RCCS+SPIDTEC2 2017. BARRIOS & OCHOA 39
Approach of Implementation using models of
analysis of main component for breeding and
reproduction of tilapia
Sergio Barrios1, Alberto Ochoa2
Abstract—Nowadays, aquaculture projects are beginning to be carried out in many parts of Mexico, where the main obsta-
cle to its success is the lack of knowledge of the basic principles and technical necessary skills to achieve maximum utiliza-
tion. In Mexico, the projection of a tilapia hatchery has required models established in other countries, making the necessary
modifications according to the natural conditions of the country. This work intends to apply multivariate analysis techniques
and especially based on main components, due to it is a method widely used to reduce the size of a group of specific data,
locating it in the specific variables according to the necessity that is required, maintaining a High-level order of the main com-
ponents which are determined and ignoring the low level for the decision making. They optimize according to the natural con-
ditions of Mexico and especially the state of Querétaro in the breeding and reproduction of tilapia, constructing predictive
models, at the time of developing applicable projects. For this, the first section of this chapter is a review of different concepts
related to methods that may be applicable in decision making for the particularity of said project explaining methods of similar
solutions giving different points of view for the solution of the same, in later sections will apply numerical methods of analysis
that work with the data generated from the analysis based on main components giving a solution of the problem showing
concrete results as desired. Finally, it is presented conclusions and references consulted for the accomplishment of this in-
vestigation.
Index Terms—Tilapia reproduction; implementation; models of analysis.
—————————— ——————————
1 INTRODUCTION municipality of Alvarado, Veracruz where Fifteen cages
were installed inside a rustic pond of 0.5 ha, and each
In recent years, the global aquaculture production has
cage was planted with 7 000 offs of 6 g average weight
increased at a sufficiently high rate to compensate for
yielded results Positive in terms of profits generated, Que-
declining catches in fisheries, so aquaculture production in
rétaro as a state, has characteristics similar to that of the
many countries has contributed greatly to the annual
municipality Alvarado, currently in Querétaro through the
production of fishery products at the level national. The
media, have been given more publicity and is quoted in
current situation of world aquaculture is characterized by
the market between 35 mxn and 45 mxn per kilogram [6].
the progress in the cultivation of shrimp and marine fish;
This is a very good alternative to improve the economic
and in several countries the economic income of aquacul-
conditions of local fishing communities, directly benefiting
ture as a result of the export of its products represents the
families by generating permanent jobs, offering a better
most important source of foreign exchange in its econo-
quality of life, producing low cost protein food as well as
my. Aquaculture projects are beginning to take place in
being a production alternative in the fishing activity. It is
many places, where the main obstacle to their success is
worth mentioning that the reproduction of the tilapia in
the lack of knowledge of the basic principles and the nec-
the fattening phase can lead to the collapse of the cultiva-
essary technical skills. In Mexico, the projection of an aq-
tion system, due to the large number of tilapias that are
uaculture farm requires models established in other coun-
born in the ponds and due to this the tilapias in cultiva-
tries, making the necessary modifications according to the
tion present a low growth and a Bad conversion of food,
natural conditions in the country. The development of
due to the process of reproduction in which great energy
aquaculture in Mexico compared to the world aquaculture
is invested, a good option is to fatten lots of masculinized
development shows a lag in both the diversity and use of
tilapias (The male grows faster than the female) which is
resources as in the modernization of the sector. Mexico is
achieved by supplying masculinizing hormones in the
in an ideal situation for the cultivation of several species
early stages when given Sexual differentiation. Although
because it has extensive coastlines, abundant wetlands
the most common practice is to keep males and females
and optimal climates and fish farming has become a ne-
together indeterminately by separating with the nets the
cessity in many places where this activity was not previ-
small fry that are born in the pond, it is best that the incu-
ously practiced [8]. Investigations were carried out under
bation be carried out in a controlled manner. One way to
commercial conditions in an intensive tilapia farm in the
achieve this is by milking the fertilized eggs from the
———————————————— female's mouth, which incubates them until they are born,
• 1Universidad Autónoma de Querétaro, Facultad de Informática Av. de the eggs are incubated in clean, oxygenated water to
las Ciencias S/ N, Campus Juriquilla, Querétaro, Qro. C.P. 76230 Mé- prevent the onset of disease, the ad
xico.
• 2Universidad Autónoma de Ciudad Juárez, Maestria en Cómputo
Aplicado, Ciudad Juárez, Chih. E-mail: alberto.ochoa@uacj.mx.
xxxx-xxxx/0x/$xx.00 © 200x IEEE Published by the IEEE Computer Society
RCCS+SPIDTEC2 2017
vantage of this system is that tilapia Are fed with hor-
mones from the time they hatch and can eat what results Description1 Description
in a good% of male tilapia, this process can take place Cp Number of fish for the crop
approximately one month after spawning. So, in this case Pi Initial budget
will work with samples of masculinized issues fry for PR Actual budget (suggested by the
the maximum profit and profit of the business. It is worth algorithm)
emphasizing that when the stocking density of the tilapia Com Cost per square meter
is low, it is possible to dispense with oxygen aerators and Cmd Number of square meters available
only to carry out water refills, in large areas, the low in- CmR Actual square meters (suggested
tensity crop can shed interesting production volumes by the algorithm)
that are the importance to perform a good study to IE Estimated cost of infrastructure
and equipment requested for culti-
achieve maximum efficiency in breeding and reproduc-
vation
tion of tilapia. Apply several techniques to apply when
Cop Cost of each Alevin (0.5 g) (Con-
getting the product present quality when it reaches its stant Value mxn 0.75)
final destination that is marketing for it tilapias must have DmT Diameter of the pond to be used
complete fins without fraying, no white spots or ulcers or (3,6,9,12 meters of Diameter)
scratching injuries behavior against the wall or the back- CoAl Generalized feeding cost per indi-
ground [5] [8]. vidual (Constant Value 1.7 kg -
Nowadays, there are not mathematical models to opti- 12.50 mxn / kg)
mize resources of scientific projects, so the present re- EBlo Existence of blower in the project
search is a milestone in the subject seeking a mathemati- (1 (SI), 0 (NO))
cal solution. Additionally, although it will be tested on Cpm Number of fish that occupies one
tilapia breeding projects already implemented, the re- cubic meter (Constant Value 50-
search will serve as a basis for any similar problem that 100 individuals)
requires cost optimization. Finally, it will serve to focus CAg Quantity of general food
the use of economic resources in a more real way. The CantT Number of ponds to be used ac-
main social contribution of the research will be to expand cording to diameter required
the knowledge of the subject in this branch that serves to M²T Metro Square according to pond
the future investors. It will be achieved as the budget of (Area of pond = 3.14 * r²)
each project is determined in real form, to avoid over- MtCult Cultivation Methodology to use
charging and underestimating them.
The main objective of this work is to determine the best
implementation of a breeding and reproduction project of
2 METHODOLOGY
tilapia depending on the budget to be invested applying 2.1 Methodology implemented
mathematical algorithms that help the decision making in When the number of pond is equal to or greater than 7,
carrying out the project. the pond capacity is maximized at the time of planting of
1.3 Initial conditions. the fry as it can plant the pods in full according to the
For the implementation of this project it is worth saying construction follows:
that the investor must take into account that the budget
Sta-
that wishes to invest will have to consist of a certain limit
ge 1
since it is necessary to invest in minimum tools indispen-
sable for the control and monitoring of the process, in
addition to taking into account the distance in which our
source of supply will be found to determine the cost of
the piping system to be applied. The study is based on
tanks of geomembrane supplied by professional compa- Stage Stage
nies in the sector and it will take into account the different 2 3
capacities of the same that are tanks of (3, 6, 9, 12) m wide
and 1.20 m high because they are the most used in This
type of projects applied to the creation of tilapia (Exten-
sive, Intensive, Semi-Intensive, Super-Intensive) [5].
Stage Stage Stage Stage
4 5 6 7
Table 1. Elements of the Mathematical Model. It is worth
to say that it is more feasible to use a methodology of
planting of the crop according to the number of ponds
Fig. 1. Pond assignations (Source: own elaboration)
that are implemented for the maximum use of the space
In which the capacity of the pond is fully exploited, re-
of the ponds for example.
specting the planting rate per cubic meter (100 u / m³)
SERGIO BARRIOS, ALBERTO OCHOA: APPROACH OF IMPLEMENTATION USING MODELS OF ANALYSIS OF MAIN COMPONENT FOR BREEDING AND
REPRODUCTION OF TILAPIA
where at the end of the breeding stage the fish reach a MtCult²= 𝑀𝑜𝑑(𝐶𝑎𝑛𝑡𝑇/7) Amount of times I can applym-
weight of 150 g / u (Pond 1) Dividing the population of ethodology 2 according to ponds.
individuals in the following ponds (Pond 2 and Pond 3), MtCult = MtCult¹ y MtCult² Number of times each meth-
thus respecting the suitability of individual space, and in odology can be applied.
turn, at the end of the pre-fattening stage (300 g / Other
ponds (Pond 4, Pond 5, Pond 6, Pond 7) until reaching the
Mathematical model for methodology 1
weight per individual of 500 g / u which would be the best
marketing weight [10].
Amount of fish per cubic meter:
2.2 Methodology 2
𝐶𝑝𝑚 = 100 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑜𝑠
When the number of ponds is less than 7 does not com-
ply with the methodology above exposed and as you
cannot divide populations equally as the previous method Cost of alevin per cubic meter general:
does not maximize the capacity of the pond at the time of 𝐶𝑜𝑚 = 𝐶𝑝𝑚 ∗ 𝐶𝑜𝑝 (𝟒)
planting because you have to think in terms of Commer- The general cost of planting the alevin.
cialization so that it is necessary to plant the optimal ca- Cp = 𝐶𝑎𝑛𝑡𝑇 ∗ 𝑀3 𝑇 ∗ 𝐶𝑝𝑚 (𝟓)
pacity by square meters that support individuals of 500 g
/ u in the pond so the planting that is carried out in the Amount of feed to be used throughout the breeding cycle
pond will not cover the whole of the pond space since the up to 500 g per fish.
fry would be sown to Lower amount per cubic meter of 𝐶𝐴𝑔 = 𝐶𝑝.∗ 𝐶𝑜𝐴𝑙 (𝟔)
water and should be adequately concentrated. A UML The estimated cost for infrastructure and equipment is
modeling that explains such a situation is as follows [10]: estimated. 𝑛 𝑚
𝐼𝐸 = ∑ 𝐶𝑜𝑒𝑖 + ∑ 𝐶𝑜𝑖𝑗 (𝟕)
𝑖=1 𝑗=1
First Stage
The cost of investment of the fry and feed will comprise
between 50% and 60% of the initial budget.
𝑃𝑖 ∗ 0.5 ≤ CAg + Cp ≤ 𝑃𝑖 ∗ 0.6 (𝟖)
The cost of infrastructure and equipment will comprise
Third Stage
Second Stage between 40% and 50% of the initial budget.
𝑃𝑖 ∗ 0.4 ≤ 𝐼𝐸 ≤ 𝑃𝑖 ∗ 0.5 (𝟗)
Mathematical model for methodology 2
Amount of fish per cubic meter:
Fig. 2. UML Modeling (Source: Saavedra, 2013)
𝐶𝑝𝑚 = 50 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑜𝑠
Function Purpose.
𝑧 = min( ∑𝑛𝑖=1 𝐶𝑜𝑚𝑖 + 𝐼𝐸 + CAg ) (𝟏) Cost of alevin per cubic meter general:
𝐶𝑜𝑚 = 𝐶𝑝𝑚 ∗ 𝐶𝑜𝑝 (𝟏𝟎)
Model Restrictions
The actual budget cannot exceed the initial budget. The general cost of planting the alevin.
𝑃𝑖 ≤ 𝑃𝑟 (𝟐) Cp = 𝐶𝑎𝑛𝑡𝑇 ∗ 𝑀3 𝑇 ∗ 𝐶𝑝𝑚 (𝟏𝟏)
The number of square meters used cannot exceed those Amount of feed to be used throughout the breeding cycle
available. up to 500 g per fish.
𝐶𝑚𝑟 ≤ 𝐶𝑚𝑑 (𝟑) 𝐶𝐴𝑔 = 𝐶𝑝.∗ 𝐶𝑜𝐴𝑙 (𝟏𝟐)
Where The estimated cost for infrastructure and equipment is
Quantity of ponds to be used according to Cmd. estimated. 𝑛 𝑚
𝐶𝑎𝑛𝑡𝑇 ≃ Cmd /3, 14*r² Calculation of the number of 𝐼𝐸 = ∑ 𝐶𝑜𝑒𝑖 + ∑ 𝐶𝑜𝑖𝑗 (𝟏𝟑)
ponds per m² available. 𝑖=1 𝑗=1
𝐶𝑚𝑟 = 𝐶𝑎𝑛𝑡𝑇 ∗ 3.14 ∗ 𝑟² Referes to each meter used with
The cost of investment of the fry and feed will comprise
respect to the diameter of the pond used.
between 50% and 60% of the initial budget.
𝑃𝑖 ∗ 0.5 ≤ CAg + Cp ≤ 𝑃𝑖 ∗ 0.6 (𝟏𝟒)
Estimation of the architectural method to be implement-
ed. The cost of infrastructure and equipment will comprise
MtCult¹= 𝐶𝑎𝑛𝑡𝑇/7 Amount of times I can apply method- between 40% and 50% of the initial budget.
ology 1 according to ponds. 𝑃𝑖 ∗ 0.4 ≤ 𝐼𝐸 ≤ 𝑃𝑖 ∗ 0.5 (𝟏𝟓)
RCCS+SPIDTEC2 2017
2.3 Analysis Based on Main Components often occurs between variables: if we take too many varia-
The so-called Common Principal Component Analysis bles (which usually happens when you do not know too
(ACP) is where you collect information from a sample of much about the data or only have an exploratory spirit), it
data, most often taking as many variables as possible. is normal that they are related or that they measure the
However, if we take too many variables on a set of objects, same from different points of view. For example, in medi-
for example 20 variables, we will have to consider 180 cal studies, blood pressure at the exit of the heart and at
possible correlation coefficients; If there are 40 variables,
the exit of the lungs is strongly related. It is necessary,
that number increases to 780. Obviously, in this case it is
therefore, to reduce the number of variables. It is im-
difficult to visualize relationships between variables. An-
other problem that arises is the strong correlation that portant to highlight the fact that the concept of greater
often occurs between variables: if we take too many varia- information is related to the one of greater variability or
bles (which usually happens when you do not know too variance. The greater the variability of the data (variance),
much about the data or only have an exploratory spirit), it the more information is considered, which is related to
is normal that they are related or that they measure the the concept of entropy [2].
same from different points of view. For example, in medi-
cal studies, blood pressure at the exit of the heart and at
the exit of the lungs is strongly related. It is necessary, 3 EXPERIMENTATION
therefore, to reduce the number of variables. It is im- 3.1 Calculation of main components
portant to highlight the fact that the concept of greater
information is related to the one of greater variability or It is considered a series of variables (x¹, x²... xp) on a group
variance. The greater the variability of the data (variance), of objects or individuals and try to calculate from them a
the more information is considered, which is related to the new set of variables y¹, y²... yp, between each other, whose
concept of entropy [2]. variances are decreasing progressively. Each yj (where j =
1... p) is a linear combination of the original x¹, x²... xp, that
2.4 Principal Components
is:
These techniques were initially developed by Pearson at
the end of the 19th century and were later studied by Yj = aj¹x¹ + aj²x² + ... + ajpxp = a0jx
Hoteling in the 1930. However, the appearance of com-
puters did not begin to popularize. In order to study the Where aºj = (a¹j, a²j... apj) is a vector of constants, and
relationships that exist between correlated variables (that
measure common information), the original set of varia- Obviously, if we want to maximize the variance, as we shall
bles can be transformed into another set of new variables see later, a simple way might be to increase the coeffi-
that are not correlated with each other (which does not cients aij. Therefore, in order to maintain the orthogonally
have a redundancy or redundancy in the information). The of the transformation it is necessary that the vector mod-
new variables are linear combinations of the previous ule.
ones and are constructed according to the order of im- A0j = (a¹j, a²j... apj) is
portance in terms of the total variability they collect from
1. That is, 𝑝
the sample. Ideally, we look for m