trabalho completo - 52ª Reunião Anual da Sociedade Brasileira de

52a Reunião Anual da Sociedade Brasileira de
Zootecnia
Zootecnia: Otimizando Recursos e Potencialidades
Belo Horizonte – MG, 19 a 23 de Julho de 2015
Comparação dos Modelos de Wood e Polinomial de Quarto Grau para estimar
Parâmetros da Lactação de Gado Holandês Puro de Origem1
Rafaela Maia Moreira2, Carla Regina Guimarães Brighenti3, Wexley Presley da Fonseca4
1
Parte do Trabalho de Iniciação Científica do primeiro autor, financiada pelo CNPQ
Graduanda em Zootecnia – Universidade Federal de São João Del Rei, São João Del Rei-MG, Brasil. Bolsista CNPQ. e-mail:
[email protected]
3
Departamento de Zootecnia – Universidade Federal de São João Del Rei, São João Del Rei-MG, Brasil. e-mail: [email protected]
4
Graduando em Zootecnia – Universidade Federal de São João Del Rei, São João Del Rei-MG, Brasil. e-mail: [email protected]
2
Resumo: O presente trabalho objetivou comparar ajuste dos modelos de Wood e polinomial de quarto grau para
estimar a parâmetros e índices ligados à lactação de animais do rebanho Holandês puros por origem. Foram
selecionadas de forma aleatória 19 primíparas da mesma fazenda das quais foram resgatadas as pesagens mensais a
partir das quais foram feitos as análises. No caso do modelo de Wood, 18 dos 19 casos obtiveram ajuste
significativo, já o polinomial de quarto grau não foi significativo para 6 deles, além disso quando comparados no
ajuste da mesma unidade experimental o modelo de Wood mostrou-se mais eficiente. A junção dos dados
observados possibilitou fazer a análise média do rebanho, que pela quantidade de dados obteve parâmetros
próximos nos dois modelos. Para todos os casos os coeficientes de grau 3 e 4 do modelo polinomial foram muito
próximos do valor zero, evidenciando pouca influência destes na análise. Observou-se que o ajuste do modelo de
Wood foi mais satisfatório e expressou os parâmetros de melhor forma, sendo o mais recomendado para tal
finalidade.
Palavras–chave: gerenciamento de produção, pecuária brasileira, produtividade
Comparison of Models Wood and Polynomial Grade Four to estimate
Lactation parameters for Holstein cattle Pure by origin
Abstract: The study aimed to compare adjustment of Wood and polynomial models of fourth grade to estimate the
parameters and indices related to lactation pure Dutch animals pure by origin. They were randomly selected 19 gilts
of the same farm of which the monthly weight measurements were rescued from which the analyzes were made. In
the case of Wood model, 18 of the 19 cases obtained significant adjustment, since the fourth degree polynomial was
not significant for 6 of them also compared the adjustment of the same experimental unit Wood model was more
efficient. The junction of the observed data to make possible the average of the flock analysis that the amount of
data obtained near parameters in both models. In all cases the degree coefficients 3 and 4 of the polynomial model
were very close to zero, indicating little influence of these in the analysis. It was observed that adjusting Wood
model was more satisfactory, and the parameters expressed in a better way, most suitable for this purpose.
Keywords: Brazilian livestock, productivity, production management
Introduction
Within the Brazilian livestock, milk production in cows is one of the activities that stands out. The Holstein
cows, of European origin, are naturally very productive with levels and duration of lactation highly significant.
However, for better management of the activity, the ideal would be that the producer esteemed indexes linked to
animals and their productivity. In the case of lactation, multiple indexes can be estimated in advance since it is
available in an effective, simple and complete method, as well as the data needed for this. A difficulty that must be
emphasized is that most of those involved in this activity are smallholders with missing controls or complete bit
about their animals, leaving those who keeps up to date provide access to research.
Since taking up the an animal lactation data, with weightings of production and time intervals between them
can be traced lactation curve of this animal, breed or herd. There are numerous alternatives to the knowledge and
use of the lactation curve of a herd; one of them is the establishment of a breeding program based on full and partial
production of the animals, which would be evaluated biological and economic aspects of creation (Guimarães et.
al., 2006). This is graphically expressed in such production and it can estimate the total lactation values, peak
production, the initial and final production, among others. To make the estimates referred to can use a regression
adjustment from reported data, about which you can find the variables needed to predictions of interest. This
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52a Reunião Anual da Sociedade Brasileira de
Zootecnia
Zootecnia: Otimizando Recursos e Potencialidades
Belo Horizonte – MG, 19 a 23 de Julho de 2015
process can be performed with linear models like the fourth degree polynomial used in commercial software
management of dairy farming as IDEAGRI® or nonlinear models such as Wood (1967), cited by many authors,
already tested in work Previous having quite satisfactory answer.
Importantly, the delivery order is a big factor influences for adjusting the lactation curve. According Durães
et al. (1991, cited by Lopes (1996)), the calving order affected significantly (p<0,01) estimates of the parameters to
model Wood. The animals first order had lower initial production and peak later, while in the other orders (second
to fourth) there was no significant difference. As for the maximum output of the third and fourth orders, which did
not differ from each other, they were statistically superior to the first and second, the first representation of the
initial potential of the animal.
The objective of this study was to compare total production, peak time and peak lactation estimated by the
models of Wood and the fourth degree polynomial, for primiparous Dutch cattle pure of origin.
Material e Methods
The weights used were the animals database of Fazenda Campo Alegre located in Ritápolis, state of Minas
Gerais. This initially contained 3615 records of their animals of the Year 1998-2012, filed in IDEAGRI® program.
All animals were under the same environmental and management conditions, and this high level.
Initially the animals were separated by level of blood, race and who possessed start and end dates of
lactation. Among the animals were randomized 19 Holstein breed they were pure of origin and those the weights
were rescued, only for the first lactation of each contemporary group.
For each animal were separated with the weighing time after the corresponding delivery and then set the
parameter estimation by R® software, following the models described below.
y  t b exp ( a ct )

Model Wood:

Model Polynomial Degree Four:
y  a0  a1t  a2t 2 a3t 3  a 4t 4
In both models y is the production of milk (kg / day) and t is the lactation time (days). In Wood's model has
a is a constant associated with the average production in early lactation, ba average production rise up to reach full
production, c is the average rate of decline in production after peaking and exp the basis of logarithms neperianos
(Lopes, 1996). values: ai, i = 0, ..., 4 are parameters from which one can obtain estimates peak, rate of rise and / or
fall, peak time and cumulative production 305 days.
Results and Discussion
By adjusting the Wood model, only one of 19 cases, did not obtain significant results at 5% confidence
level (p<0.05). Since the fourth degree polynomial model resulted in no significant six cases, moreover, the degrees
of coefficients 3 and 4 function components were estimated values very close to zero, thus having little influence on
the graphic representation of the curve. For the 13 patients who had significant adjustment with two models, the
Wood showed better visual representation and estimation.
The animal represented by the number 12, received no satisfactory adjustment on both models, whose
estimated average was 19.9 kg per day, for the first and last of their lactation were weighing around 20 kg, which is
a situation outside the standards representation of a lactation, but showing very high production capability and
capacity to maintain the level of production over the recurring cycle. Another unusual case occurred with the unit
number 4, although it achieved significant adjustment was not possible to estimate the peak of lactation, as well as
time to him, the weighing registered for this already started to 32 days after delivery. Thus, the curve assumed by
the possibility of decreasing expression its peak being located around the time that was first weighing.
To estimate the mean Dutch pure flock was made to juntion all the data for all experimental units. Both
models were used to calculate production indices of lactation and both were significant at the 5% level of
confidence (p<0.05). The values were similar due to the number of data involved. Though, even with larger
samples, the degree of coefficients 3 and 4 of polynomial function were very close to zero showing little interaction
of these and so on analysis evidencing viability of Wood model.
Table 1. Lactation parameters of pure Holstein cows by models Wood and polynomial of degree four
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52a Reunião Anual da Sociedade Brasileira de
Zootecnia
Zootecnia: Otimizando Recursos e Potencialidades
Belo Horizonte – MG, 19 a 23 de Julho de 2015
Production total
(Kg)
Time the peak
(days)
Production in the
peak (Kg)
Wood
25.00
7611.88
90
27.18
Polynomial degree four
24.90
7598.84
113
27.32
25
a0=
a1=
a2=
a3=
a4=
20.798
0.142
-9e-04
2e-06
-1e-09
10
10
15
a= 2.655
b= 0.185
c= 0.002
polinomial
20
Milk Production (kg)
20
Wood
15
Milk Production (kg)
25
30
Average Daily
(Kg)
30
Model
0
50
100
150
200
Time (day)
250
300
350
0
50
100
150
200
250
300
350
Time (day)
Figure 1. Lactation curve and parameters estimated by Wood model and polynomial
fourth degree, respectively.
The observations and the way weighings are made are determinant for the study of lactation curve, so the
more explanatory and effective model will be the best estimates. By obtaining values unrepresentative of said low
coefficients arises the possibility that the polynomial function of degree two reach similar estimates simplest form.
But the Wood model was more satisfying and lighter in determining production indices found with the lactation
curve, being a more efficient and appropriate tool than the fourth degree polynomial.
Conclusions
Based on the results, although there are commercial software using the fourth degree polynomial, it was
seen that the Wood model is able to represent and estimate the parameters and desired factors more clearly and
objectively that the polynomial model of fourth degree. Furthermore, the visual expression of the curve, except for
the general case for a fourth degree polynomial model differed from the expected pattern.
In this way, it would be more feasible and trustworthy use Wood model to represent lactation curve
parameters in both analyzes for academic purposes, such as software that may be developed.
References
GUIMARAES, V. P., RODRIGUES, M. T., SARMENTO, J. L. R.e ROCHA, D. T. Utilização de funções
matemáticas no estudo da curva de lactação em caprinos. R. Bras. Zootec., v.35, n.2, p. 535-543, 2006.
R Development Core Team. R: A language and environment for statistical computing. R Foundation for
Statistical Computing, Vienna, Áustria, 2014.
DURÃES, M.C., TEIXEIRA , N. M., FREITAS, A. F. Curvas de lactação de vacas da raça Holandesa mantidas em
confinamento total. Ar. Bras. Med. Vet. Zootec., Belo Horiznte, 1991; Apud LOPES, M. A., NEIVA, R. S.,
VALENTE, J. MARTINEZ, M. L., VEIGA, R. D., SILVA, A. R. P. da, FREITAS, A. F. Aplicação da função gama
incompleta no estudo da curva de lactação de vacas da raça Holandesa, variedade preta e barnca mantidas em
sistema intensivo de produção.
WOOD, P.D.P., Algebric model of lactation curve in cattle. Nature, 216, 1967
LOPES, M. A., NEIVA, R. S., VALENTE, J., MARTINEZ, M. L., VEIGA, R. D., SILVA, A. R. P., FREITAS,A.
F. Aplicação da função gama incompleta no estudo da curva de lactação de vacas da raça Holandesa, variedade
preta e branca, mantidas em sistema intensivo de produção. R. Bras. Zootec., v.25, n.6, 1996.
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