Instituto Español de Oceanografía
Centro Oceanográfico de Canarias
Santa-Cruz-de-Tenerife, Canary Islands (Spain)
26–30 July 1993

edited by

T. Do Chi
Fishery Resources Officer
Marine Resources Service
Fishery Resources and Environment Division

FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS

1. INTRODUCTION

The CECAF Workshop on the application of traditional and recent methods for evaluation based on trawl surveys was held at the Centro Oceanografico de Canarias of the Spanish Institute of Oceanography, Santa-Cruz-de-Tenerife from 26 to 30 July 1993 at the kind invitation of the Government of the Kingdom of Spain. The Workshop was convened following a recommendation of the Twelfth Session of CECAF (Accra, Ghana, 27 April-1 May 1992).

The opening ceremony was performed by Madame M.T.G. Santamaria, Acting Director of the Centro Oceanografico de Canarias, who welcomed participants on behalf of the Director of the Spanish Institute of Oceanography.

Twenty-eight experts from fourteen coastal States, consultants from France (Dr. P. Petitgas), Norway (Dr. T. Stromme) and Spain (Drs. L.J. Lopez Abellan and J. Ariz Tellerias) as well as experts from FAO participated in the Workshop (Annex 1).

2. ACTIONS AND OBJECTIVES OF THE WORKSHOP

The workshop noted that the exploitation of the West African coasts and waters started in the nineteenth century. However, intensification of the work leading to the assessment of the resources of the region by research vessels using trawl (and acoustic) surveys is recent and is related to the provision of advice for management of marine resources. It requires monitoring of the resources and assessing of the effects of fishing on the stocks by providing quantitative measures of the fluctuations in relative abundance and structure (age and length) of the stocks. These measures complement those obtained from commercial catches which frequently have shortcomings in accuracy as indicators of stock abundance and recruiting year-class sizes.

The workshop also noted that three workshops were organized in the region on the same subject:

1. Course on statistics and sampling (ICCAT/ICSEAF/CECAF), April-May 1978, Tenerife;

2. Acoustic methods for fish detection and abundance estimation (TF/RAF/106/NOR), June-July 1978, Casablanca;

3. Training course on acoustic and trawling surveys (CECAF, INT/79/019 and MOR/78/018), June 1980, Casablanca,

which provided the background knowledge and application in the design and operation of surveys for assessment of the fishery resources.

Reviews of the theory are given e.g. Gulland (1975), Saville (1977), Troadec (1980), Doubleday (1980), Grosslein and Laurec (1982), Fogarty (1985). These reviews also give guidelines for planning, design, data collection, data recording, analysis and reporting of surveys.

As a follow-up, the objectives of the present workshop were therefore to provide:

1. (i) a short account of the theory necessary to perform stock assessment based on trawl survey data (paragraph 3);

2. an overview of demersal trawl survey planning (paragraph 3) and guidelines for data recording and for field work (paragraph 4);

3. applicátion and comparison of standard and geostatistical methods in relation to fish survey data (paragraph 5).

An introduction to demersal trawl surveys and to standard and geostatistical methods was given.

Emphasis was placed on the issues related to logging, editing, processing and analysis of scientific trawl survey data (trawl-catch data and length-frequency data). In order to ensure the fullest use of survey data, it is essential that flexibility of analysis be achieved by the use of computers. Thus, selection of subsets for analysis and complex mathematical manipulation can be carried out with high accuracy and low cost. The creation of a survey data base also permits their use for future special studies. Exercises were performed using NAN-SIS (Survey Information System), a general PC data base system developed by the R/V Dr.F. NANSEN Programme (NORAD/FAO) for scientific fishery research surveys.

Geostatistical methods, which are commonly used for ore-reserve estimation in the mining industry, were also used by participants for analyzing bottom trawl surveys as traditional methods do not take into account the spatial structure of the stocks and the autocorrelation between close samples. Examples of problems currently encountered in fishery resources surveys, e.g., those related to the estimation of the mean density or the mean catch (either in weight or in numbers), use of a random or regular grid for selection of trawling stations, spatial structure, mapping fish density, etc. Which can thus be solved using geostatistical techniques, were presented to the workshop.

With the assistance of the trainers/lecturers, participants processed survey data on PCs, using NAN-SIS and EVA software provided to the workshop. Sets of real data were made available to the participants on hard-copy and on diskettes. These data concerned trawl surveys carried out on demersal resources of the continental shelf off West Africa. The workshop aimed at answering questions related to fishery surveys, by comparing methods used for processing and analyzing data collected in order to map and assess the stocks.

3. INTRODUCTION TO DEMERSAL TRAWL SURVEYS¹

The present chapter does not seek to provide an detailed discussion of all issues relating to trawl surveys, but rather focuses on their most relevant aspects.

The acceptability of this type of operation has fluctuated over the years in tandem with changing techniques. Working on the assumption that any carefully planned and well conducted study is valid, and that there is always room for improvement, the usefulness of a result ultimately depends on how it is interpreted and used.

While the results of trawl surveys may not provide the whole truth, they can furnish data that cannot be acquired by any other means. Broadly speaking they can determine not just the relative size of a fish population, but also its components and where and when it was found and these data should cover the whole stock rather than just the fraction caught ordinarily, as occurs with data obtained from commercial fishing activity. Such surveys can thus play a key role in monitoring the distribution and relative abundance of marine populations. Moreover, surveys can be closely controlled, using standardized methods and selecting the target areas - which may cover the range of the relevant stocks.

There is a range of literature describing trawl survey methodology. The present authors have drawn mainly on the works of Ulltang (1977), Saville (1978), Bazigos (1980), Doubleday (1981), Grosslein and Laurec (1982), Sissenwine et al. (1983), Fogarty (1985), and Sparre et al. (1989), which give a good idea of both specific and general aspects of trawl surveys. Additional methodology has been taken from Cochran (1971) and Laurec and Le Guen (1981).

The paragraphs which follow consider the traditional aspects of trawl surveys. However, the methods are evolving. For example, at present, trawl survey research focuses on:

• new techniques for data analysis and the estimation of abundance indices using space-based models;

• the planning and precision of surveys, the interaction between resource and sample distribution, the relation between stratification and the target species and post-stratification procedures;

• standardization of survey operations, and gear and vessel calibration.

¹ by L.J. Lopez Abellan and J. Ariz Tellerias, IEO, Centro Oceanográfico de Canarias, Santa-Cruz-de-Tenerife, Spain

3.1 Survey objectives

Trawl surveys can have a variety of objectives, all of them designed to improve information on the biology and dynamics of marine populations currently being fished or liable to be fished in the future.

Survey objectives will depend, to a large extent, on whether a stock is being exploited and on the quality and quantity of available information concerning that stock. Given the wide range of possibilities that may arise, it is not feasible for a single survey to achieve all the objectives at once. Accordingly, the first step in planning a trawl survey is to establish clear, attainable primary objectives, distinguishing these from secondary objectives.

The planning of a survey of a virgin stock about which little is known should use a different approach to that of a partially, or well known stock. As general objectives, the survey may seek to ascertain:

• the species found in a given area;
• their seasonal and spatial distribution;
• population structure, and some of its biological characteristics;
• potential yield;
• absolute abundance, in terms of fish numbers and biomass;
• the most suitable fishing methods;
• annual sustainable stock production.

In addition to these primary objectives, trawl surveys may provide information on the biology and dynamics of the target species. The catch per haul can be used to obtain information on the relative abundance (weight or number of fish caught in a certain trawling time or area), depth-related distribution of the target species and by-catch, size-weight ratio, sex ratios, maturity, fat content, parasites, morphometric characteristics (gillrakers, etc.), nature of stomach contents, collection of hard parts to be used to determine age (bones, scales, otoliths, statoliths and vertebrae), presence of other fauna, etc. Another important aspect is the possibility of relating data obtained in each sample to the environmental parameters prevailing at that site (e.g., temperature, salinity, dissolved oxygen, nutrients, current, wind, etc.) or to the bottom type.

At the same time, the objectives should relate to the means available, i.e., a research vessel with a large scientific staff may collect oceanographic data that a commercial vessel with limited equipment and few scientific staff is unable to collect.

3.2 Defining the study area - period and frequency of surveys

Once the target species and survey objectives have been decided, the next step is to define the sampling area so that it fits within the general framework of the survey. The choice of the sampling area will depend on the geographical and bathymetric distribution of the stocks, as the survey area should contain all or a desired fraction of the stocks to be surveyed.

A single survey provides a “sample” of the situation at a given moment which cannot be extrapolated to other seasons or to the whole year. However, a series of survey operations conducted over several years using the same methods and sampling in different seasons will provide a “view” of the evaluation of the stocks and their distribution.

The frequency of the surveys may vary depending on their objectives and the variability of the stocks being studied; different sampling patterns may be established, varying between each cruise.

The need for standardization of methods in long-term surveys means that samples must be taken at the same time of the year, to minimize possible distortions caused by seasonal variations though information on intra-annual variation can be of great interest. Similarly, given possible stock variability, the surveys should be repeated in subsequent years in order to identify changes in stock over time.

Since many marine species migrate annually, their distribution and availability can vary greatly. If knowledge of the target stocks permits, the surveys should be conducted when the stocks are least mobile.

3.3 Choice of gear and factors affecting catches

The choice of gear to be used for sampling will depend on the stocks being surveyed. Although trawls are perhaps the least selective type of gear catching most fish in their path, various factors nevertheless affect their selectivity. The relevant technical characteristics are:

• the material used for the net, as buoyancy and rigidity will vary with different types of material (nylon, polyamide, blend of materials, etc.);

• number, size and distribution of floats on the headrope (which determine the vertical opening);

• number, weight and arrangement of weights on the footrope (which increase penetration in sandy or muddy bottoms);

• size, shape and weight of otter boards (which affect the horizontal opening);

• length and weight of the bridles, length of the spreaders, size and shape of the spreader bars, etc.

Generally, all factors that affect the construction and operation of the gear will affect its selectivity. Other relevant factors include: trawling speed, direction of trawl (at a constant depth, or increasing or decreasing depth), and trawling times (day or night, or over 24-hour periods), strength and direction of current, etc.

The codend of the gear allows fish to escape in inverse relation to size, i.e. larger fish are retained but an increasing proportion of smaller fish may escape. Other factors also play a part, notably filling of the codend when catch is very abundant. If this happens, few of the fish caught will escape. One way of preventing this is to trawl for the minimum period needed to obtain a sample (usually half an hour to one hour).

If the aim is to make the net less selective or totally non-selective, one must use either a 10 to 20 mm codend liner or cover the codend with an extra bag to catch fish which escape.

If the survey is repeated at other times of year or in subsequent years, the same gear and rigging should be used, and the characteristics of the fishing operations must be firmly established in order to minimize biases. If the survey involves several vessels with different gears, or a vessel with more than one type of gear, it must be ensured that the data collected from each vessel and/or gear are comparable. To do this, comparative fishing should be carried out at the same station, keeping all relevant factors (depth, speed, duration, etc.) constant in order to obtain valid conversion factors between gears and/or vessels.

These many factors make the choice and use of gear a key decision. Several international fishery resource management commissions work on the establishment of “standard” sampling methods for the different resources to standardize trawl surveys conducted within their jurisdictions.

3.4 Survey design

A statistical population is the total number of individuals, within a clearly defined, spatially and temporally limited sampling area, from which inferences are drawn by means of samples taken from the population. To obtain good estimates, the sample and the sampling method must fulfil certain requirements.

The statistical parameters which the samples and sampling scheme are to estimate are usually the arithmetic mean and the variance, or equally, the standard deviation.

The distribution of marine species can follow three basic types of spatial distributions:

-   random distribution (variance = mean): there is an equal chance of an individual occupying any point in an area of bottom and the presence of an individual does not influence the position of a nearby individual. The striking feature of a random distribution is the lack of any system; some individuals occur in groups and others are equally spaced; some individuals are very close together and others are very far apart.

-   regular distribution (under-dispersion, or uniform distribution, or even distribution): the dispersion of a population is regular when the individuals are relatively crowded and move away from each other. Under these conditions, the number of individuals per sampling unit approaches the maximum possible (variance < mean), and the positive binomial is an approximate mathematical model. The characteristic feature of a regular distribution is the uniform spacing of the individuals in the population.

-   contagious distribution (= over-dispersion, or clumped distribution, or aggregated distribution): the spatial dispersion of a population is seldom random or regular, but is frequently contagious (variance > mean). There are always definite clumps or patches of individuals in a contagious distribution, but the final pattern varies considerably. Therefore, there are diverse patterns of contagious distributions and the negative binomial is probably the most useful of mathematical models which can be applied to a wide range of dispersion patterns.

Three main types of sampling schemes may be used in trawl surveys, depending on the survey objectives:

-   systematic sampling: this entails taking samples at regular intervals. It is used to ensure coverage of the entire distribution area of the species and to determine areas of discontinuity, or to carry out regular monitoring of relative abundance indices. Since the sampling points are not selected randomly, estimates of biomass must be treated with caution. This is the best method for mapping a resource.

-   simple random sampling: once the sampling area and the number of samples to be taken have been decided, the position of the sampling stations are selected at random, giving equal probability to all possible sites. Population estimates will be unbiased.

-   stratified random sampling: this involves identifying aspects of the sampling area which might affect stock distribution and hence abundance. Homogeneous strata are established in the light of this aspect (abundance, depth, latitude, etc.). This homogeneity reduces the variability of the values obtained in each stratum, so that greater precision is obtained than with random sampling. The data collected in each stratum are then combined, taking account of the size of each stratum, to obtain the desired population estimates. When planning a survey using this type of sampling, one must decide on the target species before establishing the strata, as stratification is unlikely to cater for the spatial distribution of several species at once. The precision of the estimates will depend on how closely the spatial distribution of stocks coincides with that of the strata.

On board sampling: organization of work on board research vessels and commercial vessels conducting a survey differs little, although some considerations will affect the choice of which type of vessel should be used. Commercial vessels are usually more efficient at fishing than research vessels, but the lay-out of commercial vessels may cause problems for use of specialized equipment. Commercial vessels often cannot accommodate a large number of scientists which may limit the number of cruise objectives. Research vessels, on the other hand, have more space and more sophisticated measuring equipment, and can house more scientists. Whichever type of vessel is used, duties must be carefully organized in the light of the number of participants and the objectives pursued, to make the sampling as effective as possible.

Before the start of the survey, one must decide exactly how the data collected at sea are to be recorded. The record sheets must cover fishing operations, catch sampling, size sampling, biological sampling, and environmental data.

The units of measurement for the variables to be studied must be precisely defined. Bearing in mind the species and the norms laid down by the fisheries bodies in the particular area, these will involve the establishing the manner of making measurements, e.g., fish length (total, fork, cephalothorax, carapace, mantle, etc.), accuracy of measurement(to the nearest cm, ½ cm, mm, to nearest unit, to nearest unit below), and weight (gram/kg).

The scientific staff must be clear about their tasks. A practical approach is to set up sampling teams with clearly defined jobs to do and a fixed place them, bearing in mind that such teams are unlikely to reach maximum output in the first few days of operation. The daily sampling load should therefore be increased gradually in order to get the system operative without initial errors which could affect species identification; this will also ensure that lack of time between hauls does not mean that data go unrecorded.

The time spent reaching the sampling stations (where the hauls will be taken) should be reduced to a minimum, so that the sea time available is used most profitably and more sampling operations can be conducted. This is the joint responsibility of the chief scientist and the vessel's captain. They should scrutinize the cruise programme before the start of the survey and discuss the each day's work programme throughout the trip. They should agree on a substitution system for stations that cannot be sampled (e.g., bottoms which cannot be trawled).

Work on board, from one haul to the next, will involve the following stages:

-   the haul itself:

• starting position and tack of the gear;
• initial and final depth of the trawl;
• trawl time;
• direction;
• other.

-   catch sampling: the purpose of the trawls is to obtain a sample of the species found in the area in sufficient quantity to determine their relative and absolute abundance. If the sample is large, it may not be possible to examine it all, and a sub-sample should be taken. In this case, all the larger fish and species of special interest should be picked out.

The related work will involve identifying the species, counting and weighing them, and sorting them for further study:

-   Size sampling: this is done with random samples of the target species, using the chosen measurement method. Where possible (e.g. for crustaceans), species should be separated by sex. The size distribution obtained will correspond with the total catch of the species.

-   Biological sampling: the samples used in biological studies must cover the size range present according to a predetermined rate (for example, 10 fish at 1 or ½ cm intervals). The data to be obtained will include:

• individual length and other measurements;
• individual weight;
• sex;
• sexual maturity;
• collection of hard parts (otoliths, scales, statoliths, bones, etc.);
• extraction and conservation of gonads;
• extraction and conservation of stomachs.

-   Sample collections and conservation: it is generally useful to make photographic collections of the species caught. It may be required to preserve them, either in formalin or frozen, for further study. Samples can also be taken for use in laboratory studies ashore.

3.5 Data analysis and validation

The data collected on the different forms or record sheets (fishing operations and catch results, biological data, oceanographical conditions and types of bottom, weather conditions, etc.) for each trawl undergo several stages of processing. Ideally - and this is increasingly common - data processing facilities may exist on board, and portable computers can be installed on commercial vessels being used for research. The next step is thus to process the data and store it electronically.

It may be necessary to prepare the raw data for automatic processing, although the normal practice is to use procedures which carry out the intermediate calculations, so that manual processing is not necessary. Some data bases are designed for specific cases and are used only for certain types of study or geographical areas, while others are designed for more general use and can be adapted to different needs. The general aim of all these applications is to generate a series of output data which present the results in the light of the relevant objectives.

Onboard data processing is a further step in processing that can provide a preliminary idea of the findings. However, the work does not end here, and time must be allowed for research centres to complete data processing and analyze the findings, and to start parallel studies with additional information gleaned from the research programme.

Checks must be made at different stages of the process in order to ensure that the data used in the analyses are valid. The first check should come after each haul, to ensure that the haul is valid in terms of trawl time, position of the gear on the sea bottom, lack of gear damage, etc. A second check should be made when processing the data to establish likely value ranges. A third check would ascertain that the data processed on the computer correspond with those contained in the written records of each haul. Similarly, the computer applications should include procedures for tracing errors during entry. Finally, experience and common sense are important for checking the information obtained.

3.6 Estimation of biomass and cartography

Biomass is estimated by extrapolating to the survey area the values obtained in catches, according to the sampling scheme used (e.g. simple random or stratified random). The basic sampling unit is the haul, so it is necessary to know the horizontal opening of the gear, trawl speed, duration of the tow, and catch.

The swept area is the product of the duration of the tow multiplied by the trawl speed and by the horizontal opening of the gear. The same units of time (e.g. hours) must be used to measure both duration and speed, and the spatial units used to measure horizontal opening and speed must also be the same (square nautical miles, square metres, etc.). The values per haul will be expressed in terms of number or weight of fish per surface unit (density). By adding together all the hauls made in the same stratum one can calculate the relative biomass and abundance values for that stratum. Combining the values obtained in the various strata will yield the biomass for the survey area.

Haul densities represent the relative abundance or biomass, since the gear does not catch all fishes in the swept area because of varying vulnerability of fish. The vulnerability of a population is the probability of a fish (or fraction of a stock) encountered by the gear that is retained. If all fish encountered are caught, their vulnerability = 1. The vulnerability of fish of different ages or sizes will depend partly on the selectivity of the gear. The availability of a stock is that proportion that is accessible to the gear. For example, if half of the stock stays in rocky bottoms, then the availability to a trawl will be 0.5. These factors can depend on season, age, etc.

If enough data are available to carry out a Virtual Population Analysis (VPA) for a stock, a relation can be established between the abundance obtained from surveys and the (absolute) abundance estimates given by analytic models. In this way one can obtain transformation factors for the biomass estimated by direct methods.

The estimate of the relative average biomass or total biomass of an area is that which applies to the overall area. Cartography is necessary to analyze biomass distribution within the survey area. This is done by taking the haul as the basic value and using various techniques to calculate, by interpolation, the values in a predetermined grid covering the whole study area. By joining together the points of equal value by isolines, one can obtain a picture of the spatial distribution of abundance.

Fisheries management (e.g. protection of areas or of fractions of population) will require utilization of data obtained from surveys for mapping the demersal resources. This is not only necessary for determining the geographical distribution of fish abundance but also for mapping spawning grounds, recruitment area, etc.

3.7 Precision of biomass estimates

Estimates obtained from trawl surveys are affected by two types of error:

1. sampling error, due to variance between hauls;
2. systematic error or bias.

Sampling error affects the precision of the estimate, measured by the standard deviation of the statistics. Precision can be improved by increasing the number of hauls and/or the use of stratification to improve the precision with the same number of hauls, thus satisfying “maximum precision for fixed cost” survey objective. Stratification will depend on what is known about the spatial distribution of the target species and this will determine strata boundaries. By altering the stratification one may reduce the variance associated with spatial variability.

If a fixed degree of precision is required and knowing the sampling variance, the number of samples to be taken in each stratum or area can be defined prior to the survey.

3.8 Biased estimates

Estimates which are precise may not be unbiased. The degree of bias is independent of the number of samples and is a measure of the accuracy of the estimate, i.e. the difference between the estimated value and the population value.

The importance of bias depends on the use to which the estimator is put. It has less impact on the study of changes in relative abundance over time than it would on an estimate of absolute abundance. It is usually difficult to evaluate a bias or demonstrate its absence. Biases can only be discovered by comparing the results with others estimates obtained independently (e.g., VPA), although these too may be subject to sources of bias.

The sources of systematic error are:

• bias due to behaviour of the species studied;
• bias due to operation of the net;
• bias due to spatial distribution of the species in relation to the area and time of sampling.

These sources of error are linked to the efficiency of the gear and the vulnerability of the target species.

The proportion of fish caught in a given area by a given gear varies with the behaviour of each species. Relevant factors include their vertical distribution in the water and ability to escape. Behaviour may follow a regular pattern (e.g. daily, seasonal, migrational) or may be subject to less regular factors such as food availability or temperature which make behaviour more difficult to analyze.

To minimize effects of errors in estimates, changes in vulnerability and availability should be minimized in using standardized methods as regards vessel and gear used and the time of day and year when the hauls are to be made.

4. TRAWL SURVEYS AND USE OF DATA BASE SYSTEMS²

A scientific investigation typically entails the following steps:

1. Formulation of hypotheses, objectives.
2. Data collection.
3. Data validation.
4. Data structuring.
5. Analysis:

• descriptive analysis of patterns in data, estimates on present state (abundance, composition, etc.);
• analysis of correlations and trends;
• system analysis;
• theory formulation.

The creative part of this process is in a) and e), and this is where the scientist can use her/his creative capabilities to discover hidden relationships in nature. This is also the most interesting part of the process and the personal driving force of the scientist is usually curiosity, backed up by the society's need for applicable results. The analytical phase is also the common field for scientific working groups.

The main part of the labour in the scientific process is however in b), c) and d), i.e. in collection of data, their validation and structuring. This process usually consumes most of the time and economic resources available. In fisheries surveys data collection requires more than 90% of the economic resources available.

Often in fisheries science there is a tendency to forget the amount of work and discipline that is necessary to invest in the data collection process, in order to make a meaningful analysis possible. We all agree that the data collected must be representative, that they must be validated and that they must be structured in order to make conclusions about the state of a resource. But in working groups we often face the problem of incomplete, unrepresentative and unstructured data sets. There is a tendency-that scientist rather focalize on analytical part of the work and perhaps look away from the needs for proper data sets. Analytical models, sophisticated estimation tools such as geostatistics and GIS require solid, validated and ordered sets of data.

² by T. Stromme, Institute of Marine Research, Bergen, Norway

In fisheries science data collection is not a one time task. In order to monitor the stocks there is a need for a continuous and consistent program for data collection both from the fisheries and from independent survey programmes.

4.1 Why a data base system?

Data bases, on paper or computerized, are established in order to store, edit, sort and retrieve data in a systematic manner.

Until the early 1970s, fishery data analysis were usually a one time process. The hand-written data records were usually stored in files and the sorting of data was done manually by going through these files and making up tables with a specific objective in mind. With the introduction of mainframe computers most national research laboratories in the industrialized world had their capacity for analysis drastically improved, while smaller laboratories and institutes in the developing world still had to follow manual methods. With the spread of personal computers from the early 1980s, a new age in fisheries science started. Computing power could be available everywhere, even on board the research vessel, and with improved storing capacity in the computers, data base systems could be developed that could keep all the research data of an institution easily accessible. Data analysis ceased to be a one time task: data could easily be re-analysed with different options and parameters, the original data could be corrected and one could immediately see the new results. With the introduction of general data base systems, data collected for a specific purpose could easily be made available for analysis for other purposes, through interface systems.

In some laboratories, especially in developing countries, one can still see today that data collection and storing is left to the responsibility of the individual scientist, with the result that within an institution there are different storage formats such as home-made data files, commercial data bases, spreadsheet and even simple word processor files, used to store the data. It is clear that such a jungle of different formats does not make exchange of data easy. In order to take care of all data collected and to make them available for various purposes, all laboratories should have a reference database that is the responsibility of their institution to maintain. With the vast inflow of data that occurs today the only way to avoid chaos is to have such databases established as soon as possible. If not, one will remain at the level that science was in the 1960s when one time analysis of data was the common practice.

4.2 Different philosophies in data base systems

The main advantage of an electronic data base system is to make data quickly available for analysis. Such an analysis can be rigid or flexible (interactive) and the database system itself can be simple or comprehensive.

A rigid analysis system forces the analysis to follow a strict order and procedure, while a flexible system allows the scientist to compose her/his own analytical procedure.

A rigid system has the advantage that it forces untrained scientist into the most common types, and this is usually the safest way of analyzing a data set. On the other hand, a flexible system allows the scientist to play with options, giving possibilities for a more in-depth analysis, but at the same time one may try to pull more information from the data sets than they can contain. Flexible systems are more dependent upon the skills and experience of the scientist.

A simple data base system would basically be a unit for storing, editing and sorting data, with limited analytical powers, but with interfaces to various types of other analytical packages. Comprehensive systems will on the other hand have more developed analytical powers built into the system, and can more easily stand as self contained units. Simple database systems are easy to maintain and can easily link up to new software developments through interfaces, while the comprehensive systems are more vulnerable to the availability of expertise for servicing and development of the data base. In this context the survey information system used in the Nansen Programme (NAN-SIS), is a flexible system that allows the scientist to vary search routines and parameters interactively. NAN-SIS is not a comprehensive system and does not incorporate more sophisticated analytical tools as advanced statistical analyses and modelling. On the other hand, the system is open ended and allows export of raw data or data in preprocessed form to various other more specialized analytical packages.

4.3 The history of NAN-SIS

The NAN-SIS software package has been gradually developed in the course of the Dr. FRIDTJOF NANSEN research programme since the late 1970s. It developed from a critical need to have continued access to the data records as the mass of data stored was rapidly expanding. The history of this project may represent an important reference for younger institutions in fisheries research.

After the first four years since the beginning of the programme, as the amount of collected data grew and because of the need to access the data for further analysis, these were transferred onto electronic computers and specialized software for analysis was developed. This was in the late 1970s and then mainframes were mainly available at universities or governmental institutions. The data and the programs were entered onto punched cards, delivered to the computer centre and the printouts from the run were received one or two days later. Interactive use of computers was still a privilege for the very few. Some years later terminals were made available that could be connected to the mainframe through modems. This speeded up greatly the data entry and the analytical process, and it was possible to rerun programs with different parameters within a short time period, thus providing the scientist with a picture of patterns and spacial structures in the set of data, that could provide ideas for further analysis. This was the first step into the great advantage of interactive computing, where the scientist uses the computer to gradually develop his hypotheses by getting immediate feedback from the computer.

The next step in the development of NAN-SIS was the introduction of intelligent data terminals on board the vessel. These terminals had limited computing capabilities and allowed a limited data analysis to be carried out on board. The great step forward took place when the database and the software were transferred to the DOS-environment in 1987. Most of the analysis needed to make a survey report could now be done on board at the end of the survey. The last step that brought NAN-SIS to its present stage was the introduction of a menu-driven shell from which the various programs of the package could be run, without typing commands from DOS.

4.4 The main philosophy of NAN-SIS

The purpose of the package is to provide a PC-based database where data from fisheries surveys, particularly trawl surveys, can be stored for later retrieval, sorting, listing and analysis on different levels. These levels can be:

Species
Species genus
Species family
User defined species groups (commercial, non-commercial, etc.)
Seasons
Geographical sectors
Depth zones
Gear types
Fish densities
Purpose of the investigation (trawl survey, catch trials, etc.)
Surveys
Projects

The survey data are organized into projects, which typically incorporate a series of surveys from a country or region within a time frame that can be analyzed as a time series. A project is accessed through the so-called PROJECT CODE, a two character alpha-numerical code that opens all the files connected to a project. The database can contain as many projects as two-letter/symbol codes that can be used in DOS; this should be at the order of 40², that is about 1600 different projects. For practical reasons the projects seldom contain more than 2000 trawl stations, but by grouping projects together the database can serve the basic storage need of trawl survey data for most research institutions. For instance all trawl data collected in the course of 18 years of surveys with the R/V Dr. FRIDTJOF NANSEN are stored under 24 projects and can easily be stored in one PC hard disk.

The main objective of the software package associated with the database is to provide the necessary information to produce survey reports on the spot at the end of a survey and to provide a query system where specific information can be retrieved quickly.

The routines inside the package are mostly using simple arithmetics on sometimes a high number of arrays and matrices. Combined with an unusual quick retrieval system this makes a simple but powerful data base system. In brief, most of the programs apply various sorting routines based on set limits directed by the user. This is the type of sorting that 15 years ago had, in most cases, to be carried out manually on spreadsheet. With tools such as NAN-SIS, work that previously took days or even weeks, can be executed in seconds or minutes. For the type of analysis that cannot be carried out inside the package there are various export facilities where data can be routed to more advanced analytical tools.

4.5 The main function of NAN-SIS

The most common type of output from NAN-SIS would be:

For survey reports:

• Station lists with species and catch information, in order of sequence by-catch rate.
• Species list with reference to stations and catch rates.
• Tables with catch rates by user defined species groups, as target catch, by-catch, commercial species, etc.
• Frequency distribution of hauls by catch rate classes, depth zones, day/night hauls and gear types.
• Swept area estimates, by total species and species groups and by surveys, seasons, depth strata and user coded strata.
• Length frequency histograms. Single samples or pooled samples by seasons, depth strata, regions or user-defined groupings. The samples can be pooled using different weighting factors, of which the most common is the catch rate of the species.
• List of length frequency samples, in raw data form or in processed form (mean length, maximum and minimum length, condition factor).

For special studies:

• Inventory for a species of its occurrence, catch rates, maximum catch rates, depth distribution, seasonal fluctuations, etc.
• Co-occurrence tables that can show expected catch rates of by-catch species in targeted species fisheries.

Through the various export programs one can do other special analysis:

• Export to STATGRAPHICS provides additional descriptive statistics, analysis of variance, regression analysis, correlation analysis and various plots. By using the inbuilt APL functions as SELECT and the relational operators, one can retrieve virtually any combinations in the dataset for analysis.

• Export to CORNELL format (occurrence matrix in compressed form). Prepares a selected subset of catch data to be analyzed for community structures, i.e. pattern of recurring species groups or assemblages.

• Export to plotting packages, GIS (Geographical Information Systems) and geostatistical software. Plotters and GIS usually use coordinates in decimal form. This group of programs in NAN-SIS export catch data of selected species with coordinates in decimal form together with other parameters as depth and time of the day. Programs that may use this data are SURFER, IDRISI, GRASS, ARC-INFO, MAPVIEWER, GEO-EAS and EVA.

• Export of length data. Samples of length data can be exported to the LFSA format and further into ELEFAN. The new FiSAT program package from FAO/ICLARM has an import option where one can import the ASCII format of the length frequency data from NAN-SIS. In the sub-program that produces pooled length frequency histograms these frequency tables can be exported to files that can be used as input for cohort and modal progression analysis.

Other programs: NAS-SIS incorporates several programs that do not access the database but because they were useful in preparing survey reports, have been incorporated in the menu shell. Especially worth mentioning is a program that on the basis of a given biomass, a representative length frequency distribution and a lenght/weight relationship gives the biomass in number and weight by length classes. If cohort parameters on normal distributed cohorts are entered, the program will also give estimated biomass and numbers by cohorts. Cohort parameters are mean length and sigma in the assumed normal distributed cohort, together with the fraction the cohort makes up of the total number of fish in the population. These parameters can be obtained through various programs of which MIX (Analysis of Mixed Populations) is one of the most used.

Other features: it has been previously mentioned that before the actual analysis and reporting can take place, various steps have to be undertaken, i.e. data collection, data entry and ordering and data validation. NAS-SIS contains a lot of inbuilt validation routines to check that the data are within expected range both during the entry and editing phase as well as during several of the programs that produce lists and summary statistics. For instance, if a mean body weight in a length sample differs from the mean body weight in the catch record to which it belongs, a warning is given.

4.6 NAN-SIS and geostatistical analysis

An introduction to geostatistics was given during the workshop as well as its applicability to trawl surveys, and the imminent issue of geostatistical package EVA (Estimation of Variance) was announced. This package has since been issued and the Nansen Programme has prepared an export routine that format the data for analysis by EVA. Below follows a description on how to get NAN-SIS data into EVA:

1. Copy the program file EVA.RUN into your NAN-SIS directory.

2. If “Export to EVA” is not in the NAN-SIS menu, select the option “Run Program” under the “Util.” option in the main menu. At “Enter Program Name” key EVA <Enter> and the export program starts.

3. The program menu allows selection of species by species codes and those stations one wants to include. The export menu also gives the possibility to group several species together under one group.

4. The data are exported to an ASCII file, that the user is asked to name. This file is then imported into an EXCEL spreadsheet. This is done by starting EXCEL from WINDOWS, then choose Open File in the File menu and point at the ASCII file you have just stored from the EVA-export programme in NAN-SIS. Once the data are in the spreadsheet you start EVA without exiting EXCEL. You then copy the data from EXCEL to EVA by highlighting a data series (one column in the spreadsheet) and by using the WINDOWS based Copy and Paste functions in the Edit menu. This is also explained in the EVA documentation.

4.7 Importing data into NAN-SIS

On several occasions there have been requests on how to import into NAN-SIS trawl survey data that already are on computer format. The main menu gives access to two sub-programs that will import ASCII data, if they are given in a special format, which will be described below. In the file structure of NAN-SIS, the data have to be split into two files, one containing station reference data and the other the species catch records. To make use of the sorting mechanism in NAN-SIS, the species names must be coded following the system described in the NAN-SIS manual. Both files must be of fixed record length, the station file must have a length of exactly 109 characters, of which the two last ones are the ASCII characters CR and LF to facilitate readability and possible direct editing. Likewise the fish record file must have a record length of 40 characters, including CR and LF.³ When the data files are ready for input, the record length can be checked by dividing the size of the file (obtained by DIR command of DOS) with the record lenght. If the file is correct, an integer number should be the result. You may now import the data into a NANSIS data file with a project code. If this file does not exist you must create the new project files before you do the import. If the files already exist and contain data the new will be added to the old. In the menu you can initialize the files in which case all old data will be deleted before the new are imported. The description of the mandatory format of the ASCII files that can be imported is given as follows:

³ If your version of the NAN-SIS shows another record length other than 40 in the entry screen for the import of fish record data, you have by mistake received an obsolete version of the program. Then, please contact the Nansen Programme at IMR, Bergen for an updated version.

Structure of the flat ASCII files from the Nansen database.

Station file: 109 characters, including CRLF
Example:
      10       20       30       40       50       60       70       80
1234567890123456789012345678901234567890123456789012345678901234567890123 4567890
WA     1    1OA81    4301235N2040W 171431PT11235 3029862987    16 39 36 39 39 90 200

      90       100       110
123456789012345678901234567890
301^*       55       1732       3464

Structure of the flat ASCII FISH data files from the Nansen database.

Record length 40 including CR and LF Example:     10     20     30     40
1234567890123456789012345678901234567890
1WA00000ANGAA00   31.50   64   M

Structure of the fish species catalogue.

Record length: 95 including CR LF
Example:
    10     20     30     40     50     60     70     80
1234567890123456789012345678901234567890123456789012345678901234567890123 4567890
BALBA01Balistes capriscus       Grey triggerfish       Baliste cabri

      90       100
12345678901234567890
      20       45

An import program for fish catalogue data is not accessible in the menu but can be started from the start program option in the Util block. In the main menu the programme name is SPECIMP. The data file to import must be named SPECCAT (no extension) and must be stored in a directory called C:\PASCAL\LOG\ that you must create for the occasion.

5. PRESENTATION OF THE GEOSTATISTICS METHOD

Geostatistics is an application of probability theory to estimate statistics relating to spatial variables. Spatial distributions (regionalization) generally have two aspects: one structured, the other complex and erratic. Geostatistics is done in two stages. First, the structural analysis characterizes the different aspects of the spatial distribution. During this stage, a model is chosen to interpret the data. The second stage involves using the model to derive the estimates.

The structural analysis is the cornerstone of the method. During this stage the scientist characterizes the observed variable on the basis of data properties. The spatial structure model describes the average correlation between two points in space, regardless of their specific geographic position. The model choice provides a physical interpretation of reality. While the data only provide a fragmentary indication of reality, our objective is to characterize this reality, not the data. The move from the description of data to the description of reality involves estimating an average, and hence the use of a probability approach.

The second phase, estimation, uses a computerized mathematical algorithm. The estimates depend on the model chosen, but similar models give comparable results.

5.1 Structural analysis - The Variogram

The spatial distribution of fish density can be represented as a complex density surface. The variogram is a useful tool to describe the structural properties of this surface.

The variogram measures the level of dissimilarity between points as a function of the distance between them. The variogram is formally equivalent to a variance. If the variogram increases as the distance increases, then closer points are more similar than more distant points and therefore there is spatial structuring; If, the variogram is flat, then close points have as different values as distant ones and therefore there is no spatial structuring. The variogram can be calculated along several directions to highlight structural anisotropies.

There are three types of variogram: the regional variogram, the experimental variogram and the model variogram. The regional variogram is the variogram function that would be obtained if we knew all values of the surface under study. This is the variogram of interest as it characterizes the real regionalization. The experimental variogram is the estimate of the regional variogram, the function that we calculate from the data. It can always be calculated and provides information about the structure. The model variogram is a probability interpretation characterizing two major types of structural properties: (1) the behaviour of the model for short distances indicates the roughness of the density surface (small scale irregularity); and (2) the behaviour over larger distances indicates the size of patches (range of correlation).

Modelling is based on probability interpretation. Consider a density surface sampled at a given time with a given sampling grid. Later, new samples are taken at the same grid of points. The underlying phenomenon is the same each time, but the values will have changed. The density surface that has been sampled is interpreted as one of the outcomes of a random function which characterizes the underlying phenomenon. The difference between the sample and the model is similar to that of a result of a simulation and the model.

The procedures for calculating variograms are given by Matheron (1971), Journel et al. (1978) and Armstrong et al. (1992). The main points are summarized below.

5.1.1 The Experimental Variogram

The variogram measures the mean square value of the difference between two separate points at vectorial distance h. The computation can be performed as follows. Take two sample points. Compute the norm and the direction of the vector they define. Also compute the square of the difference between their values, c². Repeat this for all pairs successively. Doing so, group the directions in angle classes and for each angle class group the norms in distance classes. For each distance class of each direction class, compute the average of the c² values and divide by two. The variogram has so been calculated as a function of distance and direction. The classes are selected so as to calculate the average c² from a sufficient number of pairs.

with f(x_i) = value measured in x_i, n(u,h) = number of sample pairs for direction u and distance h.

We define the angle classes by selecting an angle and tolerance (±tolu) around this angle. Let u be the selected angle and tolu, the tolerance. From each sample, x, each other sample, y, will be used to calculate the variogram in direction u if the point y is located in the mapping sector centred on x defined by

]u-tolu,u+tolu]   and by   [u+π-tolu,u+π+tolu[.

We define the distance classes by choosing a lag p and a tolerance, ±tola, around it. The variogram is calculated for n successive lags. Class i includes all the distances belonging to the interval ]ip-tolp,ip+tolp]. The variogram values are given for the successive distances i. The variogram at the origin (h=0) can be estimated by considering an extra distance class ]O,tolp] in the calculation.

5.1.2 Variogram models

The models currently used (Journel et al. 1978) describe physical properties of the spatial distributions. These properties are characterized by the behaviour of the variogram at short distances (i.e. at the origin for h=0) and at large distances to show whether or not there is a sill.

The existence of a sill means that there is a maximum level of heterogeneity. Theoretically, this means that the random function model has a variance, measured by the sill. The sill is not always equal to the variance shown by the function over a given zone.

The sill is associated with another parameter, the range, which is the distance at which the sill is reached. Two points separated by a distance greater than the range are independent while closer points are correlated. The range gives a quantitative measurement of the “Zone of influence”. In general terms, it is the average diameter of aggregates.

Models without sills relate to random functions without variance (infinite variance): the greater the distance, the greater the variance between the points, without limit. However, we can always calculate the variance for a given zone if we know the variogram. This is the average of the variogram for the distances applied to the surface.

Near the origin, the behaviour of the variogram model will indicate the degree of irregularity. Vertical tangent behaviour indicates very high irregularity while horizontal tangent behaviour indicates great regularity. Between the two, the linear behaviours indicate “medium” irregularity.

The nugget is a discontinuity with amplitude C₀ at the origin on the variogram (γ(0)=0;γ(h)=C₀>0 as soon as h>0). It is a random component of the spatial distribution with variance C₀. The nugget has three physical interpretations which are in practice inseparable. These are (1) a purely random component of the regionalization and/or (2) a measurement error and/or (3) a sum of structures which have ranges smaller than the sampling mesh grid.

The model choice is an act of characterization: we insert in the model our impressions of the underlying phenomenon. We select a type of model for its properties at large and small distances, which is why the uer generally has to select his model, then its parameters. Automatic fits are not recommended.

The common models and their physical properties are listed in Table 1.

Table 1

Variogram models and their physical characteristics

A model can be the sum of different nested models.

5.1.3 Anisotropies

Some regionalizations show anisotropic structures. Anisotropy means that not all spatial directions are equivalent in their characteristics. An anisotropic variogram has different characteristics in different directions. Journel et al. (1978) consider two types of anisotropy, geometric and zonal, with reference to the models with sills.

In geometric anisotropy models, the sill is the same in all directions but the range varies elliptically according to direction; i.e., all directions are equally non-homogeneous, but the shape of the aggregates is elliptical rather than circular as in an isotropic case. With zonal anisotropy, the variance of the function (i.e. the sill) is a function of direction, i.e., the phenomenon is more heterogeneous in certain directions. The two anisotropies can be combined.

Geometric anisotropy is characterized by an angle of rotation and has an anisotropic coefficient (X) for the direction of anisotropy, and a (Y) coefficient for the perpendicular direction. The angle defines the rotation needed to bring the abscissa axis onto the major (or smaller) axis of the ellipse of the ranges. The coefficients indicate the expansion or contraction needed on the major and minor ellipse axes to change the ellipse into a circle. For example, suppose that in direction 45° the range is twice that in the perpendicular direction, then the rotation is 45° and the coefficients are: 1 for X and 2 for Y, or equivalently 0.5 for X and 1 for Y.

Zonal anisotropy is modelled by a nested structure model. There is one model less in one direction. This is done by cancelling the anisotropic coefficient in this direction. To avoid abrupt discontinuities, it is preferable to avoid models made up of two nested models where each is only valid in one sector. Journel et al. (1978) recommend using a model where neither X nor Y are zero and to adding other models where either X or Y is zero.

5.2 Use of the variogram - Calculation of variances

The variance between values is a function of their autocorrelation. Thus the variance of the density surface can be computed in any given area by using the variogram and the geostatistics formulae. The variance is always computed over a given area and will depend on the dimensions of the area as well as on the variogram model. Matheron (1971) distinguishes two types of variance: the dispersion variance and the estimation variance.

The dispersion variance for a given zone, V, is the variance of all the values of the density surface found in V. It is a theoretical value given by the model for zone V. It is the variance of the random function over zone V. It equals the average of the variogram

for all the distances in V and is denoted γ_vv.

γ_vv can also be estimated by a set of n random samples, z_i in V, by the usual formula

The estimation variance is the variance of the error between the zone mean and the estimated value. It is a variance of interpolation. This can be represented as follows. Suppose that we undertake repeated surveys during a season, at the same sample points, in the same zone. Each survey provides a spatial distribution of densities but the underlying phenomenon generating these is considered the same during the season. We therefore have the same model and the spatial distribution for each survey corresponds to an outcomes of the same underlying process. The real value for the zone varies somewhat for each survey, as the density values for each outcome vary. We therefore make an error between the real zone value and the estimated value at each survey. The estimation variance is the variance of these errors.

The estimation variance is expressed as a function of the variogram. Supposing we estimate the mean for zone V and that the chosen estimator is the average of the data, then the variance of this estimation is:

σ²_E = 2 γ_iV - γ_W - γ_ij     (I)
where,

is the mean of the variogram for all the distances in zone V,

is the mean of the variogram for all the distances between the samples (i and j are the sample indices),

is the mean of the variogram for all the distances between the sample points and all the points of zone V.

Equation (I) has three terms. The estimation variance depends on (1) the variogram model and the shape of zone V (term γ_vv), (2) the position of the samples in relation to each other (term γ_ij), and (3) the location of the samples in relation to the limits of the zone (term γ_iV). The more regular the structure (the smoother the density surface) and the tighter the sampling, the smaller the variance.

When the structure is known, equation (I) can be used to evaluate sampling strategies. The estimation variance can be computed for different sampling schemes and the sampling scheme giving lower estimation variance retained. The sampling grid can thus be adapted to the anisotropy of the structure and the range of the spatial correlations.

Equation (I) has been computed for different types of regular sampling and variogram models. The nomographic charts are available in Matheron (1971) and Journel et al. (1978) and were distributed to the working group. The estimation variance values can be read, if necessary, after having made the required anisotropic adjustments. Equation (I) can also be computed by computerized numerical integration, whatever the sampling configuration. Not all IBM-PC geostatistic software can do this, and we have developed a software at ORSTOM (the EVA: Estimation of V Ariance) to calculate equation (I) to evaluate and optimize sampling.

Equation (I) does not take into consideration the estimation errors made at the limits of the stock distribution zone. These errors affect the mean and are another source of variability of the mean estimate. A new term, a geometric error term, should thus be added to the estimation variance calculated with equation (I). Matheron (1971) provides the form of the error term to be added for systematic sampling. In practice, this term is often low when the sampling effort is sufficient.

The estimation variance is a linear function of the variogram. It mainly depends on the behaviour at the origin of the variogram model and on the behaviour at large distances (Matheron 1971, 78). Slightly different models with similar behaviours will give similar estimation variances.

5.3 Use of the Variogram - Kriging

Kriging is a method of interpolation. From the values recorded at the sample points we wish to estimate the density surface at the nodes of an interpolation grid. A map will then be derived using a contouring procedure. The sampling grid is not necessarily that of the interpolation grid. As for any interpolation method, kriging allows us to move from the sampling configuration to a regular configuration which will automatically provide a map. Kriging allows us to estimate, on the interpolation grid, the values of the underlying process. The kriged estimated values correspond to the average values of the random function. It must be noted that the polynomial adjustment methods do not estimate exactly the same density surface.

We use the values of neighbouring sample points to estimate the values of the density surface at non-sample points. The neighbourhood is the area around the point to be estimated in which we find the samples to be used for the estimation. The kriging estimator is a weighted average of the neighbourhood samples. The kriging weight given to each neighbourhood sample depends on spatial structure, its position in relation to the point to be estimated and its position relative to the other neighbourhood samples. The kriging weights are functions of the variogram and of the sampling configuration. In linear estimation (linear kriging) the kriging weights are independent of the value of the samples but in the non-linear estimation (disjunctive kriging) the kriging weights also depend on the sample values.

The kriging weights are determined by a mathematical procedure of optimization. At unknown point x₀ we estimate the value of the underlying process by the weighted mean of the neighbouring samples of The estimation variance at x₀ is expressed as a function of the variogram and of the weights μ_i. The kriging weights are those that minimize the estimation variance. In addition to the density surface map, kriging allows us to derive the map of the estimation variance at each point. This map is a summary of the quality of the estimation obtained with the sampling configuration and the highlighted spatial structure. Kriging is the only interpolator giving a map of estimation accuracy.

There are different types of kriging. First, different neighbourhood configurations can be used. Kriging can be conducted in a unique neighbourhood, where all the samples are used to estimate each point of the interpolation grid. Close and distant data are used and a variogram model is needed for all distances, whether large or small. Kriging can also be done for a moving neighbourhood, in which case the neighbourhood is like a small window that we move and kriging can be compared to a form of weighted moving average. In this case only the samples close to the point to be estimated are used and only a variogram model for small distances is needed.

Second, when computing the weights μ_i that minimize variance, it is possible to consider different constraints that the μ_i must satisfy. This uses an algorithm of optimization under constraints. There are different types of kriging according to the constraints used. For instance, when the entire zone mean is not known but estimated as

is generally the case in fisheries, it is judicious to impose the condition on the weights. This ensures unbiasness of the estimator and kriging with this constraint is called ordinary kriging. Ordinary kriging is widely used for moving neighbourhood as the previous condition has the physical effect of keeping the estimator close to the (local) average of the neighbourhood samples.

Third, we may wish to estimate the values of the process at the points of the interpolation grid which is Point Kriging; or we may wish to estimate the mean value in each block of the interpolation grid which is Block Kriging.

As for any interpolation method, we must define the grid and neighbourhood parameters. We need to select the mesh size of the interpolation grid. If the grid node distance is too small, the map will appear to be very detailed, but the details will be unrealistic. We cannot reproduce the heterogeneity of reality on a smaller scale than the sampling mesh size. It is therefore reasonable to choose a mapping scale that is compatible with the sampling one.

There are generally four neighbourhood parameters: the shape and size of the neighbourhood, the number of neighbourhood sample points used for the estimation and a selection criteria according to their location. All these parameters can influence the estimation and their choice is largely dependent on the sampling configurations and spatial structure. The important thing is that the estimator be always well supported by sample values. Systematic sampling is appropriate for this requirement.

5.4 Models other than the variogram

Not all regionalizations can be described by variograms and other structural models are needed. The previous sections deal with linear and stationary geostatistics. The two basic assumptions are the homogeneity of spatial correlations, at least for short distances (kriging with a moving neighbourhood), and the possibility of studying all the value ranges together. The variogram gives the average measure of variability between two points as a function of the distance between them. This means that the variogram is regardless of the specific location of samples and of their values.

Consider a density surface with a maxima in the middle of the zone. Is this maxima randomly located? If yes, repeated surveys would show that we may find it elsewhere, otherwise we would always find it at the same spot. The model of random occurrence is a stationary model: the same physical process takes place at all points. The fixed occurrence model is non-stationary: all regions do not have the same structural process.

The methods of universal kriging, FAI-k theory and external drift (grouped under the term of non-stationary geostatics) propose models that characterize a random stationary component of regionalization associated with a non-stationary deterministic component.

Consider now that the density surface is made of two components: on a relatively smooth surface of low and medium values there appear patches of high values that have their own structure. The structure of the low values is not the same as that of the high values and different structural models for different parts of the histogram would characterize the regionalization better than a mean model for all ranges of values. The non-linear models (disjunctive kriging models) specify the structure for each part of the histogram and the structural relations that exist between them.

A description of the non-stationary and non-linear methods and examples of their use in fisheries can be found in Armstrong et al. (1992) and Petitgas (1991).

REFERENCES

Anon., 1991. Report of the workshop on the applicability of spatial statistical techniques to acoustic survey data. ICES, Doc. C.M.1991/D:40

Anon., 1992. Report of the workshop on the analysis of trawl survey data. ICES, Doc. C.M. 1992/D:6, 96 p.

Armstrong, M., Renard, D., Rivoirard, J. & P. Petitgas, 1992. Geostatistics for fish survey data, course publicised by ICES, Centre de Géostatistique, Fontainebleau, France, 90 p.

Bazigos, G.P., 1980. El disenos de reconocimientos de pesca con redes de arrastre. FAO Communicacion al Congreso Regional sobre Recursos emersales de Peru: 16 p.

Cochran, W.G., 1977. Sampling techniques. John Wiley and Sons, New York, 428 p.

Doubleday, W.G., 1981. Manual on groundfish surveys in the NAFO area (revised). NAFO SCS Doc. (81/VI/7):77 p.

Fogarty, M.J., 1985. Statistical considerations in the design of trawl surveys. FAO Fish. Circ. (786): 21 p.

Grosslein, M.D. and A. Laurec, 1982. Bottom trawl surveys: design, operation and analysis. Rome, FAO, CECAF/ECAF Ser.81/22, 25 p.

Journel, A. & C. Huijbregts, 1978. Mining Geostatistics. Academic Press, London, 600p.

Laurec, A. and J.C. Le Guen, 1981. Dynamique des populations marines exploitées. Tome I. Concepts et modèles. Rapp.Sci.Tech.CNEXO (45), 118 p.

Matheron, G., 1971. La théorie des variables régionalisées et ses applications. Les Cahiers du Centre de Morphologie Mathématiques, fasc.5. Centre de Géostatistique, Fontainebleau, 212 p.

Petitgas, P., 1991. Contributions géostatistiques à la biologie des pêches maritimes Thèse de Coctorat. Centre de Géostatistique, Fontainebleau, 211 p.

Petitgas, P. and A. Rampart, 1993. EVA (estimation variance): A geostastical software on IBM-PC for structure characterization and variance computation. ORSTOM, 32p. and figures.

Sissenwine, M.P., T.R. Azarovitz & J.B. Suomala, 1983. Determining the abundance of fish. (In) Experimental Biology at Sea. A.G.McDonald & I.G.Priede (Eds): 51–102.

Stromme, T., 1992. NAN-SIS: Software for fishery survey data logging and analysis. User's manual. FAO Computerized Information Series (Fisheries) No 4, Rome, FAO, 1992. 103 p.

Stromme, T., 1994. EVA-RUN: Export program for data from NAN-SIS to EVA. IMR, Bergen.

Ulltang, O., 1977. Mesure de l'abondance des stocks par d'autres méthodes que le recours aux données commerciales de capture et d'effort. FAO Doc.Tech.Pêches, (176): 25 p.

ANNEX 1
LIST OF PARTICIPANTS

ANGOLA

KILONGO, Mr Kumbi
Ministerio das Pescas
Instituto de Investigaçao Pesqueira
Caixa Postal 83
LUANDA, Angola
FAX: 00244 2 39 46 84

FREIRE MONTEIRO JARDIM,
Ms H.de F.
Ministerio das Pescas
Instituto de Investigaçao Pesqueira
Caixa Postal 83
LUANDA, Angola
FAX: 00244 2 39 46 84

CAMEROON
DJAMA, Dr Theodore
Fisheries and Oceanographic
Research Station
B.P. 343
Kribi
Cameroon

CONGO
MALOUEKI, Mr Lucien
Service des Pêches/ORSTOM
B.P. 1286
Pointe-Noire
Congo
FAX: (+242) 94 39 81
Tel. (+242) 94 02 38

COTE D'IVOIRE
KONAN, Mr Jacques
C.R.O.
BP V 18
ABIDJAN
Cote d'Ivoire
Tel. 35 50 14/35 58 80
FAX (225) 35 11 55

FRANCE
CAVERIVIERE, Dr A.
ORSTOM
911 Av. Agropolis
B.P. 5045
34032 Montpellier Cedex
FRANCE
Fax: (+33 67) 54 78 00
Tel. (+33 67) 61 74 00

PETITGAS, Dr P.
ORSTOM
Services Scientifiques Centraux
70/74, route d'Aulnay
93140 Bondy
France
Fax: (+33 1) 48 47 30 88

GHANA
KORANTENG, Mr Kwame
Fisheries Research and
Utilization Branch
Fisheries Department
P.O. Box B-62
Tema
Ghana
FAX: (+233) 221 2982

GUINEA
BAH, Mr Amadou
Chercheur
Centre de Recherches Halieutiques de
Boussoura
B,P, 3738
Conakry
Guinée

GUINEA BISSAU
MALABE DA FONSECA, Mr Luis
CIPA
Ministère des Pêches
CP 102
Bissau
Guinée Bissau
Tel. 212184/215789/201157
Telex: 267 ESTR MAR BI
Fax: 201157

MOROCCO
IDRISSI, Mr M'hammed ISPM
Institut Scientifique des
Pêches Maritimes
2, rue de Tiznit
B.P. 21
Casablanca
Maroc
Fax: 26 69 67
Telex: 23823M ou 25708M OFNAPECH
Tel. 26 81 92/27 60 88

MEHDI, Mr El Ouairi ISPM
Institut Scientifique des
Pêches Maritimes
2, rue de Tiznit
B.P. 21
Casablanca
Maroc
Fax: 26 69 67
Telex: 23823M ou 25708M OFNAPECH
Tel. 26 81 92/27 60 88

MAURITANIA
JOUFFRE, Mr D.
ORSTOM
c/o C.N.R.O.P.
BP 22
Nouadhibou
Mauritanie
Tel. (2222) 45–124
Fax: (2222) 49 050
Telex: 415 MTN