International Council for the Exploration of the Sea ICES CM 2003/V:07 Conseil International pour l’Exploration de la Mer

An EXCEL-based software toolbox for stochastic fleet-based forecast

Per Sparre *)

Abstract. This toolbox of Visual Basic routines using EXCEL as user-interface, is designed to meet the requests for assessments of mixed fisheries and assessment of the effect of management measures (catch quotas and technical management measures). With one species, one fleet, one area, a time step of one year and with no account of bio-economics or fisher’s behaviour, the toolbox will execute the traditional forecast model applied by ICES WGs. The toolbox allows for extending the simple ICES model with one or several of the options listed above. The toolbox contains a suite of modules to assess the effect of technical management measures, such as minimum mesh size, minimum landing size, closed areas, closed seasons and effort regulations. The toolbox contains a module to assess the effect of discard practice of the fishing industry. The toolbox allows for deterministic as well as stochastic simulation. The user has the option to assume a probability distribution of most of the vital input parameters, which by stochastic simulation is transformed into probability distributions of output. The intension was to produce a user-friendly software, utilizing the fact that EXCEL is already a standard tool familiar to all ICES working group members. The toolbox is a stand-alone ordinary ECEL-workbook, which can be run without any installation procedure. It does not contain any EXCEL formulas, it is based solely on macros written in Visual Basic. The tool box is based on open source Visual Basic sub-routines, which can be inspected and possibly modified by the user. In preparation of the code, it has been attempted to achieve the highest degree of transparency, for example, by choosing self-explanatory variable names. The toolbox includes a comprehensive on-line help-facility and a comprehensive user’s manual. *) Danish Institute for Fisheries Research. Department of Marine Fisheries. Charlottenlund Castle, 2920 Charlottenlund. Denmark. pjs@dfu.min.dk

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LIST OF CONTENTS 1. INTRODUCTION ..................................................................................................................................................3

1.1. The objectives of the TEMAS .......................................................................................................................3 1.2. The family of models in TEMAS.....................................................................................................................5

2. THE BIOLOGICAL/TECHNICAL MODEL of TEMAS........................................................................................ 13 2.1. LIST OF SYMBOLS .................................................................................................................................... 16 2.2. GROWTH AND MATURITY OF INDIVIDUALS AND NATURAL MORTALITY ........................................ 18 2.4. NUMBER OF VESSESLS, EFFORT AND CAPACITY .............................................................................. 23 2.5. FISHING MORTALITY................................................................................................................................ 30 2.6. STOCK NUMBERS, MIGRATION AND STOCK BIOMASS . ................................................................... 31 2.7. CATCHES................................................................................................................................................... 33 2.8. MEAN STOCK BIOMASS AND SPAWNING STOCK BIOMASS ............................................................. 33 2.9. STOCK AND RECRUITMENT MODEL...................................................................................................... 34 2.10 LANDINGS AND DISCARDS .................................................................................................................... 34 2.11. THE BASIC BIOLOGICAL/TECHNICAL ALGORITHM OF TEMAS......................................................... 35

3. ECONOMIC SUBMODEL OF TEMAS .............................................................................................................. 39 Figure 3.1. Summary results of a TEMAS simulation. ....................................................................................... 40 3.1. PRICES....................................................................................................................................................... 40 3.2. VALUE OF LANDINGS............................................................................................................................... 41 3.6. BEHAVIOURAL MODEL OF FISHING FIRMS........................................................................................... 41

4. STOCHASTIC SIMULATION ............................................................................................................................ 43 4.1. INPUT TO STOCHASTIC SIMULATION.................................................................................................... 43 4.2. OUTPUT FROM STOCHASTIC SIMULATION .......................................................................................... 44

5. OUTPUT FROM SIMULATIONS...................................................................................................................... 46 6. REFERENCES .................................................................................................................................................. 48

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1. INTRODUCTION The acronym “TEMAS” stands for “Technical measures – Development of evaluation model and application in Danish fisheries”, which is a national Danish Research project, funded by the Ministry of Food, Agriculture and Fisheries. Although TEMAS has the technical management measures as it primary objective, the “TEMAS model” covers most aspects of fisheries management. Management measures interfere and the TEMAS model aims at assessing the combined effect. To that end, the TEMAS-project is developing a software tool which can assess the combined effect of management measures in a multi-species, multi-fleet fishery accounting foe spatial and seasonal aspects. As you will see in the following, the TEMAS toolbox contains a large suite of elements, and the description given here is far from comprehensive. The idea is not to present a full reference manual or full documentation, but to give the reader an “impression” of TEMAS. The basics behind the development of the TEMAS software is given in Sparre, P., 2003, which is a collection of Lectures notes on EXCEL and Visual Basic system development for fisheries. The lecture notes starts from scratch under the assumption that the reader knows nothing about Visual Basic, but something about fisheries and EXCEL. They contain many examples and each lecture is supplemented with exercises. 1.1. The objectives of the TEMAS The objective of TEMAS is to facilitate the implementation of a models belonging to a family of models for fisheries assessment. The objective is not to implement a particular model or method or methodology. Mathematically, the TEMAS family of models share a number of features with the traditional ICES forecast model. Actually, the ICES forecast model, is a member of the TEMAS family (the oldest and smallest one). However, this applies to the mathematical formulas only. When it comes to the philosophy of using models and the applications, the TEMAS approach is quite different that of ICES, as will be explained below. When one suggest an alternative to something, it implies that this something is not considered the best possible choice. TEMAS is an alternative to the methodology currently applied by ICES WGs for provision of advice on management.

Figure 1.1. User-form from the input workbook of TEMAS.

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TEMAS is made for the Fish Stock Assessment workers who want to develop a model, specific to the fisheries system under study. This development should be facilitated by using TEMAS as the starting point, and then to modify, remove or ad modules. Most fisheries models have a long suite of components in common. The idea is that the developer should only care for the details which are specific to the case study in question. Furthermore, TEMAS can be used as a tool to train fisheries assessment workers in development of model and software. By being involved in the development of software, the Fish Stock Assessment workers will better understand the model she/he is using. The software has been programmed in Visual Basic. The idea is not to educate all-round Visual Basic programmers, but to give the user just enough knowledge to do the specific job. Therefore, TEMAS has been developed as macros in EXCEL, the most common spreadsheet-software used by fisheries scientist. (EXCEL has been selected only because it is common, and the author does not, by any means, recommend EXCEL relative to alternative spreadsheets or other computerized systems). Figure 1.1 shows an example of a TEMAS worksheet with a userform by which the user can control the program execution.

INPUTDATA TEXT FILES

OUTPUT

VB(VISUAL BASIC

MODULE)

INPUTHAND-LING

VB(VISUAL BASIC MODULE)

DATA PROCESSING

TEXT FILES

VB(VISUAL BASIC

MODULE)

OUTPUTHAND-LING

Figure 1.2. The data flow between the screen image, Visual Basic and the text files on the hard disk. Figure 1.2 illustrates some features of the TEMAS implementation, which may not occur in a simple conventional spreadsheet application. You may not use the macro-language at all, and in that case the worksheets will contain the data, i.e. you will not store data on text-files in the hard-disk. It is the author experience that making large applications with EXCEL formulas only, will end up in something extremely complicated. Using Visual Basic makes it easier for you to control, test and check your application. It has been attempted to avoid “smart” or “advanced” programming style. A goal has been to make the code easy to understand. This implies, for example, that the macro-programs are heavily commended). The program execution has bee facilitated by so-called user-forms. The user-forms are activated by a “Click” on a button. All sheets of TEMAS contains a button with the logo of TEMAS on it (shown in column “E” rows 3 and 4 in Figure 1.1. Next to the buttons in the user-form, are small buttons with “?”. If you click on a “?” you will get some explanation displayed on the screen. The package is composed of two workbooks which at starts displaying the “Opening forms” shown in Figure 1.3. The creation of such user-forms is something you can do on your own, and it is not very complicated (once you have learned a few rules). There is a tool-box in EXCEL to facilitate the creation of user-forms.

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There are no installation procedure for TEMAS, you just click on the work-book-name and it will run. You control the execution by the user-forms, and you enter the input values from the worksheets.

Figure 1.3. The opening user-forms for the input-workbook (“TEMAS_INPUT.XLS” and the calculation workbook “TEMAS_CALC:XLS”). 1.2. The family of models in TEMAS The family of TEMAS models is characterized by all members containing the traditional ICES forecast model as a subset. The traditional ICES forecast model can be attributed to e.g. Baranov (1918) or Thompson & Bell (1934). The main characteristic of the Thompson & Bell model is the account of age structures and cohorts in the description of the population dynamics. TEMAS, however, is not a competitor to the ICES model, as it is not the intension that the TEMAS model should be used to make quantitative predictions, as is done with the ICES prediction models. The intension is less pretentious, namely only to make qualitative predictions, which can be used to support or contradict potential management measures. That is, the ambition is to predict whether a management measure will have a “positive effect” according to some management strategy, but not how big the effect will be. This low level of ambitions is caused by the experiences from ICES WGs. During the last 30 years the ICES approach has hardly changed, - basically the methodology is the single species VPA (Derzhavin, 1922, ) and the Forecast (Thompson & Bell, 1934). For a review of ICES assessment methodology, see, for example, Lassen & Medley, (2000). The ICES approach is based on the assumption that fish stock assessment leads to precise

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estimates of, for example, SSB, and that there is a unique relationship between SSB and recruitment. Some limited new terminology has been introduced in ICES, but the essential features have remained unchanged for many decades. The present author acknowledges that the ICES approach would be ideal, if its assumption could be met in reality. Unfortunately, the assumptions appear to me not to be met, - the advice on management given by ICES is, based on comparison of quantities which are measured (SSB or F) with unknown confidence limits to quantities which cannot be defined in a statistical sense (the so-called reference points, Bpa or Fpa). Therefore, the level of ambitions with the TEMAS model has been lowered from “quantitative deterministic prediction” to “qualitative stochastic prediction”. The fisheries/ecosystem is so complicated and has so many unpredictable elements that quantitative deterministic predictions are very problematic. It is important to keep this feature of TEMAS in mind, - that the quantitative deterministic approach of ICES cannot be extended with a long suite of additional details in a statistical model. If that was the intension with TEMAS, it would lead to something even more questionable than the ICES approach. TEMAS can execute a complete traditional ICES assessment, but this option is there for comparison only. It is not suggested that you should use it as basis for advice on fisheries management. 1.3. The dimensions of the ICES model The TEMAS family of models can be said to extend the dimensions of the ICES model. The ICES model has (in most cases) the dimension: Number of Stocks: One Number of Fleets: One Number of Areas: One Time step: One Year This is a simplification of the actual situation in ICES, and it should be noted that: Number of Stocks: Multi-species assessment (E.g. Multi-species-VPA, Sparre 1991) has been made in ICES, but has not

really been used in fisheries assessment. Number of Fleets: There are, however, a few cases of multi-fleet forecasts in ICES). Technical interaction between

fishing fleets is ignored. Aspects of mixed fisheries is largely ignored. Number of Areas: Spatial aspects are usually ignored in ICES models. The herring in North Sea/Skagerak , for example,

is an exemption from the rule. Time step: There are, however, a few examples in ICES where the time step is a quarter of the year. The simplifications introduced by the ICES set-up, has complicated the communication between the researchers and the fishers, administrators and the public in general. The entire world of the fishers (Fleets, vessels, gears, fishing operations, fishing practices, etc.) has been reduced into one single abstract symbol, “capital F”, and the links between the experiences of fishers and scientific investigations are not obvious. Furthermore, it seems that this extreme simplification has prevented the use of big amounts of data collected from the commercial fishing vessels (e.g. logbook-data). TEMAS is an attempt to improve the use of available (but hitherto un-used) data from commercial fishery. 1.4. Dimensions of TEMAS TEMAS allows for the extensions of all dimensions relative to the ICES set-up: Number of Stocks: Any number Number of Fleets: Any number Number of Areas: Any number Time step: Any division of the year (Quarter, Month, Week, … etc.)

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In addition, Fleets can be further subdivided into: Country Fleets within a country Vessel size classes within a fleet Vessel riggings within a fleet Vessel age groups within a fleet

Figure 1.4. Data entry worksheet for dimensions of TEMAS case study.

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Input to the model is fishing effort, which in turn is converted into fishing mortality. The ICES model uses fishing mortality as input. By letting Fishing mortality be equal to fishing Effort, the TEMAS mathematical model become equivalent to the ICES model. This model-design is believed to make the model closer to the world of fishers, and to facilitate the communication between researchers and fishers. Furthermore, this model-design allows for utilization of data from the commercial fishing vessels, to a much higher degree than in traditional ICES assessment. The cohort structure of fish stocks, has been extended to the fishing fleets in TEMAS. Figure 1.4 shows a part of the dimension-spreadsheet of TEMAS, where the fleets are defined. As appears (Figure 1.5), you must specify the number of “Vessel-age-groups”. If you, however, want to ignore this aspect, you assign “one” to the number of vessel age groups, and you are back in the traditional ICES set-up. The age structure of fishing vessels is required to model the “structural behaviour” of fishing fleets. The “structural behaviour” refers to the “rules” which determines the number of vessels by

fleet, and thereby the the capacity of the fishing fleets. These structural rules deals with investment in new vessels, dis-investment, attrition and de-commission programmes. A basic feature behind TEMAS, is the belief that the most important quantity to control in fisheries management is the capacity of fishing fleets. One reason for suggesting this change in paradigm, is that control of the capacity is within the power of man, whereas the control of SSB appears to outside the power of man. There are a long list of different reasons why capacity should play a more important role models used for advice on management of fisheries, and the reader is referred to the “Green Book” from the EU Commission of Fisheries. This is an example of the “model-family”-structure of TEMAS. You may or you may not choose to consider structural behaviour and capacity features when using TEMAS. There is an option to nullify all behaviour algorithms (“rules”) of the model, and you are back in the traditional ICES set-up.

Figure 1.5. The fleet definition of TEMAS 1.5. Stochastic simulation TEMAS offers three types of predictions:

1) One single Deterministic prediction 2) One stochastic prediction 3) Multiple stochastic prediction

Stochastic simulation means that some (or all) parameters are drawn by a random number generator. The parameters of the probability distributions of parameters are given as input. TEMAS offers (in its present version) two probability distributions: (1) Normal distribution (2) Log normal distribution. The most prominent stochastic term is that which accounts for the stochasticity of recruitment. Although no stock recruitment model is suggested, the Beverton and Holt model (1956) has been implemented in TEMAS. The only reason for this is that it passes through the (0,0)-point on the stock-recruitment graph, the only point we can be sure about. However, with a stochastic variation around the stock-recruitment model, it does not matter so much which model you choose.

text

Draw Parametersfrom Random

Number Generator

EXECUTE TEMAS

save results

Repeat1000times

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A problematic element of the current ICES approach, is the assumption of a unique stock recruitment-relationship, which is the basis for the definition of the reference points. There may be some sort of weak relationship between stock and recruitment, but the only point we know for sure is the (0,0)-point. “With no parents there can be no children”, but apart from that we know (almost) nothing about the shape of the stock-recruitment relationship. What we know is something about the distribution of recruitment, and TEMAS admits these limitations of our knowledge basis. TEMAS therefore uses only the knowledge we have, namely the accumulated knowledge on the probability distribution of recruitment. The Beverton and Holt S/R-model is not very important, and can easily be replaced with any other S/R model. However, it would probably not improve the prediction power to use any alternative S/R-model. 1.6. Model of fishing mortality The TEMAS model gives the option to model fishing mortality as a function of fishing effort by the relation, which is stock and fleet specific:

Fishing mortality = Catchability * Selection * Effort The selection in turn depends on selection parameters (for example mesh sizes). Furthermore, Fishing mortality is divided into landings and discards mortality, dependent on the minimum landings size and discard practice parameters. Fishing mortality = Landing mortality + Discard mortality TEMAS allows for various models which relates catchability to the technical development and the stock biomass. This model of partial fishing mortalities allows for assessment of management regimes which are based on effort regulations, and it allows for assessment of multi-species fisheries (mixed fisheries). 1.7. Spatial aspects of TEMAS The concept of Fishing mortality relates to the stock. As TEMAS allows for division of the stock area into smaller part, TEMAS works with a concept relating mortality to sub-stocks. We call this concept “Area-mortality” (Sparre & Hart, 2002). TEMAS allows for modelling migration of fish between areas through so-called migration coefficient using the same type of model as that of Quinn, Deriso & Neal (1990). The migration is modelled in a time discrete manner:

a) Migration takes place at the end of each time period and the process of migration takes zero time. b) During a time period the stock is assumed to be homogeneously distributed within the area.

The "Migration Coefficient", MC, from area A to area B is defined as the fraction of the animals in area A which moves to area B. In this definition, the "movements" include the "move" from area A to area A, i.e., the event that the animal does not move.

The migration coefficient depends on (or has the indices): FAr: Starting area TAr: Destination area.

Note that the sum of migration coefficients over destination areas always becomes 1.0, as the starting area is also considered a destination area: 1 where a = age group and q = time period (division of year). ∑=

ArTArAr qaTFMC ),,,(0.

To illustrate the concept, an example is considered with three areas, A, B and C and a migration from A to B and from B to C. To simplify the example, the time period index has been left out, so that migration takes place at the end of the year only. If the migration from A to B takes place

gradually over the age groups 2 to 4 and no fish return to area A, the migration coefficients for movement out of A could be those shown in Table 1.7.1.

A B C

If the migration from B to C takes place gradually over the age groups 6 to 8 and no fish return to area A or B, the migration coefficients for movement out of B could be those shown in Table 1.7.1.b. If the fish stay in area C, the migration coefficients for movement out of C are those shown in Table 1.7.1.c.

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Age group From area A to area: 0 1 2 3 4 5 6 7 8 9 A (TAr=1) 1 1 0.8 0.5 0.2 0 0 0 0 0B (TAr =2) 0 0 0.2 0.5 0.8 1 1 1 1 1C (TAr =3) 0 0 0 0 0 0 0 0 0 0Total 1 1 1 1 1 1 1 1 1 1Table 1.7.1.a. Migration coefficients for migration out of area A, MC[a,1,TAr,-].

Age group From area B to area: 0 1 2 3 4 5 6 7 8 9

A (TAr=1) 0 0 0 0 0 0 0 0 0 0B (TAr =2) 1 1 1 1 1 1 0.8 0.5 0.2 0C (TAr =3) 0 0 0 0 0 0 0.2 0.5 0.8 1

Total 1 1 1 1 1 1 1 1 1 1Table 1.7.1.b. Migration coefficients for migration out of area B, MC[a,2,TAr,-].

Age group From area C to area: 0 1 2 3 4 5 6 7 8 9 A (TAr=1) 0 0 0 0 0 0 0 0 0 0B (TAr =2) 0 0 0 0 0 0 0 0 0 0C (TAr =3) 1 1 1 1 1 1 1 1 1 1

Total 1 1 1 1 1 1 1 1 1 1Table 1.7.1.c. Migration coefficients for migration out of area C, MC[a,3,TAr,-].

Age A B C Total 0 1000 0 0 10001 1000 0 0 10002 800 200 0 10003 400 600 0 10004 80 920 0 10005 0 1000 0 10006 0 800 200 10007 0 400 600 10008 0 80 920 10009 0 0 1000 1000

Table 1.7.2. Numbers corresponding to the migration coefficients given in Tables 1.1.a,b,c, a recruitment of 1000 in area A and zero mortality

To highlight the migration aspect, and de-emphasise other features, which may complicate the picture, an (unrealistic) example where mortality is zero is considered. If 1000 fish in a batch recruit to area A and no fish recruit to areas B and C and mortality is zero the numbers from that batch during its life in each age group become those shown in Table 1.7.2. The model of migration is general. Using this technique any route between any configuration of areas can be made. The movements, however, are approximations to reality as they are not continuous processes. These features of TEMAS allow for assessment of the effect closed areas (boxes). However, if you want to ignore spatial aspects, you just enter “1” for the number of areas, and you are back in the traditional ICES set-up (see Figure 1.7.3).

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Figure 1.7.3. Definition of “Areas” in the dimension-sheet of TEMAS. 1.8. Bio-economics in TEMAS The TEMAS model extends the Thompson and Bell model with a bio-economic sub-model and a sub-model for the behaviour of fishing fleets. The use of these sub-models are optional. The current bio-economic model is that developed by FAO under the name of BEAM (Bio-economic analytical model, Sparre and Willmann, 1993 and 2001). The economic sub-model, however is not presented here, as the emphasis in this paper are the biological/technical aspects. The software available from the author contains the economic sub-model. Here only, some indications of the economic sub-model will be presented. 1.9. Technical management measures The acronym “TEMAS” stands for “Technical Management Measures”. Technical management measures are all the measures which are not catch quotas or catch rations. Originally, the TEMAS was designed to analysis the effect of technical management measures. Examples of technical management measures are:

1) Minimum mesh size (and other regulations changing the selectivity of a gear). 2) Minimum landing size 3) Closed areas (boxes) 4) Closed seasons.

TEMAS offers various options for assessing the effect of most technical management measures. 1.10. Behaviour algorithms There are two options in TEMAS to control the effort (in fishing/sea days): 1) Give effort as input parameters (the ICES approach) 2) Let effort be determined by the behaviour algorithms In case 2) the program will decide the effort of “next” time period, based on the “history” of the fishery. The model used to predict the effort is called “The behaviour algorithms”. The are two groups of behaviour algorithms: 1) Structural behaviour (investments in new vessel, dis-investment, attrition and decommission) 2) Trip related behaviour (where to fish by which gear at which time of the year)

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Often it is observed that fisheries regulations do not lead to the anticipated results. This may be caused by the reaction of the industry to management measures. The behaviour algorithms attempts to account for the reaction to regulations. The behaviour algorithms are not described in details in the present paper, but they are implemented in the EXCEL-application. 1.11 Quota regulations versus effort-regulation TEMAS aims at modelling fleet based management covering all aspects of technical interaction and mixed fisheries. The traditional ICES approach of stock management by TACs is not obviously converted into fleet-based management. Essentially this is about converting catch quotas into effort quotas, and there is no tradition for effort quotas in ICES. We have no idea of how ICES might handle setting of effort quotas. The harvest control rules applied by ICES refers only to total fishing mortality and gives no indication of how this total F should be distributed between fleets. We shall not try to address this crucial question for fleet based management. Changing from stock-based to fleet-based management represents a complete change of paradigms for advice on management given by ICES. 1.12. Tuning TEMAS contains a very large number of parameters. Parameters should be estimated by strict statistical methods as e.g. done in software packages like “R+” and “SAS”. To estimate all parameters in one go (the ideal solution) appears to be impossible, simply because the problem does not have one unique solution. Some parameters of TEMAS can be estimated outside the model, such as growth parameters and maturity parameters. Other parameters may be estimated or rather “guesstimated” within the TEMAS model. The word “guesstimate” is used to indicate that a proper statistical estimation may not be possible. What TEMAS does is to make a prediction for a historical period and then compare predicted to observed values. The test criterion is the “modified ksi-squared criterion” (Sokal & Rohlf, 1981). The tuning is not described in details in the present paper, but is under implementation in the EXCEL-application, and parts of it has been implemented. 1.13. β-version The present version of the TEMAS software is a β-version (a preliminary prototype). As indicated above the TEMAS software has a considerable size (many thousand lines of Visual Basic). So far, only the author has contributed to the coding. To complete the job, a team of programmers would be required for several man-months, and an extensive testing on various levels is required. The development of TEMAS is simply too big a job for one person. It is hoped that by making it open source software, the further development and testing will be made by a larger group of contributors on various levels.

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2. THE BIOLOGICAL/TECHNICAL MODEL OF TEMAS Probably the most concise and comprehensive description of the model behind TEMAS is the VB (Virtual Basic) program, which implements the TEMAS. The names of variables and the structure of the VB program are designed to make the algorithms easy to grasp. The reader, who really wants to know what TEMAS does, is recommended to study the VB program. To get access to the code of the VB-modules you click on the icon VB-button in the tool bar of EXCEL. Although the reader may not be familiar with the VB-language, it still makes some sense to study the codes, as it is often intuitively clear what the codes means. Figure 2.0.1 shows the list of VB modules as it appears in the so-called “Project window” of the VB system. Figure 2.0.2 shows an example of VB-code, namely the “corner stone of TEMAS”, the subroutine, which executes a single simulation over a suite of years. A very large part of the TEMAS-code (say 90%) deals with the administration of input and output, and that part of the code is of interest only to the VB-programmer. The subroutines of interest to the model are all stored in the modules with “C_COMP” in their name (see left hand side of Figure 2.0.1). The modules with “C_OUT” contains the routines to display results on the worksheets.

Figure 2.0.1. List of the VB modules of the TEMAS program Figure 2.0.2 shows the (simplified) central algorithm in VB, for a single simulation over a suite of years. Note that the variables of the VB-program have been given names, which should immediately tell the reader what it is about. The VB program is conveniently structured by “Subroutines” (“Sub”), which can “Call” each other. The subroutines are started from the spreadsheet by clicking on the “Calculate”-button in the user form.

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Sub MAIN_SINGLE_SIMULATION ‘ ‘ --- This routine is the basic algorithm of the model. It executes the biological as well as the economic calculations -- ‘ --- Year one, is special, as special actions are required to start up the dynamics (by routine: INITIALIZE_SIMULATION) ‘ Call INITIALIZE_SIMULATION ‘ For y = 1 To Number_of_Years For Q_Time = 1 To Number_of_Periods ' --- Read period-specific parameters, execute simulation for one time period, and store results on diskfile Call READ_ALL_PARAM_FROM_FILE_YQ ' --- "_YQ" indicates one single period --- Call COMPUTE_ALL_RESULTS_YQ Call WRITE_ALL_RESULTS_ON_FILE_YQ Next Q_Time Next y Call SUM_UP_NPV_ECONOMIC_MODELS_BY_TYPE ' --- Compute NPV : Net Present Value ------ End Sub ‘ --- Note: A line starting with “ ’ ” is a comment, ignored by the VB compiler. “Call” means that a subroutine, with ‘the ‘ --- name following “call”, is executed. The names given here should be self-explanatory. Figure 2.0.2. Example of Visual Basic code. Note the code of the so-called “For, next – loop”:

For y = 1 To Number_of_Years …….. “Do something for a given year, y” ………….

Next y This code makes the program repeat a set of instruction one time for each value of the variable, y (Year) starting with “1“ and ending with “Number_of_Years”. Computer languages of the type Visual Basic, Pascal, Delphi etc. are not too difficult to understand, even if you do not have a background in computer science. These languages are “userfriendly”, also for a beginner. Other languages like the C++, are (to the authors opinion) designed for professional programmers. To start the subroutine in Figure 2.0.2, you must click on some buttons in the worksheet. All worksheets of TEMAS has a button placed in the first rows (you may move it). The button has the logo of TEMAS on it. If you click on the button, a user-form will be shown on the screen. Figure 2.0.3 shows the userform emerging in the calculation part of TEMAS. If you click on “One deterministic simulation” that will activate the routine in Figure 2.0.2. In principle, this could be done by the subroutine:

Sub CommandButton1_Click() Call MAIN_EXECUTE_SIMULATION

End Sub When the “event” that you click on “Commandbutton1” occurs, the statements in the routine will be executed. Actually, the code in the TEMAS program is a bit more complicated, but the code above would have worked. In the real TEMAS you would after the selection of type of simulation click on “Select Output”, and a new user-form will appear, and when you finish this user-form the routine above will be executed. Anyway, you activate the routines, by clicking on buttons in user-forms, and user-forms can be created by the (advanced) user of TEMAS. The VB-system provides a suite of facilities which makes it easy for you to create user-forms. For example, you do not need to write the two lines,

Sub CommandButton1_Click()

End Sub You are requested to provide only the text between the lines.

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Figure 2.0.3. User-form to select simulation type. This paper is not intended to develop into a textbook on VB-programming, the intension is just to give you a feeling for the complexity of VB-programming. VP-programming does not need to be very complicated, and it can be done by most scientists provided they are willing to invest a little time in learning. An example on a textbook on applied EXCEL and Visual Basic (from the world economics) is “Advanced Modelling in Finance using EXCEL and VBA”. (Jackson & Staunton, 2001). This textbook starts from scratch, introducing the basic concepts of VBA (VBA = Visual Basic for Applications, adapted for Microsoft's Office Applications: Access, Excel, Word, Outlook and PowerPoint). Then the textbook gradually introduces a long suite of VBA implementations of models applied in finance, some of which may also be useful in fisheries bio-economics. Another example of a textbook in modelling in EXCEL and VBA from the world of fisheries science was given in Sparre, 2003. This textbook introduces the basics of the TEMAS model with respect of programming in VBA. On the webside of the Fisheries Centre - The University of British Columbia, (http://fisheries.ubc.ca/events/workshops/vbcoursemat.php). You can find “Visual Basic Programming Course Material”, which is a second example of modelling in fisheries by Visual Basic and EXCEL.

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2.1. LIST OF SYMBOLS Below follows a list of variables of the TEMAS model. The symbols are grouped, and in alphabetical order within each group. Note that dot “•” instead of an index means summation over the index in question. Thus

∑=•u

juiXjiX ),,(),,( Indices in alphabetical order:

Index Explanation Range Index group 1 a Age group a = 0,1,2,…,amax(St) Age 2 Ar Area Ar = 1,2,…,Armax Area 3 Ct Country Ct = 1,…,CtMax Fleet 4 Fl Fleet Fl = 1,2,…,Flmax(Ct) Fleet 5 Q Time period (as time) q = 1,..,qmax Time 6 qa Time period (as age) qa = 1,..,qmax, Age 7 Rg Rigging of gear Rg = 1,…,Rgmax(Fl,Ct) Fleet 8 Y Year y = yfirSt, yfirst+1,…,ylast Time 9 St Stock St = 1,…,Stmax Stock 10 Va Vessel age group Va = 1,…Vamax(Fl,Ct) Age 11 Vs Vessel size group Vs = 1,…Vsmax(Fl,Ct) Fleet

Note that the sequence of indices will be X(Fl, Vs, Rg, Ct, St, y, a, qa, Va, Ar) for all variables, “X”. Variables will apply only subsets of the eleven indices, but the sequence will remain the same, irrespectively of the subset. The indices “q” or “qa” stand for divisions of the year, such as “month”, “quarter”, “half year” etc. The time period concept may be used to indicate absolute time, and time relative to the birth of a cohort, that is the age of the cohort. The age of the cohort, however, is given in years and time periods only for the first two years of life, as the from age two and onwards, it is assumed that the difference between (year, period)-cohorts is so small that it can be ignored. In the case of the time period being a quarter of the year, the time (and age index) can be illustrated by a result table from the output workbook of TEMAS:

In this case, the stock produces recruits in quarters 1 and 2, whereas quarters 3 and 4 gives no recruitment. This somewhat complicated age-concept is introduced to enable the model to make a fair approximation for length at age of juvenile fish. This is necessary for the analysis of gear selection aspects, which are most important for juvenile specimens.

16

The indices are grouped: (Fleets, Stock, Area, Time, Age) where

1) Fleet group: (Fl, Vs, Rg, Ct) 2) Stock group: (St) 3) Time group: (y) or (y, q) 4) Age group: (a, qa, Va) or (a, Va) 5) Area group: (Ar)

In order to reduce the complexity of formulas, the indices Vs, Rg and Ct will be tacitly assumed, when the index Fl occurs. Only when considered necessary for the understanding of the formula, shall we used the complete set of indices to identify a fleet “(Fl, Vs, Rg, Ct)”. Time Variables in alphabetical order:

Symbol Explanation dt Basic time step (fraction of year). dt < 1.0. dt = 1/qMax yfirst First year ylast Last year

Biological Variables (Variables related to stocks) in alphabetical order: Symbol Explanation Age Age of the fish (or cohort) in units of years amax(st) Oldest age group of stock St Armax Number of areas B(St, y, a, q, Ar) Total biomass of stock “St” , age group “a” at the beginning of time period “q” of

year “y” in area “Ar”. BH1(St) First Parameter in the Beverton and Holt Stock/Recruitment model for stock “St” . BH2(St) Second Parameter in the Beverton & Holt Stock/Recruitment model for stock “St”. C(Fl, St ,y, a, q, Ar) Numbers caught (landed or discarded) CDisc(Fl, St, y, a, q, Ar) Numbers discarded CLand(Fl, St, y, a, q, Ar) Numbers landed DIS(Fl, St, y, a, q) Discard selection ogive , that is, the fraction of fish caught, which are discarded. DISCARDS(Fl, y) Total discards (summed over stocks, areas and time periods) Dis1(Fl, St, y) Parameter in the logistic model of discard Dis2(Fl, St, y) Parameter in the logistic model of discard E(Fl, y, q, Ar) Effort EDistribution(Fl, q, Ar) Distribution of effort on areas: E(Fl, y,q,Ar)/ E(Fl, y,q,●). In the present version of TEMAS

this distribution is assumed to remain unchanged from year to year, when effort is given as input. EYMAX(Fl, y,q) The maximum number of effort units per vessel. Fdisc(Fl, St, y, a, q, Ar) Discard area-mortality Fland(Fl, St, y, a, q, Ar) Landing area-mortality” Flmax Number of fleets FStock(Fl, St, y, a, q) Fishing mortality (of stock) K(St) Von Bertalanffy curvature parameter L∞(St), Von Bertalanffy parameter, L-infinity LANDINGS(Fl, y) Total landings (summed over stocks, areas and time periods) Lgt(St, y, a, q) Mean Body length LGT50%(Fl, St, y) Body Length at which 50% of the fish entering the gear are retained LGT50%Disc(Fl, St, y) Body Length at which 50% of the fish caught are discarded LGT50%Mat(St) Length at which 50 % of the stock is mature LGT75%(Fl, St, y) Body Length at which 75 % of the fish entering the gear are retained LGT75%Disc(Fl, St, y) Body Length at which 25% of the fish caught are discarded

17

LGT75%Mat(St) Length at which 75 % of stock “St” is mature M(St, y, a, q) Natural mortality Mat(St, a, q) Maturity ogive Mat1(St) Parameter in the logistic model of maturity Mat2(St) Parameter in the logistic model of maturity MC(St, a, q, FAr, TAr) Migration coefficient migrating from area “FAr” (From Ar) to area “TAr” (To Ar) MS(Fl, y) Mesh size NJuv(St, y, a, q, Ar) Stock number , Age gr. 0-1 N(St, y, a, Ar) Stock number, Age gr. 2+

),,,,( ArqyStFlQ Catchability coefficient

),,(Re ArStFlQ f Reference catchability, which remains constant over time.

),,,,(Re ArqyStFlQTimelative Relative catchability time-multiplier.

{ } 0.1),,,,(Re),( =ArqyStFlQMAX lativeqy .

),( ArStXQArea Stock-specific catchability area-multiplier

),( StFlXQFleet Stock-specific catchability fleet-multiplier

),( ArFlX Con Year and period independent effort multiplier (Constant): )(*)(),( 21 ArXFlXArFlX ConConCon =

),,( ArqFlX Per Period (Per) dependent (Year independent) effort multiplier: ),(*),(*)(),,( 321 ArqXqFlXqXArqFlX PerPerPerPer =

),,,( ArqyFlX Time Year and period (Time) dependent effort multiplier ),,(*),,(*),(),,,( 321 ArqyXqyFlXqyXArqyFlX TimeTimeTimeTime =

Parameters used to create stochastic and biased variables:

Symbol Explanation εK(St, y) Stochastic factor of von Bertalanffy parameter K, which is normally distributed with mean value 1.0

and standard deviation σK(St) εQ(Fl, St, y)

Stochastic factor of catchability, a year, fleet and stock dependent normally distributed with mean value 1.0 and standard dev. σQ(Fl, St).

ε’QF(St, y) Stochastic term of condition factor, of stock “St” and year “y” dependent normally distributed with mean value 1.0 and standard dev. σQF (St, y)

εQF(St, y) Stochastic factor in length weight relationship: (εQF(St, y) + ε’K(St, y))/2 εSR(St) Stochastic factor of stock/recruitment relationship, of stock “St”, a stock dependent log-normally

distributed with mean value 1.0 and standard dev. σSR (St). σK(St) Standard deviation of εK(St, y) σQ(Fl, St) Standard deviation of εQ(F, St, y) σQF(St) Standard deviation of ε’QF(St, y) σSR(St) Standard deviation of εSR(St, y)

2.2. GROWTH AND MATURITY OF INDIVIDUALS AND NATURAL MORTALITY 2.2.1. Von Bertalanffy growth model: Mean Body length of stock “St”, in the middle of time period q of year “y” of age group “a”, LGT(St,a,y) is given by the Von Bertalanffy equation (1934), as an alternative to the weight at age used in the conventional ICES model, in order to simplify the model:

( [ ] )))(),,((*)(exp1*)(L q)a,y, Lgt(St, 0 StTqaqaAgeStKSt −−−= ∞ (2.2.1) The age of the fish (or cohort) in units of years is defined:

18

qa) iod(St,RecDistPer*)1()(

2*)5.0()(

2*)5.0(),,(

max

1∑=

−=

≥−+−

<+−+=

q

qaMean

Mean

qaStdawhere

aifdtqStdaa

aifdtqaqaqaqaAge

(2.2.2)

RecDistPeriod(St,qa) is the fraction of the annual recruitment which occurs in period qa. The texttable shows an example of calculation of the “time correction term” daMean(St)”, used to merge four quarter cohorts into one year cohort.

qa 1 2 3 4 RecDistPeriod(St,qa) 0.63 0.03 0.31 0.03

daMean(St)

(qa-1)* RecDistPeriod(St,qa) 0.0000 0.0313 0.6250 0.0938 0.7501

19

Note that after age group 1, the influence of the birth period is assumed to be negligible. This elaborate definition of the age concept is made to accommodate the need from both short lived species, and the need the describe the relationship between age and length for juveniles. This need for a good description of growth of juveniles is caused by the fact that the selection of fishing gears takes place for the younger specimens. The growth curve (and several other curves) should be written in two versions, one when a < 1 and one when a > 2

{ ( [ ] )

{ ( [ ] ) 2))(),((*)(exp1*)(L q)a,y, (St,Lgt

1))(),,((*)(exp1*)(L qa)q,a,y, (St,Lgt

0

0

≥−−−=

≤−−−=

∞

∞

aifStTqaAgeStKSt

aifStTqaqaAgeStKSt

However, in order to reduce the number of equations, only the simple version of the equation, for a > 2 will be presented, and the version for a < 2 is tacitly assumed. The index qa is irrelevant in the case a > 2, and has therefore been omitted. The figure shows output from TEMAS, a growth curve in the special TEMAS format when the time period (P) is a quarter of the year. The figure also illustrates another feature of the software TEMAS. TEMAS does not produce any graphical output

automatically. Any graphs must be prepared by the user, who thus must know how to make EXCEL display graphs, e.g. by the “Chart wizard” of EXCEL. This is one the advantages of using a commercial software package everybody knows. The programmer does not need to care about graphics, but can safely leave it to the user. On top of that, the user now has the freedom to use any graphical presentation on her/his choice.

The length at age can be made a stochastic variable in TEMAS, by introduction of the stochastic factor, εK

( [ ] )( [ ] ) 2))(),,((*),(*)(exp1*)(L qa)q,a,y, (St,Lgt

2))(),((*),(*)(exp1*)(L q)a,y, (St,Lgt

0

0

≤−−−=

≥−−−=

∞

∞

aifStTaqqaAgeyStStKSt

aifStTqaAgeyStStKSt

K

K

ε

ε (2.2.1.b)

where εK(St, y) is Year and stock dependent normally distributed stochastic variable with mean value 1.0 and standard deviation σK (St). When the growth model is deterministic, the stochastic factor εK(St, y) has the constant value 1.0, that is, the standard deviation σK (St), is assigned the value zero. Body length is assumed to be the same for stock, landings and discards. This is a simplification of the model relatice to ICES, which usually operates with separate weight at age keys for landings, stock and discards. As TEMAS aims at quantitative predictions rather than the quantitative predictions of ICES, it was not considered worthwhile to have a very detailed description of weight at age in TEMAS. Furthermore, this approach reduces the number of parameters. Actuall, three weight at age keys (each of, say 10 parameters) are replaced by only 3 growth parameters. Whether “Body length” refers to “total length”, “fork length”, “Carapace length”, “Mantle length” or any other length measurement is not essential for the calculations in TEMAS, as long as the length matches to the length/weight relationship. Nor is it essential which length units (say, mm or cm) are used as long as the length matches to the length/weight relationship, and the weight units used in the simulation. It is the sole responsibility of the user of TEMAS to apply consistent definitions of length, weight and units. That the index “y” is used means that the user has the option to let length at age vary from year to year, but that also includes the option to let the length at age remain constant from year to year. This and similar options are given in TEMAS in order to let the user perform sensitivity analysis on the concerned parameters. 2.2.2. Length/weight relationship Mean Body weight is defined

)(),,,(*)(),,,( StQEqayStLgtStQFqayStWgt = (2.2.2.a)

The length/weight relationship can be made stochastic in TEMAS through the stochastic factor, εQF )(),,,(*),(*)(),,,( StQE

QF qayStLgtystStQFqayStWgt ε= (2.2.2.b)

20

where εQF(St, y) = (εK(St, y) +ε’QF(St, y))/2 and where ε’QF(St, y)) is a year and stock dependent normally distributed stochastic variable with mean value 1.0 and standard deviation σQF(St). When the length/weight relationship is deterministic, the value of one is assigned to εQF. Note that the K and the condition factors are positively correlated, so that a fast growth is associated with a good condition. Body weight is assumed to be the same for stock, landings and discards. Which units to use for length and weight are entirely up to the user of TEMAS. It is not essential for the calculations which units are used (Cm, mm, gram, kilo, tons etc.). It is the user’s responsibility to ensure that the units are matching each other. 2.2.3. Maturity ogive The relationship between age and maturity, is modelled by the logistic curve. in TEMAS and not by a key as is the standard of ICES. This is done in order to reduce the number of parameters, and because TEMAS does not aim at quantitative predictions. . The maturity is usually linked to the length of the fish, so that fast growing fish will mature at a younger age than slow-growing specimens. Maturity ogive, that is the fraction of mature fish as a function of body length is

)),,,(Lgt *Mat2(St) t)exp(Mat1(S 11 q)a,y,Mat(St,

qyaSt−+= (2.2.3)

where Mat1(St) = ln(3)* LGT50%Mat(St)/( LGT75%Mat(St) - LGT50%Mat(St)), Mat2(St) = ln(3)/( LGT75%Mat(St) - LGT50%Mat(St)) and LGTX%DMat(St) = Length at which X % are mature, As the length at age can vary from year to year so can the maturity ogive. 2.2.4. Natural mortality The natural mortality is assumed to remain constant from year to year, and depend only on stock and age group. M(St, a, q) = Natural mortality. The expression for predation mortality in multi-species VPA (see e.g. Sparre, 1991), could be used here, and if the TEMAS-approach is further developed, the model of predation mortality is likely to be incorporated, as there are no technical or theoretical problems involved. The reason why it is not in the present version is the simple one, that there are so many other components in the model, that we have yet found no time to deal with predation mortality. 2.3. GEAR- AND DISCARD SELECTION OGIVES 2.3.1. Discard selection ogives. That is the fraction of fish discarded (for any reason) as a function of body length, is modelled by “one minus the logistic curve”:

)),,(Lgt * y)St,Dis2(Fl, y) St, (Fl, exp(Dis1 11- 1 q)a,y,Fl,DIS(St,

qaSt−+= (2.3.1)

where Dis1(Fl, St, y) = ln(3)* LGT50%Disc(Fl, St, y)/( LGT75%Disc(Fl, St, y) - LGT50%Disc(Fl, St, y)) Dis2(Fl, St, y) = ln(3)/( LGT75%Disc(Fl, St, y) - LGT50%Disc(Fl, St, y)) LGTX%Disc(Fl, St, y) = Body Length at which X % of the fish caught are discarded The model of discarding illustrates a feature about the TEMAS toolbox. One can think of several ways to extend the model for fishers discard practice, and the idea with a “toolbox” is that the user should be able to select alternative models for discarding. The discard model might account for high-grading due to quota or ration limitations or due to economic reasons (low commercial value of discards). Also the influence of minimum legal landing size could be accounted for in the discard-model. The current implementation of TEMAS has the minimum landing size as an input parameter, and the model lets all undersized fish be discarded. Currently, this is the only additional “tool” yet available to handle discard practice, but more tools can be implemented.

21

2.3.2. Gear selection ogives. The logistic curve is used to model the selection of fishing gears

)),,,(Lgt * y)st,Sel2(Fl, y)St,(Fl, exp(Sel1 11 q)a,y,St,SEL(Fl,

qaySt−+= (2.3.2)

where Sel1(Fl, St, y) = ln(3)* L50%(Fl, St, y)/( L75%(Fl, St, y) - L50(Fl, St, y)) and Sel2(Fl, St, y) = ln(3)/( L75% (Fl, St, y)- L50%Disc(Fl, St, y)) LGTX%(Fl, St, y) = Body Length at which X % of the fish entering the gear are retained LGT50%(Fl, St, y) = MS(Fl, y) *SF(Fl, St, y), LGT75%(Fl, St, y) = LGT50%(Fl, St, y) * SR(Fl, St, y) MS(Fl, y) = Mesh size of fleet Fl in year y SF(Fl, St, y) = Selection factor SR(Fl, St, y) = Selection range (=LGT75%/LGT50%) The term “Mesh size” may mean a real mesh size, for example the size of the meshes in the codend of a trawl, or the mesh size of a gill net. But, “mesh size”, in the context of TEMAS, is a general concept. It should rather be considered a “parameter in the model” for gear selection. Even if, for example, hooks have no meshes, the parameter “mesh size” in TEMAS, can still be used to describe the selection of the gear. A gear may not catch certain size groups or species either because they escape the gear, or because they are not located where the gear is operated, or for some other reason is not available to the gear. For example, the species may be buried in the sand. The selectivity of a fleet is thus the combined effect of gear selection and availability of the size/species in question. The combined effect is called the “resultant” curve. This curve is derived as the product of the gear selection ogive and the availability ogive. In TEMAS, however, these features of selection are not explicitly accounted for in the current version of TEMAS. TEMAS, tacitly assumes that the gear selection parameters (selection factor and selection range) are chosen so that they produce the resultant ogive (Hoydahl et al, 1982, McLennan, 1992). The parameters, Sel1 and Sel2, are the parameters in the logistic model, but actually they are not really necessary. Equation (2,3,2) can be rewritten:

),,(),,(),,,(),,(L

%50%75

50%

3 1

1 q)a,y,St,SEL(Fl,yStFlLyStFlLqayStLgtyStFl

−−

+

= (2.3.2.a)

and introducing the mesh size, the selection factor and the selection range gives a third version of Eq. 2.3.2.

)1),,((*),,(*),(MS),,,(),,(*),(MS

3 1

1 q)a,y,St,SEL(Fl,−

−

+

=yStFlSRyStFlSFyFl

qayStLgtyStFlSFyFl (2.3.2.b)

22

2.4. NUMBER OF VESSESLS, EFFORT AND CAPACITY The tradition of ICES WGs is to give F, the fishing mortality as input to the catch prediction. Usually, ICES WGs will operate with the total fishing mortality (the combined effect of all fishing fleets). The ICES WG will not use, say, the number of vessels or the number of vessel days at sea or any other data behind the “F”. Information on fishing days (or days at sea) has been available for more than a decade, from the logbook databases of EU member states and also from several other states. The model to be presented below is an attempt to utilize the available data. One objective of this is to introduce models which can be related the fishing industry and thereby makes better use of the information collected by the fishers. In terms of number of observations, the fishers collect many more data than scientists will ever be able collect. This model is a suggestion for utilization of the enormous amounts of data piled up in the logbook databases, sales slip data bases and other databases which have not yet been fully exploited for the scientific analysis of fisheries in the ICES WGs. The basic idea presented here is not new in general, but is new relative to ICES WGs. The model does the very obvious thing, namely, relates fishing mortality to fishing effort, and in turns the model relates fishing effort to the number of vessels. This is all so obvious that it hardly need to be said, and one can wonder why this type of thinking has never been considered in ICES WGs. Anyway, here comes the simple model. The TEMAS model (kind of) treats the fishing fleets as if they were fish stocks, in the sense that it keeps track of the age distributions of vessels in a fleet as the ICES model keeps track of the age distributions of fish. The information on age distributions of vessels (and many other vessel data) are available from the national vessel registers, so there are no hard data problems with the vessels as there are with the data for fish stocks. 2.4.1. Number and age distribution of vessels: The number of vessels , NUVessel(Fl, y), is in TEMAS composed of “vessel age groups”, that is

∑=

=•MaxVa

VaNesselVessel VaqyFlNUqyFlNU

1),,,(),,,( (2.4.1.1)

where NUVessel(Fl, y, q, Va) = Number of vessels which has age “Va” in period “q” of year “y”. Thus, TEMAS keeps continuously track of the age distribution of the vessels. Like the fish, vessels have a mortality, which can be due to having reached the end of their techno-economic lifetime (attrition), withdrawal because of bad financial performance or decommissioning through a buy-back programme. The number of vessels is updated once per time period, at the beginning of the time period. In the following only one index of time, “y” is used. To be complete the formulas should also have had the period index, “q”. The number of vessels, NUvessel(Fl, y,Va), is defined by iteration: For Va = 0: NUvessel(Fl, y,0) = NUNew_Vessel(Fl, y) (2.4.1.2) For Va = 1,2, ……,Vamax-1 : NUvessel(Fl, y,Va) = NUvessel(Fl, y -1,Va -1) – NUWithdrawal-Vessel(Fl, y, Va) - NUDecommission(Fl, y, Va) - NUAttrition(Fl, y, Va) For Va = Vamax : NUvessel(Fl, y,Va) = NUvessel(Fl, y -1, Vamax ) + Uvessel(Fl, y -1, Vamax -1) – NUWithdrawal-Vessel(Fl, y, Vamax) - NUDecommission(Fl, y, Vamax) - NUAttrition(Fl, y, Vamax) Where:

1) NUDecommission(Fl, y, Va) is the number of vessels withdrawn due to a vessel decommissioning. 2) NUAttrition(Fl, y,Va) is the number of retired vessels having reached the end of their techno-economic lifetime. 3) NUWithdrawal-Vessel(Fl, y, Va) is the number of vessels withdrawn , due to bad financial performance. 4) UNew_Vessel(Fl, y) is the number of new vessels introduced to fleet “Fl” in year “y”

23

The numbers may be either given as input parameters or be determined by the “Structural Fleet behaviour rules”. When the number of vessels are computed according to the so-called “structural behaviour rules of fishing firms, they are computed as a fraction of the existing number of vessels. In that case, it becomes essential in which sequence numbers are computed. For example, the number of decommissions are computed before the number of withdrawals are computed. If a vessel-owner has the choice between decommission and withdrawal without compensation, it is assumed that he will choose the decommission.

1 2 3 4 5 6 7AGE 01 2 3 4 5 6 7 8 9AGE 1

1 2 3 4 5 6 7 8AGE 2

AGE 3

1 2 3 4AGE 4

1 2 3 4 5 6 7 8 9 10AGE 5

1 2 3 4AGE 6

1 2 3 4 5AGE 7

1 2 3 4 5 6 7 8AGE 8

1 2 3 4 5 6AGE 9

1 2 3 4 5 6 7AGE 01 2 3 4 5 6 7 8 9AGE 1

1 2 3 4 5 6 7 8AGE 2

AGE 3

1 2 34 AGE 4

1 23 4 5 6 7 8 910 AGE 5

1 2 3 4AGE 6

1 2 3 4 5AGE 7

1 23 4 5 6 7 8AGE 8

1 2 3 45 6AGE 9

1 2 3 4 5 6 7AGE 01 2 3 4 5 6 7 8 9AGE 1

1 2 3 4 5 6 7 8AGE 2

AGE 3

1 2 3AGE 4

1 2 4 5 67 8 9AGE 5

1 234 AGE 6

2 3 4 5AGE 7

1 2 4 56 7 8AGE 8

1 2 3 4 6AGE 9

1 2 3 4 5 6 7AGE 01 2 3 4 5 6 7 8 9AGE 1

1 2 3 4 5 6 7 8AGE 2

AGE 3

1 2 3AGE 4

2 4 5 6 8 9AGE 5

1 2AGE 6

2 3 4 5AGE 7

1 2 4 5 7 8AGE 8

12 34 6 AGE 9

Decom-missions

Dis-in-vestments

1 2 3 4 5 6 7

AGE 0

1 2 3 4 5 6 7 8 9

AGE 1

1 2 3 4 5 6 7 8

AGE 2

AGE 3

1 2 3AGE 4

2 4 5 6 8 9

AGE 5

1 2

AGE 6

2 3 4 5

AGE 7

1 2 4 5 7 8

AGE 8

1 3AGE 9

1 2 3 4 5 6 7

AGE 0

1 2 3 4 5 6 7 8 9

AGE 1

1 2 3 4 5 6 7 8

AGE 2

AGE 3

1 2 3AGE 4

2 4 5 6 8 9

AGE 5

1 2

AGE 6

2 3 4 5

AGE 7

1 2 4 5 7 8

AGE 8

1 3AGE 9

1 2 3 4 5

1st January 31st December 31st December

1st January 1st January31st DecemberAttritions Transition Recruitment

2001 2001 2001

2001 2002 2002

RECRUITMENT

Figure. 2.4.1.1. Illustration of the fleet dynamics (one fleet in one year). Figure 2.4.1.1 illustrates the different steps of the calculation of number of vessels. The example deals with a single fleet with 10 age groups, of which the oldest age group is a plus group. The vessels are symbolized by numbered circles. The starting situation is shown in the first rectangle. This is the numbers of vessels in each vessel age group, after transition from an age group to the next age group and the recruitment (arrival of new vessels). Then the model (as an approximation) assumes that the number of vessels remain unchanged, and only at the end of the year (or a shorter time period) will changes take place. Vessels removed from the fleet are symbolized by circles next to the rectangles. The time unit for vessel dynamics is one time period, irrespectively of which time step is used as the basic time step for the simulation. The change in number of vessels is assumed to take place at the end of the period (symbolized by “31 December” in Figure 2.4.1.1). The transition from one vessel age group to the following vessel age group takes place at the beginning of the period (immediately after the change of number of vessels, symbolized by “1st January in Figure 2.4.1.1). Also the recruitment takes place at the beginning of the period. The sequence of the different changes in the number of vessels is crucial, when numbers are computed as fraction of the number of survivors.

24

Figure 2.4.1.2. Example of input to TEMAS: Number of vessels.

25

Figure 2.4.1.2 shows an EXCEL worksheet with the number of vessels as input to TEMAS, in the simple case of only one fleet with nine age classes. The first four tables contain the input, and the last two tables contains the “Resulting number of vessels”. The cohort structure of the fleet is highlighted by the frames around the 2000-year class of vessels. The last table summarizes the number of vessels over age groups. 2.4.2. Number of vessels multipliers. The TEMAS model considers the number of vessels by fleet and their capacity to create fishing mortality as key-parameters. The parameters are (in principle) under the control of man, and therefore we have introduced a number of auxiliary variables by which the number of vessels can be manipulated (this is similar to the approach used by ICES WGs to manipulate the input F to the catch prediction). The number of new vessels (investments) is created from a “reference number” multiplied by a

“Multiplier” .

),(Re yFlNU ferenceVesselsNew

),(* 10 yFlXX VesselsVessels

),(*),(*)0,,( Re

10 yFlNUyFlXXyFlNU ferenceVesselsNew

VesselsVesselsVessel =

The multiplier is composed of two factors and , where the first factor is independent, and applies to all fleets in all time periods, whereas the second factor depends on fleet and time period. The same factor is applied to the initial number of vessels (in first time period of first year):

VesselsX 0 ),(1 yFlX Vessels

),(*),(*),1,( Re

10 VaFlNUyFlXXVaFlNU ferenceVessels

VesselsVesselsVessel =

2.4.3. Fishing days or sea days: The variable Effort concepts of TEMAS relates to two purposes:

1) To convert fishing activity into fishing mortality 2) To convert fishing activity into costs of fishing.

Effort is designated E(Fl, y, q, Ar). Effort and number of vessels are the control parameters in the fisheries management model. Effort can be controlled in TEMAS in two ways

1) Giving effort as input 2) Let the “Effort-rule” decide the effort

In the following we shall deal with only the first way of entering effort in the TEMAS model, although the second one may be the most relevant one for practical applications.

∑=

=•AreaNU

ArArqyFlEqyFlE

1),,,(),,,( is the total effort exerted during time period q of year y

The input effort in the present version of TEMAS is E(Fl, y,q,•), that is the total effort summed over areas, together with the relative distribution of effort over areas: EDistribution(Fl, q, Ar) = E(Fl, y, q, Ar)/ E(Fl, y, q, •). (2.4.3.1) This distribution is assumed to remain unchanged from year to year. Thus, effort is derived from the product of the two input parameters, E(Fl, y,q,•) and EDistribution(Fl,q,Ar) E(Fl, y, q, Ar) = E(Fl, y, q, •)* EDistribution(Fl, q, Ar) (2.4.3.2) The concepts used for the definition of effort is illustrated in Table 2.4.3.1. The distribution on areas for each time period is given in the left hand side of the table. These distributions do not change from year to year, when you give effort as input parameter. Note that the distributions on areas are relative (sum up to one). The effort distribution on time periods are given

26

in the last row of the right side of Table 2.4.1. The effort distribution is in absolute numbers (e.g. fishing days) and can vary from year to year.

EDistribution on areas Effort 1999 Effort 2000

Area

distribution on areas in

period 1

distribution on areas in period 2

distribution on areas in period 3

distribution on areas in period 4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

1 0,20 0,10 0,35 0,30 200,0 110,0 455,0 270,0 230,0 125,0 507,5 315,0

2 0,25 0,25 0,25 0,25 250,0 275,0 325,0 225,0 287,5 312,5 362,5 262,5

3 0,35 0,25 0,20 0,25 350,0 275,0 260,0 225,0 402,5 312,5 290,0 262,5

4 0,20 0,40 0,20 0,20 200,0 440,0 260,0 180,0 230,0 500,0 290,0 210,0

Total 1.00 1.00 1.00 1.00 1000 1100 1300 900 1150 1250 1450 1050Table 2.4.3.1. Illustration of effort distribution for two years. Numbers in bold are input, and number in italics are derived fron the input. The distribution on areas, EDistribution(Fl,q,Ar), however, may well in reality vary from year to year, so Eq. 2.4.3.2 represents an approximation to reality. Later versions of TEMAS may relax on the assumption that the effort distribution remains unchanged between years. Effort will usually be measured in sea-days (days away from port) or fishing days (=sea-days – days to steam to and from the fishing grounds). The definition of Effort might have been more closely related to the fishing operation, such as the “number of trawling hours” or “number of gill net set”, but in that case two measures of effort may be required, one for the derivation of fishing mortality and one for the derivation of cost of fishing. There are several potential extensions of the TEMAS model in relation to the effort definition. 2.4.4. Fleet capacity The capacity is the maximum number of fishing effort units (fishing days or sea days) that a fleet can exert in a time period. It is given by the variable: EYMAX(Fl, y,q) =The maximum number of effort units per vessel per time unit.

Thus: (2.4.4.1) ∑=

•≤MaxAr

ArMaxVessel qyFlEYyFlNUArayFlE

1),,(*),,(),,,(

Eq. 2.4.4.1 secures that the effort level simulated by TEMAS will never exceed a level higher than the physical capacity of the fleets. This obvious constraint, however, is often not imposed on simulations in fisheries models, such as, for example, the Beverton and Holt Yield per Recruit model (1957), or in the catch prediction tables of ICES WG reports. 2.4.5. Effort multipliers: Assessing the effect of changing effort by fleet, rigging, area and season is the key-exercise of TEMAS. Therefore, a number of “multipliers” (“X’es”) to facilitate the manipulation of effort has been introduced. Actual effort used in the simulation is thus defined as the product of a “Reference-effort”, ERef(Fl , y, q, Ar), and a suite of multipliers (X):

),,,(*),,(*),(*),,,(),,,( Re ArqyFlXArqFlXArFlXArqyFlEArqyFlE TimePerConf=

where the three principal multipliers are defined: TimePerCon XXX ,,

Year and period independent multiplier (Constant): )(*)(),( 21 ArXFlXArFlX ConConCon =

Period (Per) dependent (Year independent) multiplier: ),(*),(*)(),,( 321 ArqXqFlXqXArqFlX PerPerPerPer =

Year and period (Time) dependent multiplier: ),,(*),,(*),(),,,( 321 ArqyXqyFlXqyXArqyFlX TimeTimeTimeTime =Figure 2.4.5.1 shows an example of the time in-dependent multipliers, with two fleets, each with two vessel size classes and two riggings.

27

Figure 2.4.5.1. Effort multipliers and distributions independent of time, for a hypothetical example.

28

2.4.6. Reference effort The reference effort will (arbitrarily) be defined as the maximum possible effort the current number of vessels can exert. As the effective effort is the results of a multiplication with one or more multipliers, the absolute value of the reference effort is in theory irrelevant. However, using the maximum possible value is believed to make it easier to operate the model. We shall laver give an exact definition of the reference effort, after the capacity of a fleet has been defined. We are now in a position to define the “reference effort” of a fleet (for all areas combined). ),,(*),,(),,,(Re qyFlEYyFlNUqyFlE MaxVesself •=• Using only multipliers less than or equal to one and, summing up to less than one over areas:

),,,(*),,(*),(*),,,(),,,( Re ArqyFlXArqFlXArFlXqyFlEArqyFlE TimePerConf •=

will guarantee that the condition 2.4.4.1 is met. Figure 2.4.6.1 continues the example of Figure 2.4.5.1. It shows the time dependent multiplies, the reference effort and the “resulting” effort, that is the product of multipliers and reference effort (From Figures 2.4.5.1 and 2.4.6.1).

Figure 2.4.6.1. Time dependent Effort multipliers and resulting effort, for a hypothetical example.

29

2.5. FISHING MORTALITY The concept of fishing mortality refers to the concept of a stock. The mortality refers to the entire stock. It should therefore be noted that when mortality is assigned to an area smaller than the area occupied by the stock, the conventional fishing mortality concept is no longer applicable, as that concept is associated with the stock, not a part of the stock. Therefore, we shall use the terminology “Area-mortality” and “Stock-mortality”. In Section 2.6 we shall give the mathematical formula for the relationship between area-mortality and stock-mortality (Eq. 2.6.5). 2.5.1. The relationship between effort and fishing mortality: The simulated area-fishing mortality is derived from the effort and the selection ogive in the case of management based on effort regulation. F(Fl, St, y, a, q, Ar) = E(Fl, y, q, Ar)* Q(Fl, St, y, Ar) * SEL(Fl, St, y, a, q) (2.5.1.a) where E(Fl, y, q, Ar) = Effort , SEL(Fl, St, y, a, q) = Gear selection and Q(Fl, St, y, a, q, Ar) = Catchability coefficient. In the case of quota regulations, one will need to convert catch quotas into effort quotas. There is no tradition for this exercise in ICES, and we have no idea about which approach ICES would choose, if it was to give effort-qoutas. We shall however, leave this crucial question of fleet based management, and return to the easy case of effort-based management. In the case of stochastic simulation, the relation between effort and area-fishing mortality is assumed to be subject to stochastic variation: F(Fl, St, y, a, q, Ar) = E(Fl, y, q, Ar)* Q(Fl, St, y, q, Ar) *εQ(Fl, St, y) * SEL(Fl, St, y, a, q) (2.5.1.b) where εQ(Fl, St, y) = Stochastic factor of catchability, a year fleet and stock dependent normally distributed stochastic variable with mean value 1.0 and standard deviation σQ . In the case of deterministic simulation the parameter εQ(Fl, St, y) is assigned the constant value one (σQ= 0). Eq. (2.5.1) represents the simplest mathematical model for the relationship between effort and fishing mortality (proportionality). TEMAS, however, offers a model, which also accounts for the relationship between catchability and stock abundance, as well as the technical development of efficiency of fishing operation (fishing power). If the fish distribute over the same area irrespectively of the stock size, one should expect the catchability to go down at low stock sizes. This is reflected by the model:

),,exp(1 ),1,,(*),,,,(),,,,( yStFlQBArqyStBArqyStFlQArqyStFlQ −= (2.5.2)

where B is the biomass. The exponent QBexp(Fl, St, y), which reflects the tendency of the catchability to go down when stock biomass is high. QBexp will most often be less than one and often close to zero. The higher QBexp is the more dependent is Q on the biomass. As Biomass, B, is dependent on fishing mortality, which in turn is dependent on catchability, Q, is related to the biomass of last time period “q-1”. TEMAS can furthermore account for the technical development in fishing efficiency of fishing vessels and fishing gears by a simple exponential growth of catchability, Q.

)),,(*exp(*),1,,(*),,,,(),,,,( ),,exp(1 yStFlQyarqyStBArqyStFlQArqyStFlQ DevTech

yStFlQB−−= (2.5.3)

Note that when the parameters, QBexp(Fl, St, y), and QTech-Dev(Fl, St, y) are given the value zero, we are back to the simple model of Eq. (2.5.1). 2.5.2. Catchability Multipliers As for the number of vessels and effort, assessment of the effect of changes in catchability is a key-exercise, and therefore a sutie of facilities has been introduced to facilitate manipulations of catchability. The catchability (Q or Q1) is in the input-part of TEMAS given as the product of four factors:

),(*),(*),,,,(*),,(),,,,( ReRe StFlXQArStXQArqyStFlQArStFlQArqyStFlQ FleetAreaTimelativef=

),,(Re ArStFlQ f is a reference catchability, which remains constant over time.

),,,,(Re ArqyStFlQTimelative , the relative time-multiplier, is a factor to raise/lower the reference values by

period (and year). The maximum value of the reference value must be one:

30

}{ 0.1),,,,(Re),( =ArqyStFlQMAX lativeqy

),( ArStXQArea

),( StFlXQFleet

. If you do not enter a set with this maximum, the program will normalize the input values so that maximum becomes one.

is the stock-specific area multiplier for catchability.

is the stock-specific fleet multiplier for catchability. Figure 2.5.1 shows an example of absolute and relative catchability together with the multipliers, as they appear in the worksheet of the input-part of TEMAS.

Figure 2.5.1. Absolute and relative catchability tables from the input-part of TEMAS. 2.5.3. Landing and discard area-mortality Area-Fishing mortality is the sum of area-landing mortality and area-discard mortality: F(Fl, St, y, a, q, Ar) = Fland(Fl, St, y, a, q, Ar) + Fdisc(Fl, St, y, a, q, Ar) (2.5.2) Where Fland(Fl, St, y, a, q, Ar) = Area-landing mortality, Fdisc(Fl, St, y, a, q, Ar) = Area-discard mortality and F(Fl, St, y, a, q, Ar) = Area-Fishing mortality. They are defined by : Fland(Fl, St, y, a, q, Ar) = F(Fl, St, y, a, q, Ar) * (1 - DIS(Fl, St, y, a, q)) (2.5.3.a) Fdisc(Fl, St, y, a, q, Ar) = F(Fl, St, y, a, q, Ar) * DIS(Fl, St, y, a, q) (2.5.3.b) Where DIS(Fl, St, y, a, q) = Discard selection ogive that is, the fraction of fish caught, which are discarded. 2.6. STOCK NUMBERS, MIGRATION AND STOCK BIOMASS . TEMAS offers the opportunity to account for spatial aspects, in the sense that fish and fleets can be allocated to a number of areas in a given time period. TEMAS uses a simple “box-model” to handle spatial aspects. However, the inclusion of spatial

31

aspects is optional, and the user may choose to consider the sea as one homogenous area. If several areas are considered, this will require a number of additional input parameter, for example “migration coefficients” 2.6.1. Stock number at end of time period, (before migration): Number of survivors (before migration) is modelled by the traditional exponential decay model:

)*),,,,(exp(*),,,,(),,,,(1 dtArqayStZArqayStNArqayStN −= (2.6.2) where Z(St, y, a, q, Ar) = Area specific “Total mortality” and N(St, y, a, q, Ar) = Stock number at beginning of time period q. Note that the indices of N and N1 remain unchanged when considering the death process during a time period of the year. The transition between time periods in the model is dealt with “just before migration” and “just after migration”.

If q = < qMax then ),,,,(1*),,,,(),1,,,(1

ArqayStNTFqaStMCTArqayStNMax

Ar

Ar

FArAr∑

=

=+

(2.6.3)

if q = qMax (and a < amax(St)) then ),,,,(1*),,,,(),1,1,1,(1

ArqayStNTFqaStMCTArayStN Max

Ar

FArArMax

Max

Ar

∑=

=++

where MC(St, a, q, FAr, TAr) = Migration coefficient for moving from area “FAr” to area “TAr” and N1(St, y, a, q, Ar) = Stock number at end of period (“just before” migration). 2.6.2. The relationship between “area specific mortality” and “stock mortality”: The concept “Mortality” as it is traditionally applied, refers to the entire stock, not to the fraction of a stock, which is in a certain area. Consequently, the number of deaths in a sub-area of the total distribution area of a stock, should not be associated with a “mortality”, but with some other concept. Here we use the term “area-specific mortality”, as the concept required to describe the death process within a sub-area, which naturally, is closely related to the real mortality concept. Let Zstock(St, y,a,q) indicate the traditional total mortality of the stock. The relation ship between Zstock and the area specific total mortalities, Z(St, y,a,Ar,q), is given by:

−

−=∑

∑=

=Max

Max

Ar

Ar

Ar

ArStock

ArqayStN

ArqayStNdtArqayStZdt

qayStZ1

1

),,,,(

),,,,(*)*),,,,(exp(ln1),,,( (2.6.5)

Table 2.6.4.a shows a numerical example of Eq. 2.6.5 with three areas. If the natural mortality remains constant from area to area, the equation above also holds for the stock fishing mortality:

−

−=∑

∑=

=Max

Max

Ar

Ar

Ar

ArStock

ArqayStN

ArqayStNdtArqayStFdt

qayStF1

1

),,,,(

),,,,(*)*),,,,(exp(ln1),,,( (2.6.6)

Table 2.6.4.b shows a numerical example of Eq. 2.6.6 with three areas. If M varies from area to area then the following relationship gives the F for the stock (omitting indexes, except for the area index):

−+−

−=∑

∑=

=Max

Max

Ar

Ar

Ar

Ar stockStock

ArN

ArNdtarMMArFdt

F1

1

)(

)(*)))()((exp(ln1

(2.6.7)

32

Ar(Area) N(Ar) F(Ar) M(Ar) Z(Ar) exp(-Z) N*exp(-Z) 1 1000 0.5 0.2 0.7 0.4966 496.62 500 1.0 0.3 1.3 0.2725 136.33 250 1.5 0.2 1.7 0.1827 45.7

= 1750 ∑ =−MaxAr

ArArNArZ

1)(*))(exp( = 678.5

{ }∑ ∑= =−−= Max MaxAr

Ar

Ar

ArStock ArNArNArZZ1 1

)()(*))(exp(ln = 0.95

∑ =

max

1)(Ar

ArArN

Table 2.6.4.a. Numerical example of calculation of Zstock (Eq. 2.6.5, skipping constant indices), with variable M

Ar(Area) N(Ar) F(Ar) M(Ar) Z(Ar) exp(-Z) N*exp(-Z) Exp(-F) N*exp(-F) 1 1000 0.5 0.2 0.7 0.4966 496.6 0.6065 606.52 500 1.0 0.2 1.2 0.3012 150.6 0.3679 183.93 250 1.5 0.2 1.7 0.1827 45.7 0.2231 55.8

Total 1750 Total 692.9 Total 846.3 Zstock = 0.93 Fstock= 0.73

Table 2.6.4.b. Numerical example of calculation of Zstock (Eq. 2.6.5, skipping constant indices), with constant M 2.7. CATCHES 2.7.1. Mean number of survivors:

dtArqayStZdtArqayStZ

ArqayStNArqayStN Mean *),,,,()*),,,,(exp(1

),,,,(),,,,(−−

= (2.7.1)

where Z(St, y,a,q,Ar) = F(St,•,y,a,q,Ar) + M(St,a) = Total mortality and N(St, y, a, q,Ar) = Stock number at beginning of the time period. 2.7.2. Number caught: C(Fl, St , y, a, a, Ar) = F(Fl, St, y, a, a, Ar)* NMean(St, y, a, a, Ar) (2.7.2) where C(Fl, St, y, a, a, Ar) = Numbers caught (landed or discarded) and F(Fl, St, y, a, a, Ar) = Area-Fishing mortality 2.8. MEAN STOCK BIOMASS AND SPAWNING STOCK BIOMASS Mean stock biomass is

∑=

=)(

0),,,(*),,,,(),,,(

Sta

aMean

Max

qayStWgtArqayStNArqyStB (2.8.1)

The conventional stock biomass, is the sum over areas:

∑∑==

=•)(

01),,,(*),,,,(),,,(

Sta

aMean

Ar

ar

MaxMax

qayStWgtarqayStNqyStB (2.8.2)

The spawning stock biomass in area “Ar” is:

∑=

=)(

0

),,(*),,,(*),,,,(),,,(Sta

aMean

Max

qaStMatqayStWgtArqayStNArqyStSSB (2.8.3)

The conventional spawning stock biomass is the sum over areas:

(2.8.4) ∑∑==

=•)(

01

),,(*),,,(*),,,,(),,,(Sta

aMean

Ar

Ar

MaxMax

qaStMatqayStWgtArqayStNqyStSSB

33

2.9. STOCK AND RECRUITMENT MODEL The recruitment is in TEMAS derived by the Beverton and Holt model (Beverton & Holt, 1957) from the stock SSB (summed over areas and time periods) of last year.

),,1,(*)(21),,1,(*)(1

),,,(Re••−+

••−=••

yStSSBStBHyStSSBStBH

yStcSIM

SIM (2.9.1)

where BH1(St) and BH2(St are the First and second Parameter in the Beverton and Holt Stock/Recruitment model. After the total stock recruitment is derived, it is subsequently distributed on areas and time periods by the input parameter, RecDistArea(St,Ar) and RecDistPeriod(St,q),, the relative distribution of recruitment on areas and time periods as will be discussed below. The relationship between recruitment and spawning stock biomass remains a complete mystery to science. The only point which is known for sure is the origin (0,0), as zero parents can produce only zero offspring. Therefore, TEMAS offers the option to let recruitment becomes a stochastic variable, through the stochastic factor )(StSRε , as shown in Eq. 2.9.2.

)(*),,1,(*)(21

),,1,(*)(1),,,(Re StyStSSBStBH

yStSSBStBHyStc SRSIM

SIM ε••−+

••−=•• (2.9.2)

where εSR(St) = Stochastic factor of stock/recruitment relationship, of stock “St”, a stock dependent log-normally distributed stochastic variable with mean value 1.0 and standard deviation σSR Eq. 2.9.1 represents the conventional Beverton & Holt model. In TEMAS, however, the recruitment of stock “St” in year “y”, Rec(St, y, q, Ar) = N(St, y, 0,q,Ar) is modelled by the “Area-specific and seasonalized version” of the Beverton and Holt model:

)(*),,1,(*)(21

),,1,(*)(1*),(Re*),(Re),,,( StyStSSBStBH

yStSSBStBHqStcDistarStcDistArqyStc SRSIM

SIMPeriodArea ε

••−+••−

=Re (2.9.3

∑=

==MaxAr

i

Area

iqyStN

ArqyStNNumbercruitmentTotal

arareainnumbercruitmentArStcDist

1),,0,,(

),,0,,(Re

""Re),(Re (2.9.4)

Thus, RecDistArea(St, Ar) is assumed to be independent of time period, “q”. The distribution on time periods is defined the same way, RecDistPeriod(St, q) is assumed to be independent of time area, “Ar”. The Beverton & Holt model could be replaced by any other stock-recruitment model, but we do not think it would enhance the predictive power of the model. This specific choice of S/R-model is somewhat arbitrary, as the only reason for choosing this particular one is its mathematical simplicity. We believe that it makes little sense to squeeze such a complex phenomenon as variation of recruitment into a two-parameter model. However, making stock-recruitment stochastic somehow reflects the present knowledge or understanding of the stock-recruitment relationship (which probably only accounts for a very small fraction of the explanation of recruitment varitions). 2.10 LANDINGS AND DISCARDS 2.10.1. Number landed and discarded: Numbers landed CLand(Fl, St, y, a, q, Ar) = Fland(Fl, St, y, a, q, Ar) * Nmean(St, y, a, q, Ar) (2.10.1) Where Fland(Fl, St, y, a, q, Ar) = “Landing mortality” Numbers discarded CDisc(Fl, St, y, a, q, Ar) = FDisc(Fl, St, y, a, q, Ar) * Nmean(St, y, a, q, Ar) (2.10.2)

34

2.10.2. Weight of landed and discarded fish: Weight of fish landed (Yield) is

),,,(*),,,,,(),,,,,( aqyStWgtArqayStFlCArqayStFlY LandLand = (2.10.3) Where CLand(Fl, St, y, a, q, Ar) = Numbers landed The total annual fleet specific landings of all age groups caught in area “Ar” becomes

),,,,,(),,,,,()(

1

max

ArqayStFlYArqyStFlYSta

aLandLand ∑

=

=• (2.10.4)

Weight of Numbers discarded ),,,(*),,,,,(),,,,,( qayStWgtArqayStFlNArqayStFlY DiscDisc = (2.10.5)

The total annual fleet specific discards of all age groups caught in area “Ar” becomes

),,,,,(),,,,,()(

1

max

ArqayStFlYArqyStFlYSta

aDiscDisc ∑

=

=• (2.10.6)

Where CDisc(Fl, St, y, a, q, Ar) = Numbers discarded and Wgt(Fl, St, a, q, Ar) = Mean Body The landings and discards for the stock summed over areas and age groups become

),,,,,(),,,,,(

),,,,,(),,,,,(

)(

11

)(

11

max

max

ArqayStFlYqyStFlY

ArqayStFlYqyStFlY

Sta

aDisc

Ar

ArDisc

Sta

aLand

Ar

ArLand

Max

Max

∑∑

∑∑

==

==

=••

=••

(2.10.7)

And the annual landings and discards of the stock become

),,,,,(),,,,,(

),,,,,(),,,,,(

)(

111

)(

111

max

max

ArqayStFlYyStFlY

ArqayStFlYyStFlY

Sta

aDisc

Ar

ar

q

qDisc

Sta

aLand

Ar

ar

q

qLand

MaxMax

MaxMax

∑∑∑

∑∑∑

===

===

=•••

=•••

(2.10.8)

Eventually we arrive at the total landings and discards by fleet Fl

),,,,,(),,,,,(),(

),,,,,(),,,,,(),(

)(

1111

)(

1111

max

max

ArqayStFlYyFlYyFlDISCARDS

ArqayStFlYyFlYyFlLANDINGS

Sta

aDisc

Ar

ar

q

q

St

StDisc

Sta

aLand

Ar

ar

q

q

St

StLand

MaxMaxMax

MaxMaxMax

∑∑∑∑

∑∑∑∑

====

====

=••••=

=••••=

(2.10.9)

2.11. THE BASIC BIOLOGICAL/TECHNICAL ALGORITHM OF TEMAS The basic biological/technical algorithm “MAIN_SINGLE_SIMULATION “ in Visual Basic was shown in Figure 2.0.2. Some details have been omitted in order to make the presentation easier to comprehend. Figure 2.11.1 shows the central subroutine of “MAIN_SINGLE_SIMULATION”, namely the sub routine “COMPUTE_ALL_RESULTS_YQ” This routine executes the calculations for one time period, as indicated by the extension “YQ” in the mane. It is called from routine "MAIN_SINGLE_SIMULATION" as shown in Figure 2.0.2. The choice of names is (apart from some formal rules of VB) a matter of taste. You can give them any name you like, but if you want other people to understand your program, you should be careful in selecting names which gives the reader the

35

right idea of what the subroutine does. You may also introduce conventions on names, which will make it easier to understand their meaning. For example, the extension to the name "_YQ" indicates that calculations are made for one time period only, or “has index (y,q)”. Sub COMPUTE_ALL_RESULTS_YQ() ' ' --- This routine is called from userform "F03_Select_Output" which calls ' ------ MAIN_EXECUTE_SIMULATION, which calls ' --------- MAIN_SINGLE_SIMULATION, which calls ' ------------ COMPUTE_ALL_RESULTS_YQ ' '--- It computes a simulation of system for one time period for all stocks, fleets and areas '--- The extension to the name "_YQ" indicates that calculations are made for one time period '--- Note the order of routines --------------------------------------- ' Call COMPUTE_ALL_OGIVES_YQ ' -------- growth curves, gear selection, discard and maturity ogives Call COMPUTE_AREA_FISHING_MORTALITY_ALL_STOCKS_YQ ' --- Convert effort into area fishing mortality Call COMPUTE_STOCK_NUMBERS_LAND_DISC_SSB_ALL_STOCKS_YQ ' ---- Population dynamics for one period Call COMPUTE_F_STOCK_FROM_AREA_MORTALITY_YQ ' ----- aggregate area-F's into stock-F's ---------- Call COMPUTE_FAO_ECONOMY_FL_VS_Ct_YQ ' -- Compute economic results for one time period ' --------------------------------------- "FAO" indicates that the model was developed by R. Willmann ' --------------------------------------- of FAO Fisheries Department, Rome ----------- ' ----- Suffix "_FL_VS_Ct_YQ" in the name "COMPUTE_FAO_ECONOMY_FL_VS_Ct_YQ" indicates that the calulation ' ----- are made for one time period for each combination of Fleet, Vessel size and country ----------- If Effort_Capacity_Rules Then '---------- Apply the behaviour algorithms (optional) ------------------- Call APPLY_STRUCTURAL_RULES_YQ ' ---- Note that structural rules comes before effort rule --- Call APPLY_EFFORT_RULE_YQ ' --------- Note that effort rules comes after structural rule ---- Call CHECK_EFFORT_CAPACITY_AND_REDUCE_IF_REQUIRED_YQ ' --- check that effort is feasible with the ' ------------------------------------------------------------------------------------------------------- current number of vessels End If End Sub

Figure 2.11.1. The routine “COMPUTE_ALL_RESULTS_YQ” exactly as it appears in the Visual Basic in module “M06_C_COMP_MAIN” in workbook “TEMAS_CALC” The intension is that the advanced user of TEMAS should understand the logics of the VB-code, and be able to modify and/or further develop it. But perhaps most important, the user should be able to check the calculations so that she/he knows what the program does. To see the real Visual Basic sub-routine, you should inspect the VB-module with “_CALC” in their names (See Figure 2.0.1), in workbook “TEMAS_CALC. Note that the variable and sub-routines have been assigned names, which should make them easy to comprehend. Do also note the extensive use of comments (lines starting with “’”), which is an invitation to the user to study the Visual Basic code. The division of the program in subroutines can be done in many ways. It has been attempted to make the split in subroutines so that it becomes easier to see the structure of the program. How to achieve this goal is to a certain degree a matter of taste. The routine “COMPUTE_STOCK_NUMBERS_LAND_DISC_SSB_ALL_STOCKS_YQ” executes the population dynamics. It is reproduced in Figure 2.11.3. The first time period of first year in the time series is treated separately, as the stocks here are given as input parameters, Thereafter, the stock numbers are compute by three subroutines

COMPUTE_RECRUITMENT_YQ

COMPUTE_STOCK_JUV_NUMBERS_MIGRATION_YQ COMPUTE_STOCK_2PLUS_NUMBERS_MIGRATION_YQ As the juveniles are modelled differently from the adults (the 2+ groups), they are handled by different routines, but in principles they are similar. The routine for the population dynamics of the 2+ groups is hown in Figure 2.11.2.e.

36

Sub COMPUTE_STOCK_NUMBERS_LAND_DISC_SSB_ALL_STOCKS_YQ() ' ----- Called from subroutine "COMPUTE_ALL_RESULTS_YQ" ' ----- This routine computes a set of stock-numbers (by age and time). For St = 1 To Number_of_Stocks If Not ((y = 1) And (Q_Time = 1)) Then '---- (y = 1) And (Q_Time = 1) --- handled by Sub "COMPUTE_CREATE_CONSTANT_INITIAL_N" --- Call COMPUTE_RECRUITMENT_YQ Call COMPUTE_STOCK_JUV_NUMBERS_MIGRATION_YQ Call COMPUTE_STOCK_2PLUS_NUMBERS_MIGRATION_YQ End If Call COMPUTE_LAND_DISC_AND_VALUE_BY_FLEET_AND_AREA_YQ Call COMPUTE_AGGEGATED_LAND_DISC_AND_VALUE_BY_PERIOD_YQ Call COMPUTE_ACCUMULATED_SSB_YQ Next St Call COMPUTE_AGGEGATED_LAND_DISC_AND_VALUE_BY_YEAR Call COMPUTE_TOTAL_YIELD_VALUE_BY_FLEET_SUMMED_OVER_STOCKS End Sub Figure 2.11.2. The algorithm for calculation population dynamics of all stocks during one time period. Sub COMPUTE_STOCK_2PLUS_NUMBERS_MIGRATION_YQ() ' ----------- This routine is used only when "Number_Of_Areas > 1" ---------------- Dim Aa As Integer, Zdt As Single, ExpZ As Single Aa = Number_of_Age_Groups(St) If Aa < Min_Adult_a Then Exit Sub ' --- only two age groups in population ----- For Ar = 1 To Number_of_Areas For a = Min_Adult_a To Aa Zdt = (F_Area_YQ(St, Ar, a) + M_Nat(St, a)) * Dt ExpZ = Exp(-Zdt) ' ---- Transition from foregoing period: Q_age = 1 ---------------- If Q_Time = 1 Then Nstart_YQ(St, Ar, a) = Nend_After_Mig_YQ(St, Ar, a - 1) Else ' ---- Transition from foregoing period: Q_Time < Number_of_Periods --- Nstart_YQ(St, Ar, a) = Nend_After_Mig_YQ(St, Ar, a) End If ' ----- Mean N (Used to compute catches) ---------------------- Nmean_YQ(St, Ar, a) = Nstart_YQ(St, Ar, a) * (1 - ExpZ) / Zdt ' ----- N at end of period ------------------------------------ Nend_Before_Mig_YQ(St, Ar, a) = Nstart_YQ(St, Ar, a) * ExpZ Next a Next Ar ' --------------------------- MIGRATION 2+ ---------------------------- For a = Min_Adult_a To Aa For Tar = 1 To Number_of_Areas X1 = Zero ' ----- Total number migrating to area "Tar" ---- For Far = 1 To Number_of_Areas X1 = X1 + Nend_Before_Mig_YQ(St, Far, a) * Mig(St, Far, Tar, Q_Time, a) Next Far If Not ((a = Aa) And (Q_Time = Number_of_Periods)) Then '------ Not oldest age (+) group ---------- Nend_After_Mig_YQ(St, Tar, a) = X1 Else '----------- oldest age (+) group -------------------_ Nend_After_Mig_YQ(St, Tar, Aa) = Nend_After_Mig_YQ(St, Tar, Aa) + X1 End If Next Tar Next a ' ------------------------ Sum over areas ------------------------------------ For a = Min_Adult_a To Number_of_Age_Groups(St): X1 = Zero For Ar = 1 To Number_of_Areas X1 = X1 + Nstart_YQ(St, Ar, a) Next Ar: Nstart_Stock_YQ(St, a) = X1 Next a End Sub Figure 2.11.3. The algorithm for calculation of stock numbers of the 2+ groups of one stocks during one time period

37

Figure 2.11.4 shows the EXCEL worksheet with ”stock-output”, that is, the results of ”COMPUTE_STOCK_2PLUS_NUMBERS_MIGRATION”

Figure 2.11.4. Stocks and catch numbers as they appear on the EXCEL sheet, computed by the routine of Figute 2.11.2.

38

3. ECONOMIC SUBMODEL OF TEMAS The economic sub-model implemented so far in TEMAS, is not described in details here. Only the part of it which links the economic model to the biological/technical model is given a presentation. The link between biology and economy is the value of the landings, which in turn are derived from the prices of landings. The model for the value of landings is presented in full, whereas other parts of the economic model is only briefly described. There are 3 economic models in TEMAS, reflecting the views of three groups of stakeholders

(1) The fishing industry (2) The Government (3) The society (as a whole).

The three models are named:

1) FINANCIAL ANALYSIS OF FLEETS: The financial performance of fishing fleets (i.e. from the point of view of vessel owners)

2) GOVERNMENT BUDGET ANALYSIS: The impact of the fleets on the government budget 3) ECONOMIC ANALYSIS: he economic performance of fishing fleet(s) and the entire fishery

(i.e. from the point of view of the economy as a whole.

All three models operate with the same concepts of costs, earnings and investments, but (possibly) with different parameters There are 10 groups of costs:

1. Costs depending on effort 2. Costs depending on costs of effort 3. Costs depending on yield (weight of landings) 4. Costs depending on the value of the landings 5. Costs depending on the divisible earnings 6. Costs depending on the number of vessels (fixed annual costs) 7. Independent fixed annual costs 8. Costs of investment in new vessels 9. Cost of decommissioning of crew members 10. Cost of decommissioning of vessel

The economic model calculates the cash flow (Revenue – costs) for each time period and eventual it computes the net present value over the time horizon simulated. The economic model was designed by Mr. Rolf Willmann, of the fisheries department of FAO, Rome (Sparre and Willmann, 1993). This paper focuses on the biological technical aspects of the model, and the description of the economic model is indeed very superficial (written by a biologist). Figure 3.1 shows a part of the so-called “Summary output” from TEMAS, with cash flows from the three economic models and some other key indicators. The first table show key indicators in the first and the last year of the time period simulated, and the second table shows values for each year.

39

Figure 3.1. Summary results of a TEMAS simulation. 3.1. PRICES In order to make the provision of input easy, ex-vessel prices are given as the product of a maximum price over age groups and a relative price by age: Pmax(Fl, St, y) = Maximum Price (over age groups) P Rel(Fl, St, a, q) = Relative price of age group “a” in time period “q”.

40

Note that Pmax depends on the year, but not the age group, whereas P Rel depends on the age group of the animals but not the year. The product becomes the age-dependent absolute price: Price per weight unit P(Fl, St, y, a, q) = P max(Fl, St, y)* P Rel(Fl, St, a, q) (3.1.1) In the current version of TEMAS, prices are given as input parameters. They can either be assumed to remain constant (i.e. no changes in response to changes in supply) or to vary as a result of changes in supply (i.e. in landings). Constant prices may apply where the supply of the fishery under investigation is small relative to the total supply (and market) of this species (or group of species) and thus there is no or a negligible effect on price formation. Where variations in supply are assumed to have an effect on prices, TEMAS provides a simple price formation function that, however, disregards changes in demand. 3.2. VALUE OF LANDINGS The value of fish landed (Yield) by fleet “Fl” of age group “a” of stock “St” during time period “q” of year “y”, caught in area “Ar” is

),,,,(*),,,,,(),,,,,( qayStFlPArqayStFlYArqayStFlVAL Land= (3.2.1) The total annual fleet specific value of all age groups caught becomes

),,,,,(),,,,,()(

1

max

ArqayFlStVALArqyFlStVALSta

a∑=

=• (3.2.2)

The value for the landings from the entire stock (all areas combined) caught by fleet “Fl” becomes

),,,,,(),,,,,()(

11

max

ArqayStFlVALqyStFlVALSta

a

Ar

Ar

Max

∑∑==

=•• (3.2.3)

And the annual value of the stock caught by fleet “Fl” become

),,,,,(),,,,,()(

111

max

ArqayStFlVALyStFlVALSta

a

Ar

ar

q

q

MaxMax

∑∑∑===

=••• (3.2.4)

The total revenue (from all stocks combined) of fleet Fl in year Y is

∑∑∑∑====

=••••= (3.2.5)

The total value of landings (all stocks combined) during a time period is one of the quantities which determines the effort exerted.

VAL (3.2.6) ),,,,,(),,,,,()(

111

max

ArqayStFlVALqyFlSta

a

Ar

Ar

St

St

MaxMax

∑∑∑===

=•••

3.6. BEHAVIOURAL MODEL OF FISHING FIRMS TEMAS contains several options to model the behaviour of fishing firms during the fishing season and from year to year. The behavioural rules are not explained in details here. One reason for that is that we still have not made up our minds on how they should be constructed. We intend to use the textbook by Vani K. Borooah (2002), as a general reference in behaviour theory. We also expect to apply elements from various papers dealing with fishers behaviour (e.g. Mistiaen & Strand, 2000, Wilen et al, 2002, Bockstael & Opaluch, 1983, Dupont, 1993). There are short-term and long term behaviour rules in TEMAS. For the short term (trip) behaviour we want a model by which we can predict the probabilities of the different choices a fisher makes on the trip-level.

),,,(ˆ γβ WXFp tBeforetj = where X is associated with the fishing trip (the so-called characteristics of the trip, for

41

example the size of the vessel) and W is associated with the “attributes” of the trip, for example the catch or the revenue from the catch. X and W may be vectors: and W),...,,...,( 21 Rr XXXXX = ),...,,...,( 21 Ss WWWW=

im

a

{ }iMi U,...,2

Yi =Priim UMax 1=

jmMjallfor ≠= .,...,1

∑=

== M

Jij

imi

U

UjY

1exp(

)exp()Pr(

ij

S

choiceofAttributesjsisW εγ +∑

= )(1

The parameter β (which may be a vector) is associated with the trip characteristics and the parameter γ is associated with the attributes. The common approach in literature is to use a “Random Utility Model . Utility, U is “something” which

determines the choice. To each choice is allocated a utility.U is the utility of trip “i” when selecting choice “m”, where

the number of choices is final, 1 ≤ m ≤ M. Thus, there are M altern tives (choices). The random utility model postulates

that the fisher will select choice (alternative) m if U,U

Let Yi denote the choice made by vessel i. Then the probability of vessel i choosing m is denoted . { }mThus { } { }UUmYp ijimiim >=== PrPr

We intend to apply the general logit model: )

The utility of the “general logit model” is composed of three terms, (1) Related to the characteristics of the trip (2) Related to the attributes of the choices, and (3) The error term

R

sticsCharacteririrjrChoicejtripi XU β += ∑

= )(1)()(

i: Trip index, j: Index of alternative (or Choice) made by trip i. , r: Index of trip-characteristics and s: Index of choice-attribute. ijε is the error term, which capture the inexact elements of the model (e.g. measurement errors) If β is positive it means that more of X will give more utility and higher probability that the corresponding choice is made. If β is negative the opposite effect will show. Similar conclusions hold for γ. We intend to use similar models for the long-term behaviour. The five rules currently in the TEMAS package are: Fishing effort rule: This is a rule for where to fish at which time with which gear. So far, the rule implemented only decides whether to fish or not to fish. The remaining behaviour is fixed by input parameters. We plan to make a model for the “trip-related” behaviour where the decisions are based on a mixture of “tradition” and “recent experience”. “Tradition” here means what was done last year (at the same time) and recent experience means the value of landings in the foregoing period relative to the costs of fishing. Decommission (Rule). This (and the three following rules) are the so-called long term rules, which determines the capacity of the fishing fleets. The decommission rules takes the decision on accept of a decommission compensation based on the recent economic performance of the fleet and the age structure of the fleet. Dis-investment rule. This rule decides on the bankruptcy of a vessel based on the recent economic performance of the fleet. Attrition rule: The attrition rule takes the decision on scrapping a vessel due to old age based on the age structure of the fleet. Investment rule: This rule decides on the investment in a new vessel based on the recent economic performance of the fleet. When predicting the effect of management measures, it is obviously very interesting to predict both the short-term and the long-term reaction of fishers.

42

4. STOCHASTIC SIMULATION Nothing is known for sure when trying to predict the events of the future. In case you possess knowledge on the probability distribution of input parameters, TEMAS can provide probability distributions of the output (based on the assumption that the TEMAS model reflects the reality, (which, needless to say, is questionable). 4.1. INPUT TO STOCHASTIC SIMULATION TEMAS can operate in two modes (1) Deterministic and (2) Stochastic. “Stochastic” means that selected parameters are drawn from a random number generator. For example, the growth parameter, K, is assumed to be normally distributed, with a relative standard deviation (=(Standard deviation)/(Mean value)), given as input to TEMAS. The mean value is also given as input to TEMAS. TEMAS is capable of drawing random numbers with two types of probability distribution, namely: (1) Normally distributed and (2) Log normally distributed A selection of input parameters of TEMAS have been made stochastic variable by multiplication with a “stochastic factor” with mean value 1.0 and a standard deviation, which is an input parameter to TEMAS (the blue cells in the input worksheet). The growth parameter K, for example, is made stochastic by replacing K (the input parameter) with: K * εK(St,y). That means that a new value of K * εK(St,y) is drawn by the random number generator, for each stock every year. K is assumed to be normally distributed. That a new K is drawn every year may result in negative growth, if no prevention of negative growth is made. TEMAS, however, allocates the growth rate 0, in case the random numbers generating K produces negative growth. εK(St,y) , σK Stochastic factor of von Bertalanffy parameter K, of stock “St” and year “y” dependent

normally distributed stochastic variable with mean value 1.0 and standard deviation σK εQ(St,Fl,y) , σQ

Stochastic factor of catchability, a year, fleet and stock dependent normally distributed stochastic variable with mean value 1.0 and standard deviation σQ .

εQF(St,y) , σQF Stochastic factor of condition factor, of stock “St” and year “y” dependent normally distributed stochastic variable with mean value 1.0 and standard deviation σQF . εQF(St,y) = (εK(St,y) +ε’QF(St,y))/2, where ε’QF(St,y)) is a year and stock dependent normally distributed stochastic variable with mean value 1.0 and standard deviation σQF. Note that the K and the condition factors are positively correlated, so that a fast growth is associated with a good condition .

εSR(St) , σSR Stochastic factor of stock/recruitment relationship, of stock “St”, a stock dependent log-normally distributed stochastic variable with mean value 1.0 and standard deviation σSR .

Table 4.1.1. List of stochastic factors available in TEMAS. Table 4.1.1 presents a list of the variables of TEMAS which (in the present) version of TEMAS have been made stochastic parameters. It should be stressed that this choice is the subjective choice of the present authors. Any input parameter is a candidate for a stochastic status, as all parameters are subject to estimation errors and variation, which is not explained by the model. Recruitment is perhaps the most famous stochastic (unpredictable) variable in fisheries science. It is a fact that yet no reliable model exists, which can predict recruitment with a known precision. Fisheries managers simply have to live with the fact that recruitment cannot be predicted. The Beverton & Holt model applied in TEMAS does not imply that we believe it has any predictive power, except when SSB (Spawning Stock Biomass) is very low. The only thing we know for sure about stock and recruitment is that if there are no parents there will be no offspring. That is about all the Beverton and Holt model says. When SSB is very low, it may affect recruitment, but otherwise recruitment is independent of SSB.

43

4.2. OUTPUT FROM STOCHASTIC SIMULATION Stochastic output means a probability distribution of an output variable.

SSB IN LAST YEAR (10000 simulations)

0

200

400

600

800

1000

1200

1400

1600

27 1275

2523

3770

5018

6265

7513

8761

10008

11256

12504

13751

14999

SSB

FRE

QU

ENC

Y

Figure 4.2.1. Example of output from stochastic simulation with TEMAS. Frequency diagram produced by 10000 run of the TEMAS model. Figure 4.2.1 shows the distribution of SSB in the last year of the simulation. In this case, the TEMAS simulation has been repeated 10000 times, each time with new values of the stochastic input parameters. Each simulation produces a new value of the SSB, and the 10000 values of SSB can be organised in a frequency diagram like Figure 4.2.1. From this diagram one can derive conclusions like “The probability that SSB < X where X is a given value of SSB. The probability distribution corresponding to Figure 4.2.1 is shown in Figure 4.2.2. Thus, with the management strategy given as input to TEMAS, we can conclude that the SSB will fall below (as an example) 3770 (weight units) with a probability of 60%. It is then up to the managers to decide if they will accept that risk. The graphs shown in this chapter are not produced automatically by TEMAS, but have to be made by the user, applying the graph “wizard” of EXCEL.

44

Probability that SSB < X

0

20

40

60

80

100

120

27 1275

2523

3770

5018

6265

7513

8761

10008

11256

12504

13751

14999

X (Weight unit)

Pro

babi

lity

(%)

Figure 4.2.2. Example of Output from stochastic simulation with TEMAS. Derived from the frequency diagram of Figure 4.2.1 Figure 4.2.3 shows another example of output from stochastic simulation. In this case is shown the time series of total revenues from the fisheries. In this case 1000 simulations were made, and the graph shows the mean value of revenue each year, together with the standard deviations and extreme values simulated.

TOTAL REVENUE (1000 simulations)

0

50000

100000

150000

200000

250000

300000

350000

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

VALU

E

Minimum

Mean - SD

Mean

Mean + SD

Maximum

Figure 4.2.3. Example of Output from stochastic simulation with TEMAS.Time series of Total Revenue.

45

5. OUTPUT FROM SIMULATIONS. As appear from the foregoing, the TEMAS model can produce enormous amounts of output tables. the full output is so voluminous that it becomes incomprehensible. therefore there is a need to aggregate and combine output. Figure 5.1 shows the userform, by which you can select the output in the case of a single simulation.

Figure 5.1. Userform to select outputformat from TEMAS. For the multiple stochastic simulation, only selected summary key-results are produced, and there is no need to de-select part of the output, as it is relatively small compared to that of single simulations. The summary output (last choice in Figure 5.1), is the default output, which will fit to two or three A4-pages, depending on the dimensions of the case study. The first part is a “summary of the summary”, which can fit to a single A4-page. The second last option is the “economic output”, where all biological/technical information has been skipped. Also this output is limited in size, although more comprehensive than the summary output. Then follows (starting from the bottom) four options to get stock structured output, where the options are to disaggregate on time periods and/or areas. The four options for “fleet-output”, gives the highest level of disaggregation. Output is structured as for the stock-output, but with output for each individual fleet. The first 3 options (“Rules”, ”Tuning” and “Ogives”) are reports on the program-execution. “Rules” provides a logbook of the application of the behaviour rules. “Tuning” gives details on the parameter estimation (“Diagnostics” in ICES terminology). Note that there are also options to select output for a single stock or and/or a single fleet. A single stock and a single fleet will produce output matching that of the ICES software. Each option in Figure 5.1 represents a worksheet. E.g. the economic output appears only in worksheet “Economic_Output”, which contains no other output. The output tables are organized in the usual hierarchical order. The main menu of the calculation-part of TEMAS gives a list-box (“Select Table” in Figure 5.2), which allows you to find any table by clicking on the name of the Table (Figure 5.3.a). Figure 5.3.b shows the last part of the Table-list, of the 1134 Tables, of the present case study of 2 fleets (each with two vessel sizes and two riggings), 2 stocks and two areas.

46

Figure 5.2. Main menu for calculation module of TEMAS.

Figure 5.3.a.The first part of list box “Select Table” from the main menu (Figure 5.2).

Figure 5.3.b.The last part of list box “Select Table” from the main menu (Figure 5.2).

47

48

6. REFERENCES Baranov, F.I., 1918. On the question of the biological basis of fisheries. Nauchn.Issled.Ikhtiol.Inst.Izv., 1:81-128 (in Russian) Bertalanffy, L. von, 1934. Untersuchungen über die Gesetzlichkeiten des Wachstums. 1. Allgemeine Grundlagen der Theorie. Roux'Arch.Entwicklungsmech.Org., 131:613-53 Beverton, R.J.H. and S.J. Holt, 1957. On the dynamics of exploited fish populations. Fish.Invest.Minist.Agric.Fish.Food G.B.(2 Sea Fish.), 19: 533 p. Bockstael, N.E. and J.J. Opaluch: 1983. Discrete modelling of supply Response under uncertaincy: The case of fisheries.

Journal of Environmental Economics and Management 10. 125-137 (1983). Derzhavin, A.N., 1922. The stellate sturgeon (Acipenser stellatus Pallas), a biological sketch. Byulleten' Bakinskoi Ikhtiologicheskoi Stantsii, 1: 1-393 (In Russian) Dupont, D.P., 1993: Price Uncertaincy, Expetations Formation and Fishers’ location Choices. Marine resource Economics,

Vol.8 pp 219-247. EU Commission, 2001: Green Paper: On the future of the common fisheries policy. Brussels 20.3.2001 COM(2001)135 Fisheries Centre, 2003. Visual Basic Programming Course Material.

Webside: (http://fisheries.ubc.ca/events/workshops/vbcoursemat.php, Fisheries Centre, NW Marine Drive Research Station, 6660 NW Marine Drive, Building 022, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4

Hoydal, K., C.J. Rørvig & P. Sparre, 1982: Estimation of effective mesh sizes and their utilization in assessment. Dana, Vol. 2: 69-95.

Jackson & Staunton, 2001: Advanced Modelling in Finance using EXCEL and VBA”. John Wiley & Sons, Ltd. (260 pp) Lassen, H. and Medley, P., 2000. Virtual Population Analysis FAO Fish. Tech. Pap. No. 400. Rome, FAO, MacLennan, C.N. (ed.), 1992. Fishing gear selectivity. Fisheries Research, Special issue. Fish.Res., 13(3):201-352 Manly, 1998: Randomization, Bootstrap and Monte Carlo Methods in Biology. Second edition. Texts in statistical sciences.

C R C Press LLC. 400p Mistiaen, J.A. and I. E. Strand, 2000: Location choice of commercial Fishermen with heterogenous risk preference.

Amer. J. Agr. Econ. 82(5). 1184-1190. Quinn, T.J.II, R.B. Deriso and P.R. Neal.1990, Migratory Catch-Age Analysis. Con.J.Fish.Aquat.Sci, (47):2315-2327. Ricker, W.E., 1975. Computation and interpretation of biological statistics of fish populations. Bull.Fish.Res.Board Can., (191):382 p. Sokal, R.R. and F.J. Rohlf, 1981. Biometry. The principles and practice of statistics in biological research. San Francisco, California, Freeman and Company, 2nd ed. Sparre, P.,1991: Introduction to Multispecies Virtual Population Analysis. Rapp.- P.-v. Cons.int.Explor.Mer. Sparre, P., 2003, Lectures: EXCEL (Visual Basic) system development for fisheries, ICES CM 2003/V:11 Sparre, P. and S.C. Venema, 1992: Introduction to tropical fish stock assessment. Parts 1 and 2. Manual, Revision 1.

FAO.Fish.Tech.Pap. No. 306/1 and 2. Rev.1 Rome, FAO.376+94 p. Sparre, P. and P. Hart, 2002. Choosing the best model for fisheries assessment. Chapter 12. in Handbook of Fish and Fisheries, Volume 2. Blackwell Science. Sparre, P and R. Willmann, 1993: Software for bio-economic analysis of fisheries. TEMAS 4 manual. Analytical bio-

economic simulation of space-structured multi-species and multi-fleet fisheries. Vol.1: Description of Model. Vol.2: User's manual. FAO Computerized Information Series (fisheries), No. 3. FAO, Rome. Vol.1 186 p, Vol.2: 46 p

Thompson, W.F. and F.H. Bell, 1934. Biological statistics of the Pacific halibut fishery. 2. Effect of changes in intensity upon total yield and yield per unit of gear. Rep.Int.Fish. (Pacific Halibut) Comm., (8):49 p. Vani K. Borooah, 2002: Logit and Probit, Ordered and Multinomial Models (In the series: Qunatitative Applications in the

Social Sciences). Sage publications. Wilen. Smith, Lockwood and Botsford, 2002: Avoiding surprises: Incorporarting Fishermman Behaviour into

Management Models. Bulletion of Marine Science, 70(2): 553-575.