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F!e,^!e^AAFAASAAAN`N`FAAA`BBBBBBBBD.66JJJJJJEFIMAS MEETING ATHENS GREECE 2006 OCTOBER 1920
A proposal for a EFIMAS prototype simulation model applied to Mediterranean Case Studies
Vincenzo Placenti HYPERLINK "mailto:placenti@irepa.org" placenti@irepa.org; HYPERLINK "mailto:placenti@argosrl.eu" placenti@argosrl.eu
INTRODUCTION
The proposal for a EFIMAS prototype simulation model applied to the Mediterranean Case Studies is a bioeconomic simulation model. No optimisation issues have been take into account. The prototype model takes into account a number of species (target and complementary species), fishing systems (fleet segments) and fishing gears, and replicates the main features of the its bioeconomic structure, as well as fishermen behaviours, and effects of the main/alternatives management measures on the sector. Main/alternatives management measures are based on a effort control policy and also on a economic incentives basis. The formers are mainly restrictions on the fishing effort in terms of activity (fishing days) and capacity (gross registered tonnage), but also technical measures, such as variations in gear selectivity. Economic measures comprises taxes and subsidies. The prototype model evaluate the overall performance of such measures by estimating biomass effect variations, and economic outputs as social costs due to employment variations and public enforcement costs management. Uncertainty of the system is considered into the biological dynamics by means of stochastic simulations.
The model is arranged into four main modules and three different dimensions.
The four modules are the following: (1) Management module; (2) Biological module; (3) Economic module; (4) State variation module.
The management module enables us to mimic the Public Administrations intervention on the sector and to measure the effects of the different management policies. The biological module simulates the evolution of the state of the biomass among the stocks exploited by the fishing activity and gears. The economic module simulates the evolution of the state of the fleet segments within the geographic area of interest. The state variation module permits to draw the dynamic relationships between the overall variables of the model, by means of simple predetermined behaviour rules. More sophisticate rules could also be considered into the state variation module as compliance and entryexit rules.
The dimensions taken into account are the following: (1) Temporal dimension, monthly for the biological and yearly for the economic aspects; (2) Structural dimension of the fleet segments, fishing systems and fishing gears; and (3) Structural dimension of target species by species, groups of species and length classes.
The present document describes the general scheme of the model and its arrangement into modules, as well as the functional relationships between variables, connecting the different dimensions and modules.
GENERAL SCHEME
The structure of the model is aimed at reproducing the main features of fisheries within the Mediterranean. The most relevant aspects of the model can be summarised as follows:
The model is bioeconomic in order to consider both the natural dynamics of ichthyic resources and the economic relationships which influence Mediterranean fishery;
The management is implemented mainly in connection with the restrictions on the fishing effort. Nevertheless, specific technical and economic measures are also taken into account;
Variations in the fishing mortality are simulated by means of variations in the fishing effort expressed in terms of fishing activity and capacity and of efficiency variations. Increases in vessel efficiency are achieved by investing in technology. These variations are influenced by a predetermined and generalized fishermen behaviour, via net profits and investments, which is aimed at maximizing shortterm profits;
The model is multispecies and multigears.
The general pattern of the model, arranged into three levels, is shown in Fig. 1. The green level represents the natural trend of the sector, which consists of the biological and economic boxes and the state variations. The biological component affects the economic outcome of the model and this determines a series of variations in the operators choices which, in turn, influence the state of the system and the biological component.
The central and core level, marked in red, represents the management affecting both the biological and the economic components which may also influence the operators decisions included in the state variation box. The different management tools pertaining to the Public Administration are the main component of this process.
The third level, marked in yellow, enables us to consider the overall performance of the fishery system, thats cannot be evaluated only on the basis of the economic outcome, but requires an assessment of the social and biological costs, as well as the costs borne by the Public Administration to enforcement the management measures. The latter could be a effort management control and/or economic incentives based policies.
ELEMENTS OF THE MODEL
As said before, the model consists of four modules: the biological box, the economic box, the state variation box and the management box.
At the generic time t, the biological box includes selection figures per species. These figures are related to the different fishing gears/systems and to the level of effort, considered as the product of the number of vessels of a given fishing system and the average days of activity. On the basis of these figures and of the initial fixed input parameters, the biological box determines the level of catches for each species as its own output.
The catches are the main input variable of the economic box thats connect the biological and the economic modules. Besides the catches, other inputs affecting the economic box may come from their effort management as well as from subsidies or variations in taxes. The output of the economic box is the level of net profits.
The outputs of the economic module may determine changes in the state of the system module, in terms of decisions concerning the effort to be exerted on the resources. Fishermen behaviour can also be influenced by the management module, which could enforce restrictions on the effort and on selectivity of gears and/or applying for subsidies and taxes.
BIOLOGICAL BOX
The biological box could consists of two biological submodels. The first, structured into length classes (lengthage structured model), is applied for each of the target species defined by the user. The second is a generalized global model that simulates the catches of the aggregate of all the other species landed by the fishing gears by the fleet segments. The latter is a consequence of that the length structured biological model requires a considerable number of input biological data which are not always available for all species captured by each gears and fleet segments. It is straightforward that a supplementary biological model to assess the catches for the species whose biological data are unknown has been foreseen, v. g. of a generalised global model. Note that, to date, no virtual biological models have been investigated to be applied, as well as its economic box interactions and well being performance.
Model structured into length classes
The proposal prototype Efimas Mediterranean model applies a length classes biological model to the target species. This model performs an internal simulation on a monthly basis. This time interval takes into account the monthly lifecycle of the species considered and it is different from that of the temporal scale of the economic box. The differences between the two temporal scales are matched during the simulation phase of the general model, given that both the input and the output of the biological box have a yearly time interval. A further significant aspect of the length structured model is the fact that different gears can be simultaneously included in a single simulation. The gears and fleet segments taken into account are those considered into the updated version of the Delivery matrices of the Efimas Mediterranean casestudies.
The main components of the length structured model are listed below:
Recruitment, determined on the basis of a priori experimental data or associated with the relationships between parental stock and recruits and by the parameters of the stockrecruitment relationships determined by Beverton & Holt (1957), Ricker (1954) and Deriso (1980) ;
Growth defined by the von Bertalanffy model;
Lengthweight ratio defined according to a power model;
Ratio of mature individuals broken down by age/size classes and defined by an ogive model;
Natural mortality (M), constant or variable as a function of the age/size, according to the model designed by Pope et al. (2000), and implemented in Samed (2002).
Selectivity of gears defined according to three main models: an ogive, a product of two ogives and a Gaussian curve.
Total mortality Z as estimated by trawlsurvey (MEDITS and/or others based estimates);
Fish mortality (F) by fishing gear, which is defined according to the ZM ratio and the percentage of selection; and
Total landings by gear/fishing system per month according to the available statistics.
Included in the module structured into length classes, the input data of the biological box are the following:
Initial Recruitment value expressed as number of individuals;
Vector 12x1 of the monthly coefficients (ranging between 0 and 1) associated with the Power of Recruitment;
Vector 12x1 of the monthly Number of Recruits, which is to be used in absence of the StockRecruitment ratio.
Two parameters concerning StockRecruitment ratios as in the Beverton & Holt or Ricker model and three parameters as in the Deriso model;
Four population growth parameters as in the von Bertalanffy model;
Two parameters relating to the lengthweight ratio;
Total mortality (Z) and natural mortality (M) parameters;
Vectors F and M in case of rejection of the simulationderived vectors;
Two parameters pertaining to the maturity ogive;
Length of retention and range of selection values per gear considered and the value relating to the deselection length in case of trawlers;
Sexratio value; and
Coefficient for the initialisation of the population.
Besides the input data entered directly by the user, the length structured model receives from the generalized model the catches and the variations of the overall days per fishing gear.
The main link between the lengthclasses structured component biological box with the other components of the model is a function linking the nominal fishing effort per fishing system (expressed in terms of overall fishing days, i.e. fishing activity) and its fishing mortality estimated per gear engaged. This effortmortality relationship derives from the assumption that a constant elasticity equal to 1 subsists between the two variables. The input variables of the biological box concerning fishing mortality involve the single fishing gear rather than the fishing systems.
Initialisation phase of the model
Within the initialisation phase, an initial population in steady state is reproduced on the basis of both the Initial Recruitment provided by the user and the above other biological inputs considered. Then, the model performs a preliminary simulation by applying the number of years obtained from the product of the lifespan of the species considered and the initialisation mortality coefficient provided by the user. This simulation permits to rectify the fishingrelated and total mortality values, the resulting estimates of population based on monthly catches and the fishing days per gear in relation to the12 months of the base year.
For the 12 moths of the base year, the initialisation phase produces the following outputs for each target species and length class: (1) average length vector; (2) natural mortality vector; (3) fishing mortality vector; (4) total mortality vector; (5) current initial population and average current population; (6) virgin initial population and average virgin population; (7) current population of reproducers; (8) current biomass; (9) virgin biomass; (10) current biomass of reproducers; (11) current biomass of reproducers; (12) yield for each of the four gears considered; and (13) correction factors for each of the gears considered.
Simulation phase of the model
During the simulation phase, the length structured model receives the following variations from the general prototype model:
Variations occurred within the aggregate days per gear;
Variations in the gear selectivity parameters; and
Variations of vessels efficiency.
These variations directly affect the fishing mortality and, consequently, the catches per gear. During this phase, the output resulting from the length structured model equals the corresponding output of the initialisation phase, except for the correction factors per gear which remain constant throughout the simulation years. To date, no simulation within economic incentives interactions is modelled.
Unstructured biological model
The species whose biological data are not available cannot be considered by applying the biological model structured into length classes. Hence, these species have been classified as a aggregate denominated as other species. Within this aggregate, the catches are estimated using a logistic model (the Schaefer model), which has been modified to take into account also their shortterm effects.
The biological model used to estimate the other species group is formulated as follows:
EMBED Equation.3 ,
where Ct are the total catches of the other species group resulting from all the fishing system considered, Et is the equivalent fishing effort expressed as aggregate days, and k0 , k1 are parameters of the longterm component.
The first part of the formula expresses the longterm effect according to the Schaefer model. In order to consider the shortterm effect, the estimate of the longterm catches is rectified multiplying it by the percent variation over the aggregate fishing days from the time t1 to the time t.
The equivalent fishing days are obtained using the weighed sum of the total days per system. The use of the equivalent fishing days is needed in order to consider the different productivity of the days per fishing systems and gears. The equivalence is expressed in terms of trawlers taken as reference fishing gear .
To obtain the equivalent fishing days, the aggregate days of each system are multiplied by a correction factor obtained using the ratio between the productivity of each of the systems considered and the productivity of the trawlers. At once, the productivity (CPUE) is measured as the ratio between the catches and the fishing days by each system.
EMBED Equation.3 .
The correction factors (FC) are then obtained by the following ratio:
EMBED Equation.3 .
The equivalent effort in terms of equivalent days is obtained using the formula:
EMBED Equation.3 .
Parameters k0, k1 are entered by users out of estimates attained outside of the model. These parameters represent the only input to the model concerning the unstructured biological model. The parameters k0, k1 entered by users are then modified in order to obtain an equilibrium solution. The only information deriving from these parameters is the ratio:
EMBED Equation.3 .
Assumed the input parameter a as fixed, the parameters k0 and k1 are updated by the model in order to guarantee the coincidence between the estimated and the actual catches throughout the base year and to follow the steadystate hypothesis also defined within the unstructured model. The new values of k0 and k1 are obtained using the following system of equations:
EMBED Equation.3 ,
The system can also be represented by the following matrix:
EMBED Equation.3 ,
or, more briefly:
EMBED Equation.3 ,
where A is the matrix of the coefficients, k is the vector of the unknown and b is the vector of the known quantities.
Within the model, the equation system is solved within the initialisation phase. Then, the new parameters k0 e k1, calculated during this phase are kept constant over the simulation phase.
THE ECONOMIC BOX
The economic box consists of the prices and costs functions. As further described, the prices function defines the evolution of prices over time. The production value per each fishing system are obtained by multiplying the prices and the quantities produced defined as an input of the economic box at the time t = 0. Earnings are considered in the costs function. The output of the economic box is represented by the level of (net)profits. Net profits is determined by the natural dynamic of the system as well as by the management policies defined in terms of subsidies and taxes.
The initial input data are the following:
A matrix of catches by species or group of species identified using 12 lines (a line per month) and n columns, where n is the number of the systems considered;
A matrix of prices defined using m lines (where m is the number of species or group of species) and n columns (where n is the number of fishing systems);
A matrix of fishing days defined using 12 lines (a line per month) and n columns, where n is the number of the systems considered;
A matrix of technical data defined using 3 lines (tonnage, number of vessels and number of fishermen) and n columns, where n is the number of the systems considered;
A matrix of costs defined using 7 lines and n columns, where n is the number of the systems considered. The 7 lines correspond to the following costs headings: commercial, fuel, other variable costs, maintenance expenses, other fixed costs, amortizations and interests.
During the initialisation phase, the model estimates the coefficients defining the relations between the variable costs and the activity, and between the fixed costs and the fleet size. In this phase, at the same time as it considers the prices broken down by commercial category, the model estimates these prices. In the latter case, further inputs to the economic box are the definition of the number of commercial categories and the relations between the prices of these categories by single species. Finally, other input data can be the price flexibility coefficients catches, average days revenues and tonnage revenues.
The following paragraphs describe the functions which determine the trend of the economic variables within the model.
Prices function
In the proposal EFIMAS prototype model for the Mediterranean case studies, prices are broken down by species or group of species and by fishing system. It is also possible to consider a price differentiation by commercial category, in which these categories are associated to the length classes of a single species. Obviously, the latter price differentiation is feasible only with the species for which a biological model structured into length classes is foreseen.
Generally speaking, price dynamics can follow two different hypothesis. In the first hypothesis, the prices by fishing system (and possibly by commercial category) are assumed as constant and equal to the prices registered over the base year:
EMBED Equation.3 .
In the second hypothesis, the prices are assumed as a function of the quantity produced, that is, the catches. The functional relation between prices and catches is defined using a flexibility coefficient per each species and fishing system. The flexibility coefficients are to be estimated offline and included in the model as input parameters. The flexibility between prices and catches is considered as the per cent variation in prices due to the unitary per cent variation in the catches:
EMBED Equation.3 ;
where EMBED Equation.3 is the flexibility coefficient per a given species and fishing system.
The prototype model could enables us to consider prices by commercial categories, as a proxy of length classes. Over the initialisation phase, prices are estimated on the basis of a series of inputs requested to the user. These prices are then used in the simulation phase.
In order to break down the prices by commercial categories, the following input data are requested:
Number of commercial categories by species;
First length class by category;
Relation between the prices of each commercial category and the price of the last category.
The price estimate by each commercial category is performed using a system of simultaneous equations subject to the restrictions on the relations between prices introduced by the user. The other limitation, given the quantities simulated by the biological box, considers the average price equal to the price registered throughout the base year. As an example for four fishing system and four commercial category, the system of equations by each species per each fishing system is formulated as follows:
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 ,
where C represents the catches of the species considered and performed using a specific fishing system, Cs the catches of a specific set of length classes or a specific commercial category, ps the average price to be estimated and the a coefficients, the ratios between the prices provided by the user.
The first equation enables us to prevent the average price registered for the species and the fishing system from being varied, whilst the other equations bind the estimate of the single prices to respect the relations defined by the user.
The system of equation can be represented using the following matrix:
EMBED Equation.3 .
By identifying the coefficient matrix as A, p the unknown matrix and b the known quantities vector, the system can be synthetically formulated as follows:
EMBED Equation.3 .
As previously defined, the prices by commercial category will vary over time on the basis of the total catches according to a single flexibility coefficient.
Structure of the costs
As shown in following table, the costs subtracted from the returns to obtain the added value and the revenues per fishing system are divided into groups. The variable costs are a function of the effort as to the components related to fuel and lubricant while the component of the commercial costs is a function of the level of catches.
Table SEQ Tabella \* ARABIC 1: Structure of the costs based on the sector economic account
Fixed costs, instead, are a function of the tonnage, both as regards maintenance expenses and other fixed costs. The labour cost is calculated as a quota equal to 50% of the full amount, within Mediterranean fisheries, that is the difference between returns and variable costs. This statement is justified by the prevalence of party contracts over other payment systems governing the fishery sector.
Gross profit is then obtained from the difference between revenues and intermediate costs; that is, between the sum of variable and fixed costs and the labour cost.
Finally, to obtain net profit, amortizations and interests are subtracted from gross profit. The amortizations are equal to 4% of the value of the fleet below 25 years of age and 2% of the fleet over 25 years of age. The interests, considered as cost opportunity, are calculated as the yearly bond interest rate applied to the vessel value. The vessel value is then estimated as a replacement value.
During the simulation, amortizations and interests will undergo some variations as a consequence of tonnage variations (i.e., variations in number of vessels).
The costs of each fishing system are broken down into the following four groups: variable costs; fixed costs; labour costs; amortizations and interests. Net taxation (that is, taxes minus subsidies) is to be added to these costs.
Variable costs are then classified under three headings: fuel and lubricant costs, commercial costs and other variable costs. The former, identified as Cc (fuel costs), and the other variable costs (Acv) are a function of the fishing effort, (that is, tonnage multiplied by average days):
EMBED Equation.3 ,
EMBED Equation.3 .
Conversely, commercial costs (Cco) are defined as a function of the total catches of the fishing system:
EMBED Equation.3 .
Variable costs (CV) can also be estimated in an aggregate way, with the exception of the details of their composition, indeed:
EMBED Equation.3 ,
EMBED Equation.3 ,
EMBED Equation.3 ,
where EMBED Equation.3 .
Fixed costs (CF) can, in turn, be subdivided into maintenance expenses (Cm) and other fixed costs (Acf). In both cases we assume that these costs are a function of the tonnage and are independent from the level of the activity:
EMBED Equation.3 ,
EMBED Equation.3 ,
EMBED Equation.3 ,
Where EMBED Equation.3 .
Labour cost (CL) is not estimated on the basis of coefficients, but is calculated as 50% of the total amount, that is the difference between returns (R) and variable costs in which the returns of the fishing system considered clearly result from the product between catches and prices per each of the species considered:
EMBED Equation.3 ,
EMBED Equation.3 .
This statement is justified by the prevalence of party contracts over other systems of labour remuneration.
Gross profit (PL) is obtained by subtracting revenues from labour cost and intermediate costs, i.e. the total amount of variable and fixed costs:
EMBED Equation.3 .
Net profit (PN) ) is obtained by subtracting amortizations (AM) and interests (I) from gross profit. The former are equal to 4% of the value of the fleet below 25 years of age and 2% of the fleet over 25 years of age. The latter, considered as cost opportunity, are calculated as the yearly bond interest rate applied to the vessel value. The vessel value is then estimated as a replacement value. Both for the amortizations and the interests, the estimation based on the age of the fleet is rather difficult. Consequently, the initial version of the model foresaw an estimate based on the overall tonnage of the fleet:
EMBED Equation.3 ,
EMBED Equation.3 .
Thus, net profit will be obtained using the following equation:
EMBED Equation.3 ,
where TN stands for net taxation; that is, the difference between taxes and subsidies as established by the Public Administration:
EMBED Equation.3 .
RELATIONSHIP BETWEEN THE ECONOMIC AND THE BIOLOGICAL BOXES
The biological and the economic boxes show different structures both with the temporal dimension of the simulation and the structure of the input data.
The simulation of the biological box works on the basis of monthly intervals, whilst the economic box shows a yearly dynamic. This distinction is justified by the different features of the two subsystems. Indeed, the biological aspects of the system are linked to the seasonal nature of natural phenomena. The lifecycle of the species exploited, the reproduction periods and the weather conditions affecting fishing mortality must all be taken into account and need to be arranged into time intervals lower than a year. On the other hand, the economic variables are hardly discernible on the basis of monthly intervals. In particular, the costs of the fishing activity can barely be subdivided into single months unless applying specific estimates. Besides, the decisions made by the operators concerning the investments are usually based on the economic outcome of the preceding year.
As for the structures, the relationship of the biological box concerns gears and species. On the contrary, within the economic box, where a single system can use different gears, the distribution/classification of the vessels is defined as a function of the fishing system. These systems are generally defined as a function of the main gear, but it is possible that in some periods of the year the main gear is supported by others. Besides, some systems, such as the smallscale and the polyvalent, fisheries are characterized by the use of different gears, which, in some cases, work simultaneously. In particular, one of the main feature of the Mediterranean fishery, polyvalence, makes the vessels classification by singlegear group simply impracticable.
Within the model, the differences between the biological and the economic boxes have been managed using a series of matrixes that allow converting catches and fishing days per system into catches and fishing days per gear. In particular, for each month and species, the catches per gear are obtained by a linear combination of catches per system according to a series of coefficients which identify the percentages of catch distribution per system among the different gears. This equation system can easily be represented with the following matrix:
EMBED Equation.3 ,
which can be more concisely expressed as follows:
EMBED Equation.3 ,
where Cs represents the vector of catches by system, Ca is the vector of catches by gear and Ds,a is the matrix of catch distribution by system among gears. This matrix, estimated offline, is included into the model as an input datum.
The model performs this operation whenever entering the biological box. When the model returns into the economic box, it performs the parallel operation; that is:
EMBED Equation.3 ,
which can be expressed by the following matrix:
EMBED Equation.3
where Ca and Cs have the same meaning as the previous matrix, whilst D1a,s represents the matrix of catch distribution by gear among systems.
Note that Matrix D1a,s is not the inverse of matrix Ds,a. It is the transposed matrix of B:
EMBED Equation.3 ,
The matrix B has the same dimension of matrix D, s x a, and its generic element EMBED Equation.3 is obtained as follow:
EMBED Equation.3 ,
where EMBED Equation.3 is the generic element of the matrix D, EMBED Equation.3 is the ith element of the vector EMBED Equation.3 and EMBED Equation.3 is the jth element of the vector EMBED Equation.3 .
Matrix Ds, a e D1a,s are estimated on the basis of the data recorded over the base year and are kept constant throughout the years of simulation.
STATE VARIATION
The variations in the state of the system involve the variations that occur within the structural variables as a consequence of the fishermen behaviour and the overall market trend. On the basis of the level of profits, the operators will make their decisions on the average number of fishing days and also on the entry/exit rules of fleet over the following year. In other words, their decisions will affect the overall tonnage exploited in the fishing activity.
The operators behaviour is aimed at maximising the profits: (a) in agreement with the regulations, the level of activity at sea should tend to increase with the increasing of profits; (b) the entry/exit from the sector will be based on the comparison between the profits made over the current year and the profits of the preceding year. Thus, average fishing days and tonnage become a function of the variations of profits according to flexibility coefficients assessed offline and included by the user as input data.
As for the average fishing days and the overall fleet tonnage, the model foresees two possible dynamics. The former assumes the average days and the tonnage as constant and equal to the values registered for the base year:
EMBED Equation.3 ;
EMBED Equation.3 .
The latter hypothesizes a relation between the variations in the average days and the variations in the profits made over the preceding year:
EMBED Equation.3 .
A relation between the overall tonnage variations and the variations in the profits made over the preceding year can also be assumed:
EMBED Equation.3 ,
The coefficients a and b respectively measure the flexibility of the average days and the flexibility of the overall tonnage in comparison with the profits.
The state variations also concern the hypotheses formulated on price dynamic and the differentiation of prices by commercial categories.
Finally, the state variation hypotheses include also assumptions concerning the effects of technology investments on fishingrelated mortality. In this case, the model requires to specify the percentage of profits that, on average, are invested to enhance vessel productivity. The introduction of a flexibility coefficient between investments and fishing mortality is also required.
MANAGEMENT
The main objective of the model is the simulation of the management measures generally adopted at a national and international level within the sector. As for the Mediterranean fishery, these measures are directed at restricting fishing effort in terms of fleet capacity and activity. Besides, the EFIMAS prototype model allows simulating both the technical measures concerning gear selectivity and economic measures, such as variations in tax level and allocation of subsidies to the sector.
In particular, the management measures implemented are the following:
Variation in selectivity: among the gears considered, the model considers a selectivity function for each gear. The input parameters that define this function can be modified by the user for a given year of simulation. This permits to simulate the management measures directed at increasing the selectivity of gears.
Temporary withdrawal: this measure is implemented within the model in relation to a single fishing system(gear). Its implementation is structured into monthly levels and permits to determine the maximum number of fishing days foreseen for each month and fishing system(gear).
Permanent withdrawal: the model simulates this measure by means of a proportional reduction in the number of the vessels that use a specific gear. The percent variation on the gear specified by the user is applied on all the fishing systems that use the same gear.
Levy variations: this is an economic measure that can be implemented both as an increase or a reduction in the taxes imposed on the fishing activity.
Variation subsidies: as with the taxation, this is an economic measure whose implementation allows evaluating the effects of subsidy variations on the sector. The initial value is nil.
Moratorium: this measure represents a ban on a specific gear or the introduction of a ban on its use.
Gear suspension: this measure can be coupled with temporary moratorium. To strengthen its effect, this measure can be associated to a temporary withdrawal. Indeed, temporary withdrawal is implemented with reference to the fishing system, whilst suspension affects the gear. The simultaneous selection of both permits to simulate a withdrawal affecting the whole system and all the vessels of the fleet, though they belong to different systems, but which use the prevalent gear of the system considered.
The management measures are implemented according to the following specifications:
As for the technical measure concerning the selectivity, the model permits to modify the length of retention by 50% by gear per species:
EMBED Equation.3 .
As regards temporary withdrawal, the model allows defining the maximum number of average days by system per month. The variation affects the sector dynamic only in case this number exceeds the maximum limit established.
EMBED Equation.3
where EMBED Equation.3 represents the highest number of average fishing days for the month considered.
With permanent withdrawal, the overall tonnage of the vessels belonging to the systems which use the gear affected by the measure will be reduced by a percentage equal to that specified by the user.
EMBED Equation.3 ,
where EMBED Equation.3 is the percentage variation of tonnage specified for the management measure.
The economic measures may consist of variations in tax levels or subsidies. The model considers taxes as an additional fixed cost. Within the base year, taxes come under the fixed costs heading. For this reason, the value of the additional cost Taxes (T) is nil:
EMBED Equation.3 .
During the simulation, this value can be modified in order to reproduce the associated management measure:
EMBED Equation.3 ,
where EMBED Equation.3 measures the variation introduced into the level of taxation.
Likewise, subsidies can be considered as an additional revenue granted by the Public Administration to a specific fishing system. This revenue is to be added to the income of the system affected by the measure. At the time t = 0, the value of subsidies is nil. Subsides could undergo variations over the simulation phase:
EMBED Equation.3 ,
EMBED Equation.3 ,
where EMBED Equation.3 is the variation in the amount of the granted subsidies.
The moratorium on a gear is simulated by deleting the catch percentages that determine the transformation of catches per system into catches per gear. For instance, if the moratorium affects gear 4 as from time t, the percentages of catches of the distribution matrix shown above will be modified as follows:
EMBED Equation.3 .
Likewise, the simulation of gear suspension is also obtained using the matrix of the catch percentages per system. In this case, the variation will be solely temporary and include only specific months.
MANAGEMENT COSTS, SOCIAL COSTS AND BIOLOGICAL COSTS
At the current stage the proposed EFIMAS prototype model applied to the CS7 and CS8 Mediterranean case studies consider only the production costs. Notwithstanding, the prototype EFIMAS model could also consider the other costs of the system, like the management, social and biological costs.
An idea as to be considered the above costs could be follow the underlines.
Management costs
The management costs are those undertaken by the Public Administration to put into effect management measures. In particular, the management costs considered in the model could represent the financial support granted to the vessels that comply with temporary withdrawal and the costs of decommissioning foreseen by the permanent withdrawal schemes.
With reference to temporary withdrawal, the crew of the vessels affected by this measure are granted the minimum wage provided for by collective agreements. Accordingly, the model would requires the insertion of the minimum monthly wage. This value can be estimated at the mean of the wage scales established by the contract for the different crew working on board. Then, the model adjusts the monthly cost for each worker to the overall number of workers affected by the measure and the duration of the measure in number of days.
As to the permanent withdrawal, the EC Regulation provides for a financial support differentiated into LFT classes and that varies in proportion to the age and tonnage of the vessel. The model would requires an average value for TSL units per system considered. The estimate of the total cost for the implementation of the measure is obtained multiplying these values by the overall amount of tonnage forgoing the fleet.
Social costs
The social costs could be considered exclusively in terms of variation in the number of workers employed in the sector. The number of workers per system is linked to the number of vessels using the parameter employed per vessel. This parameter is assumed as constant and is defined in relation to the base year.
The variations in the tonnage of each system are an outcome of both the natural sector dynamic (tonnageprofits flexibility) and the effect of management measures. These variations determine changes in the number of vessels and therefore in the number of workers.
Biological costs
The biological costs are exclusively considered in terms of total biomass. The model does not allow to estimate the actual sea biomass, but it calculates a simulated biomass whose relevance is referred to the internal structure of the population. Nevertheless, this estimation is proportional to the actual estimate on the basis of a coefficient that proves constant in time. Accordingly, the simulated variations can be directly associated to the variations that would really occur within the biomass. Consequently, the model permits to verify the effect of the management measures on the actual biomass. The model considers the changes in the biomass as a consequence of the variations in fishing mortality. This is a function of gear selectivity, fishing days of the systems and variations occurred at the technology level.
OUTCOMES OF THE MODEL
The model permits to view and save the historical series of output. The outputs considered are divided into 5 typologies: biological variables, economic variables, technical variables, biological indicators and economic indicators. The outputs connected to the biological dimension show a monthly recurrence, whilst those linked to the economic and technical dimensions have a yearly recurrence.
Biological variables per species and, as for the yield, per gear: (1) fishing mortality; (2) population; (3) SSP; (4) biomass; (5) SSB; (6) yield; (7) total mortality.
Economic variables per fishing system and, as for catches, prices and income, per species: (1) catches; (2) prices; (3) revenues; (4) costs; (5) profits; (6) crew.
Technical variables per fishing system: (1) number of vessels; (2) grt; (3) total fishing days; (4) average fishing days; (5) effort.
Biological indicators per species: (1) SSB/SSBV
Economic indicators per fishing system and species: (1) catches/grt; (2) catches/days; (3) catches/effort; (4) revenues/grt; (5) revenues/days; (6) revenues/effort.
STOCHASTIC NATURE OF THE MODEL
The uncertainty linked to the system is dealt with by adding an error term to the model. In its current version, the model has taken into account the error only in the equations which calculate the initial recruitment. This may be assumed as constant or it may follow a specific stockrecruitment relationship. The relationship considered by the proposed EFIMAS prototype biological box are that of Beverton & Holt (1957):
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Consequently, the error is distributed as a normal/perpendicular of mean 0, e~N(0,s2). The model permits to specify the variability of the error measure included in the estimate of the initial recruitment.
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