J.A. Gulland

Fisheries Department

FAO, Rome

The first objective in sampling fish - using sampling in the general sense of this manual, of catching a batch of fish with some type of fishing gear as part of some research programme - is usually very simple. That is, to find out what fish exist in the body of water being studied, roughly how many these are, of what species, and what are the more striking characteristics (size, feeding habits, etc.) of each species. At this stage of sophistication, when little is known and any information is useful in adding to general understanding, the choice of gear and sampling design is not critical.

Although in the world as a whole the number of bodies of water for which our knowledge is still minimal are probably much more numerous than those that have been subject to proper scientific investigation, this reconnaisance stage does not last long for any particular body of water. Soon a general, if somewhat superficial knowledge of the fish stocks will be obtained. Further study, if it is to be useful and carried out at reasonable cost, must be directed to some few special aspects, for example, the estimation of the potential yield that might be taken by commercial, artisanal or sports fishermen; monitoring the effects of pollution; studying the behaviour of some particular species, etc. Each specific study will require certain types of information, and these in turn will be best collected by specific sampling procedures. At this stage the choice of gear used, and the procedures to be followed becomes important. Later chapters are concerned with the choices that need to be made under different circumstances; the present chapter will discuss how this choice should be made, looked at from two aspects - the biological aspects, particularly defining the basic objectives of the sampling work, i.e., the information that is to be collected, and the statistical aspects, including the criteria that can be used in judging how well a given sampling procedure achieves those objectives.

The simplest objective concerns the provision of qualitative or semi-quantitative information about one species at one moment of time and at one place. This is a common objective of self-contained biological investigation, covering matters such as maturity, feeding habits, growth, etc. The important matter, so far as any sampling programme is concerned, is that enough fish are obtained to provide useful information. This information will come from the detailed examination of these fish, either in the field, or in the laboratory. In some cases the observation made on each fish is meaningful in itself - for example, it is of some interest to know that the stomach of a 60 cm pike contained two small perch, though it would need to be followed by the examination of many more fish (particularly of different sizes). In such a case the main demand of the sampling gear is that it should provide the scientist with plenty of fish to examine. More often it is some frequency distribution that is of interest, e.g., the length composition of the stock, or the proportion of the population of fish of a given size that are in different maturity stages. For this the requirement is that the sampling gear should provide fish of all sizes, or in all maturity stages, and that particular sizes or maturity stage are not seriously under-represented or over-represented in the samples obtained, i.e., the samples are unbiased.

Most research programmes are somewhat more sophisticated, and are more concerned with comparisons between different places, or between different times at the same place. In itself it is not really very interesting to know that 50 percent of the male pike of 60 cm in length in a certain lake in 1975 were mature. This information becomes much more meaningful, as an indication of changes in the biological characteristics of the pike population (as a result of pollution, or heavy exploitation of the pike - or the food of the pike) if it is known that only 30 percent of the 60 cm male pike were mature in 1970.

Similarly, the value of knowing that the bream in one river average 15.2 cm, with a maximum size of 28 cm, is increased if it is known that the bream in another river (generally rather similar, but with a considerable influx of domestic waste) is 19.6 cm, with a maximum size of 31 cm.

In making comparisons of this kind the consistency of the sampling procedure is clearly important. The scientist needs to be sure that the observed difference of 4.4 cm in the example above has not occurred just because in the second river the sampling gear used, or the time or place at which it was used, were particularly favourable for catching larger fish; perhaps because fishing was done on a spawning concentration. This consistency may be achieved by using fairly simple and standardized gear, and (so far as year-to-year comparisons are concerned) sampling at the same times and places in each year.

(a) __Parts of population__

Studies of the abundance present special problems. The ultimate objective is usually to know the abundance in absolute terms (e.g., numbers or weight per hectare) of the fish population. In practice, because the total population of a given species covers a range from egg through adult, in which differences in size, shape, habits, etc. are enormous, the total abundance cannot be estimated in a single operation, but has to be built up from separate estimates of distinct stages - eggs, larvae, juveniles, adults.

In some cases, the distinction between stages is very clear (e.g., the point at which eggs hatch), but the point at which small fish have grown big enough to be considered as part of the adult and sub-adult population, and to be adequately sampled by the gears used for sampling the larger fish is often difficult to determine (see Chapter 3). Since the smallest sizes of the fish in the adult and sub-adult part of the population (i.e., all those which are included in what is popularly referred to as the fish stock by fishermen and others) often make the biggest contribution to the biomass (and even more to the production), it is important, before starting sampling, to determine clearly what part of the fish population is to be sampled, and then to determine what gear will adequately sample these fish. The first may be done in terms of size, e.g., all fish longer than 6 cm fork length, but sometimes the two stages are combined. That is the part of the total fish population being considered is defined as the fish that are vulnerable to a beach seine. Operationally, this makes things simple, but can be dangerous. Not only can the results obtained be changed by a small alteration in the sampling gear, e.g., an increase in mesh size, but they can provide a biased estimate of the real quantity of interest - for example, of the quantity of some small species available to a predator, if the predator eats fish smaller than that caught by the sampling gear used.

(b) __Absolute abundance__

Given that the segment of the total population to be examined and the sampling gear
have been determined, the estimation of __absolute__ abundance is still some way off. Many gears
(e.g., gillnets, traps) catch fish from an area or volume of water that is ill-defined and
variable, depending for example on the distance from which a fish may be attracted to and
enter a trap, which can change with season, time of day, etc. (see Chapters 4 and 5). Where
the sampled area is definable, e.g., beach seine or trawl, it is seldom certain that all the
fish in the area covered will be retained by the gear (see Chapter 6). Results can therefore
be expressed as numbers caught per standard length of gill, or as per ½-hour trawl haul,
but seldom as numbers per hectare, even if the size of the trawl and the distance covered in
half an hour are known. In the latter case the sampling results do provide a lower bound;
if 400 fish are caught, and the trawl covers a width of 8 m and a distance of 1.5 km, the
number per hectare is 400/1.2 = 333, plus whatever fish escaped from the path of the trawl.
For well-behaved fish, i.e., those that stay sufficiently close to the bottom not to escape
over the net, but not so close that the net passes over them, the degree of under-estimation
of density per hectare from the catch of a trawl may be small enough to be acceptable. Thus,
there can exist suitable circumstances - clear areas of water in which to operate gears like
trawls and seines, and well-behaved species - under which absolute measures of abundance
may be obtained directly by sampling with carefully chosen gear.

(c) __Indices of abundance__

More often it has to be accepted that sampling alone will not estimate absolute numbers (or weight). This estimation has then to be a matter of applying more sophisticated techniques (e.g., tagging, analysis of mortality rates) which lie within the field of population dynamics, and outside the scope of this manual. The use of these techniques will require a variety of data to be obtained from sampling the fish stocks. Among these data indices of relative abundance are often the most important. Sampling is then concerned with obtaining these indices, and particularly with obtaining them at different times and places.

The test of the value of these indices is the degree to which the relation between the abundance and the catch per unit effort (catch per net, or per ½-hour trawl haul) of the sampling gear remains constant, i.e., whether there are changes in the vulnerability of the fish to the gear. Changes should be small from gear to gear at the same place and at the same time of year, provided care is taken to use the same gear. Seasonal changes are likely, for example changes in the behaviour of the fish can easily affect the likelihood of fish being caught by gillnets or traps. Thus seasonal changes in abundance may be more difficult to study than year-to-year changes and for the latter care should be taken to sample at the same season each year. [This is, of course, also desirable to avoid complications due to seasonal changes in real, as well as apparent, abundance.]

(d) __Multispecies sampling__

Most studies require information on more than a single species. If this information is essentially a matter of getting within-species data (e.g., regarding stomach contents) for each of several species, no new principle is introduced. However, often the relations between species, or between certain characteristics of each species, are the main interest rather than the characteristics of each species themselves. For example, the numbers of species observed, or some more sophisticated index derived from the number of species and number of individuals of each species, is increasingly being used as a measure of the stress on the environment from pollution or other human activities. The reliability of such indices will be reduced if the sampling gear fails to collect some of the species in the area. Some gears, e.g., gillnets, are obviously highly selective, and are clearly unsuitable, by themselves, for multispecies studies, but nearly all gears are somewhat selective. For these studies reliable sampling may need the use of a combination of two or more gears.

Many questions of sampling fish can be best dealt with by established statistical techniques. In particular the concepts of variance and bias should be used to evaluate the success of any sampling scheme. These provide measures of how scattered different estimates obtained by successive samples will be, and how close the central value obtained from the different samples will be to the true value. These can be used qualitatively, but quantitative measures of variance and bias provide better information on how good a sampling system is, and whether one system is better than another. Making, or even attempting to make, quantitative estimates of variance and bias forces a clear definition to be made of what the sampling system is trying to measure. This in turn can sharpen the whole research programme, as well as the sampling work itself.

Bias is more serious than variance. A high variance will soon become apparent in large differences in the results from different samples, whereas samples with large bias may appear to give good and consistent results, but which are consistent only in giving information that is wrong. Samples with high variance may give little information, but samples with large bias give misleading information which is worse than none at all.

The existence of variance can be detected from the sampling results themselves, by looking at the consistency or otherwise on the results from different samples. The existence of bias can be determined only by careful examination of the whole process of carrying out and analysing the samples. Bias can arise at all stages, perhaps most obviously at the first stage of the actual sampling gear. With the possible exception of poisoning small bodies of water, no single sampling method collects all fish, of all sizes and species, from a defined area. Any gear is selective, most noticeably in terms of size, which in turn implies indirectly selectivity in terms of other characteristics which are linked to size (e.g., maturity stage), but there can be direct selection for these other characteristics. For example, gillnets will select the more active individuals and hance their catches may be related to maturity or feeding. Baited traps will take more of those which are hungry, and the stomach contents of fish caught in traps may be completely unrepresentative of the fish stock as a whole. There are plenty of other examples; gillnets can take only fish of a certain girth, so that they will select the fatter fish in the shorter sizes, and thinner of the bigger fish. The catch of gillnets of a fixed mesh size will provide a very distorted length/girth, or length/weight relation (see Chapter 4).

Some bias, if the direction is known, and the extent is not great, can often be accepted. For example, the lower limit to the density provided by the catches taken by a trawl towed over a known area can be useful for those species for which the escape from the path of the trawl are known (or can be reasonably expected, from their behaviour and distribution) to be small. The practical solution is to determine the amount of selectivity or bias likely to be introduced by the gear in question, and to check that this is acceptable for the research programme. If it is not, some other sampling gear will have to be used.

Bias can also be introduced by the design of the sampling programme, particularly its distribution in time and space. Practical constraints often make it much easier to sample at certain places or times, e.g., near the shore, or at quiet periods in the academic programme of a university. The fish caught then may well not be typical of the whole population, e.g., the food taken by a given species of fish in late summer may be quite different from that taken at other times of the year. Before accepting the limitations imposed by practical convenience, the amount of bias that might be introduced should be examined, if possible, by taking at least a few samples at the less convenient times and places.

Finally, bias can be introduced, or the amount of bias arising from poor sampling design reduced by methods of analysis. Some of these biases and methods of avoiding them are matters of advanced mathematical techniques (for example, in expressing death rates as exponential mortality rates, rather than percentage survival) and are outside the scope of this the samples, are also useful in reducing variance, and are discussed later.

Apart from a few exceptional situations, such as where a small pond is drained and all
the fish can be examined, it is not possible to measure exactly the quantities of interest
for the whole population. The observed value will depart from the true value, and the
important question is not the fact of the departure but the average magnitude of the departure,
and its relation to the precision required. This requires a definition of the objective
of the sampling exercise. Sometimes this can be done very clearly, and it can be seen
at once whether the variance is small enough. For example, it may be desired to test whether
the growth in two lakes differs, as judged by the mean length of two-year-old fish in
September. If the two means (with corresponding confidence limits) are 23.2 cm ± 1.8 cm
and 29.4 ± 1.3 cm, then, assuming no bias has been introduced in the sampling gears and the
methods of operating them, the difference is statistically significant, and the variance of
each estimate is small enough. If the mean from the second lake was 23.7 cm ± 1.3 cm the
situation would be different; the data are not sufficient to distinguish in which lake the
growth is faster. On the other hand, the real objective is probably not to determine whether
there is a difference (which might require an almost infinite amount of sampling), but only
to detect the difference when it is __biologically__ significant, i.e., greater than a certain
value. If only differences greater than 5 cm are considered significant, than the data show
that any difference is smaller than this, and the variance is small enough; if even a 1 cm
difference is considered biologically significant, then the variance is too big.

The magnitude of the variance is determined by the natural variability in the quantity being measured, the statistical design of the sampling system, and the amount of sampling carried out. Other things being equal the variance is inversely proportional to the amount of sampling (e.g., the number of observations made), and the standard deviation of the estimates obtained inversely proportional to the square root of the number of observations. The square root means that if greater accuracy is required, the amount of sampling (and hence the costs) will go up much more rapidly than the precision achieved. Beyond a certain point it is not practicable or economical to achieve greater precision by carrying out more sampling, and improved sampling design, or a different approach to the problem is needed. Short of that point a balance needs to be struck between costs and accuracy. In fisheries there are probably no two ways in which the efficiency of research can be improved than, on the one hand reducing the amount of sampling where it is already more than adequate for the objective, and on the other, when the variance from current levels of sampling is too great to provide estimates that are accurate enough, either increasing the amount of sampling to an adequate level, or abandoning a programme that is not providing useful information.

Among the standard statistical techniques that can be used to increase the efficiency of a sampling scheme, and reduce the variance resulting from a given amount (and costs) of sampling, stratification is generally most useful when sampling fish populations. This consists in reducing the difficulties of getting an unbiased, low-variance sample from a large and heterogeneous population (using ‘population’ in the statistical sense) by dividing the whole population in a stratum within each of which conditions are more homogeneous. Samples are then taken and analysed from each stratum separately. For example, the ‘population’ might be all the positions in a lake where gillnets might be set and the ‘population’ may be stratified into depth zones, or the natural of the bottom. Similarly stratification can be applied to the fish caught when examining them for age, maturity, etc., but considering each length-group separately, e.g., in producing age-length keys. With suitable choice of stratification so that for example each sub-area of the lake has similar conditions, a small amount of sampling will be sufficient to determine the conditions within each stratum, and the total amount of sampling can be much reduced.

Sampling is an integral part of the whole process of studying fish and the environment in which they live. The previous sections have outlined a logical progression as follows:

The definition of the objective of sampling, e.g., to study the effects of increasing exploitation on the sizes of fish in a given lake

The identification of the precise quantities to be measured, e.g., the fork length of adult and subadult specimens of three species of fish

The selection of gear to be used, e.g., a set of gillnets with mesh sizes of 2, 3, 4 and 16 inches

The choice of sampling design to be used, e.g., using the nets for one night each month, at eight different sampling stations, two in each of four distinct sub-areas of the lake.

When a new sampling programme is introduced as part of a large new research project, it is likely that attention will be given to a logical development along these lines. More often research and sampling programmes develop from year to year, and the objectives and the funds available for pursuing them change. This should be followed by corresponding changes in the sampling procedures, but often this does not occur. As a result there is probably now a vast amount of sampling being carried out which is largely inappropriate to current research objectives. Since sampling can be one of the more costly parts of a research programme, the procedures (methods, gear, statistical design) should be carefully examined, not only at the beginning of the programme, but at regular intervals thereafter.