_{1}

This report introduced new concept and technics for a grid-based fishery management system. The fishing ground was first divided into small grid of equal area, each with predefined longitudes and latitudes (both 0.033 degrees or approximately 2 × 2 nautical miles in this study). All grids were laid and formatted into a Microsoft-Excel spreadsheet system, as defined by the coastline. Individual sheets were also constructed to represent different ecological characters, serving as supporting data of the main grid-map. Including individual fishing record, water depth, wind & current vector, benthic character, etc. Cellular automata (CA) mathematics was applied for simulation studies. They were programmed on the built-in Visual BASIC langrage in EXCEL. In a three-year research project, the author was able to accomplish the following major results: 1) An EXCEL-based spreadsheet system for storage of fishing effort in each grid. Provided that data of fishing yield is also available for each grid, research model for fishery management can be constructed, leading toward solutions for total allowable catch (TAC) as well as maximum economic yield (MEY). 2) A multi-layered, 2-dimentional spread-sheet system demonstrating the distribution of relative intensity for individual grids. The system can be decked up with different ecological data for more advanced studies. 3) Estimation of the nearest distance between two special grids as well as fishing harbors. This would help in more efficient navigation management and allocation of fishing rights for the fishing vessels.

This paper traced back to a research project in constructing a multipurpose fishery management system. The author discarded the traditional approaches of fish population dynamics (e.g. the dynamic pooled model and the sigmoid curve theory model). The above models utilized maximum sustainable yield (MSY) as solution for fishery management. We look for solutions of other practical targets, namely, the Total Allowable Catch (TAC), or the Maximum Economic Yield (MEY). Our major concern is the interactive performances between the fishermen and the managers. We concentrated our work on fishing ground instead of biomass of fish population. For the last two decades, remote sensing and computing techniques have been widely used in fields of agricultural sciences. It is a high time to make new changes on fishery management. The so-called adaptive fishery management [

1) Preparing the working platform

Our work begins by preparing an Excel spreadsheet as a working platform. Each cell represents a single grid of the fishing environment. The spreadsheet is created by dividing the fishing ground into unitary grid of equal area, each with predefined values of longitudes and latitudes (both in 0.033 degree or approximately 2 × 2 nautical miles in this study). Other sizes of grid can also be chosen, depending on the scale of the target area. On a high-resolution navigation map of Taiwan Island, draw horizontal and vertical straight lines, each match exactly the pre-decided values of longitudes and latitudes. This gives a grid-map paper sheet representing the target area. On the Microsoft EXCEL screen, create a spreadsheet representing the electronic image of the map above.

Referring to the navigation map above, carefully mark with mouse such that each individual cell fills up with one of the three colors, representing sea water surface, dry land or (mixed water and land) coastal area respectively (

2) Data entering

Daily records of fishing boat operation were to be collected and key in to each cell during the next step. On this study our first worksheet is the number of fishing days (as variable of fishing effort) (f). The data were from the actual daily-catching report of all fishing vessel. By regulation of the government and the insurance company, fishing vessels are required to report their daily position through special radio station [

process here. Parallel worksheets for other types of data, such as fishing yield, water depth, benthic characters, speed of wind and water current, etc. can also be constructed respectively. This depends on the purpose of the research and if adequate data are available. All worksheets can be combined as one deck (workbook). Data from all cells can be linked by referring to the same (absolute) cell address across the deck, given rise to a practically-3-dimentional operating platform. The current workbook is served as a platform for direct analysis of spatial model for the near-shored mixed fishery. It is expected that other single and multispecies model can also be constructed in the same way if adequate data is available.

3) Algorithm for data interpolation among cells

Each grid cell has four nearest neighboring cells (toward upper, lower, left and right directions) (the so-called Von Neuman neighboring system) as in

Value of each cell was first divided by the grand sum (here it is 22,823 boat-days) to transform into relative intensity values. During the CA process, value of each cell was averaged with the four neighbors, one step at a time until all cells were thoroughly processed. The averaging process repeats iteratively until no empty cells were left inside the whole area. There were various techniques named to the process of local interpolation, such as: moving averages, spline and kriging [

CA operation was done by programing with Visual Basic (Microsoft Inc.) langrage in the EXCEL system. While running the BASIC program, condition in each cell (grid) can be observed on the spreadsheet continuously.

1) Distribution of different types fishing operation.

Although no thorough scientific survey on the fishing ground distribution around Taiwan has been done, spatial distribution of capturing fishery has been well-known. And it is clearly matched with

Preparing a 2-dimentional map like this required close and well-organized communication between individual fishing boats and the radio stations. These can be improved by real-timed governmental remote sensing facilities.

Managing such a fishery system depends on the so-called right-based fishery and the individual transferable quota (ITQ) allocation system. It is the authors suggestion that an interactive relationship between managing agent and local fishermen should be developed, such that fishing licenses be issued under the condition of reporting previous fishing records from the latter. Developments of such relationship are beyond the scope of this paper and can be referred to [

2) Exploitation of fish population dynamic based on the spreadsheet platform

We begin the theoretical analysis by neglecting the traditional assumption of maximum sustainable yield (MSY) and go directly to the short-term target of total allowable catch (TAC) of the local fishing grids. The first step is to prepare the primary data sheet for one single calendar year in

In fish population biology, we have:

Z = M + F

Whereas Z, M & F stand for instantaneous total-, natural- and fishing-mortality coefficients respectively, and for value of F is

F = q × f

Which is the product of (unknown) catchability coefficient (q), and fishing effort (f) in

From traditional analysis such as Chapter 4 of [

Thus, we have F equals to q times f (F = q∙f) for each individual cell in

Y = F ⋅ B ,

where Y stand for fishing yield in weight (from the catch record) and B is the unknown biomass in each cell. Thus,

B = Y / F

The total biomass of the entire fish population during that special year is the grand sum of B over all cells.

It is expected that with annual catch record provided, a series of total biomass will be achieved. This gives rise to the theoretical base for the estimation of total allowable catch (TAC) for the manager. Estimation of maximum economic yield (MEY) can be achieved with marketing value of the fish available. During the above approach, assumptions on a balanced population, or maximum sustainable yield (MSY) will no longer be required. And fishery management moves toward more realistic considerations.

3) Transformation and integration of fishing effort data

In geographic information system (GIS) analysis, spatial interpolation is done mostly by calibration along a straight line between specific two points nearby. This method is not adequate here when, considering the cell values (number of days of fishing annually) fluctuate between fishing and are different from on solid landscape. Here we use CA operation to interpolate neighboring values of every cell. By taking moving average continuously for indefinite steps of time

until most values (say, 95% or more) of all cells were occupied [

4) Theoretical distances between fishing harbors.

Innovations and discussions

We changed the formula of interpolation on

X ′ i j = X i j + p 1 [ X i + 1 , j ] + p 2 [ X i − 1 , j ] + p 3 [ X i , j + 1 ] + p 4 [ X i , j − 1 ] 5

Whereas p_{1}, p_{2}, p_{3} and p_{4} are the weighting factor for each cell respectively. It is a more general form than the formula in _{1} = p_{2} = p_{3} = p_{4} = 1. The values of the p’s were to be assigned manually and the resulted value of (X’) would be different. The sum of all p’s can be equal to one. One example is the simulation of mullet migration to the direction of south-west along north-western coast of Taiwan, the use of empirical p-values has shown preliminary successful results. If the sum of all p’s is less than one, grid values become less and less. A CA model was constructed for demonstrating oil pollution impact (for educational purpose [

This spreadsheet model also seems suitable for the design of marine protected area (MPA) zonation and monitoring system. These new developments yet to be exploited.

The technique of CA and application has been well-developed and documented as in [

Large part of the results in this report was funded by the Council of Agriculture (COA), Chinese Taipei, between 2002 to 2004. Thanks to Shu Chia-chin, who was my graduate student in the Institute of Marine Biology, National Sun Yat-sen University, for computer data processing to create the spreadsheet maps.

The author declares no conflicts of interest regarding the publication of this paper.

Fong, S.-C. (2019) Using Cellular Automata for Grid-Based Fishery Management. Agricultural Sciences, 10, 249-258. https://doi.org/10.4236/as.2019.103021