The concept of accumulated stock

explains the fall and subsequent stabilisation

, at a lower level, of the catch in

an expanding fishery. When demand

for a particular fish increases, the trade

concentrates the effort on it.



Sekharan, K V

CMFRI Digital Repository

'. • THE ACCUMULATED STOCK The concept of accumulated stock explains the fall and subsequent stabi-lisation , at a lower level, of the catch in an expanding fishery. When demand for a particular fish increases, the trade concentrates the effort on it. When the effort increases, the catch rises for a few years, .it reaches a peak and then drops and stabilises at a lower level. The catch per unit of effort and the average size of the fish also decrease. It would be erroneous to regard such a situation as an indication of overfishing. (It may be noted that the catch does no t go on decreasing but only stabilises. But if effort goes on increasing even at this stage, the catch would go on decreas-ing, leading to the typical overfishing situation.) This may well be illustrated by considering the growth of a bank acoount under certain special conditions as mentioned below. Growth of a bank deposit In an earlier article (Sekharan, 1971), the present author had shown that , in a restricted sense , the growth of a popu-lation can be cotr'l:ared with the growth of a bank deposi t. Suppose a bank pays compound interest at the rate of 10% Published with the permission of the DirectoT1 C. M. F. R. Institute, Cochin - 18. June, 1973 Dr. K. V. Sekharan, Central Marine Fisheries Research Institute, Cochin - 18. per annum on a fixed deposit for ]Q years. Then, the growth of an initial deposit of Rs. 10,000/- will be as indicat-ed in the following Table. Table I. The growth of bank account during the first 10 years Year 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 Amount at the beginning of the year (Rs.) 10,000 II ,000 12,100 13 ,310 14,641 16,105 17,71 6 19,488 21,437. 23 ,581 Interest (Rs.) 1000 1100 1210 1331 1464 16ll 1772 1949 2144 2358 The Curve A in Fig. I shows the interest and capital at various stages during this phase of growth . The vertical lines represent the surplus ob-tained from the capital at various stages. The interest becomes greater and greater every year and the amount in the bank grows at an increasing rate (increasing absolute rate). This stage 15 is called the exponential growth phase (in the present case it would be represented by the equatio n Y = 10000 X e 0.09533 t , where Y is the '0000 32,500 z 25,000 " o " " IZSQO A 1920 1925 1m 1935 19<0 YEA R Fig. 1. The growth of a hypothetical bank account. During period A, the amount grows at an increasi ng rate and during period B, it grows at a decreasing rate. amount at the end of t years.) If the bank does not a llow compound interest then the deposit will grow only by a particular amount (Rs . 1000) every year, and the growth .of the account will be represented by a simple straight line Y = 10000 + 1000 t. The human popu-lation also grows at the rate of compound interest ; hence the term "population explosion" is used. Suppose from the 11th year on-wards, the bank reduces the interest rate , the actual rate depending on the balance. based on th e principle that the larger the balance the smaller the interest rate, except that the interest 16 rate would always be restored to 10% per year when the balance touches or goes below that of the 10th year (year 1929 in Table I); and withdrawal is allowed, but only on 1st of January every year (this makes the arithemetic simpler). Let the growth of the account, when no amount is withdrawn, be re-presented by the following Table. Table 2. Growth of the bank account when interest rate decreases Year 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 Balance at the Rate beginning of the per year year ( Rs.) 25939 28274 30536 32674 34634 36366 37821 38956 39735 40132 40132 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% 0% Actual interest (Rs.) 2335 2362 2138 1960 1732 1455 1135 779 397 o o From the 11th year onwards also the account grows, but only at a decreasing rate (provided of course there are no withdrawals) . This is shown by part B of the curve in Fig. l. The sum of Rs.40132 represents the amount accum-mulated over 19 years. A person who feels secure when the bank balance is high would no t withdraw anything, but nothing would be added to his account after th e 19th year. Let us assume that the account· ho lder decides to make withdrawals after the 19th year (which he can do only on 1st January). From SeaJood Export Journal I I' 1939 onwards, if he withdraws only Rs. 397 or less per year, the balance would remain steady at Rs. 40132. If he withdraws Rs. 397 in the first year of withdrawal and Rs. 1176 in the second years (i.e., the sum equal to the accu-mulated interests of 1937 and 1938) , the balance will be Rs . 38956 and it can be kept steady at this level by withdrawing only Rs. 779 per year afterwards. It may thus be seen that the balance can be kept steady at any chosen level (it can be kept steady even at Rs. 10 ,000 by withdrawing the accumulated interest of 19 years in one or several stages and restricting the later withdrawals to Rs. 1000/- per year). But a wise decision would be to m,lintain the stock at Rs. 235'31 , because it is this balance which g ives the maximum annual yield (Rs. 2358) . In this process the annual withdrawals would touch a peak, then it y:i11 come down and shall stabilise at Rs. 2358. But keeping the account at such a level has a drawback. The balance will have nothing to buffer the stock if a larger withdrawal in times of adversity is made, since reducing it to less than Rs . 2358 1 will automatically reduce the interest. Therefore, it would perhaps be better to main tain it at a slightly higher level. say at Rs. 25939 or Rs. 28274. It will have to be decided after c~nsidering several factors. Population accumulation If we substitute the "amount" given in the above eXlmple by "population" . we shall have a classical model of an animal stock. This is very similar to Schaefer 's model of a fish p opUlation ; only he has taken into account the June, 1973 catches (i.e., the withdrawals) in com-puting the possible net increase (net interest) at each level of the population size (balance in the account) and has shown that the biggest net increase takes place when the stock abundance is about 50% of the maximum possible abundance . In the above example it takes place at the 60% level. There are of course a number of differences between the population increase and the growth of bank account ; e .g .. the entire amount in the bank balance will fetch interest, whereas in a population only the reproductively active groups will add numbers . But, for the sake of simplicity such. differences could be ignored and the population abundance could be referred to in terms of weight. Let us assume that a virgin stock occupies 10000 sq. km. in the .sea. Thare has been no fishing in the stock and it has been allowed to accumulate over a number of years, as indicated in Tables I & 2. The population would not be able to increase at a steady rate indefinitely. After a particular level of density is reached, it would increase at a decreasing rate (as in Table 2) until it occupies the entire area of the sea available to it. After Ihis, the weight increase due to recruitment and growth and the weight loss d ue to natural causes would just balance each other. Let the weight at this steady state con-dition be 40132 kg. and let the fishing start at this stage. A particular example of fishing and the change in population (natural mortality ignored; fishing takes place only on the first day of each year) has been given in Table 3. 17 Table 3. A hypothetical population in an exploited state Year Weight of Density Catch at the Net in. crease of the stock during the year (kg. ) 1 2 3 4 5 6 7 stock at the of beginning of beginning stock the year (kg.) of (kg./sq. the year km.) 40132 40132 39735 4.01 4.01 3.97 397 1176 (2 years' accumulat-ed growth) 5101 (4 years ' accumulat-ed growth) 26366 3.64 8092 (4 years ' accumulat-ed growth) 397 779 1723 2262 30536 3.05 6955 2358 25939 25939 (3 years' accumulat-ed growth) 2.59 2358 2358 (one years' growth) 2.59 2358 2358 It is obvious that from th e sixth year onwards, we would be able to catch only a maximum of 235'8 kg. per year; other-wise the natural increase will no t be able to replace the loss d ue to fishing with the result that overfishing would develop. Much large r catches were taken in e arlie r years , but these re-presented several years ' accumulation of s tock, not one year' s g rowth. What was accumula ted over several years has largely b een fished out and the s tock has now been reduced to its most productiv e level. Now fishing will with-18 draw every year what is to be added during the course of the year. The catch trends up to this level may there-fore be represented by the curve A of Fig. 2, The peak represents the catch 9,000 , 4·00 '" 17.000 ~s.ooo J: u ~3.000 u \000 4 7 10 YEA R 13 3·00 t-o: o ~ 2·00 ~ to 5 100 ~ J: .3 Fig. 2. Catch (A) and catch per unit of effort (B) from a hypothetical fish stock. of several years' accumulation as men tioned ab ove . It is futile to hope for such large catches again, unless due to dras tic changes in environmental conditions, there is an unusually large recruitment. But we are dealing with s ituations wherein recruitment does not vary within wide limits . The assumption that the catch can be raised to the level of the previous peak within just one year, wou ld be unsound. It may be seen from Table 3 (col. 3) that the density of population has been decreasing over the years' 1-6. Therefore the catch per unit of effort (e.g., the average catch per boat per day) would decrease although the Seafood Export Journal total catch (col. 4) and the net produc-tion in the population (col. 5) inqease-a very common experience in an ex-panding fishery. However, this is the price we have to pay, if we want the fishery to prosper. Examples from marine fisheries in India There are two cases of marine fisheries in India where apparently the concept of accumulated stock applies. The first one is the prawn fishery of the Cochin area. In an interesting article, Qasim (1972) has shown that the catch of all prawns put together reached a peak in 1965-66, but later declined and came to a more or less steady state; the catch per unit of effort also declined. The same trend is seen in the catch of th e individual species also. The variation from the steady state can be attributed to recruitment variations. The " prawn rush" of the e arly sixties had taken a toll of the accumulated stock, and much of it was probably wiped out by 1965-66, the year of peak catches. A s imila r case is that of the Bombay duck. Here the catches touched a h igh peak in th e late fifties , but dropped and s tabilised around 70000-80000 tonnes in sixties (Bapat & Alawani, 1972). The introduction of mechanisation had obviously led to a big increase in the effo rt in late fifties which resulted in mopping off the stock accumulation of many years. There has however been a drastic decline in 1972. the reasons tor which have to be investigated in detail. It may also be mentioned here that the oil sardine and mackerel fisheries, the other two single-species fisheries on the west coast, also had lean seasons in 1972. June, 1973 Conclusion From the point of view of the fishing industry, a few p oints may be emphasis-ed: a) In an expanding fishery, the annual average catch per unit of effor t (e.g., the catch per boat per day) is bound to come do wn . The on ly way not to allow such a thing to happen is to stop fishing. There is s ome theoretical evidence to show that the production potential is the highest, when the mag-nitude of the stock is of the order of 40-50% of the maximum. The view expressed by some persons that the maximum potential catcli fr om a popu-lation is equal to 60% of its size in the vi rgin state, has now become scienti-fically invalid. There is no point in our making such estimates, without computing or making assumptions re-garding the potential for increase of stock and the probable loss as a result of fishing and natural mortalities. Therefore, it would be prudent to plan ahea d, taking into account the probabi-lity that when the fishery develops fully the annual catch per unit of effort is likely to decrease at least to 40-50% of that obtained from the virgin stock. In other words, a wijl e management would keep a watchful e ye on produc-tion charts , based not only on the per-formance of their vessels but also on the performance of others ' vessels. b) When th e total catch shows a slump and then stabi lises for a number of years that is the time when the indu-stry should take a serious note of the situation and then come to an appro-19 priate decision regarding conservation; for continued increase in effort at this stage would lead to reduction in the total catch. c) The need for accurate statistics is m )st urgent. The fish~ry scientists should be given complete catch and effort data so that they should be able to monitor accurately the changes in the stocks. Acknowledgement The author thanks Dr. S. Z. Qasim for his valuable suggestions. REFERENCES Bapat, S. v. & The Bombay duck fishery of Alawani, S. A. 1972. Maharasbtra with special re-ference to Versova. Symp. pelag. fish. resour., CMFRI, Cochin. Abstract: 29-30. Qasim, S. Z. 1972. Are there enough shrimps in the sea? Seafood Export Journal, 4 (I): t-12. Sekharan, K. V. The Fisheries Problem. Seafood 1971. Export Journal, 3 (7) : 31-35 .• f"""""""""'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' '' """ " " """"""'''''''''" .,'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''1 BlYT~, G~~~N~, JOU~DAIN & COmPANY, lImlHD PLANTATION HOUSE FENCHURCH STREET. LONDON. E. C. 3 • · ~~ ·'· I 1M PORTERS AND EXPORTERS OF r'" t!anlUlfJ and 7'Co]€n ::,"'1111" '11 1111111111111"'11111111""11111 ' 1""" ""'11111111""111"1111111 '11 111111 11111 11111111111111111111111 '111 111111111 IInlllllllllll1ll1~IIII "'II""'lIlIlllllIlllllllllllllllll 'llI l1l11I1111111111~ 20 Seafood Export Journal 

The accumulated stock

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The accumulated stock

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