FishRent: a Spatial bioeconomic model for Fisheries

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1 FishRent: a Spatial bioeconomic model for Fisheries Heleen Bartelings, Katell Hamon, Erik Buisman Model Description Introduction The model optimizes the catch and landings distribution of Species i by Segment j over areas n and periods p within a year t to maximise the overall net profits under management constraints. Depending on the choice of the user the model can function with monthly, quarterly or yearly time periods. The model can simulates the annual catches and landings over a time period. This means that the model will run for each year as defined by the user. Data input for consecutive years will be taken from model calculations of previous years. Objective function Total profit is maximized subject to production and balance constraints. The total profit is calculated as a sum of the profit of all fishing segments j. Objective: Profit of a fishing segment j is calculated as the revenue minus variable and fixed costs. Three types of variable costs are distinguished: fuel cost (FuC), crewcost (CrC), and other variable costs (VaC). Two types of fixed costs are distinguished: fixed cost (FxC) and capital costs (CaC). The model include a limited number of species for which the dynamics of the stock are integrated with the dynamics of the fleet. Ideally the species targeted by the fleet should be explicitly included in the model while bycatch are pooled as other species. Yearly revenue of a fishing segment j is calculated as the sum over the period of the value of the landings of the target species (Land i,j,p) times a percentage of the value of other catches (OtSpR). It is assumed that the catch of other species is linearly related to the value of landings of the target species. Thus if the total value of landings of the targeted species i increases by 10%, the value of landings of other species increases with a similar percentage. [ ] As an alternative the model can also maximize the gross cash flow (GCF) instead of the net profits. The gross cash flow is defined as the revenue minus the variable cost. Economic costs The five economic cost variables (,,, and ) are calculated on a yearly basis per fishing segment j. The cost data needed as an input to the model was based on the

2 annual economic data collected by most European countries every year. The choice to match the input needs of the model to available data was made to allow a broad use of the model. The fuel costs are calculated based on the effort in days (Eff) spend fishing and steaming. In the model the effort spend fishing determines the catch. However to catch fish the vessels need to steam to the fishing area. These steaming costs also needs to be included in the fuel costs. To calculate the total effort spend on fishing and steaming, the fishing effort is multiplied by a factor. The differs on the distance between the home port and the fishing area n. As the homeport(s) and steaming speeds differ between segments the β s can also differ between segments (see Data section for the calculation of parameters). The fuel cost are calculated as the effort spend steaming and fishing times a parameter representing the average fuel consumption per unit of effort times the indexed fuel price ( [ ( ) ] In the Netherlands the crew get a small fixed wage and a larger variable wage depending on the profit of fishing trips. To match the crew wages calculation as in The Netherlands, the crew cost are calculated as a share in the revenue minus the fuel costs. The variable cost, being e.g. costs of landings, auction and harbour fees, are determined as a fixed share of the gross revenue. The fixed costs, also named vessel costs or semi-fixed costs are administration, insurance, maintenance, etc. It is assumed that these costs depend implicitly on the value of the vessel and are constant over years per vessel. The value of the segment is calculated as a fixed amount per vessel time the size of the segment j ( times an indexed price per vessel (. The indexed price is introduced in the equation to account for inflation. The capital cost include both depreciation and interest costs. The capital cost are calculated in a similar way as the fixed costs. Production function The revenue in the model is determined by the landings and the prices of the targets species i. The landings in turn are determined by the catch of the species. Landings and catches are not per definition the same as the model takes into account the possibility of over quota discards and a fixed proportion of undersize discards. [ ] The catch of a species is calculated by a Cobb-Douglas function. Catch of species i of segment j in area n in period p depends on the fishing effort and the available biomass (CB). is a measure of the catchability of the biomass in area n and ( ) is a measure of technological creep. The value of and are set by fleet depending on the type of gear (see original fishrent manual).

3 Balance equations: Effort The use of fishing effort is limited in two balance equations. First of all the effort used per segment has to be bigger than a minimum effort calculated as a certain percentage ( of the total available effort for that segment. The total available effort is determined as either a maximum available effort (maxeff) determined by management plans or a maximum available number of days per vessel (dasm) times the number of vessels in the fleet. [ ] Second the maximum effort used per segment within a year has to be smaller than the maximum effort available to each segment. [ ] The maximum available effort per fleet segment is determined based on two parameters. First of all in the long term management plans a maximum amount of effort can be defined. Second the max effort is defined as the maximum number of seadays available to a vessel ( vessels in a segment (Fle). times the number of The size of a fleet segment is determined by the size of the fleet segment in the previous year plus the (dis)investments. Investment in a fleet segments is dependent on the profits made in that fleet segment in the previous year. Theoretically the investments should be determined by expectations of future profit, but there is no empirical data, which could be used to support such theorem in the model. Instead, perceived profitability in the preceding year, expressed as ratio between break-even revenues minus realised revenues divided by realised revenues is used to determine the (dis)investments in each year. The break revenue,, is calculated as This leads in some years to quite substantial changes in the number of vessels in a fleet segment, which could occur as vessels from other segments may enter the given fishery. At the same time, it was recognised that the inertia of the system (licensing, knowledge of skippers, etc.) does not allow such full flexibility. Consequently, parameters have been introduced to limit the maximum annual (dis)investments. Furthermore, it has been assumed that the active fleet will first achieve a certain minimum number of days-at-sea per vessel before the number of vessels will be expanded ( to avoid continuous growth of the fleet, while at same time the number of days-at-sea per vessel could be proportionately falling, as long as break-even revenues exceed realised revenues. This leads to the following investment function: If or [ ] If [ ]

4 Where is the maximum percentage of disinvestments and is the maximum percentage of investments in a year. Balance equations: Catch and Biomass is a share of the percentage of the profit that can be invested. Catch is limited by the available biomass in each area n. For each species, area and period the catch cannot exceed the available biomass. In case closures are introduced in the model as a scenario, it is assumed that the available biomass is further reduced by the percentage of the area that is closed. If no area is closed the closure parameter is set to 1, 8if closures are included the closure parameter will be smaller than 1. The biomass of species i area n and period p is calculated as the biomass of the previous period plus the growth of the biomass minus the total catch. The total catch includes undersized discard calculated as a fixed share of the catch and catches of other fishing segments not taken into account in the model ( ). Two types of species are distinguished: mobile and stationary species. The biomass is calculated differently depending on the mobility of the species. For mobile species it is assumed that after a period the biomass will be redistributed over all areas according to a predefined distribution factor. This means that within a period the biomass can be completely depleted but after the end of the period the biomass will be restored according to the overall growth of the stock. { ( ) } For stationary species the biomass within an area only depends on the stock, growth and the catches within the area. Biomass within an area can therefore be completely depleted. ( ) The growth of the stock is calculated once a year based on the biomass in the last period of the previous year. for p is last period Depending on the type of species, two types of growth functions can be used: a 3th degree polynomial growth function or a logistic growth function. 3th degree polynomial growth function: { [ ] [ ] [ ] } Logistic growth function: { } Balance equations: TAC In case a species is managed by quotas, an extra balance equation is added to the model which states that the total catch of the segment minus over quota discards has to be lower than the available quota.

5 Depending on the selected policy scenario over quota discards will either be allowed to be positive or will be kept at zero level. In long term management plans a target fishing mortality is defined to reach a sustainable catch. This target mortality is used to calculate the sustainable TAC. First of all the model calculates the current fishing mortality as the total catch divided by the total biomass. If the fishing mortality is above the target mortality the quota need to be reduced. However in most long term management plans an adjustment path towards the target fishing mortality is defined. For example in the flatfish management plan in the north sea, the fishing mortality should be reduced by 10% every year until the target mortality is reached. In the model this is taken into account in the following equation: If Where is a fixed percentage depending on value mentioned in the management plan. Based on the target fishing mortality the model calculates the sustainable TAC, using the Baranov function (Lassen, 2000). [ ] In addition, the model allows for a limit on yearly changes in the TAC if this is defined in the long term management plan. For example in the flat fish management plan north sea the yearly changes of the TAC cannot exceed 15%. If the sustainable TAC exceeds the 15% change the change will be cut of at 15% of last years TAC. Price elasticities Fish prices of species i in period p are based on the prices of those species in the same period of the previous year adapted by a price elasticity. However, this is only relevant if the fishery lands a significant share of the total supply of a species. Setting price elasticity at zero leads to constant prices. By linking the price of a species in a certain period with the price of the species in that period a year before, the model includes seasonal effects in the prices. However it is implicitly assumed that these seasonal effects will not change apart from changes due to the price elasticity. The price per species is calculated as follows: Data There are two type of data input in the model: model parameters and input data. They are both provided by the user. Initial value of variables The initial state of the system is defined by the user inputs in the base year for the following years, the model changes the system according to the equations described above.

6 The initial state of the stock and of the fishery is taken as the average of the last 3 years of data provided. Model parameters The parameters used in the model calculations are computed from the input data provided by the user. They are held constant for the time of the simulation. The description of the model parameters and their calculation is shown in table 1. Table 1 Description of the parameters used in the model Description Parameters Calculation Fleet parameters Proportion of steaming effort compared to fishing effort per fleet and fished area Minimum share of the available effort to be spent annual per fleet Maximum effort spent by a fleet Maximum number of days at sea per vessel Economic parameters Proportion of the value of landings of species not included in the simulations per fleet segment Fuel consumption per day at sea Share of the revenue minus the fuel costs spent for crew wages Proportion of the revenue taken as variable costs (e.g. costs of landings, auction and harbour fees) Annual fixed cost per vessel for each fleet Annual capital cost per vessel for each fleet Provided by the user as the proportion of total effort spent steaming per fleet depending on the fished area, it is then transformed in the model Default value to 0.8 Calculated as the initial level of effort for the fleet segment or if provided a maximum number of sea days per vessel Calculated as the initial level of effort per vessel for the fleet segment Calculated based on the value of landings of the species in the model and the total fishing revenue per fleet Calculated as the ratio of total fuel costs and number of days at sea Calculated per fleet as the ratio of crew wage divide by the revenue minus the fuel costs (to match the Dutch system) Calculated as the ratio of initial variable costs and initial revenue Calculated as the initial fixed costs divided by the initial number of vessels in the fleet segment Calculated as the initial capital costs divided by the initial number of vessels in the fleet segment Indexed price per vessel Set by default to 1 Investment parameters Maximum disinvestment as the proportion of vessels in the fleet Maximum investment as the proportion of vessels in the fleet Proportion of the profit that can be invested Biological parameters Set by default to 0.2 Set by default to 0.1 Set by default to 1

7 Species-specific coefficients of the 3rd degree polynomial function 1,,, Provided by the user, ideally calculated on biomass time series Species-specific intrinsic growth rate and carrying capacity for the logistic growth function 1, Provided by the user, ideally calculated on biomass time series Spatial distribution of the biomass of the species as a proportion of the total biomass per season Harvesting parameters Provided by the user, this can be based on survey data or if missing on commercial data Cobb Douglas effort exponent per fleet and area Cobb-Douglas biomass exponent per fleet and area Cobb-Douglas catchability coefficient per fleet, species area and period Annual technological creep coefficient per fleet Discard rate of undersized fish per species and per fleet segment Share of accounted catch per species caught by fleet segments in the model Management parameters Targeted fishing mortality per species Maximum targeted change of fishing mortality between two consecutive years Proportion of an area being closed to fishing per season depending on the fleet segment Can be provided by the user, default values for trawling fleets is 0.6 and netters is 0.4 Can be provided by the user, default values for trawling fleets is 0.4 and netters is 0.6 Calculated based on effort, biomass and catch data provided by the user Set by default to 0 (no technological advancement) Provided by the user as a proportion of the retained landings Provided by the user as the proportion of the fleet catch over the total catch for the species (including catch by fleets not in the model) Provided by the user based on management documents (if the species is managed by TAC) Provided by the user based on management documents (if the species is managed by TAC) Provided by the user 1 Only one set of parameters should be provided per species

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