Journal of Fisheries science and Technology - No.3/2016

distributions and cohort slicing analysis, the 
data were used to compute for only males. The 
total length was calculated based on the 
relationship equation with CL and then the 
asymptotic length (L∞) was estimated based 
on total length according to Sarda et al., 
(1998) [13].
The length-frequency distributions were 
plotted by year and analysed as a combination 
of cohort length distributions, each of 
which was assumed to be in the form of a 
Gaussian distribution [15]. The mean length at 
age of each cohort and the standard deviations 
was estimated and then the average growth 
rate can be modelled. The von-Bertalanffy (VB) 
growth equation was applied to the estimated 
mean length-at-age and the standard deviation 
data according to the equation:
Lt = L∞ (1− e
−k(t−t0))
(where Lt as the average length-at-age t, 
L∞ as the asymptotic length, k as the growth 
rate parameter and t0 as hypothetical age at 
length equal to 0). 
The VB growth model assumes that growth 
was faster when the species was young and 
get slow onwards after they become mature. 
In order to run this equation in R, some initial 
values as L∞, k and t0 were set and the least 
sums of squared error (SSE) was minimised 
using an iterative process [15]. The parameter 
t0 was fi xed at 0.1 as the fi rst two age groups 
were completely missing from the data series 
and t0 was always estimated really low.
To compare the estimated growth parameters 
of nephrops in this study with other studies, 
the growth performance index (Φ’) were used 
which calculated according to equation:
Φ = log10k + 2 * log10 L∞
(where k as the growth rate parameter and L∞ 
as the asymptotic length).
These data were analysed by models in the 
R software package according to Stefansson 
(2012) [14].
III. RESULTS AND DISCUSSION
1. Characteristics of age distribution
1.1. Age distribution at different years
The age distribution of lobster population 
from 1970 to 2011 had twenty fi ve age 
groups corresponding several peaks of 
carapace length (CL) frequency distribution 
(Figure 1). The mean CL of N. norvegicus at age 
estimated was ranged from 7.22 mm at age 1 
to 76.08 mm at age 25.
124 • NHA TRANG UNIVERSITY
Journal of Fisheries science and Technology No.3 - 2016
Figure 1. The age distribution of N. norvegicus based 
on CL distribution in catches from 1970 to 2011 
The growth rate of nephrops was high in 
the fi rst four years with mean increment of 
about 7.0 mm per year. After this age, they 
reached a maturity size, therefore, the growth 
rate gradually decreased. The proportions 
corresponding to relative ages revealed a 
difference between decades. In the period 
1970 - 1979, the age groups of 5 to 9 year olds 
were in high abundant as the mean CL ranged 
32.41 - 49.19 mm. The age groups of 5 to 10 
year olds of Nephrops showed a dominant 
proportion in the catches in the periods from 
1980 - 1989 corresponding to mean CL of 
32.41 - 52.42 mm. On the other hand, in 
recent years (1990 - 2009) and the whole data 
from 1970 to 2011, the landings showed high 
abundant of age groups from 6 to 10 year olds 
or mean CL of 37.26 - 52.42 mm. For the other 
groups, the age proportions were small (Table 1).
Table 1. Mean CL and age proportion of N. norvegicus in catches from 1970 to 2011
Age Mean CL (mm)
Proportion (%)
SD
1970-1979 1980-1989 1990-1999 2000-2009 1970-2011
1 7.22 3.904e-04 4.026e-04 9.454e-05 3.805e-06 1.471e-04 0.37146
2 14.51 6.690e-04 7.699e-04 1.606e-04 1.172e-04 2.719e-04 0.74646
3 21.09 0.00333 0.00135 6.967e-04 4.670e-04 0.00155 1.08544
4 27.03 0.04052 0.02019 0.02611 0.00776 0.02083 1.39185
5 32.41 0.12999 0.10445 0.09711 0.06046 0.09547 1.66882
6 37.26 0.23606 0.14914 0.20350 0.12269 0.16539 1.91919
7 41.64 0.15564 0.21745 0.19869 0.15398 0.18045 2.14551
8 45.61 0.16582 0.16544 0.14899 0.17378 0.15539 2.35008
9 49.19 0.10511 0.11656 0.11814 0.11922 0.11871 2.35008
10 52.42 0.04347 0.12218 0.10038 0.13062 0.10176 2.70215
11 55.34 0.06881 0.04140 0.06161 0.06519 0.05339 2.85326
12 57.98 0.02776 0.03125 0.03545 0.08298 0.06087 2.98984
13 60.36 6.564e-07 0.01685 1.367e-06 3.115e-06 8.279e-08 3.11330
14 62.52 0.01122 4.244e-07 0.02809 0.05616 0.03708 3.22490
15 64.46 0.00688 0.00959 2.685e-07 0.02014 1.075e-04 3.32578
16 66.22 5.898e-07 3.531e-07 4.401e-07 2.007e-06 9.292e-07 3.41697
17 67.81 2.331e-07 8.992e-08 7.086e-10 6.164e-06 0.00543 3.49939
18 69.25 5.413e-04 5.351e-08 4.058e-07 6.843e-04 0.00211 3.57391
19 70.54 9.469e-04 7.151e-08 1.810e-07 0.00549 2.967e-07 3.64126
20 71.71 3.102e-06 3.660e-08 9.089e-05 2.262e-04 3.539e-07 3.70214
21 72.77 3.665e-07 1.911e-08 2.404e-04 3.802e-06 2.488e-07 3.75713
22 73.73 3.959e-07 8.855e-08 1.732e-04 2.856e-06 7.566e-07 3.80691
23 74.59 6.670e-08 1.921e-07 3.134e-05 1.450e-06 1.331e-07 3.85189
24 75.37 9.341e-08 3.232e-07 5.930e-06 1.744e-06 1.397e-06 3.89253
25 76.08 0.00285 0.00296 4.472e-04 1.065e-06 0.00103 3.92928
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Journal of Fisheries science and Technology No.3 - 2016
The mean CL of this species caught in 1970 
was 45.10 mm and presented a fl uctuation 
onwards with minimum value of 42.60 mm in 
1973. Until 1995, the CL increased rapidly and 
reached a peak of 49.66 mm in 2010.
1.2. Age distribution at different fi shing areas
The age distributions of N. norvegicus 
were compared the Southeast with Southwest 
fi shing grounds based on the mean of CL 
frequency distributions.
In general, the mean CL of N. norvegicus in catches increased from 1970 to 2011 (Figure 2). 
Figure 2. The mean CL of N. norvegicus in catches from 1970 to 2011
Figure 3. The age distribution of N. norvegicus based on CL distribution in catches from 1970 to 2011 
at different fi shing areas (A: Southeast area and B: the Southwest area).
Figure 3 showed that the plotted of age 
distributions as CL frequency distributions 
were similar, but in the Southwest areas, the 
distribution was wider than in the Southeast 
areas, which revealed a difference in the 
proportion of age groups (Table 2).
126 • NHA TRANG UNIVERSITY
Journal of Fisheries science and Technology No.3 - 2016
Figure 4 showed that the mean CL of 
nephrops caught in the Southeast areas 
fl uctuated but did not show any consistent 
trend with the mean CL was 44.84 mm from 
1970 to 2011. Meanwhile, in the Southwest 
areas, the mean CL of this species revealed 
an increase from a minimum value of 40.27 
mm in 1970 to maximum value of 61.42 mm 
in 2003 and then gradually decreased to 50.0 
mm in 2011. The mean carapace length of 
N. norvegicus in this fi shing areas was 47.94 
which is signifi cantly higher when compared to 
Southeast areas (p<0.01).
The signifi cant difference of mean CL 
of N. norvegicus caught in Southwest and 
Southeast fi shing areas may be caused by 
different type of bottom structure in their 
habitat. This was in good agreement with 
Figure 4. The mean CL of N. norvegicus in catches at different fi shing areas from 1970 to 2011
Table 2. Age proportion of N. norvegicus in catches 
at different fi shing areas from 1970 to 2010
Age
Proportion (%)
Age
Proportion (%)
Southeast areas Southwest areas Southeast areas Southwest areas
1 2.106e-04 2.023e-04 14 0.01436 0.06853
2 3.733e-04 3.489e-04 15 0.00406 0.01124
3 0.00159 0.00144 16 4.538e-04 2.992e-05
4 0.02245 0.02029 17 7.999e-04 0.01403
5 0.11301 0.08017 18 8.431e-04 0.01562
6 0.19184 0.13409 19 6.784e-06 5.318e-08
7 0.19557 0.15062 20 3.183e-07 3.339e-07
8 0.16140 0.13479 21 1.625e-07 2.269e-07
9 0.10207 0.12198 22 1.087e-07 4.741e-07
10 0.10534 0.09338 23 4.469e-07 1.386e-09
11 0.02944 0.07735 24 1.988e-07 7.967e-06
12 0.05462 0.07474 25 0.00155 0.00142
13 5.323e-07 3.542e-07
In the Southeast fi shing areas, age groups with the highest proportions ranged between 5 and 
10 corresponding to mean CL of 32.41 - 52.42 mm, while the proportion of age groups 5 to 12 with 
mean CL ranged from 32.44 mm to 57.98 mm were most abundant in the Southwest fi shing areas.
NHA TRANG UNIVERSITY • 127
Journal of Fisheries science and Technology No.3 - 2016
previously observation by Tuck et al. (1997), 
who stated that local variations in size 
composition, density and growth of this species 
might be related to type of bottom sediment [16]. 
Moreover, the mean CL size of nephrops 
was positively correlated with increasing 
clay/silt content from 30 - 90% and showed 
an inversely relationship in the Irish Sea with 
bottom sediment ranges between 4 - 49% of 
clay/silt [16].
Moreover, the variation in mean CL of 
nephrops is also negatively correlated 
with depth [5]. In the Southwest areas, the 
depth ranged from 130 - 180 m and it could 
explain the higher average CL than found in 
the Southeast areas with depth of 180 - 250 m.
2. The growth parameters
The mean CL at ages of N. norvegicus 
obtained from the length frequency 
distribution and cohort slicing analysis were 
then fi tted to the von Bertalanffy growth curve 
model to calculate the growth parameters: 
CL∞ = 82.5 (mm), k = 0.1 (yr
-1), t0 = - 0.1 and the 
growth performance index Φ’) were 3.87.
Mytilineou and Sarda (1995), the CL∞ of lobster 
in the Catalan Sea ranged from 84.4 to 96.6 
mm [9]. Meanwhile, the asymptotic length (L∞) 
calculated based on the relationship equation 
between CL and total length in this study was 
300 mm which was higher than L∞ of 226 mm 
in Ancona Sea [13]. 
The growth rate parameter (k) of this 
species obtained in this study (0.1 yr-1) was 
higher than those stated by Mytilineou and 
Sarda (1995) in Catalan Sea (0.05-0.08 yr-1) 
but consistent with value of 0.11 in Ancona 
Sea [7]. 
On the other hand, the growth performance 
index (Φ,) calculated 3.87 in this study was 
higher than the results reported by Mytilineou 
and Sarda (1995) in Catalan Sea (2.6 – 2.8) [9] 
but lower than values of 6.33 – 6.64 in Ancona 
Sea [7]. The values of k and Φ’ (0.1 yr-1 and 
3.87) obtained in this study were in good 
agreement with observation before in Iceland 
(0.1 yr-1 and 2.81, respectively) [4]. These 
results were contrary to Pauly (1984), who 
stated that growth performance index was 
constant [11]. However, it was consistent 
with other studies on N. norvegicus which 
presented the growth rate can vary considerably 
due to environmental forces such as 
temperature, sediment particle size, food 
availability, population density and fi shing 
pressure, each of which may have different 
and possibly interactive effects [1].
IV. CONCLUSION
Age distributions of N. norvegicus in Iceland 
revealed twenty fi ve age groups corresponding 
to mean CL ranging from 7.22 mm at age 1 to 
76.08 mm at age 25. The dominant age groups 
in the catch were 5 to 10 year olds. The mean 
CL of this species increased from 45.10 mm 
in 1970 to 49.3 mm in 2011. The mean CL of 
N. norvegicus caught in the Southwest areas 
Figure 5. von-Bertalanfy growth curve of N. norvegicus 
at different ages in catches from 1970 to 2011 
(Broken lines showed standard deviation)
 Figure 5 showed that N. norvegicus 
caught in Icelandic waters had a CL∞ of 82.5 
mm that was fairly similar when compared 
with previous studies in different fi shing areas 
although using different methods. According to 
128 • NHA TRANG UNIVERSITY
Journal of Fisheries science and Technology No.3 - 2016
(47.94 mm) was signifi cantly higher than those 
of 44.84 mm caught in the Southeast areas 
(p<0.01).
The growth parameters of nephrops were: 
CL∞ = 82.5 (mm), k = 0.1 (yr
-1), t0 = - 0.1 and 
the growth performance index (Φ’) were 3.87. 
ACKNOWLEDGEMENTS
The authors would like to thank the United 
Nations University - Fisheries Training 
Programme and Marine Research Institute 
in Iceland for great supportted and excellent 
guidance for this research. 
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