scholarly journals Comparison of the parameters of the lactation curve between normal and difficult calvings in Iranian Holstein cows

2019 ◽  
Vol 17 (1) ◽  
pp. e0401
Author(s):  
Navid Ghavi Hossein-Zadeh
Keyword(s):  
Dairy Cows ◽  
Milk Yield ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Holstein Cows ◽  
Coefficient Of Determination ◽  
Lactation Curve ◽  
Non Linear ◽  
Best Fit

To evaluate effect of dystocia on the lactation curve characteristics for milk yield and composition in Holstein cows, six non-linear models (Brody, Wood, Sikka, Nelder, Dijkstra and Rook) were fitted on 5,917,677 test day records for milk yield (MY), fat (FP) and protein (PP) percentages, fat to protein ratio (FPR) and somatic cell score (SCS) of 643,625 first lactation Holstein cows with normal calving or dystocia from 3146 herds which were collected by the Animal Breeding Center of Iran. The models were tested for goodness of fit using adjusted coefficient of determination, root means square error, Akaike’s information criterion and Bayesian information criterion. Rook model provided the best fit of the lactation curve for MY and SCS in normal and difficult calvers and dairy cows with dystocia for FP. Dijkstra model provided the best fit of the lactation curve for PP and FPR in normal and difficult calvers and dairy cows with normal calving for FP. Dairy cows with dystocia had generally lower 100-d, 200-d and 305-d cumulative milk yield compared with normal calvers. Time to the peak milk yield was observed later for difficult calvers (89 days in milk vs. 79 days in milk) with lower peak milk yield (31.45 kg vs. 31.88 kg) compared with normal calvers. Evaluation of the different non-linear models indicated that dystocia had important negative effects on milk yield and lactation curve characteristics in dairy cows and it should be reduced as much as possible in dairy herds.

Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins

2013 ◽  
Vol 152 (2) ◽  
pp. 309-324 ◽  
Author(s):  
N. GHAVI HOSSEIN-ZADEH
Keyword(s):  
Dairy Cows ◽  
Milk Yield ◽  
Goodness Of Fit ◽  
The Other ◽  
Linear Functions ◽  
Holstein Cows ◽  
Lactation Curve ◽  
Non Linear ◽  
Watson Statistic ◽  
Best Fit

SUMMARYIn order to describe the lactation curves of milk yield (MY) and composition, six non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Hayashi and Dijkstra) were used. Data were 5 535 995 test-day records for MY, fat (FC) and protein (PC) contents and somatic cell score (SCS) from the first three lactations of Iranian Holstein cows that were collected on 2547 dairy herds in the period from 2000 to 2011 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using root-mean-square error (RMSE), Durbin–Watson statistic (DW) and Akaike's information criterion (AIC). The Wood and Dhanoa models provided the best fit of the lactation curve for MY in the first and second parities due to the lower values of RMSE and AIC than other models; but the Dijkstra model showed the best fit of milk lactation curve for third-parity dairy cows, FC, PC and SCS in the first three parities because of the lowest values of RMSE and AIC. Also, In general, the Sikka model did not fit the production data as well as the other equations. The results showed that the Dijkstra equation was able to estimate the time to the peak and peak MY more accurately than the other equations. However, the Wood equation provided more accurate predictions of peak MY at second- and third parities than the other equations. For first lactation FC, the Dijkstra equation was able to estimate the minimum FC and for second- and third-parity FC, the Wood equation provided more accurate predictions of minimum FC. For first- and second-lactation PC, the Dijkstra equation was able to estimate the minimum PC but for third parity, the minimum value of PC was predicted more accurately by the Wood model. The Dhanoa and Dijkstra equations for first lactation SCS and the Dhanoa equation for second- and third- lactation SCS were able to estimate the minimum SCS more accurately than the other equations. Overall, evaluation of different equations used in the current study indicated the potential of the non-linear functions for fitting monthly productive records of Holstein cows.

Introducing a sinusoidal equation to describe lactation curves for cumulative milk yield and composition in Holstein cows

2020 ◽  
Vol 87 (2) ◽  
pp. 220-225
Author(s):  
Navid Ghavi Hossein-Zadeh ◽  
Hassan Darmani Kuhi ◽  
James France ◽  
Secundino López
Keyword(s):  
Linear Model ◽  
Milk Yield ◽  
Milk Fat ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Holstein Cows ◽  
Coefficient Of Determination ◽  
Production Traits ◽  
Lactation Curve

AbstractThe aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar $, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2 $ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.

Modelling lactation curve for milk fat to protein ratio in Iranian buffaloes (Bubalus bubalis) using non-linear mixed models

2016 ◽  
Vol 83 (3) ◽  
pp. 334-340 ◽  
Author(s):  
Navid Ghavi Hossein-Zadeh
Keyword(s):  
Mixed Models ◽  
Milk Fat ◽  
Goodness Of Fit ◽  
Linear Mixed Models ◽  
Information Criterion ◽  
Protein Ratio ◽  
The Third ◽  
Lactation Curve ◽  
Non Linear ◽  
Best Fit

The aim of this study was to compare seven non-linear mathematical models (Brody, Wood, Dhanoa, Sikka, Nelder, Rook and Dijkstra) to examine their efficiency in describing the lactation curves for milk fat to protein ratio (FPR) in Iranian buffaloes. Data were 43 818 test-day records for FPR from the first three lactations of Iranian buffaloes which were collected on 523 dairy herds in the period from 1996 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly FPR records of buffaloes using the non-linear mixed model procedure (PROC NLMIXED) in SAS and the parameters were estimated. The models were tested for goodness of fit using Akaike's information criterion (AIC), Bayesian information criterion (BIC) and log maximum likelihood (−2 Log L). The Nelder and Sikka mixed models provided the best fit of lactation curve for FPR in the first and second lactations of Iranian buffaloes, respectively. However, Wood, Dhanoa and Sikka mixed models provided the best fit of lactation curve for FPR in the third parity buffaloes. Evaluation of first, second and third lactation features showed that all models, except for Dijkstra model in the third lactation, under-predicted test time at which daily FPR was minimum. On the other hand, minimum FPR was over-predicted by all equations. Evaluation of the different models used in this study indicated that non-linear mixed models were sufficient for fitting test-day FPR records of Iranian buffaloes.

scholarly journals Evaluation of non-linear models to describe development and fertility of codling moth at constant temperatures

2017 ◽  
Vol 20 (1) ◽  
pp. 3 ◽  
Author(s):  
H. Ranjbar Aghdam ◽  
Y. Fathipour ◽  
D. C. Kontodimas
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Developmental Rate ◽  
Codling Moth ◽  
Coefficient Of Determination ◽  
Temperature Threshold ◽  
Optimum Temperature ◽  
Non Linear ◽  
Lower Temperature

Developmental rate of immature stages and age-specific fertility of females of codling moth at constant temperatures was modeled using non-linear models. The equations of Enkegaard, Analytis, and Bieri 1 and 2 were evaluated based on the value of adjusted R2 (R2adj) and Akaike information criterion (AIC) besides coefficient of determination (R2) and residual sum of squares (RSS). All models have goodness of fit to data especially for development [R2, R2adj, RSS and AIC ranged 0.9673-0.9917, 0.8601-0.9861, 0.08-6.7x10-4 and (-75.29) – (-46.26) respectively]. Optimum temperature (Topt) and upper threshold (Tmax) were calculated accurately (Topt and Tmax ranged 29.9-31.2oC and 35.9-36.7oC) by all models. Lower temperature threshold (Tmin) was calculated accurately by Bieri-1 model (9,9-10,8oC) whereas Analytis model (7,0-8,4oC) underestimated it. As far as fertility is concerned the respective values were better fitted near the optimum temperature (in 30oC) [R2 ,R2adj, RSS and AIC ranged 0,6966-0,7744, 0,5756-0,6455, 2,44-3,33 x10-4 and (-9,15)-7,15 respectively].

scholarly journals Evaluation of Non-linear Models to Predict Potential Milk Yield of Beef Cows According to Parity Order Under Grazing

2021 ◽  
Vol 8 ◽  
Author(s):  
Matheus Fellipe de Lana Ferreira ◽  
Luciana Navajas Rennó ◽  
Isabela Iria Rodrigues ◽  
Sebastião de Campos Valadares Filho ◽  
Luiz Fernando Costa e Silva ◽  
...  
Keyword(s):  
Milk Yield ◽  
Milk Fat ◽  
Linear Models ◽  
Nonlinear Models ◽  
Information Criterion ◽  
Beef Cows ◽  
Total Solids ◽  
Lactation Curve ◽  
Non Linear ◽  
Milking Machine

This study aimed to evaluate the effect of parity order on milk yield (MY) and composition over time of grazing beef cows and to evaluate non-linear models to describe the lactation curve. Thirty-six pregnant Nellore cows (12 nulliparous, 2 years; 12 primiparous, 3 years; and 12 multiparous, 4–6 years) were included in the study. With calving day assigned as day 0, milking was performed using a milking machine to estimate MY on days 7, 14, 21, 42, 63, 91, 119, 154, and 203. Dummy variable analyses were applied to estimate its effects on MY, composition (kg and percentage), afternoon/morning, and afternoon/total proportions. Since multiparous cows had higher MY than nulliparous and primiparous cows, two different groups were used for lactation curve analysis: Mult (multiparous) and Null/Prim (nulliparous and primiparous). The MY estimated by the last edition of BR-Corte (Nutrient Requirements of Zebu and Crossbred Cattle) equation was compared with the observed values from this study. Five nonlinear models proposed by Wood (WD), Jenkins & Ferrell (JF), Wilmink (WK), Henriques (HR) and Cobby & Le Du (CL) were evaluated. Models were validated using an independent dataset of multiparous and primiparous cows. The estimates for parameters a, b, and c of the CL equation were compared between groups, and the BR-Corte equation used the model identity methodology. Nulliparous and primiparous cows displayed similar MY (P > 0.05); however, multiparous cows had an average MY that is 0.70 kg/day greater than that of nulliparous and primiparous cows (P < 0.05). Milk protein and total solids were higher for multiparous cows (P < 0.05). Effect of days in milking was found for milk fat, protein, and total solids (P < 0.05). The yield of all milk components was higher for multiparous cows than for nulliparous and primiparous cows. The afternoon/morning and afternoon/total proportions of milk production were not affected by parities and days in milking (P > 0.05), with an average of 0.76 and 0.42, respectively. The BR-Corte equation did not correctly estimate the MY (P < 0.05). The equations of WD, WK, and CL had the best estimate of MY for both Mult and Null/Prim datasets. The equations had a very similar Akaike's information criterion with correction and mean square error of prediction.

scholarly journals Choice of non-linear models to determine the growth curve of meat-type quail

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Marta Jeidjane Borges Ribeiro ◽  
Fabyano Fonseca Silva ◽  
Maíse dos Santos Macário ◽  
José Aparecido Santos de Jesus ◽  
Claudson Oliveira Brito ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Growth Curves ◽  
Information Criterion ◽  
Metabolizable Energy ◽  
Coefficient Of Determination ◽  
Parameter Estimates ◽  
Coturnix Coturnix ◽  
Non Linear ◽  
Meat Type

ABSTRACT: The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards’ was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.

scholarly journals Determination of the best non-linear function to describe the growth of Kajli sheep

2020 ◽  
Vol 50 (3) ◽  
pp. 452-459
Author(s):  
A. Ali ◽  
K. Javed ◽  
I. Zahoor ◽  
K.M. Anjum
Keyword(s):  
Linear Function ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Linear Functions ◽  
Coefficient Of Determination ◽  
Parameter Estimates ◽  
Early Maturity ◽  
Linear Pattern ◽  
Non Linear

The aim of the present study was to determine the best non-linear growth function to describe the growth of Kajli sheep. For this aim, the Brody, von Bertalanffy, Logistic, and Gompertz models were used to describe the sigmoidal relationship between bodyweight and age of the Kajli sheep. The records obtained from the Livestock Experiment Station, Khushab, were collected between 2007 and 2018. The records comprised 9864 age-weight observations (300 for male, 9564 for female, 7392 for single, 2388 for twin, and 84 for triplet lambs), which extended from birth to 12 months old. Candidate non-linear functions were fitted and the curve parameters were estimated by nlsfit (fit non-linear models) function in R statistical package, version 3.6.1. Goodness of fit criteria that were used to evaluate predictive performances of candidate models were adjusted coefficient of determination (R2adj), Akaike’s information criterion (AIC), Bayesian information criterion (BIC) and root means square error (RMSE). The Brody model was the best non-linear function that described the biological growth pattern of all, male, female, single, twin, and triplet lambs. Differences in curve parameter estimates between male and female suggested a definite pattern of sexual dimorphism. Moreover, a higher estimate of rate of maturity in female lambs reflects their early maturity compared with male Kajli lambs. Similarly, the single-born Kajli animals with highest maturity rate were maturing at an earlier age than twins and triplets. This is the first report on the non-linear pattern of visible changes in bodyweight of Kajli sheep from birth to 12 months old.Key words: age, bodyweight, growth curves, regression, sheep

Application of the Wood model to analyse lactation curves of organic dairy sheep farming

2014 ◽  
Vol 54 (10) ◽  
pp. 1609 ◽  
Author(s):  
Juan Carlos Ángeles Hernández ◽  
Octavio Castelán Ortega ◽  
Benito Albarrán Portillo ◽  
Hugo H. Montaldo ◽  
Manuel González Ronquillo
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Evaluation Criteria ◽  
Coefficient Of Determination ◽  
Dairy Sheep ◽  
Organic System ◽  
Dairy Ewes ◽  
Lactation Curve ◽  
Total Milk ◽  
Wood Model

The aim of the present study was to evaluate the performance of the Wood model to describe the characteristics of lactation curves of dairy ewes under organic management in Mexico. In total, 4861 weekly test-day milk yield records from 194 lactations of crossbred dairy ewes were analysed to assess the performance of an empirical model to fit their lactation curve. We used the mathematical model proposed by Wood. The evaluation criteria were the correlation coefficient (r) between the values of total milk yield observed and estimated, the coefficient of determination (R2), and the mean square prediction error (MSPE). In addition, the peak yield (PYest) and time at peak yield (PTest) were calculated. The Wood model showed adequate goodness of fit (r = 0.95, R2 = 0.92 and MSPE = 0.024). The Wood model detected that 52.06% of lactation curves had a continuously decreasing shape (atypical curve), probably as a consequence of the characteristic management of the organic system, mainly due to the genotype used and the nutritional management. Residuals were greater for atypical curves than for typical ones, indicating differences in the ability of the Wood model to fit the two types of shapes. In typical curves, the Wood model showed adequate estimates of total milk yield and time at peak yield. The peak yield was underestimated both in typical and atypical curves. The Wood model in atypical curves underestimated the time at peak yield and milk yields in late lactation. The Wood model showed a reasonable fit of lactation curve in dairy sheep in organic systems but presented deficiencies of fit in atypical curves; therefore, estimates should be interpreted carefully.

Comparing biological and linear models to estimate milk yields and lactation curve parameters

2005 ◽  
Vol 2005 ◽  
pp. 113-113
Author(s):  
B. Albarran-Portillo ◽  
G. E. Pollott
Keyword(s):  
Dairy Cows ◽  
Milk Production ◽  
Milk Yield ◽  
Linear Models ◽  
Computational Effort ◽  
Reasonable Accuracy ◽  
Early Predictors ◽  
Lactation Curve ◽  
Total Milk ◽  
Mathematical Equations

The genetic evaluation of dairy cows is based primarily on milk production and its constituents. Many models have been developed and evaluated in order to estimate total milk yield (CTMY) and other characteristics of lactation curves. Frequently, the models are based on complex mathematical equations and their use demands a huge computational effort. The development of simple models as early predictors of TMY with a reasonable accuracy is important. The objective of this research was to compare the biological model described by Pollott (2000) with two linear models.

scholarly journals Estimation of diurnal total radiation based on meteorological variables in the period of plant vegetation in Poland

2018 ◽  
Vol 23 ◽  
pp. 00032 ◽  
Author(s):  
Paulina Stanek ◽  
Leszek Kuchar ◽  
Irena Otop
Keyword(s):  
Relative Error ◽  
Linear Models ◽  
Meteorological Data ◽  
The Other ◽  
Meteorological Variables ◽  
Coefficient Of Determination ◽  
Total Radiation ◽  
Radiation Data ◽  
Non Linear ◽  
Best Fit

The paper presents selected models for the estimation of diurnal total radiation on the basis of other meteorological variables (using simple data as temperature and rainfall) in the vegetation months in the territory of Poland. For that purpose 6 meteorological stations were selected, having standard meteorological data as well as total radiation data for the period of 2001 – 2010. The stations were chosen so that two of them were situated on the coast, two in the lowland part of the country, and two in the mountains. The models were evaluated with the use of the coefficient of determination R² and the relative error of estimation RMSE with division into 6 months and 6 meteorological stations. In each of the regions the best results were obtained for models 6 and 7 which are combinations of the remaining models and additionally the constructed variable ΔT, used in other non-linear models analysed in the other studies. The best fit for those models was obtained for the mountain stations (R² from 0.67 to 0.75, RMSE from 2.7 to 4.4). The poorest estimation was obtained for the coastal stations (R² from 0.41 to 0.67, RMSE from 2.6 to 5.1). The paper does not indicate the best month in terms of the fitting, due to the high variation of results for the stations and the models.

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