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Abstract: The impact of different fishing intensities and fleet size on the stock was analyzed, allowing the assessment of management strategies and estimation of the carrying capacity. An age-structured simulation model for the skipjack tuna fishery of the eastern tropical Pacific was developed. Population parameters, boat numbers, carrying capacity, and costs and benefits of fishing operations are required as inputs. The yield response to fishing capacity is analogous to the response to fishing effort in surplus yield models. When age of first catch is increased, and assuming catchability remains constant, significant increases in yields, profit, and carrying capacity may be obtained. Given the current age of first catch and assuming constant catchability, the model output indicates that under the economic equilibrium limit (i.e. total revenues = total costs, fishing mortality = 0.62, and a catch of 132 000 ± 2 000 tonnes) estimates of the potential yield suggest that the fishery withstands a maximum carrying capacity of 74 000 tonnes. The trend of yields from 1992 to 1998 suggests a possible reduction of the fishing intensity F, from near the level required to attain maximum yield, where it seems to be not profitable, towards the level required to attain the optimum economic yield. Skipjack caught within the regional Economic Exclusive Zone represents 64 percent of total biomass, implying that the countries with capacity to fully exploit the stock within their 200-mile limits may claim exclusive rights to do so.


The increase in fishing intensity has become a major problem in many artisanal and industrial fisheries. It has contributed to overfishing and depletion of many commercially important fish stocks. An estimate of the world fleets states that they are 2.5 times larger than needed (Porter, 1998a; Gréboval, 1999), and up to 70 percent of world's marine stocks are considered to be depleted or fully exploited. When there is too much fishing capacity, each boat catches far less than its maximum potential (Porter, 1998b). Excessive fishing capacity has contributed to a decline in landings of many fisheries and also is considered as an economic waste (FAO, 1998). For this reason, its causes and definition, measuring and controlling fishing capacity has become a concern to be considered in the Plan of Action to be adopted internationally. Unfortunately, fishing capacity has not been considered as an issue of control in management practices of most world fisheries (Newton, 1999) even though overcapacity of the global fleet has a long history (Porter, 1998a).

The tuna fishery, in contrast with many other fisheries, records and identifies each fishing vessel operating on the high seas. This then gives us available historical records of fishing operations as well as catch and effort. The skipjack is the most highly captured tunid species, with 1 560 000 tonnes during 1995, mainly in the western and central Pacific. In the eastern Pacific, yields amounted to 240 000 tonnes in 1992 (Hinton and Ver Steeg, 1994). Important yields are obtained near Baja California, Islas Revillagigedo, Clipperton Island, Central America, northern South America, and the Cocos and Galapagos Islands. The identification of fleet overcapacity and optimum yield levels implies a potentially high significance related to the sovereignty of the countries exploiting this stock within their economic exclusive zones (EEZ). In the present analysis, other stocks exploited in the tuna fishery were implicitly ignored. For the purpose of the present paper, the skipjack was considered as the only stock in the fishery. Hence the results are valid specifically for this stock and any extrapolation should be made carefully.


A simulated-model-age-structure was used, following the basic principles of stock assessment described by Hilborn and Walters (1992) and more specifically by Chávez (1995), Nevárez-Martínez et al. (1999), López-Martínez et al. (2000), and Ponce-Díaz et al. (2000). This differs from the approach adopted for the measurement of capacity from an economic viewpoint (Kirkley and Squires, 1999)

The only meaningful measure of fishing capacity is the tonnage of fish that it can catch (Porter 1998b). For the tuna fishery, to which skipjack belongs, and for the goals of this paper, the fleet tonnage capacity was used instead the number of fishing days or any other measure of effort. The analysis of fleet carrying capacity (Ca) is analogous to fishing effort and, with a fleet-dependent catchability coefficient (qk), is a component of fishing mortality (F), such that:

F = qkCa


Therefore, response of yield (Y) with respect to F and Ca can be described by a surplus yield parabola, given by:

Y = ak Ca exp-(bk Ca)

where ak and bk are estimated coefficients of the equation. Once estimates of F were obtained from the last fifteen years of catch records, obtained from Hinton and Ver Steeg (1994) and from the IATTC (1999), parameters of a function analogous to those of the Fox model (1970) were obtained.

The stock size and the exploited age groups are described as:

Nt+1 = Nte-zt


where Nt is the number of fish with age t, and Z is the total mortality (where Z = M + F, i.e. natural (M) plus fishing (F) mortalities).

The yield obtained each year is the product of F multiplied by the stock size. That is:

Y = FNt wt


where Y is the yield (e.g. tonnes), tc is the age of first capture, tT is the last age group, and wt is the mean weight of fish of age t.

Apart from tuna and a few other stocks, most fisheries lack fishing-effort data records or tonnage capacity of their fleets, making estimates of carrying capacity a difficult task. The use of catch data for the last fifteen years is desirable, however, the model can use data for only one year, assuming that these data and other information such as the von Bertalanffy growth parameters (K, L¥, to), the length-weight relation coefficients, the age of first catch, age of maturity, and current data on costs and benefits of fishing operations are available or can be collected in a short term survey.

Values of the parameters L¥, to, and K of the von Bertalanffy growth model (L¥ = 83.9 cm, K = 0.6811 and to = -0.0018), were taken from Fish-Base 98 (Froese and Pauly, 1998). The asymptotic weight (W¥ = 12.1 Kg), and the average weight by group of age were estimated by the relation W = a Lb using the values a = 0.005916 and b = 3.28, also taken from Fish-Base 98.

For the analysis of age structure, longevity of the skip jack tuna was determined initially, assuming at least 95 percent of the population survives to 95 percent of its asymptotic length, which upon transforming the equation of von Bertalanffy gives the ratio 3/K, which is equivalent to only four annual groups. This value is considered very low, because for the long line fishery, Matsumoto and Skillman (1984) report catches of 12 year-old fish. Therefore, the criterion of considering eight age groups for this analysis was adopted. A factor adding certain complexity to the analysis is the fact that fish more than three years old are seldom found in the eastern Pacific (J. Joseph, pers. comm). Therefore, yield estimates must be based only on the age groups exploited, but estimations of recruit numbers should consider all adult stock.

The estimate of natural mortality (M) value was obtained after Pauly (1980). The age of first catch (tc) was identified as one year, and the reconstruction of the age groups was made under the implicit assumption that it has remained constant over time.

The model, developed on a spreadsheet as an interactive user-friendly tool and accessible to non-specialists, provides the way to estimate the Beverton and Holt (1957) recruitment model (a slightly modified version is used here) b parameter, giving a as a fixed value. The estimate of recruitment is multiplied by a random number with normal distribution, whose variation coefficient (VC = 0.056) is determined by minimizing the differences between observed and estimated catch (when there is a series of catch values to match with) and by doing a fine tuning of initial number of recruits.

The fishing mortality values (F) each year were estimated through the comparison of simulated and observed catch levels. This was undertaken once the initial age structure was defined by means of a successive approximation procedure using the solver function in the Excel spreadsheet that fits the catch recorded for every year of data with that calculated from the catch equation. Simulations were made through 15 years after the last year of data records. The mean values of the last five years of simulation were used to evaluate the effects of fishing strategies and, therefore, the fleet size over the long term.

If a single year of catch data is used, then a single F estimate value is made. Once the series of parameter values required are put in, the model estimates the potential yield under a series of F values, which is graphically shown on the screen, often describing a parabola. This way it is possible to determine the potential yield as a function of fishing mortality. Depending upon these key variables, the fleet size required to obtain a particular yield can be determined. This yield may be the maximum sustainable yield (MSY), or the optimum economic yield (OEY), corresponding to the F value giving the highest profits. If the study case is a stock whose age of first capture is larger than age of sexual maturity, then a yield parabola is found whose maximum value is usually located at F levels higher than the former one with a fleet size which is different from that required to achieve the OEY.

The fleet carrying capacity, if seen as the simple relationship described above, may be interpreted as a simplistic linear relation. However, it implies more complexity, because it really is a dynamic function of the stock and recruit sizes, age of first catch and F, elements which comprise a hypothesis to be tested. The model developed enables us to choose the age of first capture during the simulation period and corresponding yields, hence fleet sizes depending upon F are obtained.

The fleet carrying capacity can be formally represented by combining Equations 1 and 2, giving:

Ca = F/qk = (Y/nt wt)/qk


Throughout the simulation process, increasing the age of first catch also increased potential yield and profits, but the number of boats remained constant, depending upon the F value assigned. To obtain a dynamic response of the fleet size as a function of age of first capture, the Ca originally obtained was weighted by the ratio of revenue to costs.

The analysis and other pertinent considerations were made assuming the fishery relies upon a single stock, a constancy of age of first catch, and the selection pattern over time, regardless of other species exploited by the same gear, with the intention to explore the accuracy and perspectives of a general use of the method developed here.

To test the hypothesis, and used for the skipjack fishery, validity of the model was tested by a comparison between observed and recorded yields and by a minimization of errors of the former data series.


The parameter values of the Fox model linking F and Ca are ak = 2 and bk = 0.000007, with a relatively low correlation. This function was used to determine the fleet number weighted by the revenue/cost ratio for the simulation period, and the value of qk = 0.000007.

The a parameter of the parent-recruit relation equals 0.25 and was left constant, whilst b was determined with the aid of the solver function (1.04). Using both parameters, the estimation of the number of one-year old recruits to the stock every year was made. Age groups were reconstructed and catch values were evaluated for the period of analysis, observing that with a F = 0.7 average yields above 128 000 tonnes per year can be obtained over the long term as shown in Figure 1. The fleet tonnage is a variable depending upon F and also describes a parabolic tendency with a maximum fleet carrying capacity of 70 000 tonnes at F = 0.7.

Using values of F > 0.7, the stock is overexploited. The OEY is achieved at F = 0.2, when total profits are US$112 000, and the revenue/cost ratio is 1.97. There is a remarkable contrast between biological and economic optimum, given that under the current selectivity pattern and age of first catch, the biological optimum (MSY) is achieved at unprofitable levels of fishing intensity. However, analysis of potential yield shows that if age of first capture is higher than two years, yields may be much higher and no values of MSY or OEY, nor a maximum carrying capacity (not shown here) are achieved. Fishing exploitation can then be as intense as possible (Figure 1).

Figure 1. Potential yield of the skipjack stock exploited in the eastern Pacific

To maintain the fishery in the long-run, a good fishing strategy under the current selectivity pattern could be made with a fishing mortality of F = 0.2, providing the highest profits, though a significant number of boats would have to be withdrawn from the activity. Again, the estimate of potential yield obtained by simulation shows that a significant yield increase, about six times higher than the current one, could be obtained with a tc > 5 and F ³ 1.7.

Figure 2. Dynamic response of the model showing historic trends and simulations of biological, and economic levels, as well as boat numbers and fleet carrying capacity under two key fishing intensities a) With FOEY = 0.2; b) With FMSY = 0.7.

Observed and simulated catches (Figure 2a, b) show a good fit of the model. The results indicate that the stock has been progressively more exploited over time. Statistical records show that, from 1978 to 1985, there was an important drop in yields from 179 000 tonnes in 1978 to 53 000 tonnes in 1985, probably caused by overfishing. A new increase in fishing intensity began in 1991 with 66 000 tonnes caught, arriving at 145 000 tonnes in 1997 and with F values increasing from 0.149 to 0.558 (Table 1), overexploiting the stock.

Table 1. Yield data (rounded to the closest thousand), fleet sizes as number of boats and carrying capacity (after Hinton and Ver Steeg, 1994; IATTC, 1999), and estimates of fishing mortality F, adult numbers, and one-year old recruits for each year of the 1984-1998 data series.


Recorded Catch, tonnes

Fishing Mortality F

Million of Age I Recruits

Million of Adults

Number of boats

Carrying capacity, tonnes


63 000





106 701


53 000





119 937


68 000





114 366


65 000





132 188


88 000





136 616


97 000





123 955


77 000





124 805


66 000





107 575


89 000





101 348


90 000





102 752


77 000





105 885


144 000





107 543


117 000





114 957


145 000





127 257


122 000





53 949

The results of the simulations suggest that the OEY (84 000 tonnes) can be obtained under F = 0.2, and that the MSY = 128 000 tonnes can be achieved at F = 0.7 (Figure 1). At F = 0.2 the goal could be achieved with a carrying capacity of 29 000 tonnes in about 45 boats. If MSY is chosen as the target yield, then a carrying capacity of 761 000 tonnes in about 100 boats is required (Table 2). However this fishing intensity is below profitable levels. Uncertainty yield levels in each case approach ± 2 000 tonnes. Trend of yields (89 000 tonnes in 1992 and 120 000 tonnes in 1998) show the situation of a possible economic overexploitation of the stock, and the fishery seems to have switched towards the FOEY point, rather than to the FMSY level, where it seems to be unprofitable (here the revenue/cost ratio = 0.7). If current F values for the last year (1998) are around 0.45, annual yield is 122 000 tonnes and the fleet carrying capacity required is 50 000 tonnes (82 boats) with a B/C = 1.03. At the FOEY level, the fishery is more profitable (revenue/costs = 1.59).

Under a fishing intensity exploiting the stock at the economic equilibrium limit (EEY) (revenue/cost ratio = 1, F = 0.47, and a catch of 124 000 tonnes), the fishery withstands a maximum carrying capacity of 51 000 tonnes, equivalent to 84 boats.


The tuna fishery contributes to impressive amounts of all high seas catch (41 percent) and total landed value (82 percent), as stated by Newton (1999). This emphasizes the need for strengthening the regional cooperation of the countries involved in this activity to provide effective control of fishing capacity. For the tuna fisheries of the eastern Pacific, the IATTC is setting up a group working on fleet capacity limits (Porter, 1998b).

Fleet capacity and its control implies technological issues rather than only the stock dynamics (Gréboval and Munro, 1999) and though this is essentially an economic issue, before taking any management action to control the excess capacity requires an accurate assessment of the exploited stocks and their dynamics on which the economic system relies and for which it is an unavoidable input. Issues regarding fleet dynamics belong to the domain of economy, however, any assessment that does not consider the stock as a variable input may give a biased estimate.

One of the aspects often implicit in the measurement of fishing capacity is the use of the Gordon-Schaeffer model. Its conception departs from the ecological consideration that the catch per unit of effort (CPUE) is a good indirect measure of the stock density and the CPUE should often be used despite the possibility of having access to more realistic and structurally correct models (Ludwig and Walters, 1985). However, when fishing capacity is in excess, a portion of the fleet remains on dock and CPUE stops being a good estimator of stock density. Therefore the available data may not behave properly to fulfill the requirements to fit the model mentioned, and an estimate of optimum level of effort or fishing capacity (number of boats, or fishing capacity) may not be obtained or may be inaccurate. For the tuna fishery, the problem of obtaining accurate estimates of fishing effort becomes an enormous task, because not only is there a variety of boat sizes and gear types, but in the last few years, the common adoption by some fleets of fish aggregating devices (FADs) located by satellite, turns fishing effort into a stereotype different from its original traditional concept and for the same reason, of doubtful validity.

The results of the simulations may appear to show some mismatches with respect to recent data records. Values chosen, as indicators of MSY and OEY levels are lower than current yields and even worst, the EEY is higher than they are (Table 2). However, these indicators correspond to the mean values of the last five out of the fifteen years of simulations, chosen as estimators of a long term behaviour of the fishery to be used as reference points if adopted for decision making in the process of managing this fishery.

Table 2. Total yields (thousand tonnes), F, fleet sizes (as boat numbers and thousand tonnes of carrying capacity), and revenue/cost levels corresponding to current values (for the years 1997 and 1998) and estimates of potential yield at the optimum biological yield (MSY), optimum economic yield (OEY), and economic equilibrium yield (EEY) fishing intensity levels.

Fishing level




































4.1 On the fleet allocation

All symptoms of the skipjack exploitation intensity and the stock dynamics point towards the need to reduce fleet carrying capacity. For this reason, the adoption of FOEY as target of a management strategy addressed to the reduction of fishing intensity seems a desirable option. If a policy like this is adopted, the fleet carrying capacity should have to be reduced about 18 000 tonnes. Evidently, a reduction of fleet size should have to be made gradually to avoid severe social and economic impacts.

From the data produced by Hinton and ver Steeg (1994) and IATTC (1999), the mean catch of skipjack caught in the eastern Pacific Ocean for the years 1988 to 1992, summarized in Table 3, amounts to 95 000 tonnes, which is above the estimate of OEY (84 000 tonnes), but below the MSY level (128 000 tonnes). Total yields for the years 1997 and 1998 were 145 000 and 120 000 tonnes caught with total carrying capacities of 128 000 and 53 000 tonnes in 219 and 53 boats (Table 2). The mean catch for the 200-mile exclusive zone for the years 1988 to 1992 amounts to 61 000 tonnes and the catch by the main participant countries (Ecuador, Colombia, and Mexico) in this zone for the same period was 43 600 tonnes. The yield obtained within the EEZ of the region is 64 percent of the total. This implies that if FOEY is chosen as target, which seems the most convenient option to adopt, only 36 percent (31 000 tonnes) out of a yield of 87 000 tonnes could be shared by a carrying capacity of all the fleets exploiting the stock in international waters. Under these conditions, the eastern tropical Pacific countries with capacity to fully exploit the stock within their 200-mile limits may claim exclusive rights to exploit existing biomass (56 000 tonnes) within their limits. In this respect, good care should be taken setting suitable controls of fishing effort and fleet sizes to avoid overexploitation of the stock.

Table 3. Proportion of yield (61 200 tonnes, mean of the years 1988-1992), caught within the EEZ of the countries where the skip jack stocks are exploited (64 percent of total yields) in the eastern tropical Pacific (based on table 12 by Hinton and Ver Steeg, 1994). Data on the fleet sizes for these countries correspond to the year 1997 (1996 for Costa Rica), total fleet size fishing at the eastern Pacific in 1996 was 201 ships or 115 000 tonnes (after IATTC, 1999).


Yield Percent

Fleet sizes


Capacity (tonnes)




6 600

Costa Rica



n. s.




24 000

El Salvador











41 500









United States




ns. = Not specified, ------ = No data.


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[151] Centro Interdisciplinario de Ciencias Marinas (CICIMAR IPN), Av. Instituto Politécnico s/n, Col. Sta. Rita, Playa El Conchalito, La Paz, BCS 23070 México. Email: [email protected]. The author would like to thank Sofía Ortega and Francisco Arreguín-Sánchez who kindly reviewed the manuscript, and Ellis Glazier who edited the English language. The study was conducted under the partial sponsorship by COFAA-IPN.

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