Marine landing data for Karnataka during 1956-1978 were subjected to time series analysis and cyclical periodicities isolated in the case of seven fisheries namely, ribbon fish (five year cycle); Caranx spp., Leiognathus spp, and mackerel (six year cycle each); the combined landings of Hemirhamphus spp. and Belone spp.,'Lesser Sardines' and 'Other Clupeids' (seven year cycle each). 'Total' demonstrated an eight-year cyclical periodicity

Gadagkar, S.R.

Sundararaj, N.

Aquatic Commons

Tem a ral Behavio r of Marie e Lal dings Alo 
C astal Karn taka rH111. Cyclical Patterns* 
SUDHINDRA R. GADAGKAR** and N. SUNDARARAJ 
Department of Statistics, University of Agricultural Sciences, Bangalore-560065 
Marine landing data for Karnataka during 1956-1978 were subjected to time-
series analysis and cyclical periodicities isolated in the case of seven fisheries namely, 
ribbon fish (five year cycle); Caranx spp., Leiognathus spp, and mackerel (six year 
cycle each); the combined landings of Hernirhamphus spp. and Belone spp., 'Lesser 
Sardines' and 'Other Clupeids' (seven year cycle each). 'Total' demonstrated an 
eight-year cyclical periodicity. 
The availability of certain fish resources 
is known to follow a cyclical periodicity. 
The pink salmon Onchorhyncus gorbuscha 
is a widely studied one and considerable 
information is available on its biology and 
ecology. Based on his studies on this fish, 
Birman (1976) demonstrated the occurrence 
of periodicities in abundance, specifically 
a two-year and a four-year periodicity in the 
abundance of the pink salmon. The two-
year periodicity is apparently a wide-spread 
phenomenon which has been observed in 
plants (LeRoy-Ladurie, 1971) and in meteoro-
logical elements in temperate latitudes 
(Ugryumov, 1968). Birman (1976) found 
that the sock-eye salmon revealed a depen-
dency on climate, especially solar activity, 
when a four-year periodicity in abundance 
occurred. Regular rhythmic fluctuations 
in climatic conditions and consequent hydro-
graphic fluctuations possibly influence the 
life history of any aquatic population and 
fish is no exception. 
The present study was undertaken to study 
the temporal behaviour of fish landings 
along coastal Karnataka and in the process, 
to look for cyclical (of period more than one 
year) periodicities. 
Material and Methods 
Quarterly marine catch-statistics in metric 
tonnes for coastal Karnataka (12° 44' N to 
*Forms part of the first author's thesis approved 
for the award of M.F.Sc. degree of the University 
of Agricultural Sciences, Bangalore-560 065. 
**Present address: Statistics Unit, College of Fishe-
ries, UAS, Mangalore-575 002. 
14° 53/ N) were obtained from the Central 
Marine Fisheries Research Institute, Cochin, 
for the period 1956 to 1978, for 'Total' lan-
dings as well as individual figures for 21 
species/groups. The data for the period 
1956-59 however, was available only for 
eight fisheries. 
The decomposition of the time-series data 
into its components was carried out by assu-
ming a multiplicative model which is expe-
cted to fit the data better than an additive 
model (Croxton et al., 1967). Under the 
multiplicative model, an observation Ot 
(fish catch) pertaining to a specific time 
point 't' is a result of four influence, namely, 
a trend effect (T i), a seasonal effect (S t), a 
cyclical effect (Ct) and a random (irregular) 
component (I,), conceived mathematically 
in a multiplicative form, namely, 
O t = Tt. Ct. St. It 
These four components were estimated 
from the data on fish landings by standard 
methods (Croxton et al., 1967). The sea-
sonal indices were estimated first, using 
which, the original observations O t were 
deseasonalized by dividing by S t to give 
the final estimate of TCI. These estimates 
(TCI's) were then plotted on a graph against 
time, to check if any periodic (cyclical) 
pattern was discernible visually. Wherever 
an oscillatory pattern was suggestive, a cen-
tered moving average of an appropriate period 
was worked out to eliminate this cyclical 
component, leaving only T which constituted 
the secular trend of the species/group under 
consideration. 
FISHERY TECHNOLOGY 
TEMPORAL BEHAVIOUR OF MARINE LANDINGS 
	 33 
An improved and final cycli cal effect 
was obtained in the following manner. 
The TCI's were divided. by the T's to give 
CI's (the cycles along with the 'Irregular' 
component). To remove this 'I' effect 
from these cycles, that is to smoothen the 
cycles, an appropriate simple moving average 
was computed. The corresponding points 
in the different cycles were then averaged 
to give the cyclical indices for the species/ 
group under consideration. In order to 
ascribe a mathematical format to the said 
indices as well as to join them by a smooth 
curve, harmonic analysis was carried out 
using the procedure given in Douglas (1964). 
"In general, there is the result that with 'r' 
intervals it is worth carrying out this kind 
th 
of analysis only as far as the (r- 1) har- 
monic" (Bajpai et al., 1977). In the pre-
sent study, however, in spite of the fact 
that the number of intervals varied from 20 
(five year cycle) to 32 (eight year cycle), it was 
not found necessary to go beyond the fifth 
harmonic as the fit was found visually ade-
quate. 
Results and Discussion 
The results of the time-series analysis per-
taining to cyclical patterns alone are presen-
ted in this paper. The identification of 
cyclical periodicity is much more difficult 
than that of seasonal patterns, since pseudo-
cyclical periodicities are likely to be induced 
into the moving average trend due to the 
Slutzky-Yule effect (Nerlove et al., 1979). 
Hence cycles are identified and commented 
upon only wherever they are obvious. 
As many as seven out of the 21 species/ 
groups considered in this study exhibited a 
distinct cyclical pattern of period ranging 
from five to seven years. They are ribbon 
fish (five year cycle); Caranx spp. Leiogna-
thus spp. and mackerel (six year cycle each); 
and the combined landings of Hemirhatn-
phus spp. and Belone spp., 'lesser sardines' 
and 'other clupeids' (seven year cycle each). 
`Total' exhibited a cycle of period eight years. 
Since the periods were large and the data 
available was only for 19-23 years, the num-
ber of cycles in each was less. However, 
the oscillatory behaviour of the deseason.a. 
lized data was quite apparent. Table 1 
Table 1. Cyclical indices (quarterly) pertaining to seven species/groups and the 'Total' 
Year 	 1 	 2 
	 3 	 4 
species/group IQ IIQ IIIQ IVQ IQ IIQ IIIQ IVQ IQ IIQ IIIQ IVQ IQ IIQ IIIQ IVQ 
Ribbon fish 83 180 170 154 125 171 182 128 195 94 79 63 66 43 35 42 
Caranx spp. 52 113 128 165 122 121 133 137 167 133 142 140 207 143 108 58 
Leiognathus spp. 107 98 129 119 126 112 107 104 113 138 96 61 71 72 79 73 
Mackerel 94 185 264 264 112 71 77 161 151 137 76 41 49 22 30 47 
Hemirhampus spp. 
and Belone spp. 
Lesser Sardines' 
132 
104 
103 
93 
115 
221 
312 
339 
371 
328 
371 
224 
161 
85 
142 
89 
57 
72 
62 
82 
30 
98 
22 
128 
119 
110 
146 
65 
157 
61 
55 
82 
`Other clupeids' 98 92 168 191 222 157 98 142 60 72 77 86 73 71 68 68 
`Total 131 108 122 149 138 118 118 133 97 97 109 116 93 88 90 94 
5 6 7 8 
Ribbon fish 56 78 63 73 
Caranx 72 66 78 50 50 60 68 65 
Leiognathus spp. 60 63 85 82 77 45 72 78 
Mackerel 33 29 29 46 52 78 97 108 
Hemirhampthus spp. 
and Belone spp. 41 31 34 20 24 21 44 65 78 66 103 125 
`Lesser sardines' 107 167 152 139 43 27 15 25 40 73 83 63 
`Other clupeids' 107 128 127 107 90 81 91 100 119 123 103 69 
`Total' 100 92 116 86 64 55 49 86 96 125 114 115 90 70 96 113 
Vol. 23, 1986 
24 	 32 	 40 	 48 	 56 	 64 16 
400® 
3 00® 
200 
1 0 0 
0 
-I 0 
30 
20 
1 0 0 
0— 
2 00,-- 
1 00 
(f) 'Lesser sardines' 
(g) 'Other clupeids' 
',1*,91.1111411PP 
( h ) Total' 
e • •• 
100 
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(e) Flemirhamphus spp. 8i Selene spp. 
-• 	 •••••••••-• 
• * •• 
34 	 SUDHINDRA R. GADAGKAR AND N. SUNDARARAJ 
(a) Ribbon fish 
Quarters (t) 
Fig. 1. Harmonic analysis of cyclical periodicities for different species/groups (2 cycles shown) 
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FISHERY TECHNOLOGY 
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TEMPORAL BEHAVIOUR OF MARINE LANDINGS 35 
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Vol. 23, 1986 
36 	 SUDHINDRA R. GADAGKAR AND R. SUNDARARAJ 
presents the cyclical indices pertaining to 
each of the seven species/groups and the 
`Total.' Since the data presented in the 
Table are indices, the figures are not absolute. 
Instead, they are relative to the trend-a base 
of value 100. Again, the 'years' denoted 
in the Table simply pertain to the respective 
periods of the different species/group and 
do not refer to any specific point in time. 
Harmonic analysis (upto the fifth harmo-
nic only) was carried out using the cyclical 
indices for each of the seven fisheries and 
for the 'Total.' The results are presented 
in Fig. 1 and the mathematical format that 
f(t), the cylical function assumes in each 
case, is given in Table 2. 
As is evident from the Figure lA and Table 
1, the amplitude is maximum in the case of 
the combined landings of Hemirhamphus 
spp. and Belone spp., followed by 'lesser 
sardines', mackerel, 'other clupeids', Caranx 
spp. ribbon fish and Leiognathus spp. These 
amplitudes are relative to a base (trend) of 
value 100 and reflect the systematic fluctua-
tions over the years from this base. The 
quarterly average landings of these seven 
fisheries are as follows : ribbon fish (72 tonnes) 
Caranx spp. (172 t), Leiognathus spp (408 t), 
mackerel (6951 t), Hemirhamphus spp, and 
Belone spp. (17 t), 'lesser sardines' (297 t) 
and 'other clupeids' (163 t). 'Total' has 
a quarterly average of 20,617 t. Thus a 
lower amplitude of mackerel in the figure 
is of far greater significance than the higher 
amplitude of Hemirhamphus spp. and Belone 
spp. 
Explanations for such periodicities (Fig. 1) 
are perhaps to be sought in the environment 
and meteorological activity. Most fisheries, 
especially migratory ones like mackerel, are 
to a considerable extent guided by changes 
in the environment. Cyclical phenomena in 
meteorological elements in temperate latitudes 
have been reported by Ugryumov (1968). 
Investigations have shown that fish cycles 
are very closely related to meteorological 
activity. Lapin (1971) found that the curve 
of fluctuations in the abundance of pink 
salmon in the Amur Basin almost exactly 
repeats the curve of winter rainfal. Birman 
(1966, 1973) opines that in general, the two-
year periodicity in the abundance of pink 
salmon changes at the time of greatest solar  
activity and in the southern most regions 
at the time of minimum solar activity. Thus 
Birman (1976) maintains that the two-year 
cycle in the abundance dynamics of pink 
salmon is caused by the quasi-biennial cycle 
of stratospheric winds, which in turn are 
caused by changes in solar activity. Dow 
(1977) found that most of the commercial 
marine and estuarine species of the coast 
of Maine are significantly correlated with 
sea temperature cycles. While admitting 
that the two-year cycle of pink salmon could 
be an adaptive self-adjustment to the two-
year periodicity in reproductive conditions, 
and possibly also in the abundance of major 
food items for the young, Birman (1976) 
opines that regular rhythmic fluctuations in 
climatic conditions lie at the heart of fluctua-
tions in abundance of most animal popula-
tions including fish. 
The cyclical phenomena in the fish lan-
dings of the coast of Karnataka demonstra-
ted in this study are of significance both to 
the fishermen as well as the conservationist 
and planner. The presence of a periodicity 
in the behaviour of fish landings, when there 
is no reason to expect any periodicity in the 
behaviour of the corresponding fishing effort, 
obviously reflects on the behaviour of the 
available fish stock itself. However, the 
causative factors can be short-listed only 
with more information on the hydrography, 
behaviour and biology of the concerned 
species/groups in relation to corresponding 
changes in the environment. It is impor-
tant that these resources are studied as popu-
lations and not merely fisheries. 
The authors thank the Central Marine Fisheries 
Research Institute, Cochin for the catch-statistics 
for coastal Karnataka. They also thank Dr. N.R. 
Menon and Prof. H.P.C. Shetty of the College of 
Fisheries, UAS, Mangalore, and Mr. K.M.S.Sharma 
and Dr. R.Narayana, UAS, Bangalore, for their 
keen interest and helpful suggestions. This pro-
ject was successfully carried out with the help of 
the financial assistance given by the ICAR to the 
first author, in the form of a fellowship. 
References 
Bajpai, A. C., Mustoe, L. R. & Walker, D 
(1977) Advanced Engineering Mathe-
matics, p. 578, John Wiley & Sons 
FISHERY TECHNOLOGY 
TEMPORAL BEHAVIOUR OF MARINE LANDINGS 
	 37 
*Birman, I. B. (1966) Vopr. ikhtiol., 6, 43 
*Birman, I. B. (1973) Vopr. ikhtiol., 13,78 
Birman, I. B. (1976) J. Ichthyol., 16, 364 
Croxton, F. E., Gowden, D. J. & Klein, S. 
(1967) Applied General Statistics, 3rd 
edn., pp. 214-342, Prentice Hall of India 
Pvt. Ltd., New Delhi 
Douglas, A. H. (1964) Engineering Mathe-
matices - An Introductory Survey of 
Modern Developments., p. 442, Concrete 
Publications Ltd., London 
*Dow, R. L. (1977) J. Cons, CIEM, 37, 
274 
*Original not referred 
*Lapin, Yu, Ye. (1971) Features of the 
Dynamics of Fish Populations in Connec-
tions With the Length of Their Life Cycle. 
Nauka Press, Moscow 
*LeRoy-Ladurie, E. (1971) A Thousand 
Years of Climatic History. Gidrometeo-
izdat, Leningrad 
Nerlove, M., Grether, D. M. &' Carvalho, 
J. L. (1979) Analysis of Economic 
Time Series-A Synthesis. p. 468, Acad-
emic Press. 
*Ugryumov, A. I. (1968) Meteorologiya 
gidrobiologiya, No. 12 
Vol. 23, 1986 


Temporal behaviour of marine landings along coastal Karnataka 3. Cyclical patterns

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Temporal behaviour of marine landings along coastal Karnataka 3. Cyclical patterns

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