Ashley J. Mullen, Alejandro Anganuzzi, Richard B.
Deriso,
Richard G. Punsly and G. Jay Walker
Inter-American Tropical Tuna Commission
8604 La Jolla Shores Drive
La Jolla, California 92037-1508 USA
ABSTRACT
Boats of various types from several nations exploit tunas in surface waters of the eastern Pacific Ocean using different modes of operation. There is some concern regarding two of these modes. One involves taking tunas associated with dolphins, and in the other tunas are taken while associated with passive floating objects, or "logs." In both cases there is concern for non-target species, and in one there is additional concern that the fishery might be harmed because smaller individual fish tend to be taken. A spatial model has been developed to simulate the fishery. The catches from the model are compared to those from the fishery, and then to those simulated with moratoria on the modes of concern.
Two species of tunas, yellowfin (Thunnus albacares) and skipjack (Katsuwonus pelamis), are considered. The results of this study tend to confirm an earlier, simpler, study on the effect of ceasing to use dolphins in catching tunas. It appears the yield of yellowfin would increase immediately if log fishing ceased, whereas a temporary decline was expected before gaining an increased yield per recruit. The discrepancy is a result of an interaction between the fishing method and the mixed-species nature of the fishery.
The effects of fishing mode are not universal, but interact with the type and nationality of the vessels. Vessels were divided into categories based on their type and nationality, and the catches of each category were tabulated. Moratoria improve the catches of some categories of vessel while causing a decline for others. The effects of such moratoria changed quite markedly for some categories within the period of the simulation.
1. INTRODUCTION
Purse seiners seeking tunas in the eastern Pacific Ocean operate in three basic modes which are commonly termed log fishing, dolphin fishing and school fishing. Schools of tuna are the target in each case and the first two terms refer to fishing directed at schools that are associated with floating objects, or "logs," and dolphins. The fishery is prosecuted by an international fleet with boats of various sizes and levels of sophistication which are capable of different fishing modes. Log and school fishing are options available to every boat, but dolphin fishing requires additional gear which makes it impractical for some of the smaller boats. The different fishing modes exert different size selectivities on the fish. The purpose of this study is to consider the effects on catches of ceasing to use one or more of these fishing modes. Some categories of vessel may gain while others lose, so these effects will also be considered by vessel size, type and national flag. Thus, this is a study of how the relative success of different groups of vessels interacts with the fishing methods that are open to them.
The fishing methods will be explained briefly, and then the reasons why vessels might switch among fishing modes will be discussed, before explaining how such changes might affect the different categories of vessels.
Schools of tunas frequently associate with floating objects (Greenblatt, 1979). Boats fishing these logs will drift alongside them, using sonar to monitor the fish associated with them. The association of the school to the log is rather loose, and varies throughout the day. There may be more than one school associated with the log, and the boat may set its net more than once on the same log. The yellowfin (Thunnus albacares) caught in this manner tend to be smaller than those caught using the other two modes, and more skipjack (Katsuwonus pelamis) tend to be taken in log fishing than in the other modes (IATTC, 1994: Table 30). A single set close to, or around, a log will often yield a mixture of yellowfin and skipjack; non-target species are also frequently caught.
Yellowfin also associate with dolphins (Perrin, 1969); skipjack do so only very rarely. Boats described as dolphin fishing search for dolphins which are more readily seen because they regularly break the surface. Each dolphin school is investigated: if there are sufficient yellowfin, then the net is set around the joint aggregation, and the dolphin are released before the tuna are removed. These yellowfin tend to be larger than those caught using other methods.
School fish are not associated with either dolphins or logs. They can be sighted visually as a dark patch in the water, or as disturbance caused by them swimming close to the surface (Scott, 1969). Both yellowfin and skipjack are taken in this manner, as joint aggregations and as pure schools. The yellowfin tend to be of an intermediate size, between that of those caught on logs and those caught with dolphins.
Boats catching the younger, smaller fish are likely to have an effect on those catching older, larger fish. This effect will not be reciprocated if it is assumed that recruitment is density independent at the population sizes considered (IATTC, 1994: Figure 59).
Size limits are used to manage some fisheries. If recruitment is independent of spawning stock and the size limits succeed in increasing the mean yield per recruit, then size limits can increase the long-term yield of a stock. Size limits would not increase the current mean yield per recruit of skipjack (IATCC, 1994: 80-82). For yellowfin, a size limit might be desirable, but would not be practical because there is usually considerable range in the size of fish taken from a single school. If boats ceased to fish logs, the mean size of the overall catch would be increased, so a switch from log fishing to the alternative modes of fishing might be a reasonable proxy for a minimum size limit.
Dolphins are sometimes killed when fishing for tunas associated with them, despite the precautions which are taken to try to avoid dolphin mortality. As a result, dolphin fishing is not permitted for vessels registered in some nations, and many consumers refuse to purchase tuna caught in this manner Joseph (1994). If either of these decisions reduces the effort directed to dolphin fishing, then that effort is likely to be redirected to log and school fishing. This will affect the size structure of the population and the catches made by vessels currently using other methods.
In redistributing the effort from one mode to another, Anganuzzi (1996) considers each category of class and national flag separately. Nationality was included in the stratification of vessels because vessels of the same size and nationality are likely to operate under similar restraints. Boats of some class-flag combinations fish only near their home ports. Nations may negotiate licenses to fish the Exclusive Economic Zones (EEZ's) of other countries. Boats of such nations, and those of their hosts, will have access to waters that are unavailable to vessels flying other flags.
By using Anganuzzi's (1996) program, simulations are performed to estimate what would have happened to the catches of 1980-86 if dolphin fishing, log fishing, or both modes of fishing had been foregone. The displaced effort would have interacted with the effort already expended on the alternative fishing modes; these interactions are the focus of this study. It is expected that some categories of vessels will gain and others will lose from such changes, but the system is sufficiently complicated that no clear prediction can be made without a quantitative study. The overall effect of these changes is, of course, the sum of the changes that would be experienced by each category.
The period 1980-86 (inclusive) was chosen for the study. The number of sets on logs nearly equalled the number made on dolphins in the first half of the period, but log sets were relatively rare in the second half (IATTC; 1994: Table 3c). Each half was considered independently to see how the gains and losses varied with this extrinsic factor.
2. METHODS
Two species were considered, yellowfin and skipjack, within the simulation procedure. The aim was first to develop a model that was able to mimic catches of each species over the period considered. Then that model was used to predict what the catches would have been during that period if the fishery had operated under additional constraints.
Yellowfin were modelled using as a starting point the 2½° area-month model fitted to the data from years 1980-86 described by Mullen (1996). Yellowfin are recruited, they move around within the geographical constraints of the model, and suffer both natural and fishing mortality. Effort is a measured variable that is assigned to one of the three modes of fishing, each of which has a different age-specific catchability coefficient, which also varies by month and area. Movement is characterized by a field of diffusion coefficients which was estimated by Mullen (1996).
Recruitment is not knife-edge, and seems asynchronous. Representatives of a cohort are first caught in only a few cells, but may be found over a relatively large area shortly afterwards (Punsly and Deriso, 1991). Mullen (1996) deemed it unreasonable to assume the entire population was concentrated in those few cells and then dispersed extremely rapidly. It was assumed instead that the fish initially become vulnerable to capture within only a small portion of the area within which they are present. A few months after a cohort first appears in the catch, representatives are taken from a large zone within the region. From there, fields of diffusion coefficients could describe them as moving offshore and dispersing gradually to cover the entire region modelled in a manner consistent with the appearance of the cohort in the catch. Two cohorts are modelled per year, one first appearing around May, and the other in November. The fish are estimated to be approximately 6 months old at these times. The recruits that first appear in May are deemed fully recruited a year later, while those first appearing in November achieve this by the following September. The estimates of movement of the young fish are not reliable before these dates. Significant catches are made before these dates, however, particularly by log fishing.
Catches of yellowfin are described by the following equation:
where C is the catch at time t by vessels of category c, defined by flag and t,c vessel characteristics; q is the catchability coefficient; M is the instantaneous natural mortality rate; i and j are the latitude and longitude of the 2½° areas; s is the fishing mode (1-3); E is the effort in boat days; and dt is the time increment - one "week," or a fifth of a month. An annual rate of 0.8 was assumed for M; q was obtained from the work of Punsly and Deriso (1991), briefly described by Mullen (1996). Monthly effort was available from compilations of logbook records made by the IATTC; these values were divided by five to give weekly values. The catchability coefficients were in general, specific to the particular areas and months, but one run was made in which the mean value over the seven years was used as the catchability for a given cohort, area and month.
Punsly and Deriso (1991) took from cohort analysis estimates of numbers of each cohort from recruitment until they no longer appeared in the catches. The cohort analysis had been made on spatially aggregated data. They assessed the distribution of the cohorts using spatial catch statistics, employing a general linear model to take into account factors such as the power of each particular vessel and the skill of individual captains. Then, with the local abundance determined, they divided the total catch attributed to each set in each time-area stratum by the days of effort devoted to that mode of fishing. This gave the catchability coefficients, q, above. Mullen (1996) took those distributions of numbers of fish from Punsly and Deriso (1991), estimated diffusion parameters, then revised the estimates of distributions. Here, the original recruitment figures are used: those recruits then suffer time, area, and age specific mortality, Z. For 10 to 12 months, depending upon cohort as explained previously, the sum total of each of these cohorts is redistributed at the end of each month to match the distribution estimated by Punsly and Deriso (1991). The larger, fully recruited, cohorts move according to the weekly diffusion coefficients estimated by Mullen (1996)
Skipjack were modelled very simply. Analysis of yield per recruit suggests they are under-exploited within the region considered and that the yield would increase with effort even if the effort increased to two or three times current values (IATTC, 1994: 80-82). In the simulation catch per unit of effort was assumed constant through time for each area-fishing-mode stratum. For each month, the mean of the values for that month over the 7 year series was used. It was assumed that the skipjack were always available and vulnerable to capture, but were not sought when yellowfin were also vulnerable. The catch rate, however, was limited to the mean over the region for each fishing mode, because some large values were calculated for small amounts of effort. Those values might have biased the redistribution of effort and led to an overestimate of the catch when the effort allocation program was used.
Initially, the monthly effort expended in the 2½° areas of the model by vessels of each category using the three modes of fishing was obtained from the IATTC data base. For the next stage, an effort allocation program (Anganuzzi, 1996) was used to redistribute geographically the effort recorded in the data base. Finally, the effects of different fishing methods were investigated by simulating what the effects might have been had certain modes of fishing ceased. It was assumed that if this happened, then the effort which had been expended on one mode would be redirected to others. The effects of a cessation of dolphin fishing and log fishing were considered, both separately and combined. This was done by setting the catchability coefficient of the particular fishing method or methods to zero and reassigning the effort using Anganuzzi's (1996) program.
3. RESULTS
The model for yellowfin is the more complex and readily testable. It is considered first, then various scenarios are considered by looking at the predicted catches of yellowfin and skipjack combined for the entire international fleet. Having considered the global effect of changes in the behaviour of fishermen, we shall then look for interactions within the international fleet to see whether individual categories of vessels might have fared better or worse than average.
Figures 1A and 1B compare the recorded catches of yellowfin to those predicted given the estimated abundance obtained from the movement model. For Figure 1A, monthly area-specific catchability coefficients were used; while for Figure 1B, the mean value for that month and area calculated over seven years was used for each year. The sum of squares of the differences between catches and those predicted in Figure 1A, is about one half that of Figure 1B. The specific values of catchability clearly give a better approximation to the observed data than the mean values, as would be expected. The worst deviations in Figure 1A occur in 1980 and 1985, when the predicted catches are significantly less than those recorded. This may be due to the inability of the movement model to transport enough fish into the areas being fished at those times.
All subsequent runs of the model used the catchability coefficients that were used in the production of Figure 1A. The next stage was to compare the predicted catches using the effort distribution as determined by Anganuzzi's effort allocation program. This comparison is available in Figure 2 for yellowfin (Figure 2A) and for yellowfin and skipjack combined (Figure 2B). The solid lines of Figure 2 represent the catches predicted using the effort allocation program (Anganuzzi, 1996). Thus, the model predicts a similar time-series of catches when using Anganuzzi's (1996) program for allocating effort as it does when using the recorded distribution. The series predicted using the effort allocation program will henceforth be used as a standard of comparison when investigating the effects of curtailing the fishery.
The questions to be answered are: what would have happened if none of the vessels that comprise the international fleet had operated in the dolphin fishing mode; if no log fishing occurred; or if fishing involved only the school-fishing mode? These scenarios are easily set by fixing the catchability coefficient for any given mode(s) of fishing at zero. The predictions of the catches of yellowfin for these three scenarios are given in Figures 3A-5A with the predictions given by the effort allocation for unrestricted fishing. Figures 3B-5B show equivalent predictions for the sum of yellowfin and skipjack.
Finally the effects of the three postulated scenarios were compared for twelve categories of vessel: four groups of nations and three classes of vessels. The data for 1980-86 were partitioned into two segments, 1980-83 and 1984-86. Catches of yellowfin alone and of yellowfin and skipjack combined were calculated. Each scenario is compared by dividing the catch for that scenario with that predicted by the model using the effort allocation program. The results are presented in Table 1. Some of the categories defined were empty: that is there was no boat of a particular class and national group operating within that segment of the period. In other cases, the total catch predicted using all three modes of fishing was less than 5,000 tons for each segment. These cases are denoted with an asterisk: the predictions are based on so few data that they should be viewed with much scepticism.
4. DISCUSSION
Fish catches are so inherently variable that predicting catches given proposed or possible changes in the behaviour of fishermen is fraught with difficulty. Those changes could easily be swamped by other unanticipated changes, many of which will be outside human control. This problem is sidestepped by taking a past period and predicting what would have happened if the behaviour had been changed for that period. The model that has been considered is less than perfect for reasons that will be discussed. Even if it were perfect for the period modelled, future changes in external factors would render it only a rough guide to the future. But most fisheries models are only rough guides because they too are subject to externalities. By predicting what might have happened, we hope to show the general scope of effects which can be anticipated, without creating illusory precision or calculating spurious confidence limits.
In considering the sensitivity of our results to parameters, we do not consider the parameters individually. An overestimation of recruitment will not occur in isolation, for instance, but will be associated with persistent overestimation of the abundance of that cohort and underestimation of all its catchability coefficients. With such errors, our simulation would overestimate the resilience of the cohort to fishing pressure. If the errors are pandemic, then the movement model should not present a problem because the same proportion of the population will move at each time step. Errors will, however, be introduced into the movement model whenever the estimated distribution of the population is incorrect. There are so many diffusion parameters that none will have a large effect on the overall simulation. The spatial pattern of diffusion is much more important in determining the distribution of fish. If the diffusion pattern increases the aggregation of fish in the model, then this will make the model more sensitive to the fishery and accentuate the results presented.
Table 1. Predicted effects of cessation of particular modes of fishing on catches made by vessels of 12 categories (A-L) during two segments of the period studied (1980-83 and 1984-86), expressed as proportions of the catches expected when all three modes of fishing are used. The categories denoted with asterisks represent cases for which the total predicted catch with all three modes of fishing was less than 5,000 tons for both segments. The vessel categories are not identified to preserve the confidentiality of information provided by the vessel owners and captains.
|
YELLOWFIN |
||||||
|
|
No dolphin fishing |
No log fishing |
No dolphin or log fishing |
|||
|
80-83 |
84-86 |
80-83 |
84-86 |
80-83 |
84-86 |
|
|
Category |
||||||
|
A* |
0.9397 |
0.8047 |
1.1623 |
0.6002 |
1.0933 |
0.5607 |
|
B |
0.9791 |
1.0228 |
1.1703 |
1.0335 |
1.2110 |
1.1255 |
|
C |
0.8654 |
0.8142 |
1.2051 |
1.0305 |
1.2018 |
0.8815 |
|
D |
0.8935 |
0.8071 |
1.4581 |
0.9730 |
0.8426 |
0.7393 |
|
E |
0.8486 |
0.9047 |
0.9726 |
1.1887 |
0.6676 |
0.7617 |
|
F* |
0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
|
G* |
0.8854 |
0.0000 |
2.8542 |
0.0000 |
3.6875 |
0.0000 |
|
H* |
0.5517 |
0.0000 |
0.4064 |
0.0000 |
0.3473 |
0.0000 |
|
I |
0.7268 |
0.5891 |
1.0736 |
0.9673 |
0.8423 |
0.9103 |
|
J |
0.9257 |
0.9239 |
1.2091 |
1.0601 |
1.1239 |
0.9951 |
|
K |
0.8147 |
0.7577 |
1.0494 |
1.0560 |
0.8287 |
0.8482 |
|
L |
0.8417 |
0.7684 |
0.9777 |
1.0180 |
0.6722 |
0.7559 |
|
All |
|
|
|
|
|
|
|
Combined |
0.8563 |
0.7982 |
1.0610 |
1.0250 |
0.8451 |
0.8340 |
|
YELLOWFIN + SKIPJACK |
||||||
|
|
No dolphin fishing |
No log fishing |
No dolphin or log fishing |
|||
|
80-83 |
84-86 |
80-83 |
84-86 |
80-83 |
84-86 |
|
|
A* |
0.9585 |
0.8445 |
0.9666 |
0.5513 |
0.9197 |
0.5383 |
|
B |
0.9969 |
1.0435 |
1.1017 |
1.0262 |
1.1443 |
1.1297 |
|
C |
0.9766 |
0.9265 |
1.0241 |
1.0265 |
1.0601 |
0.9704 |
|
D |
0.9766 |
0.9258 |
1.0201 |
0.9423 |
0.9059 |
0.8688 |
|
E |
0.9802 |
0.9860 |
0.8959 |
0.9996 |
1.0076 |
0.9541 |
|
F* |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
|
G* |
0.9688 |
0.0000 |
1.1042 |
0.0000 |
1.4514 |
0.0000 |
|
H* |
0.7032 |
0.0000 |
0.5583 |
0.0000 |
0.5671 |
0.0000 |
|
I |
0.9446 |
0.7136 |
0.8882 |
0.9531 |
0.8646 |
1.0058 |
|
J |
0.9463 |
0.9363 |
1.0191 |
1.0070 |
0.9805 |
0.9560 |
|
K |
1.0485 |
0.7904 |
0.8626 |
1.0268 |
0.8266 |
0.8281 |
|
L |
1.1180 |
0.9873 |
0.6870 |
0.9330 |
0.6613 |
0.8585 |
|
All |
|
|
|
|
|
|
|
Combined |
1.0593 |
0.9496 |
0.8212 |
0.9717 |
0.8056 |
0.9150 |
It would be a mistake to assume that the precision suggested by Figure 1A, comparing the model output to observed catches, will apply to the hypothetical scenarios. The model is tightly constrained by the catchability coefficients, which were estimated from the observed catch rates. Catchability coefficients are available for yellowfin for a given area-month stratum only when there was effort in that stratum; otherwise, their default value is zero. As a result, effort is always confined within that zone in which it was originally recorded. The modelled effort is likely to be redistributed and may withdraw to a smaller zone, but it will not expand into areas that were not originally exploited during that particular month.
The caveats issued by Anganuzzi (1996) apply, of course, to these results which depend on his program: effort is modelled continuously rather than as discrete boats following a particular strategy in trading-off risk against expectation. Economics are assumed constant, whereas, in reality, they vary greatly. Log fishing conserves fuel, so the proportion of effort expended upon this mode will depend to some extent on the cost of diesel.
Having estimated the age, position, and time dependent movement parameters for the population over the period 1980-86, it is assumed that these parameters would not change with the behaviour of fishermen. In arguing that movement could be parameterized with variable diffusion coefficients, Mullen (1989) suggested that it is likely these parameters would be a function of local population density, which is affected by the fishermen. Unfortunately, the diffusion coefficients might not be related directly to the population density because they may also depend on the local environment. The arguments of Mullen (1989) suggest, however, that the diffusion coefficients are likely to be positively correlated with population density when considered by area-time stratum across model runs. Without further information, the parameters were not corrected for this postulated effect.
No account has been made for the fact that catches might be limited by the number of dolphins or logs. If either dolphin fishing or log fishing is foregone, the number of fish rendered unavailable by their association with dolphins or logs is likely to increase. The effort which had been expended on that mode of fishing will be redirected. Thus, if dolphin fishing ceases, then logs will be fished more intensively; and vice versa. A log which is being fished by one boat is not available to another, so it might take more time to find a suitable log when there are more boats log fishing. The same is true if boats are looking for dolphins; a school of dolphins is likely to yield few fish immediately after it has been fished. More boats fishing dolphins will reduce the mean time between any school being fished, giving it less time to recover, or "recruit," more tunas. These saturation effects are likely to cause some decline in the yield from the remaining modes if any mode of operation is abandoned.
Figure 1. Observed catches (solid line; total catch = 1,337,266 tons) compared to those calculated from the recorded distribution of effort (dotted lines), using A) monthly values of catchability (total catch = 1,178,956 tons)
Figure 1. Observed catches (solid line; total catch = 1,337,266 tons) compared to those calculated from the recorded distribution of effort (dotted lines), using B) monthly mean values of catchability (total catch = 1,222,957 tons).
Figure 2. Predicted catches for the recorded effort distributed by Anganuzzi's allocation model (solid lines) compared to those calculated for the recorded distribution of effort (dotted lines) for A) yellowfin B) yellowfin + skipjack. The predicted total yellowfin caught over the period with modelled effort was 1,151,238 tons; versus 1,178,956 tons calculated given the recorded distribution of effort. For yellowfin and skipjack combined, the totals were 1,636,232 tons for the modelled effort and 1,653,834 tons for the recorded distributions. The predictions using modelled effort, the solid lines of this figure, also appear in Figures 3-5.
A) YELLOWFIN CATCH: RECORDED EFFORT, AND MODELLED EFFORT
B) TOTAL CATCH: RECORDED EFFORT, AND MODELLED EFFORT
Figure 3. Predicted catches for distribution of effort allocated using all modes of fishing (solid lines) compared to those with no dolphin fishing (dotted lines) for A) yellowfin (total without dolphin fishing, 952,492 tons)
Figure 3. Predicted catches for distribution of effort allocated using all modes of fishing (solid lines) compared to those with no dolphin fishing (dotted lines) B) yellowfin + skipjack (total with no dolphin fishing, 1,656,560 tons).
Figure 4. Predicted catches for distribution of effort using all allocated modes of fishing (solid lines) compared to those with no log fishing (dotted lines) for A) yellowfin (total with no log fishing, 1,200,861 tons)
Figure 4. Predicted catches for distribution of effort using all allocated modes of fishing (solid lines) compared to those with no log fishing (dotted lines) B) yellowfin + skipjack (total with no log fishing 1,448,911 tons).
Figure 5. Predicted catches for distribution of effort allocated using all modes of fishing (solid lines) compared to those predicted using effort with no dolphin or log fishing (dotted lines) for A) yellowfin (total with no log or dolphin fishing: 966,537 tons)
Figure 5. Predicted catches for distribution of effort allocated using all modes of fishing (solid lines) compared to those predicted using effort with no dolphin or log fishing (dotted lines) B) yellowfin + skipjack (total with no log or dolphin fishing: 1,394,675 tons).
Some fish are discarded at sea. These fish incur fishing mortality even though they are not represented in the catch. One estimate (IATTC, 1993: 3) puts discards, by weight, of tunas during log fishing as high as 32.5%; 8.6% for school fishing and 0.7% for dolphin fishing. If these figures are valid we are likely to underestimate the effect of log fishing on other modes. Catches would be greater than the model suggests when log fishing is eschewed, and less when dolphin fishing is foregone. This effect is being investigated, but we have no results ready for discussion.
The effects of redirecting effort from dolphin fishing are similar to those obtained by Punsly et al. (1994) using a spatially aggregated model. If there had been no fishing on dolphin then catches of yellowfin would have been less for almost every month in the period considered, with the decline being greater in the latter part of the period when more dolphin fishing occurred. This decline would have been compensated by an increase in catches of skipjack, bringing the total for both species to within 2% of that predicted for the entire period with dolphin fishing as observed. The similarity of the results of the two studies suggests spatial effects are not crucial in this case. This is interesting because a concern the previous study was unable to answer was that the cessation of dolphin fishing might cause the fishery to contract its geographical range. If so, its yield would probably decline (Mullen, 1994). Anganuzzi's effort allocation program (Anganuzzi, 1996), however, suggests the range of the fishery would not contract, so the problem does not arise.
Log and school fishing were considered a single mode by Punsly et al. (1994). The effects of switching from log fishing suggested by this body of work are at first surprising, but easily explained. It was anticipated that catches of yellowfin would initially decline, but would recover after a delay, so that the overall effect on yellowfin would be positive. The model predicts instead that catches are immediately enhanced, and that the overall effect on catches is positive. However, when skipjack are added, the total catches do show an initial decline, followed by a recovery to roughly the catches predicted without changing fishing mode. Log fishing generally yields more skipjack, and there was a lot of log fishing in 1980, 1981 and 1982; catches of skipjack would have declined substantially in those years without log fishing. Effort is redirected to school and dolphin fishing, for which the catch of yellowfin is higher, that is why there is an immediate increase in the catch of yellowfin. During 1984-86, there was little log fishing, so little effort to redistribute from that mode. If the population had been more heavily exploited during the period considered then the recorded catches of yellowfin might indeed have declined more. Then there would have been more scope for improving the yield per recruit.
If fishermen had forgone both log and dolphin fishing, the catches of yellowfin would have declined immediately. Catches of yellowfin under this scenario only rarely equal or surpass those that were predicted with the observed fishing modes. Under this scenario, there is no compensation for reduced catches of yellowfin by increased catches of skipjack.
Turning now to Table 1, we can consider how individual categories of vessels might have fared. To preserve the confidentiality of the data supplied on voluntary basis by vessel owners and skippers, the identity of individual categories is not revealed. Ignoring the entries marked with an asterisk as representing too few data, there are two points that can be made. Firstly, if vessels had not fished dolphins then the catch of yellowfin would have declined for all but one category (B) in both the segments of the period. Presumably boats of categories that are unable to operate in this mode would suffer from increased competition for yellowfin unassociated with dolphins, which tend to be smaller. Secondly, increased catches of skipjack would have more or less compensated for the reduced catch of yellowfin in the earlier segment (1980-83) when log fishing was clearly a viable alternative. In the later segment, vessels of category B would have been able to make up the shortfall of yellowfin, while the others would not. For all boats combined, catches of yellowfin would have declined and those of skipjack would have increased in both segments of the period. Combined catches of both species for all boats would have increased by 6% in the first segment of the period, and declined by 5% in the second.
The case when no boats fished logs is almost the opposite of that when they eschewed dolphin fishing: catches of yellowfin would have increased for most categories, but the overall benefit would be reduced due to lower harvest of skipjack. For two categories, K and L, there would have been a marked decline in the total catch during 1980-83 when the incidence of log fishing was high.
Most categories suffer reduced catches if they forego both log and dolphin fishing, but one exception to this generalisation is particularly interesting. Category B does better in catching yellowfin and skipjack if there is no log or dolphin fishing than in any other circumstances. An increased yield per recruit can explain enhanced yield when there is no fishing of logs, but not an enhancement due to cessation of dolphin fishing. It seems that boats of category B would have done better if they had ignored tunas associated with dolphins. Thus, boats of category B were not maximising their overall yield and might have been attempting to optimise according to other criteria. For all vessels combined, catches of yellowfin declined substantially in both segments of the period. Total catches of skipjack also declined in the first segment, but increased in the second. There was a decline in the combined total catches throughout the period without log or dolphin fishing, and that decline was greater in the first segment of the period.
This work might be extended in a number of ways. Anganuzzi (1996) has discussed modelling the allocation of fishing effort on the basis of individual vessels, rather than using a mass-action type of model. A general linear model of the type used by Punsly and Deriso (1991) could then be used to determine a factor accounting for the fishing power of each vessel-captain combination. Punsly and Deriso (1991) found significant effects due to time-region strata, but did not find any significant effects due to environmental variables such as wind-speed. It would be interesting to run the analysis of Punsly and Deriso (1991), ignoring effects of time-area or time-region strata, and considering only vessel-skipper and environmental effects. The catchability coefficient would then pertain only to the area of water, and any spatial variations would be determined solely by environmental relationships. This would allow, in principle at least, catchability coefficients to be defined for time-area strata within which no effort was expended. It might still be necessary to assume zero or much-reduced catchability for some strata on the basis of environmental conditions. If so, those strata would be truly off-limits to fishing. The aim of the work would be to assign variation in catch rates to the power of the fishing vessel, environmental conditions, and then to the distribution of fish.
5. CONCLUSIONS
A discussion of the effects of curtailing modes of fishing in a particular year cannot be divorced from the peculiarities of that year. Some years are bad for fishing logs, in those years little is sacrificed if logs are passed by. In years that are very good for fishing logs, less will be lost if boats do not fish dolphins. The effects will also vary among categories of vessel. Vessels that cannot fish dolphins may suffer from increased competition if other boats switch from that mode of operation.
In considering the effects of vessels forgoing dolphins as an aid to fishing tunas with purse seiners in the eastern Pacific Ocean, this model confirms the results of a simpler aggregate model. The harvest of yellowfin is likely to be reduced, but additional catches of skipjack are likely, so the yield of both species combined is unlikely to change much.
In switching from fishing logs, increased catches of yellowfin are likely at the rates of exploitation used in this model. But skipjack catches are likely to decline more markedly, causing a reduction in the catch of tunas from the region by this fishery.
The model is complex enough to have provided some surprises for which rational explanations have been made. Unfortunately the natural system is far more complex, and any one of the many simplifications made in the model might mask a phenomenon which is crucial to any quantitative predictions.
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