10.1 Introduction
10.2 Methods of sampling
10.3 Verification of the counts obtained
10.4 Random sampling
Trawling surveys (pelagic, demersal) are carried out concurrently with the main acoustic survey aiming to supply the material needed for the verification of the counts attained at the main acoustic survey, species identification of the survey biomass and the collection of biological information concerning the survey stocks.
A variety of sampling systems have been employed in the past for the collection of the required information. In each individual case a choice is made by assessing the objectives of the overall survey system and resources available, i.e., vessel’s availability, research vessel only, research vessel plus auxiliary trawler.
From a sampling point of view, the trawling sample methods used can be grouped under the following headings:
1. Concurrent systematic sampling (CSS)In the case of CSS a systematic sample of fishing stations is selected along the sample tracks of the main acoustic survey. Fishing is usually carried out by the research vessel. For the location of the fishing stations the following criteria are used:
2. Systematic sampling with time lag (LSS)
3. Random sampling (RS)
a) Pelagic trawling: Sampling (fishing) is conducted when concentration of fish is recorded by the acoustic surveyirregular CSSIn the case of LSS, an auxiliary trawler is used for fishing operations. A time lag might be observed between the acoustic survey and trawling survey.b) Demersal trawling: Fishing is conducted either at preselected sampling stations by using supplementary information  regular CSS, or when changes in the concentration of fish are recorded by the acoustic surveyirregular CSS.
In the case of random sampling (RS), fishing operations are usually conducted after the completion of the main acoustic survey. Specifically, by using the chart of the relative fish abundance of the main acoustic survey, the survey area is first divided into a number of density domains, here called strata, and a random number of fishing stations is selected within the established strata. In this procedure every possible trawling site in each stratum has an equal chance of being selected and the probability of sampling a particular depth (or ecological niche) within a stratum is proportional to the area represented by that depth (or niche) in the stratum.
It should be noted that, behavioural changes may alter the vertical distribution of fish. Also, intensity of light (day, night) may affect the activity of fish which, in turn, affects the catchability coefficient. Because of that, sampling (fishing) in daytime and nighttime is important and the ratio of night to day may be useful in detecting anomalies in catchability or gear selectivity.
If trawling surveys based on CSS have been used in an acoustic survey programme the trawl data can be used for the validation of the obtained echointegrator readings. Specifically, simple statistical approaches can be used for this purpose. It is expected that a linear model should be fitted to the matched sample data of the two concurrent surveys (integrator readings, catches). The estimated model describes the existing association between the two variables. A critical evaluation of the findings provides some indication of the validity of the obtained echointegrator values.
10.4.1 Estimated indices
10.4.2 Estimated abundance
10.4.3 The sample size
10.4.4 The logarithmic transformation and the estimation of the confidence limits (small samples)
If random sampling (demersal trawling) has been used in an acoustic survey programme, the obtained results can be used, among other things, to calculate abundance estimates. In the sections below we describe the methodology used for this purpose.
Random sampling within each stratum provides valid estimates of sampling error (variance) and the catchperhaul indices (standard) are unbiased in the sense that every (trawlable) habitat has an equal chance to be included in the sample.
Notation:
Suffix h: stands for a given stratumStratum estimates:
Suffix i: stands for a given sample tow
A_{h}: area of the h^{th} stratum
y_{hi}: sample catch of the i^{th} standard tow
n^{h}: stratum sample size
: sample mean catch per standard tow in the h^{th} stratumThe standard abundance index is the stratified mean catch per haul for the strata which encompasses the population or stock of interest. The formulae for the stratified mean and its variance V() are: sample variance in the h^{th} stratum
, ()
, (estimated)
and
It should be noted that, unadjusted survey indices have a consistent bias in the sense that they reflect only that portion of fish in the path of the trawl which is actually caught. That is, the mean catch per haul is only a relative abundance index and must be adjusted by the average catchability coefficient (q) to represent absolute abundance. The catchability coefficient is the proportion of the fish in the path of the gear that is actually retained by the net. Values of the catchability coefficient which have been used in stock assessment studies are: Southeast Asian waters, q = 0.5, Western Indian Ocean, south of the equator, q = 1.0.
Estimation of standing stock can be calculated by using the sample observations.
Notation:
a: average area swept per standard haulThe estimated absolute abundance in the h^{th} stratum is,
A_{h}: area of the h^{th} stratum
q: average catchability coefficient
: sample mean catch per standard tow in the h^{th} stratum
The estimated variance of , is
or
where
The estimated absolute total biomass for the strata which encompasses the population or stock of interest is
The estimated variance of is
and
Sample size vs. precision
Some first approxomiations can be worked out of the relation between precision of stratified means and sample size (overall number of hauls). The calculations are based on the general formulae of stratified random sample for estimating required sample size for given precision.
Notation:
N: total number of possible standard hauls in the area represented by strata in the set (N = A_{/a}).where
N_{h}: total number of possible standard hauls in the h^{th} stratum (N_{h} = A_{h/a}).
: variance per haul in the h^{th} stratum (an estimate of is given by , above).
V_{O}: desired variance of the stratified mean. Specifically
CV(): desired coefficient of variation of e.g., 10%(An estimate of is obtained by using the results of a pilot survey or the results of a previously conducted survey)
n: required sample size (overall number of hauls for a given precision (= V_{O}).In the case of proportional allocation the required n for given V_{O} is
In the case of optimum allocation the required n for given V_{O} is
, (, negligible)
Usually, Values of n are calculated (estimated) for the set of species we are interested in and for the given V_{O} values. The estimated maximum n represents the required sample size.
Sample size for normal approximation
The distributions we usually have to deal with in trawling demersal surveys are usually highly positively skewed and because of cost considerations our samples are of a size of which the assumption that is normally distributed might be far from the mark.
A rule of thumb (Cochran) for use in the normal approximation is the sample size should be greater than 25 times the square of the coefficient of skewness G_{1} (Fisher) of the surveyed population,
where
The value of G_{1} can be estimated by using the results either of a pilot trawling survey or of a previously conducted survey.
Sample size for a given cost
In practice, largescale trawling surveys are costoriented surveys and the overall sample of the survey (= sample stations) is determined by the sample cost function
C = overall cost of the surveyFrom the above cost function the estimate of the overall sample size n_{c} is calculated by
c_{0} = fixed cost encountered
c_{1}: average travel cost between sample stations
c_{2}: average cost of sampling a given station (duration of an individual tow plus time needed to set and haul up the net).
The actual sample size
In the previous three subsections we presented the methodology for advanced sample size estimates:
n: overall sample size for a given precisionThe final decision on the actual sample size of the survey should be a striking balance between cost and the objectives of the survey.
n*: overall sample size for normal approximation
n_{c}: overall sample size for a given cost
In sample surveys the normal approximation is used primarily to calculate confidence limits. Generally speaking, when 95% confidence limits are computed for the population mean m by the normal approximation, we make the following statement:
With repeated sampling, we claim that statements of this type will be wrong only 5% of the time. Consequently we might say that the normal approximation is accurate enough if such statements are in fact wrong between 4% to 6% of the time. Some workers may be satisfied with wider limits.
For populations in which the principal deviation from normality consists of marked positive skewness, the above statement is valid under the assumption that the sample is large enough so that the distribution of shows some approach to normality.
When the samples are of a size for which the assumption of is normally distributed it is not justified, then any confidence statement using the above described procedure is wrong. In such a case the logarithmic transformation is usually employed for the estimation of confidence limits.
For a sample of n observations, the mean of the transformed values equals the logarithm of the geometric mean of the actual values.^{2} For example, if
then
or
, where g_{y} is the geometric mean of y.
^{2} For the transformation , the following relations have been worked out,Also,a)b) ,
For the calculation of confidence limits for the population mean (m) there are two compromise solutions to the problem:
1. To use the factor derived from the logarithmic transformation and apply this factor to the arithmetical mean of the sample.Example:2. As the geometric mean is always less than the arithmetical mean, the estimated confidence limits will underestimate the true confidence interval of the population mean. A solution to the problem is to adjust the geometric mean before it is used for the calculation of confidence limits of m. The adjusted geometric mean (approximation) is given by,
The catches (kg) per standard tow of a pilot trawling survey are 90, 20, 70, 220, 50. Calculate the confidence interval of the population mean (P = 90% or a = 10%):
Solution:
a) n = 5 




Sample mean, Sample variance per unit, Clearly Because there are no zeros in the raw data (sample data) the transformation^{3} used is ^{3} If there are zeros in the sample data and the transformation is used. 



b) The transformed values
for the sample data
are 




: 1.9542, 1.3010, 1.8451, 2.3424, 1.6990 (g_{y} = Antilog = 67.34) 





(i) Estimated confidence limits: 






(i) Using the sample mean: 





The estimated lower (L_{1}) and upper (L_{2})
confidence limits for a = 10% are, 













= 90 × 1.8339 =165.0510 kg 




(ii) Using the adjusted geometric mean: 






= Antilog (1.8283 + 1.15 × 0.1438) 















L_{2} = Antilog (1.9937 + 0.2600) = 179.3494
kg 