A total surface of the area

N number of strata in that area

Ai surface of the stratum i

Wi relative weight of the stratum i in the area

ni number of hauls in the stratum i

Ai,j surface trawled by the haul j in the stratum i

fi sampling fraction in the stratum i

xi,j measured value in the haul j

with and

It is possible to choice between two options. The first one is to calculate for each haul a value by surface unit and to average those values over all the hauls made in the stratum :

et

This estimate is unbiased but it is possible to reduce its variance. Actually, the surface covered by the trawl is large compared to the micro-distribution structures. Therefore, the variance of the catch is proportional to the covered surface. In other words, the number of individuals or the total weight by unit of surface, which can be considered as a CPUE, has a variance in 1/A_i,j (F. Gauthiez - IFREMER Nantes, to be published). It seems then more realistic, especially if the hauls are of different lengths, to get estimates using weighted least squares with the following formulae

The term (1- fi) could be neglected because fi is in general very small.

To know the surface actually covered by the trawl, it is indispensable to know both the real distance covered by it on the bottom and the horizontal opening of the trawl, either the door spread or the wing spread. The distance can be measured with enough accuracy by navigation devices such as GPS and, for example the wing spread by SCANMAR. Nevertheless some vessels participating in the survey did not have these equipments

The covered distance can be calculated by a simple algorithm (Annex 1) from the shooting and hauling positions. Obviously this computation gives correct results only if the course during the haul has been rectilinear. This has to be assumed, even if it was not the case but, to avoid too big errors, it is important to make as rectilinear courses as possible.

As far as the wing spread is concerned, the data available after the 1994 survey show that there is an obvious non linear relationship between the warp length and the trawl horizontal opening, at least for warp length less than around 500 meters. For longer warp lengths the wing spread stabilize around 17 meters. To take this relationship into account, it has been decided to fit a von Bertalanffy function to the data provided by France, Italy and Greece. The asymptotic relationship so obtained has been applied when the wing spread was unknown. It is as follow (with S = wing spread and L = warp length) :

These are calculated by stratum doing a simple sum of individuals caught by length class. For fish and cephalopods, the length class interval is 1 centimetre while it is 1 millimetre for crustaceans. For practical purpose, the span of these length frequencies has been limited to 100 length classes, i.e. 1 meter for fish and cephalopods and 10 cm for crustaceans. The total number caught in the strata is also calculated and this value is printed out together with the histograms.

The program to perform the above mentioned calculations has been written in standard FORTRAN 77 Microsoft® and run under MS-DOS®. The version to be used now is Version 3.0, dated 02/96. It needs four reference files and the three data files by country/area.

Two of them are common to all participants. The first one contains the list of species with their Rubbin code and scientific name (see Annex 2) ; it has been derived from the official LISTFM file used for the 1995 survey (506 species). Due to the rather small memory currently available under MS-DOS, it is not possible to extend it to much. Nevertheless, it is expected that computations will not be performed for new species added to the LISTFM file each year. However, if the user wants to run the program for one of these new species, it is possible to do it. In that case the user will be asked to give the scientific name of any species absent from the file. The file second contains only a list of species to be taken into account within a single run of the program. This file is normally limited to the 31 reference species but can be modified by any user following his own needs. The usual 31 species file is shown in Annex 3.

The two other files are peculiar to each participant in the survey. They contain respectively the list of the strata in each country/area with their respective surface and the list of the hauls with the stratum in which they have been made (see Annex 4 and Annex 5).

To correctly use the program, the user has to be sure that the file names comply with the following rules :

Examples (country : France, year 1995) :

4.3. Running the program

The user is asked to give the country code, the year and the area code (if any). Then the program asks if the user wants to make the calculation either for a single species or for some of them. In the first case the program asks the Rubbin code of the species and in the latter case the name of the file with those species. If a species is absent from the species reference file, the user has to give its scientific name.

Then the user has to choice whether he wants to calculate length frequencies or abundance indices. The possible indices are given in Annex 6. In the case of calculation of indices, an other choice is between full or reduced output. The user has to give one output file name for a full output and two for a reduced output.

The output file names are fixed : the first character is H, the following seven are the species Rubbin code, the two first of the extension are the country code and the last one is the second character of the area code. Example : Results for Merluccius merluccius, country Italy, area M3 : HMERLMER.IT3

The files are in CSV (comma separated values) format and can be easily imported into any spreadsheet. An example is given in Annex 7.

The output file names are free but it is recommended to use easy-to-remember names. The two types of file (full and reduced output) are simple ASCII files which can be easily imported into any word processor. The full output file contains two separate tables by area. The first one gives the detailed results by stratum and the second the results for the whole area, the shelf and the slope separately. In the case of a reduced output, the first file contains the same table as in the previous versions of the program giving the abundance index and its coefficient of variation by stratum and for the whole area and the second file contains a table giving index and coefficient of variation for the whole area, the shelf and the slope. Examples of these files are given in Annex 8 and Annex 9.

The INDMED program could obviously and quite easily been extended to other computations from the MEDITS data files. Being written in a standard and normalized language, its subroutines can been incorporated in new programs.

However some theoretical points could be raised. Is the calculated index relevant ? Is there a better index ? For the time being, the surfaces of the strata are estimated from maps following a ground plan. It could be better to try to estimate the actual surfaces by taking into account the various slopes. These question should be addressed to the Group of Co-ordination of the MEDITS program and/or to some of the Working Groups which have been set.