ASFB Home > 2001 > Commercial catches as an indicator of stock status in NSW estuarine fisheries: trigger points, uncertainty and interpretation

Commercial catches as an indicator of stock status in NSW estuarine fisheries: trigger points, uncertainty and interpretation

James P. Scandol and Robyn E. Forrest

(This paper was written whilst James Scandol and Robyn Forrest were at the Centre for Research on Ecological Impacts of Coastal Cities, Marine Ecology Laboratories A11, University of Sydney NSW 2006. James is now at NSW Fisheries, PO Box 21, Cronulla, 2230, NSW. Phone: (02) 9527 8540. His email is: James.Scandol@fisheries.nsw.gov.au. Robyn is now at the UBC Fisheries Centre, 2204 Main Mall, Vancouver, BC, Canada V6T 1Z4. Her email address is: r.forrest@fisheries.ubc.ca).

Abstract

NSW Fisheries has elected to use commercial catch as a temporary indicator of the state of stocks within the Estuary General Fishery until better indicators can be developed. One rule of management requires that if landed catch varies more than a pre-specified amount from the mean catch between 1984-85 and 1998-99 a review of the management arrangements is required. The trigger points have been defined for the principal species within the fishery and vary from a 10% to 50% deviation from historical catch.

Monte Carlo simulation was used to analyse the effectiveness of this catch-based indicator for the detection of recruitment failure or survival failure (of the standing stock). Simulated catch data were generated with a lagged stock–recruitment biomass model and the performance of the indicator estimated. This analysis was completed by estimating the probability of obtaining false negative and false positive outcomes in the detection of recruitment/survival failure. Results suggest that if NSW Fisheries uses trigger points of around 25-40%, it should be able to detect both recruitment failure and survival failure. However, there will be a high rate of false positive outcomes. Analyses of this type require judgments to define 1) reference points; 2) the magnitude of change that represents a problem; and 3) acceptable probabilities of false positive and negative outcomes. Stakeholders should be involved in making these judgments. The precautionary principle implies that the rate of false negative outcomes should be minimised.

Introduction

Background

For the NSW Estuary General Fishery, NSW Fisheries has elected to use landed or commercial catch as a temporary indicator of the state of the fishery. Ideally, catch rate or catch per unit effort are used as indexes of stock abundance. However, the data available on fishing effort in the Estuary General Fishery is seriously compromised by the inability to account for multiple gear use on the same day and questionable credibility of effort records. Scientific staff in NSW Fisheries are reluctant to use the effort data for the fishery and we concur with their misgivings. Indicators based on age and length structure are being developed and will be implemented in due course for species for which there is such data. Fisheries in NSW with credible fishery-dependent effort data or fishery-independent abundance data will use catch rate as an index of abundance rather than commercial landings.

Within the fisheries management strategy for the NSW Estuary General Fishery (NSW Fisheries, 2001; Table 5, this paper) NSW Fisheries has defined the trigger points for landed catches of primary species that will generate a review of the management arrangements. Should future catches be greater or less than a percentage variation (e.g. 25% for yellowfin bream, (Acanthopagrus australis) of the mean catch between 1984-85 and 1998-99 then a review will take place.

There are several advantages to this approach including:

• the aggregate catch is more accurately recorded than are most other entries in the catch records database.
• There are no elaborate calculations performed upon the catch data (such as standardising indices of abundance) and hence the process is transparent.

There are also disadvantages:

• catch is determined by many important factors that are unrelated to stock size, including targeted fishing effort, non-targeted fishing effort (where the species is landed bycatch) and price.
• The difficulty of determining what degree of variation from the mean catch should be considered important, and why.
• The concern that triggers will trip when they should not have (false positive responses) or do not trip when they should (false negative responses). Interpretation of the results will be difficult unless these errors are explored.

The following modelling study investigates these issues by developing a simple model of the stock dynamics, calibrating this model to patterns of observed catch, and then simulating a recruitment failure or increase in stock mortality. The trigger points are then tested to determine if they successfully detected these changes, and the rates of their success and failure in detecting changes are estimated.

The model used is referred to as a lagged stock recruitment model (Hilborn and Mangel, 1997). This model is more complex than the standard biomass dynamics model but less complicated than a complete delay difference model (Hilborn and Walters, 1992). Stock biomass is represented but at no point shall actual numbers be given as we are not confident that available numbers represent a real estimate of the biomass of each stock. The calibration exercise aims to determine the model parameter values that result in quantitatively similar patterns of catches. It does not represent the stock biomass.

The analysis described below (a slightly modified version of Chapter 7 of Scandol and Forrest, 2001) has logical parallels with power analysis (Peterman 1990; Underwood 1990) in which the probability of Type II error of a statistical test is estimated. Type I and Type II errors are the same type of concept as the false positive and false negative judgements described below. Underwood (1997) noted that precautionary management strategies should be based upon statistical analyses with a low Type II error, or high power, but the exact requirements will depend upon the hypothesis being tested.

Indicators and the underlying system

A relationship between an indicator and an aspect of the system of interest is shown in Figure 1. The usual 'aspect of the system of interest' is the exploitable biomass, the usual indicator is catch rate, and the expectation is that catch rate is positively correlated to the exploitable biomass.

Figure 1 Example relationship between an indicator and the system state it represents. A meaningful indicator will be correlated to the system state, but the relationship will be uncertain (represented by the ellipse). The usual state represented is the ratio of current biomass to initial biomass (B/B₀) and an indicator could be the ratio of the current catch rate to the initial catch rate (U/U₀). [Diagram modified from Stewart, 2000]

This diagram requires extension for it to be of value to decision-makers. First, a threshold state of the system needs to be specified that would be avoided by decision-makers. For example, if the system state (y-axis for Figure 1) was defined as the proportion of virgin biomass, then a limit reference point threshold would usually be 20% of B₀ (Gilbert et al. 2000). In our case the y-axis will represent a measure of recruitment failure or biomass survival failure. Second, a threshold value on the indicator axis that represents where action should be taken. Note that this value would be a trigger point, not a limit reference point. Such action would usually take place when the catch rate falls below a particular level, but in our case will represent the percentage deviation of landed catch from the historical average (Figure 2).

Once these two additional thresholds are defined, four regions are evident on the graph (Figure 2):

• True positive: the actual state is below the threshold and the indicator makes the correct inference;
• True negative: the actual state is above the threshold and the indicator makes the correct inference;
• False positive: the actual state is above the threshold and the indicator makes the incorrect inference; and
• False negative: the actual state is below the threshold and the indicator makes the incorrect inference.

Figure 2. Extension of Figure 1, with the thresholds for problems and decisions annotated. When a decision is made there are four possible outcomes: true positives (state is below threshold, and this was correctly detected with the indicator); true negatives (state is above the threshold, and this was correctly detected with the indicator); false positive (state is above the threshold and this was incorrectly detected with the indicator); and false negative (state is below the threshold and this was incorrectly detected with the indicator). [Diagram modified from Stewart, 2000]

We are not proposing to quantify the biomass in this analysis but are looking to detect a change to the fishery to which a response should be made, if catch is used as an indicator. Two example issues have been selected that represent the sort of events that could occur. (1) Recruitment failure and (2) an increase in the mortality of the stock from sources other than commercial harvesting (e.g. an increase in natural mortality, illegal harvesting, or recreational catch). In our analyses, we have termed this survival failure. As in the Fisheries Management Strategy (NSW Fisheries, 2001) we have used the deviation from average historical catches as an indicator for the stock. Once catches fall below (or exceed) this indicator then the trigger has tripped. We examine the appropriate level at which these triggers should be set to detect important changes to the fishery.

Methods

The model

The underlying model used to represent the stock is:

,

where B_t is the biomass at the end of year t, m is the annual mortality of biomass during year t, thus (1-m) is the survival of the biomass during year t. R_t-lag is the recruitment to the biomass with a time lag reflecting the number of years from spawning to recruitment to the fishery. Recruitment error, R_err, is described below. Catch during year t is represented by C_t and the difference equation is initialised with a starting value B₀.

The initial recruitment is estimated by assuming:

The stock-recruitment relationship used is a Beverton-Holt model that has been re-parameterised to the steepness of the stock recruitment relationship and the initial biomass/recruitment. Thus:

, , and ,

where z is the steepness of the stock recruitment relationship and a and b are the parameters of the standard Beverton-Holt stock recruitment curve.

This transformation of the stock recruitment relationship is common (Hilborn and Walters 1992), as it enables the steepness of the Beverton-Holt stock-recruitment relationship to be altered without changing the recruitment at initial stock size. The parameter z is defined such that when R_t = z⋅R₀ then B_t = 0.2⋅B₀, where R₀ and B₀ is the initial recruitment and biomass respectively.

Two types of error are introduced in the system dynamics. Recruitment or process error (R_err) is a lognormal variate of mean 1 and standard deviation σ_R, which is calculated by transforming a normal variate N (mean 0, standard deviation 1) using:

The second type of error is catch error C_err. This error is a mixture of the usual process error and observation error because catch is the observable indicator used to assess the fishery, but variation in catches will also affect the system dynamics. The following calculations are performed in sequence:

,

where represents a catchability type constant (defined differently to the usual catchability), σ_C is the standard deviation in the catch error, and C_t is the catch during year t.

2.2 Model calibration

Non-linear optimisation was not used to calibrate the model because both process and observation errors were included in the model. Sampling-importance-resampling methods (McAllister et al. 1994) would have been ideal but were too technically complicated for this exercise. In lieu of these a simple random search strategy was used. The appropriate algorithm was:

select random values of σ_C , σ_R and from random distributions (see Table 1 for a summary of these sampling distributions). The value of was assumed to equal ;

calculate ten replicate simulations for those particular parameter values, for each replicate calculate the mean and standard deviation of the simulated catches;

calculate the average mean catch and the average standard deviation over those 10 replicate simulations. This results in an overall measure of the mean and variability of the simulated catches for the selected parameter values;

calculate a goodness-of-fit criterion between the average of the simulations and observed catches using:

this goodness-of-fit criterion captures differences in both the average catches and the standard deviations of the catches for replicate sample i;

repeat the sampling process 2000 times and sort the results in ascending order by Δ_i;

select the best 5% (the top 100 replicates) of the smallest difference between the observations and the simulations of the samples (Δ_i). This gives values of σ_C , σ_R andthat generate similar patterns of simulated catches to observed catches.

Table 1. Summary of the parameters used and the distributions from which their values were sampled.

Parameter	Distribution	Minimum	Maximum
	Uniform	0	100
σC	Uniform	0	0.5
σR	Uniform	0	0.5

Once a set of parameter values are available that generate time-series of catches that are quantitatively similar to the observed catches for that fishery, the trigger point analysis can be completed. This analysis involved two stages: modelling stock failure and estimating the error rates of various trigger points. These are discussed below in turn.

2.3 Modelling recruitment or survival failure

Biomasses and catches are projected for an additional five years from the last year of recorded catches. However during that time an 'impact' was imposed on the biomass dynamics to reflect either recruitment failure or increased mortality.

Given an impact value φ_r that varied from 0 to 1, recruitment failure was modelled with:

,

and survival failure was modelled with φ_m,

Thus φ = 0 reflected complete failure, and φ =1 indicated no failure. The threshold of what represents a significant failure is somewhat subjective but needed to be defined. We have assumed that a failure of φ < 0.5 should be detected unless otherwise specified.

Simulated catches were generated using with the underlying biomass impacted by recruitment failure or survival failure.

2.4 Error rates of trigger points

The outcome of this exercise was to estimate the probabilities of true positive, true negative, false positive and false negative results for various levels of the trigger point. The trigger point level (τ %) is the deviation of future catches beyond the mean catch between 1984-85 and 1998-99, as this is the reference point set by NSW Fisheries in the Estuary General Management Strategy (NSW Fisheries, 2001). Should the value of τ be set close to zero, the trigger point would trip every time (any future catch would be greater than a 0% deviation from the past). In this case we would expect all false positives or true positives. Alternatively, if the trigger point level was extremely high (~100%), the trigger point would never trip and we would expect all false negatives or true negatives.

The sampling process was similar to the scheme used for model calibration. For each type of impact (recruitment failure and survival failure) one hundred φ_r and φ_m values were given random uniform values between 0 and 1. Each of these 100 values was used in association with the 100 best solutions from the model calibration exercise. For each replicate calculation, 10 samples were calculated from the model and if a future simulated annual catch was less than (or greater than) τ % of the simulated mean historical catch between 1984-85 and 1998-99 then the trigger point was tripped. For each of these 10×100 calculations the overall result (e.g. numbers of false positive, false positive) was counted and then converted to probabilities by dividing by 10×100. These calculations were repeated for τ% values ranging from 0% to 100% in steps of 10%.

Results

Example calculation

We give an example using the NSW estuarine catches of dusky flathead (Platycephalus fuscus) before the formal results are presented.

Figure 3 illustrates observed catches of dusky flathead in NSW and also includes three replicate simulations of a stochastic model. Model parameter values were selected by the random search routine described earlier. The important advantages of this method are that the temporal dependencies associated with the observed catch time-series are retained in the simulated data and the data can be projected into the future. Figure 3 also illustrates these projected time series when there have been no changes to recruitment or annual biomass mortality (m).

Unless otherwise stated, the assumed value of m was 0.9, the steepness of the stock-recruitment relationship (z) was 0.8, and the time lag between spawning and recruitment to the fishery was three years. The impact of these assumptions is evaluated in Section 3.3.

Figure 3. Observed catches for the NSW Estuary General dusky flathead fishery (solid bold line). Three replicate simulations of catches are annotated on the plot. Projected values of simulated catches (starting in 2000) with the same system dynamics are also illustrated.

The random search routine provides valuable insight into the sensitivity of the simulated catches with the values of the parameters. Following from the dusky flathead example, frequency histograms of the three parameters for the best fitting 100 sets of parameter values sampled (Figure 4). Figure 4a indicates the samples values of where, apart from small values of this ratio, there is essentially random uniform distribution within the domain of the sampled distribution. The peak for values between 80 and 90 is probably sampling variation, but this is not an issue of importance. In contrast, Figure 4b indicates that the variation in successful values of catch error σ_C, is tightly constrained compared with the sampled distribution (uniform between 0 and 0.5). Only values less than 0.15 were permissible and the median of the distribution was 0.06. Similarly, only small values of recruitment error σ_R contributed to the better fitting models, though in this case values close to zero were frequently included. We have not included correlation plots of these optimal parameter values but report that there was no marked correlation between these parameters. The lack of marked correlation indicates that the model had sufficient but not excessive numbers of parameters.

a)

b)

c)

Figure 4. Frequency histograms of the parameter values of the best 100 simulations from the random search routine or model calibration procedure. (a) Parameter , (b) Catch error σ_C, (c) Recruitment error σ_R.

Using these best 100 solutions from the model calibration procedure the stock dynamics were projected into the future with recruitment or survival failure included (as discussed above). Figure 5 illustrates the consequences upon various outcomes when using τ % as the deviation from mean historical catches as the trigger point for dusky flathead in NSW. These examples illustrate that recruitment failure and survival failure yield quantitatively different results and should therefore be treated separately.

a)

b)

Figure 5. Examples of graphs showing the probability of false positive, false negative, true positive and true negative outcomes for a range of trigger points (τ) from zero to one, in the events of a) Recruitment Failure and b) Survival Failure for dusky flathead throughout NSW.

Figure 5a indicates that when τ is zero, then any deviation from historical catches will trip the trigger. Since the values for recruitment failure (φ_r) are sampled from a random uniform distribution bounded between zero and one, approximately half will be less than 0.5 (which we have defined as the threshold for a problem) and the converse proportion will be greater than 0.5. When the value of the catch trigger is 0.0 we expect approximately 50% true positives and 50% false positives as there will always be an indicated effect, but only half the time will there be an actual effect. In contrast, when the trigger value is 1.0, we will never detect an effect (0% of any catch is zero, and catches will always be above zero), and there will be a 50:50 ratio of false negatives and true negatives. Intermediate values of the trigger value generate intermediate results.

For recruitment failure (Figure 5a) the rate of false positives decays rapidly as we increase τ and the rate of false negatives does not become significant until the τ value is greater than about 0.5. Intermediate values of τ between 0.3 and 0.7 resulted in low error rates and high probabilities of successful detection of recruitment failure. Survival failure, where φ_m is similarly sampled from a uniform distribution, illustrates the same behaviour at the minima and maxima of τ as does the response to recruitment failure. Behaviour for intermediate values is however very different. False and true positives, and false and true negatives, essentially trace each other. Thus, there is no real differentiation between them. Trigger points can be set to minimise the number of false negative results but will do so at the expense of getting large numbers of false positive results.

This result enables us to discuss the selection of appropriate trigger points. Figure 5 shows that the probability of false negative outcomes tends to increase as the probability of a false positive outcome decreases. A decision needs to be made about acceptable probabilities for each of these types of error before an appropriate trigger point can be selected. The method we suggest is to select the largest probability of a false negative that is smaller than a previously agreed minimum probability (say 5%). In this way, the probability of false negative result is kept below an acceptable standard, whilst minimising as much as possible the probability of false positive result. An alternative is to select the trigger point under which the curves for false positive and false negative outcomes cross. In this way, the sum probability of making either type of error is minimised. This method, however, has a certain level of risk as the curves are likely to cross where neither probability is below an acceptable standard. This situation is illustrated in Figure 5b: here the curves cross at a trigger point where the probability of both outcomes being false is 20%, which in either case is likely to be an unacceptably high probability of error.

Evaluation of simulated catches

To evaluate the sensitivity of the analysis with differing types of data, four sets of simulated catch data were generated and the analysis done using each of these datasets. The four data sets had different, known properties, and showed either a) a decreasing trend in catches, b) an increasing trend in catches, c) constant catch with little variation, or d) random catches with large variation. Graphs of the four datasets are shown in Figure 6.

a)

b)

c)

d)

Figure 6. Graphs of the four simulated data sets showing trends in catches that are a) decreasing; b) increasing; c) constant; and d) variable.

Analyses of performance of trigger points for the events of recruitment failure and survival failure were done using each of the above fictitious datasets. Graphs of the results are shown in Figure 7.

Figures 7a and 7b illustrate the outcomes of the catch trigger analysis with these simulated datasets. These figures indicate that the results from the analysis are extremely robust and that similar results are generated for each type of stock failure regardless of the catch trend. Detection of recruitment failure is slightly more unreliable with decreasing catches, but survival failure is difficult to detect regardless of the catch history.

A similar comparison can be made with constant catches versus random catches. Figures 7c and 7d illustrate the results for constant catch history versus a highly variable catch history. With constant catch history recruitment failure can be reliably detected, but when the fishery has a highly variable catch history, recruitment failure is much harder to detect using variation in catches as an indicator. This is an intuitively reasonable result. As before, survival failure is difficult to detect under both catch scenarios.

a)

b)

Figure 7. Examples of graphs showing the probability of false positive (bold solid line), false negative (bold dotted line), true positive and true negative outcomes for a range of trigger points from zero to one, in the events of Recruitment Failure and Survival Failure for data with a) decreasing catches; and b) increasing catches.

In each case, the most appropriate trigger point selected was that which produced the largest probability of a false negative result less than 0.05. In this way, an acceptably low probability of a false negative was returned, whilst a low probability of false positive errors was maintained (see section 3.1). Table 3 gives the trigger points selected using this criterion for the events of recruitment failure and survival failure for the four fictitious data sets.

c)

d)

Figure 7 (continued) Examples of graphs showing the probability of false positive, false negative, true positive and true negative outcomes for a range of trigger points from zero to one, in the events of Recruitment Failure and Survival Failure for data with c) constant catches; and d) variable catches.

Table 2. Appropriate triggers for a i) decreasing trend in catches; ii) increasing trend in catches; iii) constant catches; and iv) variable catches, for the events of recruitment failure and survival failure.

	Event
Trend shown by data	Recruitment Failure	Survival Failure
Decreasing	0.7	0.5
Increasing	0.7	0.3
Constant	0.6	0.1
Variable	0.7	0.5

Table 2 indicates that a relatively high trigger point value can be set to detect recruitment failure that will allow an acceptable level of false negative outcomes whilst generating very few false positive outcomes. Survival failure is much more difficult to detect and there is no consistent value of a trigger point that will allow for small rates of false positive and false negative responses.

Sensitivity analyses

The sensitivity of the analyses to the assumptions in parameter values z (the steepness of the stock recruitment relationship) and m (the annual mortality of biomass during a given year) was also evaluated. The sensitivity analyses was completed using the dataset for dusky flathead in New South Wales. Performances were evaluated for intermediate values of z and m, then for four combinations of large and small values for these parameters. In each case, the most appropriate trigger point was selected to be that which produced the largest probability of a false negative that was less than 5%. Table 3 gives the trigger points selected using this criterion for five combinations of values for z and m. The multiplying nature of the mortality constant m led us to distribute the values of m in the sensitivity analysis with the logarithmic scale (i.e. 0.5, 0.9 and 0.95).

Table 3. Appropriate catch trigger point values for dusky flathead in NSW with i) intermediate z and m; ii) low z and intermediate m; iii) high z and intermediate m; iv) intermediate z and low m and v) intermediate z and high m for the events of recruitment failure and survival failure. In all cases, recruitment lag was set at 3.

	Event
Value of parameters	Recruitment Failure	Survival Failure
z = 0.8; m = 0.9	0.6	0.1
z = 0.4; m = 0.9	0.7	0.1
z = 0.95; m = 0.9	0.5	0.1
z = 0.8; m = 0.5	0.5	0.4
z = 0.8; m = 0.95	0.6	0.0

Table 3 continues to illustrate the robust nature of detecting recruitment failure and the difficulty of detecting survival failure. Large changes to z or m cause little impact of the appropriate catch trigger point value when attempting to detect recruitment failure. A large reduction in the annual mortality of biomass (to m = 0.5) infers greater variation in catches should be accepted before we assume that an impact on the stock survival has occurred.

The parameters z and m cannot be calculated directly or easily estimated from available data. The steepness of a stock-recruitment relationship is difficult to estimate unless data with sufficient contrasting observations of stock size and recruitment are available. Access to all of this information is rarely the case, so z has to be assumed, and the sensitivity of results to this parameter evaluated. Values of m could be inferred if information about natural mortality and individual growth was available, but again, since natural mortality is often a ‘guestimate’, a similar strategy for dealing with this parameter is required. Fortunately the time lag from spawning to recruitment can be easily determined by inspecting catch-at-age data and noting how many years it takes for most (~ 80%) of the fish to recruit.

Analyses by species

Landed catch data were extracted from the NSW Fisheries catch records database. For dusky flathead, the analysis has been completed for the entire State and for three individual estuaries: Camden Haven River estuary (Northern Zone), Lake Illawarra estuary (Central Zone) and Tuross Lake estuary (Southern Zone). For the other finfish species examined in this report, data were only analysed for the whole State. This strategy was selected because the analysis is only preliminary and it appears that the results are quite general. Analyses were completed using the intermediate values of z and m given in section 3.3. Figure 8 shows the catches of flathead for NSW and for the three estuaries.

a)

b)

Figure 8. Time series of total landed catch of dusky flathead from 1984 to 1999 for a) all of New South Wales; and b) Camden Haven River, Lake Illawarra and Tuross Lake estuaries.

The appropriate trigger points for dusky flathead for New South Wales and for the three estuaries are shown in Table 4. Graphs of the performance of triggers for dusky flathead in New South Wales comprise Figure 7.

Table 4. Trigger points for dusky flathead selected as the most appropriate for i) all of New South Wales; ii) Camden Haven River estuary; iii) Lake Illawarra estuary; and iv) Tuross Lake estuary for the events of recruitment failure and survival failure.

	Event
Location	Recruitment Failure	Survival Failure
i) New South Wales	0.6	0.1
ii) Camden Haven River	0.6	0.2
iii) Lake Illawarra	0.7	0.3
iv) Tuross Lake	0.7	0.4

Time-series of catches for luderick (Girella tricuspidate), yellowfin bream (Acanthopagrus australis), sand whiting (Sillago ciliata) and sea mullet (Mugil cephalus) are shown in Figure 9. Graphs of the performance of triggers for these four species in New South Wales comprise Figure 10. The trigger points selected by the analytical process for each species and trigger points proposed for each species by NSW Fisheries are given in Table 5. Table 5 indicates that the trigger points proposed by NSW Fisheries will easily detect recruitment failure and are also within, or very close to, the boundaries required to detect survival failure.

a)

b)

c)

d)

Figure 9. Time series of total landed catch from 1984 to 1999 for a) luderick; b) yellowfin bream; c) sand whiting; and d) sea mullet in New South Wales.

Table 5. Trigger points selected as the most appropriate for dusky flathead; luderick; yellowfin bream; sand whiting; and sea mullet in New South Wales, for the events of recruitment failure and survival failure. For comparison, trigger points proposed by NSW Fisheries are also shown (Source: NSW Fisheries, 2001)

	Event
Species	Recruitment Failure	Survival Failure	NSW Fisheries, proposed trigger point
Dusky flathead	0.6	0.1	0.1
Luderick	0.6	0.2	0.25
Yellowfin bream	0.7	0.2	0.25
Sand whiting	0.6	0.1	0.25
Sea mullet	0.6	0.2	0.1 (for 2 consecutive years)

a)

b)

Figure 10. Probability of false positive, false negative, true positive and true negative outcomes for a range of trigger points from zero to one, in the events of Recruitment Failure and Survival Failure for a) luderick; and b) yellowfin bream.

c)

d)

Figure 10 contd. Probability of false positive, false negative, true positive and true negative outcomes for a range of trigger points from zero to one, in the events of Recruitment Failure and Survival Failure for c) sand whiting; and d) sea mullet in New South Wales.

4. Discussion

The most important point about the practice of using catch as an indicator of stock biomass is that the outcomes appear to be extremely robust with regards to catch history. Failure of the existing biomass to survive is difficult to detect and requires that trigger points be set rather low (greater than 10%-40% variation in historical catches). This will result in a high probability of false positive declarations. In contrast, detection of recruitment failure is straight forward and can be completed with trigger points set at 50%-70% variation from historical catches. Such values will see relatively low probabilities of false negative or false positive results. The trigger points proposed by NSW Fisheries (Table 5) are well within the boundaries required to detect recruitment failure with very low probabilities of false negative outcomes for all species. They are also within or very close to levels required to detect survival failure.

Two parameter values, z (steepness of the stock recruitment relationship) and m (survival of existing biomass) need to be assumed in this modelling study. Sensitivity analysis indicates that the conclusions for detecting survival failure are impacted by altering assumed values of m, but are robust to changes in z. Given that z is, for all intents and purposes, impossible to estimate from empirical sources, this is a welcome result. In principle, the values of m could be estimated from individual growth data and estimates of natural mortality, but these were not addressed in this study.

The contrasting results for survival failure and recruitment failure are very important. Survival failure is somewhat analogous to growth overfishing, whilst recruitment failure is essentially the same as recruitment overfishing. Thus, although survival of the stock is important, as long as there is sufficient spawning stock, the population will continue to recruit and the impact may not be seen in landings. In contrast, successive recruitment failure will eventually cause the collapse of a fish stock and have an obvious impact on landings. Triggers could be set at low values in an attempt to detect survival failure (~30%) but there will be a high frequency of false positive alarms.

Should such triggers be used within an operational scenario for finfish, once a trigger has been tripped there should be ample evidence from systematically collected catch-at-age or catch-at-length data to elucidate what type of event has occurred. Furthermore, that information will be much less ambiguous than variation in landed catches.

In fisheries where there is no other information available apart from landed catch information (for example, some low value invertebrate fisheries) use of catch as an indicator will be a valuable strategy. In the more valuable invertebrate or finfish fisheries, where catch-at-length and/or catch-at-age data is available, landed catch should only be used as a crude indicator of the state of the stock. Obviously, catch per unit effort information should also be collated when possible, even if it is a crude indicator such as catch-per-fisher. Such methods could be easily generalised to an index of catch rate.

There are several aspects of this analysis that need additional input from the stakeholders of the fishery. The first aspect is: what constitutes a problem? We have assumed in our simulations that when survival or recruitment become less than 50% of the historical value then that is the 'problem'. Like other reference points, this cut-off is somewhat arbitrary (Gilbert et al. 2000).

The other aspect requiring comment is the acceptable rate of false positive and false negative errors in the analysis. We described the conditions (Section 3.1) that we applied to the outcomes to select the appropriate trigger point value. This argument is based upon the level of commitment that stakeholders of the fishery and the NSW State Government have made to the application of the precautionary principle in the management of fisheries in NSW. Under that principle, the rate of false negative outcomes should be made as small as possible. The rate of false negative outcomes cannot be made zero as this would result in such high frequencies of false positive outcomes that the results could not be interpreted. The trigger points proposed by NSW Fisheries fall well within the boundaries required to detect recruitment failure, but managers and stakeholders need to consider the associated implication of increased likelihood of false alarms.

Appropriate trigger points for five species of finfish based upon statewide historical catches have been calculated. For dusky flathead the analysis was also completed for catches in three estuaries. To detect survival failure, a wide range (between 10% and 40%) of trigger values would have to be applied. In contrast, recruitment failure is reliably detected if a 60% deviation from historical catches is used as the trigger. These results appear to be robust across all species and estuaries.

This analysis did not use a particularly sophisticated modelling approach. An alternative method would be to base the population dynamics on a formal delay-difference model (Hilborn and Walters 1992, Quinn and Deriso 1999) and apply Bayesian sampling-importance-resampling (e.g. McAllister et al., 1994) methods to calibrate the model to the observed catches. It would, however, be surprising if the conclusions changed.

Using catch as an indicator of the stock is an acceptable strategy in low-value fisheries where catch is the only information available. Precautionary interpretations also need to be specified for quantitative and qualitative criteria within the analysis. The indicator seems particularly effective at detecting recruitment failure but is not a robust indicator of survival failure. The crudeness of the indicator, however, is such that it is absolutely imperative that NSW Fisheries continues to collect data about the age and/or length structure of commercial finfish harvests. It is only with this additional information that issues affecting the stock will be able to be elucidated. Resources also need to be applied to retrieve some historical effort information and better systems put in place to collect future information.

The tripping of a trigger point of 60% or 70% will indicate a serious problem with the stock. In such circumstances, NSW Fisheries should be prepared to take immediate and decisive action to control fishing mortality. Where possible, multiple sources of evidence should be available because the necessary decisions to control fishing mortality are likely to cause social and economic hardship.

Acknowledgements

This project was funded by NSW Fisheries as part of a research contract providing modelling services for the NSW Estuary General Fishery. The work benefited from the support of several individuals and organisations. At the Centre for Research on Ecological Impacts of Coastal Cities we thank Professor Tony Underwood, Dr Gee Chapman and Dr Mike Holloway. From NSW Fisheries, we thank Dr Kevin Rowling and Dr Duncan Worthington for their comments, and Dr Charles Gray and Ms Marnie Tanner for their extensive support. We also thank Dr Steve Kennelly for initiating this project in January 2001. Finally, we acknowledge the support of members of the Estuary General Management Advisory Committee.

References

Gilbert, D.J., Annala, J.E. and Johnston, K. 2000. Technical background to fish stock indicators for state-of-environment reporting in New Zealand. Marine and Freshwater Research 51: 451-464.

Hilborn, R. and Mangel, M. 1997. The ecological detective. Confronting models with data. Princeton University Press, New Jersey.

Hilborn, R. and Walters, C.J. 1992. Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Chapman and Hall, London. 570 pp.

McAllister, M.K., Pikitch, E.K. Punt, A.E. and Hilborn, R. 1994. A Bayesian approach to stock assessment and harvest decisions using the sampling / importance resampling algorithm. Canadian Journal of Fisheries and Aquatic Sciences 51: 2673-2687.

NSW Fisheries. 2001. Draft Estuary General Fishery management strategy. May 2001. Sydney. 112 pp.

Peterman, R.M. 1990. Statistical power analysis can improve fisheries research and management. Canadian Journal of Fisheries and Aquatic Sciences 47: 2-15.

Quinn, T.J. and Deriso, R.B. 1999. Quantitative fish dynamics. Oxford University Press, New York. 542 pp.

Scandol, J. and Forrest, R. 2001. Modelling services for the Estuary General Fishery – Draft report. Centre for Research on Ecological Impacts of Coastal Cities, University of Sydney. 114 pp.

Stewart, T.R. 2000. Uncertainty, judgement, and error in prediction. Pp 41-57, in D. Sarewitz, R. A. Pielke and R. Byerly (eds), Prediction: science, decision making, and the future of nature. Island Press, Washington D.C.

Underwood, A.J. 1990. Experiments in ecology and management: their logics, functions and interpretations. Australian Journal of Ecology 15: 365-389.

Underwood, A. J. 1997. Environmental decision-making and the precautionary principle: what does this principle mean in environmental sampling practice? Landscape and Urban Planning 37: 137-146.