Received: 09/09/2024 Accepted: 04/11/2024 Published: 05/02/2025 1 of 9
https://doi.org/10.52973/rcfcv-e35513 Revista Cientíca, FCV-LUZ / Vol. XXXV
ABSTRACT
In this study, a comparison of traditional growth methods (length-
weight relationships and von Bertalanffy growth function) with
articial neural networks in growth models was carried out in
the growth of 783 specimens of Capoeta umbla from the Munzur
River, Turkey from September 2019 to May 2021. The length-
weight relationships of C. umbla W = 0.0085L
3.013
R
2
=0.943 was
determined for all individuals. The ages of the specimens were
from 0 to 11 years old. The von Bertalanffy growth function was
L
t
= 46.15 [1-e
-0.139 (t + 2.57)
] and W
t
= 856.32 [1-e
-0.139 (t + 2.57)
]
3.013
for all
individuals. Ф' value was 2.471 all individuals. The training stopped
and the best validation performance was xed at 8.1473 × 10
-5
at
epoch 42. The validation checks were reached as 6, at epoch 48
and the gradient = 5.6566 × 10
-5
, at epoch 48. The target output
R value was 0.98584 for training, 0.98969 for validation, 0.98757
for testing and 0.9868 for all. The calculated MAPE values were
0.140 and 0.578 for articial neural networks, 1.168 and 2.726 for
length–weight relationships, 5.721 and 4.013 for von Bertalanffy
growth function, respectively. The calculated SSE values for length
and weight were 0.0128 and 30.864 for articial neural networks,
1.3985 and 350.786 for length–weight relationships. The results
of the present show that articial neural networks can be superior
estimators than length–weight relationships and von Bertalanffy
growth function. Therefore, articial neural networks models are
an effective tool to describe body weight and length in sh.
Key words: Growth properties; mean absolute percentage error
(MAPE); length–weight ratio; von Bertalanffy growth
function; Index of Average Percentage Error
RESUMEN
En este estudio, se realizó una comparación de los métodos de
crecimiento tradicionales (relaciones longitud–peso y función de
crecimiento de von Bertalanffy) con las redes neuronales articiales
en el crecimiento de 783 ejemplares de Capoeta umbla del río
Munzur, Turquía de septiembre de 2019 a mayo de 2021. Se
determinó la relación longitud-peso W = 0.0085L
3.013
R
2
=0,943
para todos los individuos. Las edades de los ejemplares fueron de
0 a 11 años. La función de crecimiento de von Bertalanffy fue L
t
=
46,15 [1-e
-0,139 (t + 2,57)
] y W
t
= 856,32 [1-e
-0,39 (t + 2,57)
]
3,013
para todos
los individuos. El valor de Ф' fue 2,471 para todos los individuos.
El entrenamiento se detuvo y el mejor rendimiento de validación
se fijó en 8,1473 × 10
-5
en la época 42. Las comprobaciones
de validación fueron alcanzado como 6, en la época 48 y el
gradiente = 5,6566 × 10
-5
en la época 48. El valor R de salida
objetivo fue de 0.98584 para el entrenamiento, de 0,98969 para
la validación, de 0,98757 para las pruebas y de 0,9868 para todos.
Los valores MAPE calculados fueron de 0,140 y 0,578 para redes
neuronales articiales, 1,168 y 2,726 para relaciones longitud–peso,
y 5,721 y 4,013 para función de crecimiento de von Bertalanffy,
respectivamente. Los valores SSE calculados para longitud y peso
fueron 0,0128 y 30,864 para redes neuronales articiales, y 1,3985
y 350,786 para relaciones longitud–peso. Los resultados del estudio
actual muestran que las redes neuronales articiales pueden ser
estimadores superiores a relaciones longitud–peso y función de
crecimiento de von Bertalanffy. Por tanto, los modelos de redes
neuronales articiales son una herramienta ecaz para describir
el peso y la longitud corporal de los peces.
Palabras clave: Propiedades de crecimiento; error porcentual
absoluto medio; relaciones longitud–peso;
función de crecimiento de von Bertalanffy; índice
de error porcentual promedio
Comparison between traditional models and articial neural networks
as estimators of the growth of the Tigris scraper Capoeta umbla
(Teleostei: Cyprinidae) in the Munzur River, Turkey
Comparación entre modelos tradicionales y redes neuronales articiales
como estimadores del crecimiento del raspador del Tigris Capoeta umbla
(Teleostei: Cyprinidae) en el río Munzur, Turquía
Ebru Ifakat Ozcan* , Osman Serdar
Munzur University, Faculty of Fisheries. Tunceli, Türkiye.
*Corresponding author: ebruozer@munzur.edu.tr
Comparison of traditional models and articial neural networks in the growth of Capoeta umbla / Ozcan and Serdar___________
2 of 9 3 of 9
FIGURE 1. Relative location of the study area
INTRODUCTION
Nowadays, with the increase in the world population, the need
for animal protein has increased [1]. In order to meet this animal
protein need, the biological characteristics of the species must
be known in order to effectively manage fish stocks. Growth
in sh can vary even among same species, different regions.
These differences may result from the physical, chemical and
biological characteristics of the environment, especially genetic
characteristics and nutrition [2].
The body of Capoeta umbla (Heckel, 1843) is slightly cylindrical
in shape. Its upper side displays a dark coloration, while its sides
appear brown-yellow. The lower side of the body is off-white and
provided with small scales [3]. The standard length is minimum
3.9 and maximum 4.7 times the maximum body length. There is a
pair of barbels on the corners of the mouth. The mouth structure
is slightly curved or straight, regardless of gender. The head is
pointed, the nose is blunt, the mouth is large. Head length is
minimum 2.5 and maximum 3.5 times mouth width. 2/3 of the
last unbranched ray of the dorsal n is toothed and slightly strong
in some individuals [3]. Previously, several studies have been
conducted on the biology of C. umbla in different aquatic bodies
[4, 5, 6, 7, 8, 9, 10, 11, 12].
Articial neural networks (ANNs) are computer systems designed
to emulate the learning function that is a fundamental feature
of the human brain. They carry out the learning process using
examples. These networks consist of interconnected process
elements (articial nerve cells). A weight value for each link. This
is the information that the articial neural network has hidden in
the weights. It is distributed throughout the network. It produces
the outputted by passing it through the activation function and
sends it to other cells (process elements) over the connections
of the network [13]. By experimenting with data, articial neural
networks can learn and generalise; it has a non linear structure
and is better shows better results than linear methods [14]. The
method determines non-linear relationships without the need
to assume them [15]. It also allows using an unlimited number
of variables. Increasing interest in articial neural networks in
sheries, especially in recent years, is due to the fact that these
issues require accurate estimates. Many studies on articial neural
networks have shown that they provide preferable results than
traditional methods [16, 17, 18, 19, 20, 21, 22, 23, 24]. ANNs
due to their ability to mimic nonlinear systems, It is more effective
than other traditional methods [25].
This study was based on the comparison of traditional equations
(LWRs, VBGF) and articial neural networks (ANNs) on the growth
of C. umbla in the Munzur River. It will determined whether articial
neural networks can used as a alternative and reliable method in
growth models.
MATERIALS AND METHODS
Turkey's Munzur River originates from the foothills of Visit Hill
on the Munzur Mountains in the north of Ovacık and merges with
Pülümür Stream in the central district and flows into Keban Dam
Lake. Uzunçayır Dam Lake was established on the Munzur River
to produce energy [26, 27].
For the study, 783 specimens of C. umbla were collected from
local shermen seasonally from different regions of the Munzur
River (FIG. 1) [28] from September 2019 to May 2021. The body
weights of the sh were determined on a scale with 1 g precision
(Dahongying, ACS-809T model, Korea), and their lengths were
determined with an ichthyometer with 1 mm graduations. Sexual
determination of sh was performed according to Lagler et al. [29].
In smaller sh sex determination was determined with the help of
a compound microscope (Nikon, ECLIPSE Ci model, Japan). The
chi-square test (χ2) was used to determine whether the sex ratio
(female/male) in the sample was statistically different from the
expected 1:1 ratio [30]. For age determination, between 10 and
15 scales taken from the sh were placed in paper envelopes.
The dirty scales have been washed in a bath of warm water. Age
readings were made with a compound microscope with glycerin
dripped slides (OLYMPUS, BX53 model Japan).
The length-weight relationships were determined equation:
W = a*L
b
[31] (W = total weight, a and b = regression constants,
L = total length).
To check if there was difference between the ages, the Index
of Average Percentage Error (IAPE) was used. The formula was
as follows [32] IAPE = 1/N ∑ (1/R) ∑ (xij-xi/xj) (N = Number of sh
whose age is determined, R = Number of readings, xij = Mean
age calculated from the jth sh, xij = ith age determination of the
jth sh).
The von Bertalanffy formulae for growth in length and weight
have been used for the mathematical calculation of growth in
length and weight. von Bertalanffy growth function: L
t
= L
∞
[1-e
-k(t-to)
];
W
t
= W
∞
[1-e-
k(t-to)
]
b
[31] (L
t
= The total length (cm) at age t, L
∞
=
the asymptotic length (theoretical maximum length), W
∞
= the
asymptotic weight (theoretical maximum weight), k = The Brody
growth coefcient (proportional to rate at which L
∞
is reached), t
= The age (years), t
0
= The age at zero length).
The growth achieved in the parameters studied in this research has
been compared with previous studies using the Phi Prime. Growth
performance (index) value (Ø’) (Phi-prime): Ø = log
(k)+2log
(L
∞
) [33].
Comparison of traditional models and articial neural networks in the growth of Capoeta umbla / Ozcan and Serdar___________
_________________________________________________________________________________________________Revista Cientica, FCV-LUZ / Vol.XXXV
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5.
0
-
9.9
10
.
0-
14.9
15
.
0-
19.9
20
.
0-
24.9
25
.
0-
29.9
30
.
0-
34.9
35
.
0-
39.9
40
.
0-
44.9
0
100
200
300
400
Total length groups (cm)
Frequency
All
Female
Male
FIGURE 2. Representation of an articial neural networks.
FIGURE 3. Distribution of total length groups-frequency of Capoeta umbla in
Munzur River
The condition factor, the feeding capacity of the fish’s
environment, is calculated as follows: CF = (W/L
b
).100 [34].
Microsoft Ofce Excel 2013 and SPSS 24.0 packages were also
used for statistical analysis of the data obtained.
Articial neural networks (ANNs)
Articial neural networks have been inspired by the human brain,
and the mathematical process of learning modeling has emerged
as a result of the effort. ANNs consists of three layers: input, hidden
and output layers. In addition, the model consisting of 8 neurons
(3 in the input layer, 4 in the hidden layer and 1 in the output layer)
is designed as fully connected feed-forward backprop propagation
algorithm. The input layer transfers the data from the sensors and
the set to the network. The information from the input layer is
multiplied by weight coefcients in the hidden layer and passed
through activation functions and then passed to the output layer.
The output layer contains the output values previously given to
the ANNs using error calculation functions. Error between values
produced by ANNs. The weighting coefcients are redone when
the error values are not good [35]. In articial neural networks,
the goal is to nd the optimal weight and bias values that yield
the best performance for the given model. These weight and bias
values influence the network’s ability to accurately map inputs to
outputs during the learning process, ultimately determining the
effectiveness of the model in solving the desired task. At each
epoch, weights and biases are updated. these calculated values
are dened as learning. Representation of an articial neural
networks is given in FIG. 2. System training uses the feed-forward
backpropagation algorithm.
Two performance measures used in the study were sum squared
error (SSE) and mean absolute percentage error (MAPE). SSE was
used as a convergence criterion during network training. MAPE is
often used to evaluate the accuracy of predicting models. MAPE
is usually expressed in percentage (%).The MAPE (%) equation
has been used for comparison between ANNs and other methods.
MAPE is an error measure, a low result is a measure that shows
high performance that is inversely proportional to power [22, 37].
SSE and MAPE are given in the equations below.
Weighting and biasing, mathematical equation of neuron model
[36] are given in the equations below.
w w
w
=
-
f
2
2N
b b
b
=
-
f
2
2N
y(k) F( wi(k) xi(k) b)·
i 0
m
=
+
=
/
SSE = e
i
2
i
=
1
n
/
MAPE =
n
1
Yi
ei
i
=
1
n
/
×100
(n= number of total observations, ei= difference between actuals
and estimates, Yi= actual observation value).
MATLAB Ver R2016a Neural Network Toolbox used in ANN
predictions consists of three parts: learning (70%), testing (15%)
and validating (15%) [17].
RESULTS AND DISCUSSION
The total length of C. umbla caught during the research were
6.8 cm to 38.5 cm in females and 7.9 cm to 40.2 cm in males.
The length frequency values of the samples of C. umbla living are
given in FIG. 3 from Munzur River. The length group is dominant
15.0-19.9 cm in female and 20.0-24.9 cm in male (FIG. 3). TABLE I
shows the total length values of C. umbla in the studies carried out
by different researchers. Differences between these values may
be influenced by the region, time, method and many ecological
factors [38]. Of the 783 samples caught, 444 were female and
339 were male. The female/male ratio is calculated as 1/0.764,
chi-square (χ
2
) test showed that signicantly different from the
theroretical 1:1 ratio (P<0.05).
yi(k)=output value in discrete time k, F=transfer function,
xi(k)=input value in discrete time k where i goes from 0 to m,
wi(k)=weight value in discrete time k where i goes from 0 to
m, b=bias.
Comparison of traditional models and articial neural networks in the growth of Capoeta umbla / Ozcan and Serdar___________
4 of 9 5 of 9
0 10 20 30 40 50
0
100
200
300
400
500
600
700
Total length (cm)
Weight
W=0.0085L
3.013
R
2
=0.943
n=783
FIGURE 4. Length-weight relationship for all individuals of Capoeta umbla in
Munzur River
Length-weight relationship of C. umbla were determined
W = 0.0084L
3.015
(R
2
=0.948, SE of b=0.0029 and 95 % condence
intervals of b=2.680–3.359) in females, W = 0.0088L
3.007
(R
2
=0.935,
SE of b=0.0033 and 95 % condence intervals of b=2.625–3.236)
in males and W = 0.0085L
3.013
( R
2
=0.943, SE of b=0.0022 and 95%
condence intervals of b=2.652–3.359) in all individuals (FIG. 4).
The growth of C. umbla is isometric in the Munzur River. The length-
weight relationships of this species studied by different researchers
are given in TABLE I. These values can different even between
same species in different locations. Differences can be observed
due to seasonal changes in nutrient levels and reproduction [39].
All environmental factors as well as reproductive period, sex,
sampling method and time, number of samples, season and region
may give different results in ‘b’ values [38]. Condition factor of
C. umbla varies between 0.894±0.007 in females, 0.911±0.008
in males and 0.901±0.006 in all individuals from Munzur River.
TABLE I
Population characteristics of Capoeta umbla in dierent regions
Habitat Sex n Age Total length (cm) a b R² L∞ k to Ф’
Hazar Lake [
4
]
180 2–13 18.70–47.20 0.0000083 3.006 0.96 68.61 0.07 -2.04 2.517
164 2–13 19.50–46.00 0.0000050 3.097 0.96 71.49 0.06 -2.63 2.486
+
346 1–13 15.00–47.20 0.0000029 3.186 0.94 68.62 0.07 -2.20 2.517
Karasu River [
5
]
506 1–12 10.40–34.20 0.0117 2.991 0.99 45.70 0.14 -0.83 2.465
665 1–10 10.90–32.30 0.0139 2.936 0.99 42.30 0.14 -0.98 2.398
Tercan Dam Lake [
6
]
165 1–6 11.62–31.84 0.000500 2.321 0.98 41.64 0.19 -0.69 2.517
158 1–6 12.35–31.06 0.000192 2.485 0.98 40.60 0.22 -0.29 2.559
+
323 1–6 12.00–31.65 0.000677 2.674 0.98 41.11 0.20 -0.54 2.528
Tuzla Stream [
6
]
161 1–6 12.11–32.67 0.000290 2.400 0.98 54.17 0.12 -1.54 2.546
146 1–6 12.67–31.00 0.000141 2.532 0.99 46.08 0.15 -1.34 2.503
+
307 1–6 12.42–32.34 0.000208 2.458 0.98 52.15 0.14 -1.35 2.580
Hazar Lake [
7
]
237 1–10 14.31–44.65 0.056 2.466 0.95 49.22 0.20 -1.88 2.685
127 1–10 13.71–44.80 0.104 2.262 0.93 56.17 0.13 -1.62 2.612
+
364 1–10 13.95–44.68 0.070 2.390 0.95 53.77 0.16 -1.84 2.665
Uzunçayır Dam Lake [
8
]
158 1–11 15.33–43.05 0.0112 2.927 0.96 47.01 0.16 -1.58 2.550
288 1–12 13.20–42.70 0.0111 2.930 0.95 44.91 0.14 -1.82 2.450
+
446 1–12 14.17–42.70 0.0110 2.932 0.96 46.85 0.14 -1.95 2.490
Özlüce Dam Lake [
10
]
153 1–12 18.35–45.55 0.0066 3.092 0.95 50.59 0.14 -1.99 2.550
223 1–11 17.30–39.70 0.0072 3.064 0.89 47.12 0.12 -2.78 2.430
+
376 1–12 17.49–45.55 0.0071 3.070 0.94 49.83 0.13 -2.13 2.510
Karasu River [
11
]
115 0–7 – 0.0086 3.070 0.98 46.05 0.133 -1.202 2.450
117 0–9 – 0.0099 3.020 0.98 53.49 0.098 -1.670 2.447
Pülümür River [
12
]
644 0–11 7.1–38.8 0.0096 2.973 0.97 49.25 0.128 -1.68 2.492
743 0–11 7.3–38.3 0.0103 2.954 0.98 44.42 0.155 -1.37 2.485
+
1387 0–11 7.1–38.8 0.0100 2.963 0.98 45.29 0.146 -1.42 2.476
Munzur River
(This study)
444 0–11 6.8–38.5 0.0084 3.015 0.948 45.45 0.116 -2.45 2.38
339 0–11 7.9–40.2 0.0088 3.007 0.935 54.61 0.086 -2.08 2.41
+
783 0–11 6.8–40.2 0.0085 3.013 0.943 46.15 0.139 -2.57 2.47
(n: sample size, a: intercept, b: slope, R
2
: coecient of determination, L
∞
: asymptotic length, t
0
: theoretical age, k: body growth coecient, Ø: growth performance index)
Comparison of traditional models and articial neural networks in the growth of Capoeta umbla / Ozcan and Serdar___________
_________________________________________________________________________________________________Revista Cientica, FCV-LUZ / Vol.XXXV
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0 2 4 6 8 10 12
0
5
10
15
20
25
30
35
40
45
Age (years)
Total lenght (cm)
Lt=46.15[1-e
-0.139(t+2.57)
]
FIGURE 6. Age-length relationship for all individuals of Capoeta umbla in the
Munzur River
0 1 2 3 4 5 6 7 8 9 10 11
0
100
200
300
400
Age (years)
Frequency
All
Female
Male
FIGURE 5. Age-frequency of Capoeta umbla in the Munzur River
FIGURE 7. Neural Network Training in MATLAB
The age range of C. umbla is 0 to 11 years, with the dominant
age group being 2 years (FIG. 5). The longest specimen was an
11-years old male, that measured 40.2 cm. Age readings are
reliable when the Index of Average Percentage Error (IAPE) from
two independent age readers is between 5% and 15% [40]. In
this study, IAPE was found 9.2% as a result of age readings of
C. umbla in the Munzur River.
The neural network training in MATLAB. Plots (performance,
training state and regression) in articial neural networks model
are given FIG. 7.
The parameters of the von Bertalanffy growth model of C. umbla
were: L
t
= 45.45 [1-e
-0.116(t+2.45)
]; W
t
= 768.22 [1-e
-0.116(t+2.45)
]
3.015
in
females; L
t
= 54.61 [1-e
-0.086(t+2.08)
]; W
t
= 941.13[1-e
-0.086(t+2.08)
]
3.007
in males; and L
t
= 46.15 [1-e
-0.139(t+2.57)
] (FIG. 6); The weight
equation for all specimens was: W
t
= 856.32 [1-e
-0.139(t+2.57)
]
3.013
.
The value of Ф' was 2.380, 2.409 and 2.471 for female, male and
all individuals, respectively. The age and von Bertalanffy growth
parameters of C. umbla by different researchers are shown in
TABLE I. The differences between the groups may be due to the
shing environment, time, method, structure of the nets, number
of sh used and the characteristics of the environment.
FIG. 8 shows change as a result of ANN training with the Matlab
program. The network training reached the optimal result in 48
iterations and increasing the number of epoch does not help the
program. The training stopped and the best validation performance
was also xed at 8.1473 × 10
-5
at epoch 42 (FIG. 8). In their study
for C. umbla from Karasu River, Ozcan and Serdar [11] reported
that the network training reached the optimum in 11 epochs and
the best validation performance was 0.00033534 at epoch 5.
Ozcan [24] reported that the training best validation performance
in epoch 4 was 0.00083535 and the validation error reached 10
epochs for A. sellal in Munzur River.
In FIG. 9, the validation checks of the articial neural network
model for training are given as 6, at epoch 48 and gradient=5.6566
× 10
-5
, at epoch 48. Ozcan and Serdar [11] reported that the
validation checks as 6, at epoch 11 and gradient=0.00053887, at
epoch 11 for C. umbla from Karasu River. Ozcan [24] reported that
validation controls for training neural networks as 6 in epoch 10
and gradient = 0.00010533 in epoch 10 for A.sellal in Munzur River.
Calculated MAPE values 0.140 and 0.578 for ANNs, 1.168 and
2.726 for LWRs, 5.721 and 4.013 for VBGF, respectively. ANNs
MAPE (%) values were calculated better than the LWRs and VBGF
MAPE values. MAPE criterium is widely used for acuracy evaluation
of model t. TABLE II shows actual data and ANNs, LWRs, VBGF
with MAPE (%) results of C. umbla. The results of the network lie
Comparison of traditional models and articial neural networks in the growth of Capoeta umbla / Ozcan and Serdar___________
6 of 9 7 of 9
FIGURE 8. Iterative representation of the mean squared error
FIGURE 9. Articial neural networks training state
TABLE II
Actual data and ANNs, LWRs, VBGF with MAPE (%) results
Sex Age
Actual Data ANNs (MATLAB) ANNs MAPE (%) LWRs CALCULATED LWRs MAPE (%) VBGF CALCULATED VBGF MAPE (%)
L W L W L W L W L W L W L W
0
8.58 5.10 8.64 5.16 0.699 1.176 8.32 5.06 3.030 0.784 9.24 5.47 7.692 7.255
9.25 7.05 9.17 6.85 0.864 2.837 8.95 6.88 3.243 2.411 8.94 6.57 3.351 6.809
1
15.69 36.40 15.69 36.39 0.000 0.027 15.83 34.94 0.892 4.011 14.99 33.99 4.461 3.777
15.69 37.60 15.69 37.59 0.000 0.027 15.98 34.84 1.848 7.340 14.71 36.18 6.246 2.308
2
19.31 63.68 19.30 63.67 0.052 0.016 19.20 64.27 0.570 0.926 18.33 62.21 5.075 1.051
19.29 64.73 19.29 64.71 0.000 0.031 19.33 64.10 0.207 0.973 17.16 64.05 11.04 2.847
3
22.78 108.20 22.78 107.35 0.000 0.831 22.88 106.01 0.439 2.024 21.30 105.12 6.497 1.601
22.57 104.30 22.56 103.48 0.044 0.863 22.56 103.21 0.044 1.045 21.32 102.63 5.538 1.239
4
25.17 145.28 25.15 154.52 0.079 6.405 25.23 144.56 0.438 0.496 23.94 143.48 4.887 7.032
24.28 137.23 24.26 135.59 0.082 1.239 24.71 129.81 1.771 5.407 22.24 127.58 8.402 4.452
5
28.28 219.69 28.25 219.69 0.106 0.000 29.09 211.14 2.864 3.892 26.30 209.91 7.001 11.36
28.09 213.29 28.08 213.24 0.036 0.000 28.01 197.00 0.285 7.637 24.90 189.06 11.36 2.882
6
29.74 236.63 29.73 236.61 0.034 0.000 29.79 234.57 0.168 0.871 28.40 229.81 4.506 4.055
29.81 237.23 29.81 237.24 0.000 0.000 29.80 235.46 0.034 0.746 27.35 227.61 8.252 4.168
7
30.86 267.53 30.87 267.46 0.032 0.037 31.05 261.63 0.616 2.205 30.26 256.38 1.944 5.412
31.32 285.44 31.31 285.47 0.032 0.000 31.74 274.18 1.341 3.945 29.60 269.99 5.492 3.862
8
33.12 318.45 33.01 318.46 0.332 0.000 32.94 324.04 0.543 1.755 31.93 306.15 3.593 5.604
34.27 318.67 34.30 318.67 0.088 0.000 32.96 308.29 3.822 3.257 31.66 300.81 7.616 2.857
9
34.70 344.40 34.72 344.41 0.058 0.000 33.80 342.12 2.594 0.662 33.41 334.56 3.718 1.439
33.10 316.80 33.06 316.91 0.121 0.032 32.90 322.60 0.604 1.831 33.55 312.24 1.360 3.343
10
36.44 386.40 36.46 386.46 0.055 0.000 36.13 381.93 0.851 1.157 34.73 373.48 4.693 3.600
35.72 387.27 35.70 387.20 0.056 0.000 35.56 406.03 0.448 4.844 35.29 401.21 1.204 4.110
11
38.23 474.40 38.20 474.07 0.078 0.084 37.90 498.14 0.863 5.004 35.90 493.90 6.095 3.101
38.53 523.43 38.35 521.90 0.507 0.287 38.33 511.86 0.519 2.210 36.88 512.20 4.282 2.145
Average MAPE (%) 0.140
0.578 1.168 2.726 5.721 4.013
Comparison of traditional models and articial neural networks in the growth of Capoeta umbla / Ozcan and Serdar___________
_________________________________________________________________________________________________Revista Cientica, FCV-LUZ / Vol.XXXV
7 of 9
FIGURE 10. Articial neural network training, validation, testing and all data
results
on a 45° line, indicating that the distribution of the data is good and
close to the target [41]. Since MAPE shows the forecast errors as
a percentage, it has more meaning than other statistical methods
[42]. Ozcan and Serdar [11] found that MAPE values 0.979 and
1.593 for ANNs, 1.637 and 3.567 for LWRs, 3.904 and 4.912 for
VBGF of C. umbla from Karasu River. Ozcan [24] found that MAPE
values 0.349 and 1.655 for ANNs, 1.267 and 3.342 for LWRs, 4.000
and 4.122 for VBGF of A. sellal in Munzur River. Models with a
MAPE of less than 10% are classed as “very good”, between 10%
and 20% as “good”, between 20% and 50% as “acceptable” and
more than 50% as “imprecise and incorrect” [43, 44].
The regression plots in FIG. 10 show the outputs of the network;
the training-validation-test groups are evaluated separately
according to their target values. If it is desired to increase the
performance of the network, the network can be retrained. The best
t between targets and outputs is shown by the linear regression
line. ANNs were randomized as follows: 548 in training (70%),
117.5 in testing (15%) and 117.5 in validation (15%) for C. umbla.
The targeted output R value was 0.98584 (training), 0.98969
(validation), 0.98757 (testing) and 0.9868 (all). As can be seen
from here, the learning process has been carried out with great
success. Ozcan and Serdar [11] found that the targeted output R
value was 0.99629 for training, 0.99765 for validation, 0.98934
for testing and 0.99399 for all of C. umbla from Karasu River.
Ozcan [24] found that the targeted output R value was 0.87275 for
training, 0.96297 for validation, 0.94942 for testing and 0.90697
for all of A. sellal in Munzur River. When the R value is between 0.95
an 1, further education is more successful [45]. The calculated SSE
values for length and weight was calculated as 0.0128 and 30.864
for ANNs. The SSE value was found 1.3985 and 350.786 for length
and weight for LWRs. MAPE and SSE were used for comparison of
ANNs and traditional methods of t and have been found to give
better results. It is estimated that a comparison of MAPE and SSE
values can give sound results [17, 46].
CONCLUSION
This study determined that articial neural networks are a
reliable alternative method for making accurate predictions and
evaluating sh growth characteristics in sheries management.
The measured and predicted data were very similar to the results
obtained by the Articial Neural Network (ANN) in this study. When
all theobtained results were evaluated together with the Mean
Absolute Percentage Error (MAPE) and the Sum Squared Error
(SSE), the ANN gave better results than other traditional methods.
For this reason, in this study it can be concludedthat the use of
ANN models is more effective and reliable than the Length-Weight
Ratio (LWR) and the von Bertalanffy Growth Function (VBGF).
Conflict of Interests
The authors declare that there is no conflict of interest.
Author Contributions
E.I.O. wrote the main manuscript, performed ANNs analysis;
contributed data and analysis, validation, review and edited the
manuscript; O.S. for shing and providing the sample, review and
edited the manuscript. All authors reviewed the manuscript.
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