Ragnar Arnason*

Calculation of Discarding Volumes

on the Basis of

Size Composition of Catch and Landings

Research Project

Discarding of catch at Sea

Working Paper 6

May 1998

DRAFT

Not to be quoted without consulting the author

* Department of Economics, University of Iceland, 101 Reykjavik

Tel. 354-525-4539

E-mail

3

0. Introduction

In a recent memorandum (Memorandum 4), Tryggvi Björn Davíðsson discussed available information on the size composition of landings and the independently estimated size composition of catch. Davíðsson describes how the Marine Research Institute (MRI) in collaboration with the Fisheries Directorate annually estimates the size distribution of cod catch for the various gear types (in particular bottom trawl and longline) with the help of sampling techniques. It is convenient to refer to this estimate simply as the Catch Distribution. For marketing purposes the actual landings of cod are similarly classified according to fish weight. The latter weight measure can be turned into a length measure using a simple formula (Davíðsson 1997, p. 6). It is convenient to refer to this measure as the Landings Distribution. In his memorandum Davíðsson provides data on the Catch and Landings Distributions (apparently as percentages of the total catch and landings volumes) and speculates that the discrepancy between these two independent measures of size distribution may be attributed to discarding of catch at sea.

This memorandum follows up on Davíðsson’s work. Its main purpose is to show how Davíðsson data can in principle be used to obtain measures of the actual volume of discards. Before turning to that, however, the paper briefly discusses possible alternative explanations of the observed discrepancy between the Catch and Landings Distributions.

1. Explanations for a Discrepancy between the Catch and Landings Distributions

An observed discrepancy between the Catch and Landings Distributions may be attributed to at least the following factors:

·  Measurement errors

·  Different fish selectivity

·  Discarding of fish at sea


Measurement errors

These data are subject to various types of errors. There are obvious sampling errors in the data collection at sea. There are similar sampling errors in the estimate of size distribution of the landings. More seriously, the only source for landings statistics used in Davíðsson’s memorandum, i.e. Islandsmarkaður (Davíðsson 1997, pp. 4-6) which first of all represents only a very small fraction of cod landings in Iceland (perhaps around 5-7%). More seriously, however, this particular market disproportionately receives catch from a certain geographical are with a size distribution of cod catches different (in fact larger fish) from other parts of the country. Also, it must be kept in mind that the fish markets in general serve certain marketing outlets with their own preference for fish sizes which consequently will be reflected in the supply.[1] In addition to this, there will be calculation errors due to the employment of a simple formula to turn weight into length and approximation errors due to discreteness of the weight and length categories.

Different fish selectivity

It is quite possible that the harvesting selectivity of the commercial vessels landing catches to the fish markets is somewhat different from that of the overall fleet that is supposedly reflected in the MRI Catch Distribution. The majority of the fleet does not normally sell their catches through the fish markets but rather on a variety of long term contracts to processing plants directly. Provided it is economical there are many ways for a vessel of a given size to alter its harvesting selectivity if that is deemed economical. Thus, if the fish market demand differs from the processing plant demand with respect to fish size distribution, the corresponding fish supply will tend to reflect this. Moreover, the composition of the fishing vessels supplying the processing plants directly is probably quite different from the vessels supplying the fish markets. (The former tend to be the larger deep sea trawlers).

Discarding of catch at sea

The third factor explaining the discrepancy is discarding of catch at sea thus altering the size distribution on the landed catch as compared with the catch itself. The data presented in Davíðsson’s memorandum suggests that it this is the main explanation then small cod are primarily discarded. This, incidently, is in conformance with theoretical predictions (Arnason 1996)

It is therefore not at clear that an observed discrepancy between Catch and Landings Distributions necessarily reflects discarding at sea. It may just as easily reflect some of the other factors discussed above.

2. Calculation of Discarding Volumes on the Basis of the Size Composition of Catch and Landings

Let a(i) represent the percentage share of size class i in the catch of a given species. For convenience let us refer to a(i) as the i-th catch share. Clearly,

(1) a(i) º y(i)/y,

where y represents the total catch and y(i) the i-th catch share.

Similarly, let b(i) represent the percentage share of size class i in the landings of a given species. For convenience let us refer to b(i) as the i-th landings share. Clearly,

(2) b(i) º l(i)/l,

where l represents the total catch and l(i) the i-th landings share.

Now, the difference between catch and landings is discards:

(3) d(i) º y(i) - l(i),

and the percentage of size class i caught and discarded (i.e. the discarding ratio) is:

(4) d(i) º 1-l(i)/y(i).

Combining (4) with (1) and (2) yields:

(5) d(i) º 1- b(i)×l/a(i)×y.

Now, b(i), a(i) and l are observed quantities. b(i) and a(i) are the i-th landings and catch shares given in Davíðsson’s memo. l is the total volume of landings obtainable from landings statistics. The actual total catch, y, on the other hand is not observed. However, there is an easy way around this problem provided there is some size class that is not discarded at all.[2] Let us refer to this size class as class I. Then, clearly

(6) d(I) º 1- b(I)×l/a(I)×y º 0.

Rearranging we obtain the following estimator for y:

(7) y = b(I)×l/a(I)׺ 0.

Substituting into (5) we can express the discarding share as a function of observable quantities only as:

(8) d(i) º 1- b(i)×a(I)/b(I)×a(i).

And the volume of discarding is found by combining equations (3) and (4) yielding:

(9) d(i) = l(i)×d(i)/(1-d(i)),

where d(i) is given by (8). Alternatively, substituting (8) and (2) into (9) and rearranging we obtain a useful equation for calculating the discarding volume directly as a function of observable quantities only:

(10) d(i) = l×[b(I) ×a(i) - b(i)×a(I)]/ a(I).

Notice ,however, that in order to calculate discarding volume on the basis of equation (10), it is necessary to have information about the landings

3. An example:

As an example let us calculate discarding ratios for Icelandic cod on the basis of the data presented in Davíðsson (1997). The following table replicates his catch and landings distribution data for the trawl cod fishery and calculates the discarding share according to equation (8):

Table 1
Calculated Discarding Shares
Icelandic trawl fishery for cod 1995-6
Length
classes (cm.) / Approximate
age
(Years) / Catch
shares / Landings shares / Discarding ratio
>90 / >7 / 3,72 / 3,85 / 0,107
70-89 / 6-7 / 30,11 / 34,87 / 0,000
60-69 / 5-6 / 27,81 / 30,75 / 0,045
55-59 / 4-5 / 13,31 / 15,83 / -0,027
50-54 / 3-4 / 11,27 / 11,57 / 0,113
45-49 / 3 / 7,99 / 2,74 / 0,704
40-44 / 2-3 / 4,04 / 0,35 / 0,925
35-39 / 2 / 1,31 / 0,04 / 0,972
30-34 / 2 / 0,33 / 0,01 / 0,987
<30 / 0-2 / 0,10 / 0,00 / 1,000

The calculated discarding shares are given in the last column of Table 1. Needless to say, the interpretation of these numbers as discarding shares rest on the assumption that the difference between the catch distribution statistics and the landings distribution ones are entirely due to discarding, undoubtedly a false assumption as discussed in section 1. Anyway, retaining this assumption it appears that in the trawl fishery, four year cod and older are for the most part not discarded. It may be noted, however, that there appears to be a slight tendency to discard the largest fish. This indication, however, may be an artificial creation of the data inaccuracies discussed in section 1. Three year cod however are to a large extent discarded (at a rate of approximately 50%). Two year cod and younger is almost entirely discarded.

Employing equation (10) we can also calculate the volume of discards corresponding to the discarding ratios. Again, however, the reader should be reminded of the strong assumptions needed to interpret the results as a measure of actual discards. The result of these calculations are listed in Table 2.

Table 2
Calculated Discarding Volumes
Icelandic trawl fishery for cod 1995-6
Length
classes (cm.) / Approximate
age
(Years) / Catch
shares / Landings shares / Discarding volume
(metric tonnes)
>90 / >7 / 3,72 / 3,85 / 324
70-89 / 6-7 / 30,11 / 34,87 / 0
60-69 / 5-6 / 27,81 / 30,75 / 1023
55-59 / 4-5 / 13,31 / 15,83 / -294
50-54 / 3-4 / 11,27 / 11,57 / 1037
45-49 / 3 / 7,99 / 2,74 / 4561
40-44 / 2-3 / 4,04 / 0,35 / 3032
35-39 / 2 / 1,31 / 0,04 / 1035
30-34 / 2 / 0,33 / 0,01 / 260
<30 / 0-2 / 0,10 / 0,00 / *
Total discarding of 2-5 years cod / 9631
Total discarding of 3-5 years cod / 8336

According to the results in Table 2 the trawl fishery in 1995 may have discarded up to 10.000 metric tonnes of cod. This represents about 12% of the actual quantity of cod caught in trawl during that year. Most of these calculated discards, about 2/3 are 3 year old cod, over 1/4 appear to be 2 year old cod and younger and the remaining discards consists of four year cod and older.

These calculated discarding volumes are significantly higher than previously estimated and reported (see Davíðsson 1996). In this connection it is important to keep in mind that due to the various simplifying assumptions, the inaccuracies of the data and the rough nature of the actual calculations the above results should not be interpreted as estimates of the actual volume of discarding. Rather they should be regarded as examples of how the particular data in question can, with the help of equations (9) and (10), be used to obtain estimates of discards. For serious estimates, the data has to be carefully screened, simplifying assumptions kept to a minimum and the calculations carefully conducted.

In interpreting the results in Table 1 and 2, it is also important to keep in mind that according to the discussion in section 1 discarding estimates on the basis of discrepancy of catch and landings statistics almost certainly overestimate the true level of discarding possibly quite dramatically. Also, as pointed out in Arnason (1996) a certain level of discarding is generally socially optimal. According to the results in Davíðsson (1997), it seems likely that this applies to most 2 year old and some 3 year old cod.


References

Arnason, R. 1996. On Selectivity and Discarding in an ITQ Fishery. Research Project Discarding of catch at Sea. Working Paper #1

Davíðsson, T.B. 1997. Estimation of Catch Discarding: Construction of Length Distribution for Landed and Caught Catch. Research Project on Discarding of Catch at Sea. Memorandum 4.

Davíðsson, T.B. 1996. Umfang Brottkasts Sjávarafla: Fyrirliggjandi Athuganir. Research Project on Discarding of Catch at Sea. Working Paper 2.

Davíðsson, T.B. 1997. Brottkast fiskafla á hafi úti. B.S. dissertation, Department of Economics, University of Iceland.

[1] Again, at least to the extent that (i) very small fish command a low market price and (ii) the saltfish sector is supplied through the fish markets, there is a certain reason to expect the fish markets to receive a fish size distribution skewed toward larger fish.

[2] This condition would normally be approximately satisfied.