Determination of the Utilization and Effort Level of Mackerel Scad (Decapterus spp) in the Bitung Waters North Sulawesi

Determination of utilization level and effort level of scad mackerel (Decapterus spp) are very important to know the status of fisheries management. This fish needs to be managed well because even as a renewable natural resources, but can undergo depletion or extinction. One of the approach in the management of fish resources is by mathematics modeling. In this research using Surplus Production Model (SPM) with 5 estimator methods, that are: Schaefer, Fox, Schnute, Walter-Hilborn, and Clarke Yoshimoto Pooley. The analysis was performed aiming to get the best estimate for the surplus production model to determine the maximum sustainable yields (MSY), utilization level, and effort level of scad mackerel. The criteria of the best model (estimator) are: sign suitability of regression equation, value of coefficient determination, validation values (residual), and significance of regression coefficients. From the best model by using the formula can be determined the maximum sustainable yields (MSY) of catching, utilization level, and effort level. The data of catch and fishing effort of scad mackerel collected from the Marine and Fisheries the Bitung City and North Sulawesi Province from 1998 2016. The best SPM, which is used to assess the potential of scad mackerel is Schaefer Model. Optimal effort (EMSY) of 4,449 trips per year, with catch of optimal CMSY19,793.601 tons per year. The effort level for 2014 is 86.58%, which shows the quite efficient effort, the utilization level of 73.10% showing the production still can be increased.


Introduction
Mackerel scad (Decapterus spp) classified as important pelagic fisheries resources and one of the non-oil export commodity in North Sulawesi. Mackerel scad production in North Sulawesi (including Bitung waters) in 2016 reach 50,000 tons per year, with a value of about 100 billion rupiahs [1]. Research on mackerel scad generally discusses the exploitation to increase production, not much research on the status of utilization (including aspects of sustainability and efficiency) resources.
Catching mackerel scad in Bitung waters has lasted long enough, with high intensity. Data on the level of utilization of the fish resources are very important, as it will determine whether the resource use is less than optimal, optimal, or excessive. Exessive utilization of fish resources would threaten its sustainability. By knowing the level of resource utilization on the mackerel scad, is expected to be done in a planned and sustainable management.
The simplest model of the dynamics of fish populations is Simple Production Model (SPM), by treating the fish as a single biomass that can not be divided, which is subject to the rules of simple increases and decreases in biomass. This model, commomly used in the assessment of fish stocks using only the data of catch and fishing effort generally available.
This study aims to get the best SPM, as well as knowing how much the result of maximum sustainable yields (MSY), Scad (Decapterus spp) in the Bitung Waters North Sulawesi utilization level, and the level of effort of mackerel scad in the Bitung waters.

Surplus Prodction Model
The simplest model of the dynamics of fish populations is surplus production model that treats the fish population as a single biomass that cannot be divided, which is subject to the simple rules of the rise and decline. The production model is dependent on the amount of four kinds, namely: biomass population at a given time t (B t ), catches for acertain time t (C t ), fishing effort at a certain time t (E t ), and the natural growth rate constant (r) (Boer dan Aziz, 1995) [2].
This model was first developed by Schaefer, who was initially the same as the form of logistic model. According to Coppola and Pascoe [3], equation surplus consists of several constants that are affected by natural growth, the ability of fishing gear, and carrying capacity. Constants allegedly using models of biological parameter estimators of surplus production equation, namely the model: Equilibrium Schaefer, Schaefer Disequilibrium, Schnute, and Walter-Hilborn. Based on four models were selected the most appropriate or best fit of the estimation of others.
According to Sparre and Venema [4], formulas surplus production model (SPM) is valid only if the slope parameter (b) is negative, which means the addition of fishing effort will lead to a decrease in the catch per fishing effort. If the parameter b positive value, then it can not be done estimating the optimum amount of stock and effort, but it can only be concluded that the addition of fishing effort is still possible to increase the catch.
Prediction of optimum fishing effort (E opt ) and the maximum sustainable catch (C MSY ) approached the SPM. Between the catch per unit of effort (CPUE) ang fishing effort can be either linear or exponential relationship [5]. SPM consists of two models, namely basic model of Schaefer (linear relationship) and the Gompertz model developed by Fox with forms exponential relationship [5].

Schaefer Model
SPM first developed by Schaefer, who was initially the same as the form of logistic growth model. The model is as follows: This equation does not include the effect of the catching, so Schaefer wrote back to: (1 ) K is the carrying capacity of the marine environment, and C t is the catch that can be written: q is catchability, and E t is fishing effort. This equation can be written: From the differential equation (2), the optimum catchment can be calculated at the time = 0, also called settlement at the point of balance (equilibrium), in the form of: (1 ) 0, From equation (3) and (5), find value of B t obtained as follow: So that equation (5) becomes: Equation (7) is simplified further by Schaefer becomes: while a = q K and 2 q K b r = This linear relationship is used widely for calculating C MSY through the determination of the first derivative of C t with E t to find optimal solutions, both to catch and fishing effort. The first derivative of C t to E t is: 2 t t t dC a bE dE = − in order to obtain the alleged E opt (optimum fishing effort) and C MSY (maximum sustainable yields of catch), respectively: By entering the value of E opt in equation (8), will be obtained as follow: by substituting a = qK and 2 , q K b r = will be obtained, The value of a and b are estimated by the least squares method approach that is commonly used to estimate the coefficients of a simple regression equation. Furthermore, by including the value of E opt in the equation (6) is obtained optimum biomass (B MSY ) as follows: The value of parameter q, K, and r can be calculated using the Fox algorithm, as referenced in Sularso [5], as follows: where the value of q is the geometric mean of q t . From the values of a, b, and q, can be calculated values of K and r.

Fox Model
Model of Fox has several characteristics that are different from the model Schaefer, that it biomass growth following the Gompertz growth model [6]. The relation of CPUE with efforts (E) follows a negative exponential pattern: Efforts optimum is obtained by equating the first derivative of C t to E t equal to zero and find: The maximum sustainable yield of catch (C MSY ) is obtained by inserting the value of the maximum effort into equation (13), and obtained:

Schnute Model
Schnute, suggest another version of the SPM is dynamic and deterministic [7]. Schnute method is considered as a modification of the model in the form of discrete Schaefer (Roff, 1983, reffered by Tinungki) [8].
where a = r, , and c = q, is the regression coefficient estimators.

Walter -Hilborn Model
Walter and Hilborn (1976) referred by Tinungki [8], to develop other types of SPM, known as the regression model. Walter-Hilborn model, using a simple differential equation, by the following equation:

Clarke Yoshimoto Pooley (CYP) Model
Estimation of biological parameter for the SPM can also be done through estimation techniques proposed be Clarke, Yoshimoto, and Pooley (Fauzi and Anna) [9]. The parameters which allegedly is r, K, and q, the model is expressed as follows: (18) can be written in the form:

Source of Data
The primary and secondary data of mackerel scad catching is collected from the Bitung waters. Production and fishing effort data collected from the Marine and Fisheries Service of Bitung City and North Sulawesi Province during 1998-2016.
Data (variables) used for the analysis of the SPM is the data of catch (C t ) per year and fishing effort (E t ) per year, and CPUE (Catch Per Unit of Effort). The data (variables) used for the analysis of the SPM is a follows: 1. The catch (C t ): weigkt of fish landed (tons) in year t 2. The effort of catching (E t ): the number of fishing boat landing (trips) in year t 3. catch per unit of efforts

Methods of Data Analysis
The models estimator who analyzed and evaluated are Schaefer, Fox, Schnute, Walter-Hilborn, and Clarke-Yoshimoto-Pooley (CYP). Based on results of statistical evaluation (mark of conformity, the value of R 2 , the validation (residual) value, and significance of the regression coefficient of the model), we get the "best" as estimator.
From the best of model can be calculated C MSY value, optimum fishing affort (E MSY ), utilization: n level, and the level of effort of mackerel scad.

Result and Discussion
Catch of mackerel scad fisheries in the Bitung waters fluctuate from year to year. Data catching in 1998-2016, are presented in Table 1. The results of the regression analysis for the SPM is presented in Appendix 1, which is described as follows:

Schaefer Model
From the analysis of regression equation 8.898 0.001 with a coefficient of determination (R 2 = 0.639) and a significance level of p < 0.01. Thus, a production model estimator catches Schaefer model according to equation (8) is: C t = 8.898 E t -0.001 E t 2 .

Fox Model
From the results of the regression analysis for Fox model is: Ln C t = 2.397 -0.000243 E t , with R 2 = 0.577 (p < 0.01). Estimates of catches corresponding to the model Fox equation (13): C t = E t . e (2.397-0.000243 E t

Schnute Model
Schnute method according to equation (16), obtained regression equation: with R 2 = 0.043, and all the regression coefficient were not significant (p > 0.05).

Discussion
The results of calculation for validation (residual) SPM of 5 models is presented in Appendix 2, which is summarized in Table 2. From the results of the calculation in Table 2, it appears that the most appropriate is Schaefer model with the largest R 2 = 0.639 and validation (residual value) is relatively small. Schaefer model obtained value of a = 8.898 and b = 0.001, with equation From the calculation, it turns out mackerel scad fishing effort at the Bitung waters in 2014 (86.58%), lower than the optimum effort so that still can be increased. The utilization level for the year 2014 (73.10%), is lower than the optimum level, its mean the catching can be increased. The researchs to know utilization level and effort level for pelagic fish, especially to little tuna in North Sulawesi waters by Kekenusa et al in Talaud and Bitung waters showing that the overfishing of production and inefficient of effort [10], [11].
The distribution of scad mackerel (Decapterus spp) in almost of regións in Indonesia, especially in Java Waters, South of Makasar, until North Sulawesi Waters [12]. As a comparison to scad mackerel in other waters in Indonesia, the catches of optimal (C MSY ) of scad mackerel in East of South East Sulawesi waters is 5,747.61 tons per year [13]. Scad mackerel in South East Sulawesi waters showing the intensive production [14]. In South Sulawesi at Flores Sea Waters, C MSY of scad mackerel is 10,456 tons per year, with the effort level 83.15% and the utilization level 76.60%, showing the intensive exploitation [15]. From these data, for scad mackerel in East Indonesia Waters (include in Bitung), generally the production still can be increased.
This research describes the use of some statistical criteria in selecting the best surplus production model. By applying some statistical criteria in selecting a surplus production model, will obtain better results. Researchers in the field of fisheries get guidelines for setting selection criteria for surplus production models, as well as avoiding the direct application of one model in analyzing the surplus production model in a waters.

Conclusion
1. The surplus production model that can be used to examine the catch of mackerel scad in the Bitung waters is Schaefer model, by the equation: C t = 8.898 E t -0.001 E t 2 . 2. The maximum sustainable yield of mackerel scad C MSY is 19,793.601 tons per year, obtained at the level of fishing effort E opt 4,449 trips. According to data at year 2014, for next years the catch and effort still can be increased.

Suggestion
1. In applying surplus production model in a waters location, not only directly using one particular model, but should use some of the models are chosen based on statistical criteria. The criteria involve, among others: suitability sign of the coefficient of models, coeffient of determination (R 2 ), the value of validation (residual), and the significance of the regression coefficients.
2. The catchs and efforts for mackerel scad in Bitung waters are lower than the optimum, so that still can be increased.