Reference Points Based on SR Relationships
For completeness, reference points based on availability of historical SR data are included here and are obviously those which require the most complete data sets, consisting of time series of agestructured catches and population sizes, often supplemented by regular biomass surveys. As noted, such reference points form the main basis for LRP definition in the ICES and, to a lesser extent, NAFO areas. For example, F_{MED} (Sissenwine and Shepherd, 1987) is the fishing pressure that reduces spawning biomass of a year class over its lifetime below the corresponding value for its parents and is estimated from the slope of the line through the origin of the SR relationship for a fishery. Others are referred to more extensively in Mace (1988), Caddy and Mahon (1995), etc., and it remains to be seen whether these are likely to have wide application for datapoor fisheries, but a brief list of common approaches to LRP formulation follows.
Reference Points Based on Y/R and SSB/R Analysis
The classical TRP for Y/R analysis is of course F_{MAX}, which again, nowadays, tends to be regarded as an LRP, with F_{0.1} commonly used as the corresponding TRP, both being subject to change as a result of changes in age distribution, recruitment and selectivity changes. Hence the need for the use of F_{0.1 }in conjunction with an LRP. In New Zealand, if an LRP cannot be estimated from a model, it is often substituted for by the relevant value of M (see later). In South Africa, F_{0.2} is frequently used and is a more restrictive exploitation rate reference point, which has been used as a target or a benchmark in a fisheries management procedure (Butterworth et al., 1997).
Spawning stock biomass/recruit reference points include F_{REP}, F_{HIGH} and F_{LOW} and these may also be subject to variability for the same reason as mentioned for F_{0.1} above (as, in fact, is true for most RPs). F_{35%} or F_{30%} are two fishing rates based on previous data sets for stock and recruitment that calculation has shown will maintain SSB/R at safe levels: the latter is an RP used by the North Pacific Fishery Management Council (Hollowed and Megrey, 1993), which is believed to be roughly equivalent to about 75% of longterm MSY as long as spawning stock size does not fall below 2060% of the unfished level (i.e. both fishing mortality and biomass need to be monitored).
Reference Points Based on Production Modelling
The classical RP (now regarded in some quarters as an LRP) is of course F_{MSY} In the past, MSY has been the classical management target, to be probably replaced now by quotas set at lower levels of harvest pressure, such as F_{0.1} or that corresponding to 2/3 MSY, (Doubleday, 1976). Although, strictly speaking, it belongs in the previous category since in the ICES area it is usually estimated by the Shepherd approach, which depends on data for fitting SR relationships, F_{CRASH} In theory could be estimated by more conventional production modelling as the point of interception of the righthand limb of the curve on the fishing effort axis. One may doubt whether this is a particularly safe LRP and certainly not one to be exceeded! More relevant here could be the economic benchmark referred to as the point of Bioeconomic Equilibrium, where costs equal revenues from fishing (e.g. Panayotou, 1988). This seems a logical LRP to use, especially in highseas fisheries where costs and revenues should be relatively easily measured.
Using size compositions to arrive at simple estimates of total annual mortality rate may allow application of production models using mortality in place of fishing effort (e.g. Caddy and Defeo, 1996). These authors show that, given reasonable time series of annual data for Z_{t} and Y_{t}, it is possible to use bootstrapping to arrive at a series of estimates for a TRP such as MSY. Ranking separate estimates and plotting them cumulatively (Fig. 7), the 50% quartile of the cumulative distribution of MSY estimates might make a suitable LRP, while the 25% or more cautious percentile could be a candidate for a TRP.
Reference Points Based on Survey Data
The trend in many fisheries where commercial data is uncertain or unreliable is to rely to a progressive extent on estimates of biomass coming from surveys. While this does not seem a readily available option for most tuna fisheries, a study of a longline fishery for sablefish (Ruppert et al., 1985) suggests a general formula for using survey data in setting harvests under thresholds, namely
Catch in year t of age group a: C_{at} = G_{t}*(S_{a}*N_{at}  T)
where G_{t} is some function of the exploitation fraction in year t, S_{a} is selectivity at age, N_{at} is the number of age group a in year t, and T is the threshold population size below which harvesting ceases. Some variation of this approach may provide elements for constructing a harvest rule whose degree of precaution will depend largely on the value of G_{t} used. Other more complex procedures for calculating quotas based on RPs are of course part of fishery management procedures (Butterworth et al., 1997), and the 'MagnussonStefansson feedback gain rule' is similar and is described in the following section.
Reference Points Based on Past Fishery Yields
Past yields from a fishery, under certain circumstances, can provide some rough indication of future potential, as long as independent biological indications support the continuity of the fishery at historical levels. Some ideas on this have been proposed by Pope (1983), and in New Zealand (Annala, 1993) several yieldbased reference points are currently used in fisheries management. These are either developing fisheries, in which case extremely precautionary criteria are used, or are fisheries with a fairly long history of exploitation, where maximum potential yields are believed to have been reached in the past but where the stock continues to produce at close to historical levels. Maximum Constant Yield (MCY) is the "maximum constant catch that is estimated to be sustainable, with an acceptable level of risk, at all probable future levels of biomass". Recognizing that this does not take into account future catastrophes, under certain constraints it nonetheless corresponds to a relatively low level of harvest and can be regarded as a precautionary target, which could be tested by stochastic simulations incorporating likely recruitment variability.
Figure 8. Relationships among Maximum Yield (MCY), Current Annual Yield (CAY) and Maximum Average Yield (MAY) (from Annala, 1993)
Current Annual Yield (CAY) is a dynamic version of MCY (Fig. 8), in which a constant exploitation strategy at F_{REF} is applied. This Fbased reference point is "the level of instantaneous fishing mortality which, if applied each year, would, with an acceptable level of risk, maximize the average catch from the fishery" and, again, would be established from simulation. According to Annala, CAY is calculated as:
CAY = [F_{REF}/(F_{REF} + M)]*[1exp  (F_{REF} + M)]*B_{BEG}
where B_{BEG} is the stock biomass at the beginning of the fishing year.
The mean value of historical annual values of CAYs is another measure, the Maximum Average Yield (MAY) (Fig. 8), which is considered to be close to MSY and is often interpreted as such by New Zealand's fishing industry (Annala, 1993).
One other useful approach to setting quotas when only commercial or survey indices are available has been referred to as the 'MagnussonStefansson feedback gain rule' (NAFO, 1998 draft report) and is reported as particularly useful for restoring a depleted fishery to productive condition which has been gradually declining in stock size over time. The rule is:
Y_{t} = Y_{t1}*(1+g(B_{t1}  B_{t2})/B_{t2})
where Y is catch and B is biomass (or commercial CPUE index) in year t, and g, referred to as the 'feedback gain', reflects the degree of proportionality between changes in biomass observed between the last and current year and, hence, the extent to which it will be reflected in the coming quota. Values for g of 1 and over seemed to contribute to precautionary approaches in simulations, but higher values of g were found to do so by leading to progressively more frequent closures.
Other Empirical Approaches
The concept of an RP as a 'conventional' value that is accepted by industry is one idea that may have to be considered if available data does not allow calculation of a 'scientific' or modelbased index (even performance of these latter is inevitably uncertain until they have been used in a management system, for reasons mentioned earlier). One example here was the use of a spawning escapement (40% of the biomass) for squid stocks in the FalklandMalvinas region, which was in a sense used as an LRP. Such a 'conventionalized' approach to setting LRPs appears more feasible, if one considers that, even with the best of analyses, a system of LRPbased management will depend for its feasibility on the degree of implementation (Fig. 1).
A further generalization that may be useful is to consider Fbased RPs in terms of the natural mortality rates that apply to a stock, since these are, after all, the natural level of risk the stock faced before fishing begins. For tunas, these values probably range from around 0.5  0.8+ annually for small tunas to 0.1 or lower for adult bluefin tuna. Several generalizations, beginning with Gulland, have examined the possibility of defining the MSY reference point in terms of natural mortality rate and biomass. Gulland (1971) proposed that M is approximately equal to M at MSY and hence, for the logistic model,
MSY = 0.5*M*B_{0 } (1)
Several authors have since questioned this equation, (e.g. Garcia et al., 1989) and hence there is also a concern that F (MSY) = P*M, for P = 1 would be too optimistic as a means of guessing at the order of magnitude for a safe fishing mortality corresponding to MSY, especially for shortlived animals. In general, various authors suggested that P should be lower for shorterlived species. Patterson (1992) proposed for small pelagics that a value of P = 0.5 (F_{MSY} = 0.5M) would be appropriate. Objective data on this point are difficult to find, but one solution proposed here is that P declines linearly with M, so that F(LIM) is smaller relative to M for shortlived than for longlived species. Based on the preceding account, a linear decline in P with natural mortality rate between two sets of extreme values was postulated, based on the following two data sets:

Apical predator 
Small pelagic fish 
M = 
0.1 
1.25 
P = 
0.9 
0.50 
Solving for these values (and admittedly other sets of 'seed' values could have been used), gives the empirical relationship below:
F_{LIM} = 0.981M0.194M^{2} (2)
A range of values for FLIM using this approach are given in Table 5.
Table 5. Predicted values for F_{LIM} from equation 2
M 
P 
FLIM 
0.1 
0.836 
0.084 
0.2 
0.803 
0.161 
0.3 
0.771 
0.231 
0.4 
0.739 
0.296 
0.5 
0.707 
0.353 
0.6 
0.674 
0.405 
0.7 
0.642 
0.449 
0.8 
0.610 
0.488 
0.9 
0.577 
0.520 
1 
0.545 
0.545 
1.1 
0.513 
0.564 
1.2 
0.480 
0.576 
1.3 
0.448 
0.583 
1.4 
0.416 
0.582 
1.5 
0.384 
0.575 
It is postulated that an Fbased LRP determined in this way (Fig. 9) might be tested against other estimators, and could be used to determine a cautious level of target fishing intensity using the methods given in Caddy and McGarvey or the simple exponential relationship given by ICES in Table 2.
A number of variations of equation (1) have been used, e.g. substituting x for 0.5. Annala (1993) notes that in New Zealand, values for
MCY = 0.25*F_{0.1}*B_{0}
have been used in new fisheries to set a conservative TRP, and
MCY = 0.5.F_{0.1}*B_{av}
has been used in 'mature' fisheries, both regarded as relatively conservative. The quantity B_{av} in the last equation is the average historic recruited biomass. Simulation results (Mace, 1988) are reported to have shown that MCY may be as low as 60% of the deterministic MSY. Does this make MCY a possible candidate as a TRP to accompany MSY (used as an LRP) in a management system?