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Universal Research Publications. All rights reserved
ISSN 2277-7729
D.NAGARAJAN
Associate Professor, Dept. of zoology, Kamaraj College, Tuticorin – 628003, Tamil Nadu
Received 29 August 2013; accepted 30 September 2013
Abstract
Age and growth of Ponyfish Secutor insidiator (Bloch) was estimated from the length frequency data. The growth parameters „L ‟, „K‟ and „t
0
‟ were calculated as per Von Bertlanffy, Bagenal, Gulland & Holt, Ford-Walford, Powel and
Wetheral methods and also through FISAT software. Von Bertalanffy growth equation fitted for the length at age data is lt
= 123.8(1-exp-3.1613 (t+0.0007)). S.insidiator
attains a length of 69, 98 and 112 mm in 0.25, 0.5 and 0.75 years. The life span (T max) is estimated to be 0.95 years.
© 2013 Universal Research Publications. All rights reserved
Keywords : Secutor insidiator , Model progressive analysis, Growth parameters, T max
1.
INTRODUCTION
Information on the growth of a fish is an important prerequisite in understanding the dynamics of its populations.
In fishery yield studies, the growth is a basic variable determining the exploitable stock and yield from the fishery. Age and growth studies in fishes help to know the age and class structure of the stock and fluctuations in the fishery caused by the presence or absence of various year classes. In the present study the age length key are derived from the length frequency analysis. Determination of growth parameters of fish requires a reliable age-length key.
The important growth parameters are „L ‟, „K‟ and „t
0
‟.
L is interpreted as “the mean length of very old (strictly: infinitely old) fish” and K is a “curvature parameter” which determines how fast the fish approaches L . The short lived fishes almost reach L in a year or two and have a high value of K. Other species have a flat growth curve with a low K value and need many years to reach L . The third parameter, t
0
also called “the initial condition parameter” determines the point in time when the fish has zero length. Biologically, this has no meaning, because the growth begins at hatching. Owing to the paucity of information on the age and growth of Secutor insidiator for
Gulf of Mannar, the present study was undertaken to estimate the age and growth of this species.
2.
MATERIALS AND METHOD
2.1.
Treatment of the data
The data were collected once in a weak by random sampling method from minimum of 10 trawlers from the
122 commercial fish landings by trawls at Tuticorin fishing harbour along with catch and effort and species composition. Total length of 2741 specimens of
S.insidiator
was measured. The weight of the fish landed was recorded by eye estimation since the fish were auctioned in lots in the auction hall. The length frequency data were grouped into 5 mm class intervals and each length group were raised for the sampling day‟s catch and subsequently for the month‟s catch by respective raising factors as per the method of Sekharan (1962).
2.2.
Model progression analysis (scatter diagram technique)
The integrated method i.e., the simultaneous application of
Peterson‟s method and the Modal progression analysis was used (Pauly, 1980) to identify the various broods in a year and their growth in subsequent period. The length frequency data during 1993-„95 for S.insidiator
are given in
Table 1 and 1a. The modes recognized in the length frequency data for various months are represented in the form of scatter diagram and the progression of mode was traced freehand through time. This line was extrapolated with reference to the inter-modal slope so as to intersect the time axis in order to trace the time of brood origin. This trend line leading from the time axis to the highest modal value in the series was the first guideline for tracing the growth history of the still older broods. When many similar trend lines were fitted, each are acted as guideline for tracing the growth history of the much older broods and also to correct, if necessary already fitted lines for the younger broods. The progression of modes through successive month along a series of trend lines, representing growth of various broods, is given in figure 1. The modes
International Journal of Research in Fisheries and Aquaculture 2013; 3(4): 122-129

thus traced were tabulated chronologically (George and
Banerji, 1968) and the average sizes were calculated as shown in Table 2. The average sizes were plotted on an arithmetic graph against the age in months and a free hand curve was fitted through the plots and this may be considered as an empirical growth curve of the species as shown in figure 2. A fresh set of lengths attained by these species from the first month of its age onwards have been obtained from these empirical growth curves which enables to obtain the missing data at lower and higher size ranges.
These data were used for further analysis to obtain the growth parameters `L ‟, `K‟ and `t
0
‟ as per von Bertlanffy
(1934), Bagenal (1955), Gulland and Holt (1959), Ford-
Walford (1946) and Powel and Wetheral (1987) methods.
Estimates of L , and K were obtained by using FISAT software (Gayanilo et al. 1995) also.
2.3.
The von Bertalanffy growth equation
The mathematical model derived by von Bertalanffy (1938) was used to calculate the length of fishes at any given time.
This equation is based on the concept that the growth is the result of anabolism and catabolism. The mathematical model expresses the length „L‟ as a function of the age of fish,„t‟: lt = L (1-e
-k (t-to)
) --------------------------------------- 1
Where L = asymptotic length, lt = Length at age t, exp = natural logarithm, K = co-efficient katabolism, t = age of fish and t
0
= age at 0 length.
2.4.
Begenal method
Begenal (1955) described the method of fitting von
Bertalanffy‟s equation for estimating the parameters L , K and t
0
. For this purpose von Bertalanffy‟s growth equation was rewritten as lt+1= L (1-e
-K
)+e
-K
lt -------------------------------- 2
This equation gives linear relationship between the lengths
123 at time „t‟ and at time „t+1‟
Where a = L (1-e l t+1
=a+b l
-K
) and b = e t
-k
Applying standard methods of regression analysis the „a‟ and „b‟ for the values of l t
and l t+1
were obtained. For this purpose the equation l t+1
=a+b l t may be written in the general form.
Y = a+bx --------------------------------------------------- 3
N XY - X. Y b =
N X
2
- ( X)
2 a = Y - b x and l t
= X and l t+1
= Y
The value of „K‟ is derived from that of „b‟ using the expression
K = - log e b ------------------------------------------------4 t
0
was estimated by rewriting the von Bertalanffy‟s Growth
International Journal of Research in Fisheries and Aquaculture 2013; 3(4): 122-129

equation as
- k t + k t l t = L - L e
- k t + k t
L e 0 = L - l t
0
L - l t e
- k t + k t
0
=
L
L - l t
- k t + k t o
= log e
L
L - l t k t o
= log e
L
+ k t
L - l t t o
= 1/k { (log e
) + k t } -----------------5
L
2.5.
The Gulland and Holt plot
Growth parameters can be derived from age/length data by graphical methods for plots, which are always based on a conversion to a linear equation. These plots are named after the authors ie.,e Chapman (1961), Ford-Walford
(1946) and von Bertalanffy (1934). The Gulland and Holt
(1959) plot is obtained from the equation
L/ t = K L - K L (t) ----------------------------------6
The length „l(t)‟ represents the length range from l(t) at an age t to l(t+ t) at age t+ t. Thus, the natural quantity to enter into Eq.(6.6) is the mean length Using l(t) as the independent variable and L/ t as the dependent variable
Eq.(6.6) becomes a linear regression:
L/ t = a+b * L (t) l(t+ t) +l(t)
L =
2
The parameters K and L are obtained from K = - b and
L = - a/b
2.6.
The Ford – Walford plot and Chapman‟s method
This method introduced by Ford (1933) and Walford
(1946) was derived from the original growth equation
(Eq.6.1) by a series of algebraic manipulations such as: l(t+ t) = a + b l(t) ---------------------------------------------7
Where a = L (1 – b) and b = exp. (- K t )
Since K and L are constants „a „and also „b‟ become constants if t is a constant. Using l(t) and l(t+ t) as (x,y)
Eq. 6.7 can be used for linear regression. The growth parameters „K‟ and „L ‟ are derived from
K= -(1/ t)
L
*
Lnb and L = a / (1 – b) can be estimated graphically from the intersection point of the regression line and the line l(t) = l(t+ t) (the 45 degree line) because for very old fish, which have stopped growing we have L = l(t) = l(t+ t).
Also the methods described by Chapman (1961) and later by Gulland (1969) are based on a constant time interval„ t‟, that is to say that the method is applicable if we have pairs of observations.
(t, L(t) ), (t+ t, L(t + t)), (t+2 , L(t+2 t)),etc.
It can be shown that the von Bertalanffy growth equation implies that:
L(t+ t) - L(t) = c
*
L - c *L(t) ----------------------------- 8
124
Where c = 1 – exp ( - K
*
t )
Thus, since K and L are constants, and if t remains constant, „C‟ will remain constant and consequently Eq.
(6.8) becomes a linear regression
Y = a + b x where
Y = L(t+ t) - L(t) , a =c
*
L , b = - c and x = L(t)
The growth parameters are derived from
K = - (1/ t)
*
Ln (1 + b) and L = - a/b or a/c
2.7.
Powell – Wetherall method
Powell makes use of variance in length of fish caught from
L
‟ onwards and he proposes the following equation to get L
and Z / K.
L – L‟ = a+b * L‟ where,
L = -a/b and Z /= - (1+b)/b
Thus, plotting L against L‟ gives a linear regression from which a and b can be estimated and hence L and Z / K.
2.8. The von Bertalanffy plot
This method can be used to estimate K and to from age/length data, while it requires an estimate of L as input. The growth equation (6.1) can be rewritten
-Ln (1 - L(t)/L ) = - K
* t
0
+ K
*
t ----------------------------9
With the age, t, as the independent variable (x) and the lefthand side as the dependent variable (y) the equation defines a linear regression, where K represents the slope and -K
*
t
0 the intercept.
K = b and t
0
= - a/b
The growth parameters are also estimated from the length frequency data by using FISAT software. The growth parameters W , K and t
0 in weight of these species is estimated from the corresponding weight obtained for the size at an interval of one month year as per their respective length-weight relationship by the method of Bagenal
(1955).
3.
RESULT
From the length frequency data (Table 1 & 1a) progression of modes can be traced for the period ranging from 2 to 5 months (Fig. 1). A mode at 62.5mm in July 1993 can be traced to 92.5mm in October 1993, and two modes at
67.5mm in January 1994 and July 1994 can be traced to
97.5mm in September 1994 and October 1994 respectively, showing an average growth 10mm per month. Further one mode at 97.5mm in October 1994 can be traced to
102.5mm in November 1994 and two modes at 102.5mm in
December 1994 and August 1994 can be traced to
107.5mm in January 1995 and September 1994 respectively, showing a monthly growth of 5 mm. Monthly growth of 10 mm between 62.5 mm to 97.5 mm in, and 5 mm between 97.5 to 107.5 mm were observed. Hence, the smallest modal length at 62.5 mm (from which growth could be traced) can be reasonably taken as three months old with an average monthly growth of 21mm. The progression of model lengths in successive months during
1993-1995 is given in the Table 2. As per the empirical growth curve (Figure 2) S.insidiator
attains 69, 99 and
112mm in 0.25, 0.5 and 0.75 years with a monthly growth rate of 23.6, 9.3 and 4.3mm respectively.
International Journal of Research in Fisheries and Aquaculture 2013; 3(4): 122-129

Fig. 1. Tracing the progression of modes by scatter diagram of modal length-month for Secutor insidiator for Tuticorin during 1993 - 1995
Table 1.
Estimated numbers for S.insidiator
during 1993 - 1994
Mid length
(mm)
Mar
„93
Apr
„93
May „93 Jun „93 Jul „93 Aug „93
Sep
„93
Oct
„93
Nov „93
Dec
„93
Jan „94
62.50
67.50
72.50
77.50
82.50
87.50
92.50
97.50
102.50
107.50
112.50
117.50
TOTAL
Feb
„94
TOTAL
0
689
0
2066
0
0
0
0
3443 0
24169 47235
34563 55187
10082 50587
3568
689
8531
0
0
0
0
0
0
704737
2401015
1722504
3334643 10660740 2184398
2316876 6179886 6861284
3691666
959854
585774
176875
0
0
0
0
2413639
5397251
4082182
1206252
1261357
0
0
0
134806
134806
1351
279669
5085953
4374594
459287
236935
1351
0
0
0
0
0
166044
1323895
710801
0
0
0
0
0
0
34678
46275
0
92904
87293
0
87293
0
7689
17145
5611
0
0
0
0
122025
667391
2047838 213181 187258 750731
1730977 165813 129272 563869
0
0
30212
48556
33142
14798
15414
23736
2200343 210870 57986 1390289 18959
3382887 256390 15378 1617517 25435
75837
4161
3546
0
6415
14967
10691
2138
4276
2138
7773
29980
29153
15217
4009
738
53709
89515
89515
53709
0
0
318046
1080563
4949353
7559428
35806 16526789
17903 17506880
17903 16853674
0 11928956
0
0
5622515
3023808
783127
6349
79269 161540 15893944 31201307 19754434 11562785 927207 687829 5111822 293796 127495 358060 86159488
Table 1a: Estimated numbers for S.insidiator
during 1994 - 1995
Mid length
(mm)
Mar
„94
Apr
„94
May „94 Jun „94 Jul „94 Aug „94 Sep „94
92.5
97.5
102.5
107.5
112.5
117.5
TOTAL
62.5
67.5
72.5
77.5
82.5
87.5
Oct „94
Nov
„94
Dec
„94
Jan „95 Feb „95 TOTAL
4925 0 0
0
4925
0
0
0
0
0
201389
0
0
0
6478170
4925 201389 6588223
0
56493
112985
225970
112985
508433
10300 0 0
10300
31906
41199
54518
0
0
437825
1167535
0
0
0
0
183147 3940429 913735
0
0
0
0
0
700628
0
0
0
0
0
14764
0
0
0
0
2197
0
0
0
0
0
0
0
0
0
0
0
0
0
15225
66793
149816
704994
8016794
13055673
4925 172619 5772824 1016866 490660 1897244 456868 350314 7382 6592 0 1092481 11268775
9849
0
4925
0
0
14385
28770
0
0
0
517753
110053
0
165080
110053
1129851 352975
451940
112985
56493
0
105011
31906
10300
0
473150
1233541
181267
181267
0
1142169
328406
1970433
328406
328406
875785
175157
1050942
175157
175157
18456
29529 327793 127571 819361
3691
0
0
93232 382713 819361
188835
30345
7185
255142
0
0
273120
0
0
5829679
3737132
4073246
947048
620801
34474 618552 19742156 3785001 1322222 9512258 5468423 3503140 73822 656179 765426 3004323 48485976
International Journal of Research in Fisheries and Aquaculture 2013; 3(4): 122-129 125

Table 2: Progression of model length (mm) in successive months for S.insidiator during 1993-1995
Curve No. Origin
4
5
6
7
1
2
3
8
9
10
11
Mean Length (mm)
March
July
March
April
1
32
33
31
32
32
2
54
55
53
54
54
3
70
70
71
71
70
89
70
73
4
82
82
84
83
82
82
81
82
82
A g e I n M o n t h s
5 6
92
92
92
93
93
92
91
90
91
92
92
101
99
99
101
99
99
98
98
98
98
98
99
7
105
105
106
104
104
104
103
104
104
8
116
111
108
108
108
110
9
113
113
Table 3: Estimated values of t
0
and calculated values of length and weight of S.insidiator by Bagenal‟s method.
Age
(month)
Lt
Total
Length mm (x)
Lt + 1
(Y) t
0
Calculated
Length
(mm)
Empirical
Weight (g)
Cube root of wt(x)
Cube root of wt+1
(y) t
0
Calculated weight
(g)
1
2
3
4
5
6
7
8
32
54
69
82
92
99
104
109
113
54
69
82
92
99
104
109
-0.01127
-0.01461
-0.00782
-0.01015
-0.01332
-0.00864
0.00346
29
51
68
81
91
98
104
113 -0.00528 109
Mean t
112
0
= -0.0085/Month; -0.0007/yr a (intercept) = 28.68 b (slope) = 0.7684
L∞ a/1-b = 123.8 mm K (annual) = 3.1613
95% confidence limits for a: (26.4870, 30.8738)
95% confidence limits for b: (0.7423, 0.7945)
126
0.371
2.087
4.689
8.293
12.128
15.452
18.183
21.234
23.918
0.718
1.278
1.674
2.024
2.298
2.491
2.63
1.278
1.674
2.024
2.298
2.491
2.63
2.769
-0.0022
-0.0046
0.0016
-0.0018
-0.0061
-0.0018
0.0106
0.3
2.0
4.8
8.2
11.9
15.4
18.6
2.769 2.881 0.0042 21.4
2.881
Mean t
0
= -0.00001/Month; -0.0000008/yr
23.7 a (intercept) = 0.7019 b (slope) = 0.7826 w∞ 1/3 = 3.2290 woo = 33.67 K (annual) = 2.9414
95% confidence limits for a: (0.6450, 0.7588)
95% confidence limits for b: (0.7555, 0.8097)
International Journal of Research in Fisheries and Aquaculture 2013; 3(4): 122-129

Table 4: Estimation of growth parameters (L∞, K and t
0
) for S.insidiator during 1993 – 1995 as per Von Bertalanffy,
Ford-Walford, Chapman and Gulland and Holt methods.
Methods Von Bertalanffy Ford-walford Chapman Gulland and Holt t" months
L(t) mm
(x)
L(t+Dt) +L(t)/2
(x)
- Ln (1 - L(t)/L¥)
(y)
L(t +Dt)
(y)
L(t+Dt) - L(t)
(y) dL(t)/dt
(y)
5
6
7
8
9
1
2
3
4
32
54
69
82
92
99
104
109
113
43
61.5
75.5
87
95.5
101.5
106.5
111
0.2991
0.573
0.815
1.0858
1.3592
1.6078
1.833
2.124
2.4391
54
69
82
92
99
104
109
113
22
15
13
10
7
5
5
4
22
15
13
10
7
5
5
4
Von Bertalanfy Ford-Walford Chapman Gulland and Holt a (intercept) = 0.0342 b (Slope) =0. 26285 a (intercept) = 28.6804 b (Slope) = 0.7684 a (intercept) =28.6804 b (Slope) = -.0.2316 a (intercept) = 32.3959 b (Slope) = -0.2614
K (annual) b* 12 = 3.1548 t
0
(annual)
(-a/b)/12 = -0.0108
K (annual)
(-Lnb/dt)* 12 = 3.1613
L∞ a/(1-b)/ = 123.8 mm
K (annual)
Ln(1+b)* 12 = 3.1613
L∞
-a/b = 123.8 mm
K (annual)
-b* 12 = 3.1368
L∞
-a/b = 123.9 mm
Table5.
Estimation of asymptotic length (L∞) for S.insidiator during 1993-1995 as per Powell Wetherall (1987).
L‟= L
1
-L
(X)
2
C(L
1
,L
2
)
(% catch
(L
1
+L
2
)/2
∑ C(L‟,∞)
(% Cumulated)
((L
1
+L
2
)/2)*C
∞
∑(( L
1
+L
2
L‟
)/2)*C L L - L‟
60-65
65-70
70-75
75-80
80-85
85-90*
90-95*
95-100*
100-105*
105-110*
110-115
115-120
0.2475
0.8521
3.7871
6.1379
18.2283
22.6985
20.8863
13.1891
6.9513
5.2709
1.285
0.4658
62.5
67.5
72.5
77.5
82.5
87.5
92.5
97.5
102.5
107.5
112.5
117.5
99.9998
99.7523
98.9002
95.1131
88.9752
70.7469
48.0484
27.1621
13.973
7.0217
1.7508
0.4658
15.46875
57.51675
274.5648
475.6873
1503.835
1986.119
1931.983
1285.937
712.5083
566.6218
144.5625
54.7315
9009.535
8994.066
8936.55
8661.985
8186.298
6682.463
4696.344
2764.361
1478.424
765.9158
199.294
54.7315
90.096
90.164
90.359
91.070
92.007
94.456
97.742
101.773
105.806
109.079
113.831
117.5.1 a (intercept) = 30.8822 sa = 1.6538 95% confidence limits for a = (25.623, 1414) b (slope) = -0.2538 sa
2
=2.7352 95% confidence limits for b = (-0.309, -0.1986)
L∞ = -a/b = 121.7 mm sb = 0.01736 * used in the analysis (n=5)
Z/K = -(1=b)/b = 2.9401 sb
2
= 0.0003
30.096
25.164
20.359
16.07
12.007
9.456
7.742
6.773
5.806
4.079
3.831
2.501
The L , K and t0 obtained by the various methods and their respective Table and Figure numbers are given below:
L
(mm)
123.8
-
123.9
123.8
123.8
121.7
122.0
K
(year)
3.1613
3.1548
3.1368
3.1613
3.1613
-
2.5000 to
(year)
-0.0007
-0.0108
-
-
-
-
-
Method
Bagenal
Von Bertalanffy
Gulland and Holt
Ford-walford
Chapman
Powell wetherall
Bhattacharya-FISAT year
1955
1934
1959
1946
1961
1987
1967
Table
No.
3
4
4
4
4
5
-
Figure
No.
2
3
4
5
6
7
8
124.0 3.0000 - ELEFAN I - FISAT
According to the von Bertalanffy growth equation lt = 123.8(1-exp
-3.1613 (t+0.0007)
)
1995 - 9
S.insidiator
is estimated to grow 68, 98 and 112 mm in 0.25, 0.50, and 0.75 years. The life span (T max) of this species is estimated to be 0.95 years as per the equation: T max = 3/K.
127 International Journal of Research in Fisheries and Aquaculture 2013; 3(4): 122-129

The growth parameters W , K and t
0
of S.insidiator
were given below:
Year Gram
0.25 4.8
Growth parameters
W (g)
K (year)
S.insidiator
33.7
2.9414
0.50
0.75
1.00
W
15.4
23.7
28.6
33.7 t
0
(year) -0.0000008
The growth in weight may be described by the following von-Bertalanffy (1938) growth equations. wt = 33.7(1-exp
-2.9414 (t+0.0000008)
) 3
As per the above equations the weight (in gram) attained at an interval of 0.25 year is given below.
Obtaining a reliable estimates of growth parameters for tropical species is hampered very much due to interference of various factors such as short life span, seasonal variations in growth within a year etc,.
Generally in nature the oldest fish in the stock grows to reach about 95% of its asymptotic length (Beverton, 1963).
Assuming the maximum size encountered in the fishery ie.,
117mm for S.insidiator
and 166 to be 95 % of the L of these then the L works out theoretically to 123 mm.
Present estimates obtained through various methods vary from 122 to 124 mm for and all these estimates are much closed to the theoretical estimates obtained for all the four species as shown above.
The estimates of growth parameters obtained in the present study and earlier work in S.insidiator
in Indian waters are given in the form of a Table here for comparison.
Growth parameters
Locality Author Year
L (mm) K (annual) t
0
(annual)
Tuticorin Present 122-124 2.5 to 3.1613 -0.0108to -0.0007
Kakinada
Portonovo
Kerala coast
Murty
Jayabalan
Abraham
1990
1991
2011
123
120
130
1.2
_
0.80
-0.01
_
-0.001
Murty (1990) has reported the growth parameters for
S.insidiator
from Kakinada to be L = 123mm, K = 1.2 per year and t
0
= -0.01 year which indicate that the L is very close and the K is lower than the present estimates obtained for the same species. Further, as seen from the K of all these species reported by other workers it appears that all these species are exhibiting much slower growth than the four species presently studied.
The short lived species has small L and a high K value and long lived species have a higher L with a low K value
(Pauly, 1985). Present study shows that S.insidiator
is having small L and higher K values indicating that these species are short lived like the Indian mackerel Rastrelliger kanagurta (Yohannan, 1982; George and Banerji, 1968), oil sardine Sardinella longiceps (Banerji, 1973); and barracuda Sphyraena obtusata (Kasim and
Balasubramanian, 1990). The long lived species like seerfish Scomberomorus commerson (Devaraj, 1982) and
Rhizoprionodon acutus (Kasim, 1991) and perch Lethrinus nebulosus (Kasim et al, 1989) have higher L and small K.
Larger perlagic fishes such as the king seer Scomberomorus commerson is reported to attain 500 to 600 mm in 6 months and about 800 mm in 1 year by Dadley et al., (1992) based on the daily growth ring. Faster growth among the tropical species is not uncommon in view of the prevalent high temperature which profoundly influences the growth of the poikilotherms. The same is true for long lived tropical species also as reported by Kasim (1991) in the case of sharks. Naturally it is true from the present study and earlier reports that the silverbellies are small to medium
128 sized fishes with short life span ranging from 1.0 to 1.5 years with small L and large K values.
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