3.1 Introduction
3.2 The vertical migratory process (daytime observations)
3.3 Night-time biomass estimates
In this chapter we examine some of the peculiarities of the target population (= population of small pelagic fish) which affect the accuracy of the calculated sample estimates.
As we have discussed(Section 2.1) temporal changes in the packing status characterize fish populations of small pelagic fish. Observations of echo records indicate that during night-time fish are spread widely forming layers of fish. During daytime small pelagic fish are packed in schools of various sizes. Schools are not randomly distributed in space but exhibit aggregation patterns which may intuitively be noted by anyone looking at echo records.
Apart from the temporal variation in the packing status of the target population, small pelagic fish exhibit diurnal (vertical) migration which is related to the light intensity. With this information, and with further knowledge that neither echo-integrator surveys nor sonar surveys can achieve a complete vertical coverage of the survey body of water1 we can readily ascertain that independent population estimates produced by these two kinds of surveys include traces of bias (underestimation).
1 In echo-integrator surveys approximately the upper 10 m are not covered by the system (4-5 vessel draft, plus 4 m before the echo-sounder operates normally). Also, sample observations obtained within the second upper layer (10-20 m) are biased (underestimation) because of the avoidance effect.Sonar surveys usually cover the upper 20 m (effective range) and the system can only be used for the detection of fish schools (daytime observations).
3.2.1. The structure of sample data
3.2.2 De-biasing sample estimates
It is of interest to examine the vertical migratory process of the schooling fish population by introducing distinct time intervals within the daytime period (during night-time the observed layers of fish are located in the upper layers of water). For purposes of illustration (Fig. 3.2a) we have first divided the survey body of water into the following three depth domains:
Domain A: |
Expresses the upper layer of water, 0-10 m. This layer is not
covered by echo-integrator surveys, it is covered by sonar surveys. |
|
|
Domain B: |
Expresses the second upper depth layer of water, 10-20 m. This
layer is partially covered by echo-integrator surveys because of the avoidance
effect (underestimation); it is covered by sonar surveys. |
|
|
Domain C: |
Expresses the remaining body of water below 20 m. This layer
is covered only by echo-integrator surveys. |
A critical assessment of Table 3.2b leads to the following conclusions:
a) If echo-integrator surveys are conducted only during the time interval one (t-1) they will produce an unbiased estimate of the population total. If echo-integrator surveys are conducted only during the time interval five (t-5) they will produce a zero value of the population total. If echo-integrator surveys are conducted within the time intervals t-2 to t-4 they will produce a biased estimate (underestimation) of the population total.Figure 3.2a The vertical migratory process of the schooling target population (daytime observations).
Table 3.2b. Temporal vertical localization pattern of the schooling target population and level of coverage obtained
t |
Depth domains (m) |
Level of Coverage |
|||||
|
0-10 |
10-20 |
below 20 |
Echo-integrator |
Sonar |
||
1 |
|
|
Ö |
below 20 m |
Complete coverage |
below 20 m |
Complete omission |
2 |
|
Ö |
Ö |
below 20 m |
Complete coverage |
below 20 m |
Complete omission |
10-20 m |
Biased coverage |
10-20 m |
Complete coverage |
||||
3 |
Ö |
Ö |
Ö |
below 20 m |
Complete coverage |
below 20 m |
Complete omission |
10-20 m |
Biased coverage |
10-20 m |
Complete coverage |
||||
0-10 m |
Complete omission |
0-10 m |
Complete coverage |
||||
4 |
Ö |
Ö |
|
10-20 m |
Biased coverage |
10-20 m |
Complete coverage |
0-10 m |
Complete omission |
0-10 m |
Complete coverage |
||||
5 |
Ö |
|
|
0-10 m |
Complete omission |
0-10 m |
Complete coverage |
If the total sample data (daytime observations) are used for estimation purposes they will produce a biased estimate (underestimation) of the population total.b) If sonar surveys are conducted during the time interval four or five (t-4 or t-5) they will produce an unbiased estimate of the population total.
If sonar surveys are conducted during the time interval one (t-1) they will produce a zero value of the population total.
If sonar surveys are conducted during the time intervals t-2 and t-3, they will produce a biased estimate (underestimation) of the population total.
If total sample data (daytime observations) are used for estimation purposes they will produce a biased estimate (underestimation) of the population total.
An insight into the basic structure of the. empirical total
sample observations (daytime) can be obtained if the data are broken down
according to the established time intervals (post-stratification). In such a
case estimates can be calculated of the overall sample mean
() e.g., echo-integrator
readings/n.mi, and of the sample means within the time intervals
(
). Observed statistical
differences among the calculated means provide an indication of the effect on
the sample observations caused by the vertical migratory process of the
schooling target population.
It should be noted that, in the case of large-scale acoustic surveys, in order to assess the structure of the empirical sample data the above kind of analyses should be worked out on a space/depth domain basis.
3.2.2.1 Matching echo-integrator and sonar estimates
As we have discussed in previous sections, original sample observations (daytime) of echo-integrator surveys and sonar surveys cannot be used independently in order to calculate unbiased population totals. A number of alternatives have been worked out for de-biasing purposes.
1. If the actual sample in the non-biased (complete population average) time interval (s) is sufficient and representative of the survey population and it. can be properly identified (post-stratification) these data can be used in order to provide an independent and unbiased estimate of the population total (echo-integrator, sonar surveys).2. Sample observations (daytime) of echo-integrator surveys can be used for the estimation of population totals (unbiased) after a proper adjustment of the original sample data.
The de-biasing process asks for an extensive use of the available echograms. Adjustment of the original sample data is made progressively, i.e., on an elementary sampling distance unit basis and by following up the vertical migratory process of the schooling sample population.
Some kind of subjectivity might be inherent in the process of adjusting the original sample observation by using the available echograms.
3. Matching the results of the concurrent echo-integrator and sonar surveys: In such a case an unbiased estimate of the population total is calculated by adding up the estimated totals which are produced independently by these two kinds of acoustic surveys:
Estimated population total = (Echo-integrator total - below 20 m) + (Sonar total - above 20 m).The mechanism of this alternative is explained in section 3.2.2.1 below.
An unbiased estimate of the population total is calculated by adding up the independent estimates produced by the echo-integrator survey (below 20 m) on the one hand, and the concurrent sonar survey (upper 20 m) on the other.
For purposes of illustration (Fig, 3.2.2.1a), the survey area has been divided into two depth domains, i.e., A1: 0-20 m, A2: below 20. Further, we have introduced three time intervals by taking as criteria both the temporal vertical localization pattern of the schooling target population and its level of coverage by the individual concurrent acoustic surveys:
T-1: |
The target population is located below 20 m. The
echo-integrator survey alone ensures a complete coverage of the target
population. |
|
|
T-2: |
The target population is located in both depth domains
A1 and A2. The echo-integrator survey ensures a partial
coverage of the total population and the concurrent sonar survey ensures
coverage of the remaining part of the target population. |
|
|
T-3: |
The target population is located in the upper 20 m. A sonar
survey alone ensures a complete coverage of the target population. |
Figure 3.2.2.1
In Figure 3.2.2.1b the overall size of the pre-selected
regular line transect sample2 (n.mi) is given by the vertical tracks
a, b, c which are equal in size; each sample transect is divided into
elementary distance sample
units (ESDUs = 1 n.mi).
2 See chapter 5.To simplify our discussion we assume that the target population is evenly distributed in the survey area covered by the pre-selected line transect sample. Also, we assume that the target population consists of homogeneous schools, i.e., the schools are equal in size and packing density.
Variate -(x) expresses number of sample schools per ESDU in the echo-integrator survey, and variate -(y) expresses number of sample schools (effective range) per ESDU in the concurrent sonar survey.
It is obvious that, in the absence of a vertical coverage problem, variable -(x) will take the same value along the sample ESDUs. An unbiased estimate of the population mean per ESDU is given by the overall sample mean
(1)
where
Because of the vertical coverage problem (Fig. 3.2.2.1a) variable -(x) will take a variety of values along the sample tracks,: Total number of selected ESDUs
track -a: |
values attained x, (mean x) |
|
|
track -b: |
values attained
|
|
|
track c: |
values attained x = 0, (mean 0); complete omission of the
target population by the echo-integrator survey |
(2)
or
(biased)
By applying Midttuns Method (see chapter 4) the
estimated number of schools per n.mi can be raised to n.mi2
(). A biased estimate of the
total number of schools in the population is given by,
(3)
where
A: total survey area in n.mi2By using the same logic as above, a biased estimate of the total number of schools in the population can be calculated by using the sample observations of the concurrent sonar survey (see chapter 4),
: Estimated total number of schools (Because of the symmetrical case in coverage of our example, this number equals with only a half of the true number of schools in the population).
(4)
where
As it has been discussed, an unbiased estimate of the population total number of schools is obtained by adding up the calculated independent estimates (totals) of the echo-integrator survey (below 20 m) and sonar survey (upper 20 m):= average number of schools per n.mi2
: Estimated total number of schools (Because of the symmetrical case in coverage of our example, this number equals with only a half of the true number of schools in the population).
Estimated population total =
(5)
As mentioned earlier, during the night-time small pelagic fish are concentrated in the upper layers of water forming layers of fish, which can only be detected by the echo-sounder (echo-integrator surveys).
The effect of bias on the accuracy of the calculated night-time biomass estimates is a function, on the one hand, of the abundance of the survey stocks and, on the other, of the observed localization pattern of fish. For example, fish very close to the surface will be subjected to all types of coverage problems; sub-surface fish will only be subjected to avoidance effect.
For de-biasing the obtained sample observations, the vertical distribution of fish should be taken into account. Specifically, the following kind of distributions can be identified (Fig. 3.3a, b, c).
Figure 3.3
Orthogonal distribution; In the above case (a) simple ratio estimate can be used for de-biasing the sample observations. In such a case, sample data of the depth domain C(= 20-30 m) can be raised to the total by using depth as the raising factor.
Skew distributions: In the above cases (b), (c) for raising sample data of the depth domain C to the total, the kind of skewness (positive, negative) should be taken into account.
Total biomass estimates are calculated by using the adjusted sample data.