% of the maximum. A model presented by Thompson (1993b) supports the use of the 50% recruitment level in that 50% is the maximum reduction in recruitment that could be observed in equilibrium for a stock that is fished at the MSY rate. Myers et al. (1994) evaluated this reference point for 72 sets of stock-recruitment data from around the world. Although these analyses all measure relative recruitment in terms of the underlying (deterministic) stock-recruitment relationship, the 50% reduction can be generalized by framing it in terms of expected recruitment, and may provide a robust safeguard against recruitment overfishing. The challenge is in estimating the maximum recruitment, analogous to previously mentioned difficulties in estimating B0.
This recruitment-based reference point can be translated into either a biomass-based or F-based reference point. When cast as a biomass threshold, this reference point has an advantage over biomass thresholds expressed as a fixed percentage of B0, in that it takes account of the degree of compensation in the S-R relationship, setting more conservative (higher) thresholds for stocks with lower compensatory reserve. Such methods should be preferred over the blanket adoption of 20% Bo, which is unlikely to be applicable across the entire range of observed levels of stock resilience. However, rarely are there stock-recruitment data with sufficient contrast to estimate stock resilience precisely. For example, Myers et al. (in press) found that the biomass at 50% Rmax sometimes appeared overly risky, particularly when the available historical data exhibited zero or negative slope, resulting in extremely high estimates of the slope at the origin of the S-R curve. Conversely, for data exhibiting a positive slope overall, the method often estimated a threshold that was extremely large. These problems are related more to a lack of contrast in the data and the validity of the fitted curve than to the definition of the reference point itself.
When cast as an F-based threshold, a reference point based on relative expected recruitment can be expressed in terms of equilibrium spawning per recruit, providing (as above) that the degree of compensation in the S-R relationship can be estimated.
There are many cases where neither F nor B can be estimated explicitly, due to lack of data. The only option in such situations is to develop proxies based on the type and quality of data that are available. Proxies that may index F include truncated age distributions and small or decreasing mean size in landings or measures of fishing effort; those indexing biomass include low commercial catch per unit effort (CPUE) and low or markedly declining research survey indices. For example, overfishing could be specified as a ratio of current commercial or research CPUE compared to the CPUE of some historic period when the stock was lightly exploited. It is sometimes difficult to use such proxies to develop measurable, unambiguous and meaningful overfishing definitions. Proxies for F may be difficult to specify and interpret due to departures from a stable age distribution (e.g., a decrease in mean size may indicate a strong incoming year class rather than high F); proxies for B may be difficult to specify, due to the problem of selecting a suitable base period and changing catchability related to the efficiency of fishing or the distribution of the stock.
One persuasive argument in favor of specifying the limit reference point for recruitment overfishing as a maximum fishing mortality rate (F) is that it relates to the act of fishing and therefore can be controlled directly. In fact, the amount and characteristics of fishing on the stock are the only components of stock dynamics that can be controlled by management. However, the ultimate intent of management with respect to conservation of the resource is to ensure that there is sufficient spawning stock remaining after the harvest for the stock to sustain itself.
Reference points that give a maximum fishing mortality rate have the further advantages that: (1) There is a theoretical and empirical basis for the selection of maximum F levels, such as Fmed, F20%, or F35% (Goodyear 1977; 1980; 1989; 1993; Sissenwine and Shepherd 1987; Gabriel et al. 1989; Clark 1991; Mace and Sissenwine 1993); (2) when the fishery is operating near the limit a maximum harvest rate strategy may not result in fishery closures, but rather require substantial reductions in catches or effort if the threshold is crossed; (3) an appropriate limit reference point can be estimated from relatively sparse fishery data and information on the life history characteristics of the stock in question; and (4) setting a maximum F can prevent the stock from depletion due to fishing in the long term.
On the other hand, there are some disadvantages in limits specified in terms of a maximum fishing mortality rate only. Maximum fishing mortality rate strategies do not increase the protection afforded to the stock when it is in poor condition. An F-based definition that is appropriate over some middle range of biomass levels, may not necessarily be appropriate at the extremes of biomass. For example, a maximum harvest rate, such as F20%, set to prevent long-term decline of the stock from its current level will not necessarily allow rebuilding of a stock that was seriously overfished in the past. Nor will it allow a fishery to develop its full potential if estimated from data obtained only from a period of light fishing. Further, changing environmental conditions and life history characteristics may necessitate changing the threshold harvest rate in the definition.
Reference points that specify a minimum biomass level for the stock, below which the fishery is curtailed or, in the extreme case, closed, have the advantages that: (1) Biomass is more directly linked to recruitment than is the fishing mortality rate; (2) minimum biomass levels provide a guide for management of stocks that are already depleted by setting a standard for rebuilding; and (3) during periods of adverse environmental conditions, a minimum biomass level provides a seed stock for eventual recovery when conditions are more favorable.
However, specifying minimum biomass levels can be difficult and is often more demanding of the data than determining a maximum harvest rate. This is particularly true if the biomass threshold is treated as absolute, i.e., the fishery is closed if the estimated biomass falls below the threshold, rather than indicative, i.e., when the stock is below and indicative biomass threshold the maximum allowable F is reduced. The problem of lack of observations over the full range of stock conditions (i.e., lack of contrast in stock abundance or changing environmental conditions) may cause the minimum biomass to be mis-estimated. The strategy of closing a fishery below a biomass limit and opening it above may also result in highly variable fishery yields and economic dislocation. Because the consequences of crossing an absolute biomass limit are so extreme, their use will often be accompanied by intense controversy about the accuracy of stock size estimates. In addition, managers and the public may misinterpret a biomass limit as the point at which the resource will collapse, heightening the controversy.
While F-based reference points applied in a multispecies fishery afford some protection to the suite of stocks fished, a biomass limit is, of necessity, set on a stock-by-stcok basis. A maximum fishing mortality rate is needed for multispecies fisheries in particular, even if a minimum biomass level is set for some of the principal species in the suite.
Using a combination of a maximum fishing mortality rate, a indicative biomass level below which the maximum allowable fishing mortality rate is reduced, and an absolute minimum biomass limit may provide good protection for the resource. This is illustrated, schematically in Figure 1 in the form a harvest control law, such as are used for some U.S. Pacific coast stocks. The harvest control law specifies a maximum fishing mortality rate for a stock in healthy condition, some strategy for reducing F progressively as biomass falls below some precautionary level of stock biomass (regardless of the reason for low stock size), and a (lower) absolute biomass threshold below which fishing must cease or be restricted to bycatch only. The option of closing down a fishery when stocks become severely depleted should always be retained. One way of incorporating such an absolute biomass limit would be to set it arbitrarily low (e.g., 10% of current biomass) to be used as a safeguard only in extreme situations of failed management, poor stock assessment or continuing adverse environmental conditions that place the stock in jeopardy.
If a control law that reduces the fishing mortality rate gradually as biomass is reduced below some designated precautionary level is used: (1) It affords additional protection for the resource when stock condition is apparently poorer; (2) the consequences of mistakes in the specification or estimation of reference points are not as serious; (3) relating F to biomass over some intermediate range of biomass should allow more time and flexibility for evaluating whether the stock is in a transition phase from one stationary state to another; (4) temporary reductions in biomass can be accompanied by temporary reductions in F that need not result unnecessarily in permanent changes in the composition or operation of the fishing fleet; and (5) small or gradual reductions (or increases) in F will be less controversial, and therefore less subject to litigation.
There are three principal sources of uncertainty with respect to the precautionary application of limit reference points for fisheries. The first is the difficulty of adequately accounting for some life history features in choosing the reference points. This means that there is uncertainty about the dynamics of the stock. In effect the determination of a precautionary limit is uncertain because of the difficulty of describing the relationship between stock and recruitment. As noted in the introduction, the choice of a null hypothesis is crucial in dealing with uncertain stock dynamics. To be cautious, it should be assumed that there is a linear relationship between stock and recruitment, such that reductions in spawner abundance (increases in fishing pressure) will reduce stock productivity directly. However, there will still be uncertainty about all parameters used to calculate the reference points, e.g., growth and maturation rates, an that uncertainty needs to be accounted for in application of any precautionary strategy.
A second major source of uncertainty that affects the use of precautionary reference points is measurement error in the determination of the current state of the stock. For many stock assessments, estimates of measurement errors are available and these should be used directly in advising managers on the probability that a stock is overfished relative to a given reference point. Such uncertainty is generally reduced with longer time series and more accurate and precise data. e.g. for relative abundance indices. The benefits of reduced uncertainty when managing a stock under a given harvest strategy show up most clearly in the expected variability of yield (Powers and Restrepo 1993) and the power and Type I error for detecting the probability of recruitment overfishing (Rosenberg and Restrepo 1993)(here, Type I error refers to erroneously concluding that overfishing is taking place). As would be expected, the statistical power of detecting overfishing is higher in more precise assesments having a longer time series and higher contrast in abundance levels. Similarly, the Type I error is lower for longer time series and higher contrast in abundance.
Assessment methods are subject to errors due to variability in input data and to model mis-specifications. In some cases, errors tend to cancel. For example, the natural mortality rate M is rarely known accurately, and errors in M result in systematic errors in assessments. However, if a reference point is based on models using the same erroneous value of M, performance of the limit reference point may prove to be robust.
A more disturbing possibility is the so-called “retrospective problem” (ICES 1991). Experience has shown that assessment methods in some cases consistently overestimate or consistently underestimate current abundance for a given stock, as compared with estimates based on subsequent information. Causes for this phenomenon are many, including mis-specification of natural mortality values, biased trends in relative abundance data, and other forms of model mis-specification such as ignoring sexually-dimorphic growth. As stocks approach a condition of being overfished, assessment methods may be prone to Type I and Type II errors (falsely indicating recruitment overfishing when it is not occurring or failing to indicate overfishing when it is occurring), due to the “retrospective problem.” The error may be recognized only after passage of several years. This leads to the question of how management should address such retrospective errors, especially when there is reason to believe the error is an ongoing phenomenon.
A third source of uncertainty relates to possibly changing environmental conditions that affect stock productivity. Such environmental changes may mean that the value of the limit reference point must be changed, but it is difficult to detect and forecast environmental trends and their impacts. Most stock assessment models and overfishing definitions assume that life history characteristics are constant and that long-term changes in stock abundance are determined principally through a stationary stock-recruitment relationship. Short-term fluctuations in the environment introduce variability into the stock-recruitment relationship, but do not create a fundamental problem for the analysis. However, long-term trends in the environment and changes in the density-dependent nature of individual growth and egg production can change the shape and scale of the stock-recruitment curve. The short duration of most time series hinders unambiguous detection of these trends and changes. In a short time series, the stock is typically observed over only a narrow range of abundance. The resulting lack of contrast in stock-recruitment data can lead to large measurement error in estimates of biological reference points, and to estimates of biological reference points that may not be applicable to other levels of stock abundance or environmental conditions. While extending the time series can alleviate problems caused by lack of data contrast, it can exacerbate problems caused by long-term trends in the environment.
Limit reference points based on an absolute minimum biomass level differ from definitions based on a maximum fishing mortality rate in terms of their ability to protect a stock during prolonged periods of adverse environmental conditions. A minimum biomass threshold may be preferable, because it can protect a stock until there is sufficient information on production capacity. However, if the environmental carrying capacity for new recruits alone has changed (i.e., if the slope at the origin of the stock-recruitment curve is unchanged), then the new climate regime may not change the appropriate fishing mortality rate. In this case, a reference point based on maximum fishing mortality rate would be robust; the corresponding yield and biomass levels would simply be scaled up or down by the change in recruitment potential.
All assessment methodologies contain some amount of error and/or bias. One aspect of the performance of a methodology for setting a limit reference point is its ability to identify accurately a condition of overfishing, even when implemented according to imprecise or inaccurate stock assessments. This property can be called robustness. It is important to evaluate the robustness of not just the method for setting a limit reference point, but the performance of the entire management procedure used for the stock, meaning everything from data collection and analysis, to the assessment results and their use in combination with target and limit reference points in harvest control laws. The reason for this is that there is feedback between all parts of the system (stock-management) over time: today's decisions affect tomorrow's outcomes and, therefore, tomorrow's decisions. The robustness of a management procedure can be best evaluated through simulation experiments, as advocated by, e.g., de la Mare (1986), Rosenberg and Restrepo (1993), and Restrepo and Rosenberg (1994).
Because all of the various sources of uncertainty interact, managers should choose a “decision rule” that sets an acceptable probability of recruitment overfishing, given the uncertainty in knowledge of the true dynamics of the stock, the estimates of current stock status, and the possibility of environmental trends. The acceptable probability of overfishing is related to the time frame considered, the consequences of crossing the limit reference point, and the action to be taken if it is concluded the stock is overfished. For example, a given probability of overfishing might be acceptable if the only consequence is a slightly increased risk of poor recruitment in one year. However, the same probability might not be acceptable if there was thought to be a high chance of recruitment failure that would affect the fishery for several years to come. Similarly, if the actions taken upon crossing the threshold are likely to redress the situation quickly (e.g., if crossing a maximum F threshold is followed by corresponding quota reductions), then the decision rule may allow a higher probability of overfishing than if the action is merely to begin a 20 year gradual decrease in fishing.
Thus, an important consideration is that all limit reference points are not created equal in terms of their inherent degree of cautiousness. As shown by Rosenberg and Restrepo (1993), there is little to be gained by setting a very low allowable probability of overfishing if a very cautious limit reference point is being used. On the other hand, overfishing could be avoided by setting a low allowable probability of overfishing when the limit reference point is not very cautious.
These types of uncertainties and the need for a decision rule on the acceptable probability of overfishing apply to both F-based and biomass-based thresholds. A control law that reduces the fishing mortality rate gradually as biomass is reduced below some designated precautionary level, as advocated in the previous section, can incorporate decisions based on the perceived uncertainty in stock status and the reference point (Restrepo and Rosenberg, 1994). For instance, the control law may reduce F in inverse proportion to the estimated probability that the stock is below a precautionary biomass-based threshold.
Estimates of stock status and the appropriate limit reference level to prevent recruitment overfishing will always be uncertain and engender substantial argument in management fora. Because of this, the management actions to be taken if the overfishing definition threshold is crossed should be explicitly stated in conjunction with the chosen decision rule. It is important that the determination of management actions be made prior to reaching the limit, so that action to protect the stock is not delayed. If this is done, and the reference point is chosen conservatively, then the time for the stock to recover from any short period of overfishing should be short. It is recommended that the expected time for a stock to recover from the limit level to the target level be considered in developing limit reference points. Calculations should be done to estimate how rapidly recovery could occur with high probability if the fishery were closed. For example, in the event of recruitment overfishing a rebuilding program could be designed to result in a high probability of recovery in not more than one generation longer than the time needed under a complete closure.
Precautionary management reference points are those intended to prevent recruitment overfishing, even if a direct link between spawning stock size and subsequent recruitment cannot be established statistically.
In order to be precautionary, the appropriate null hypothesis is that spawning biomass or egg production is linearly related to recruitment, i.e., that the stock does not compensate for reduced abundance by increasing productivity. A null hypothesis of average constant recruitment at all stock sizes (slope = 0), prevalent in the minds of many scientists and managers, can result in continued harvesting until a major decline in recruitment at low adult biomass occurs, the antithesis of precaution.
Limit reference points for biological conservation should set the constraints within which a management strategy must operate. A number of limit reference points related to recruitment overfishing have been developed based on theoretical or empirical work, or both, as detailed in the second section above. In some cases these are expressed in terms of fishing mortality rates and in other cases in terms of biomass. Both ways of expressing limits have advantages and disadvantages and how a particular limit definition performs could be case-specific. However, it is unlikely that a single limit reference point can provide protection for the resource under all foreseeable circumstances and, thus, it is useful to define harvest control laws which combine several thresholds. For instance, using a combination of a maximum fishing mortality rate, a precautionary biomass level below which the maximum allowable fishing mortality rate is reduced, and an absolute minimum biomass limit (Figure 1) may provide good protection for the resource.
A schematic harvest control law
In this example, the dashed line represents a target fishing mortality rate which may vary as a function of stock size. A stock biomass value of 2 corresponds to an absolute biomass threshold. Biomass levels below this value indicate that the stock is overfished. The solid line represents a threshold fishing mortality, or the maximum allowable F. F values above this line indicate overfishing. A stock biomass value of 4 corresponds to a precautionary biomass level below which the maximum allowable F is reduced.
A precautionary management strategy should contain, in addition to limit reference points, a priori decision rules on the acceptable probability (risk) that recruitment overfishing will take place, given the target harvest and the estimated stock status. If the acceptable probability of overfishing is not defined a priori, or if it is redefined with every new assessment, it becomes inevitable that higher risks will be taken at low stock sizes in order to maintain stable catches. What constitutes a reasonable decision on the acceptable probability of overfishing is likely to be case-specific, depending on the life-history characteristics of the stock in question, in particular on its resilience to fishing.
All of this can - and should - be investigated from available data and simulation studies. The choice for a particular definition should also be tied to uncertainty and precautionary management dictates that more uncertain situations require more conservative measures.
We gratefully acknowledge the ideas and contributions of the other members of the review panel for overfishing definitions in the U.S.:P.Mace, G. Thompson, G. Darcy, W. Clark, J. Collie, W. Gabriel, A. MacCall, R. Methot, J. Powers, T. Wainwright, L. Botsford, J. Hoenig and K. Stokes. The original idea for the review and support for it's work came from M.P. Sissenwine and W. Fox and we thank them for their guidance. Mike Sissenwine has also guided our simulation studies on uncertainty and risk assessment for several years, providing support together with the University of Miami's Cooperative Unit for Fisheries Education and Research by National Oceanic and Atmospheric Administration Cooperative Agreement NA90-RAH-0075.
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