The Precision Approach of the Lactation Curve in Sirohi Goats Using Non-Linear Models

Iranian Journal of Applied Animal Science

دوره 13، شماره 1، خرداد 2023، صفحه 105-111   

نوع مقاله: Research Articles

نویسندگان

L. Gautam^{* 1}؛ H. Ashraf Waiz²

¹Department of Animal Genetics and Breeding, College of Veterinary and Animal Science, Rajasthan University of Veterinary and Animal Sciences, Bikaner, 334001, India

²Department of Livestock Production Management, College of veterinary and Animal Science, Rajasthan University of Veterinary and Animal Science, Bikaner, 313601, India

چکیده

Lactation knowledge enables total milk yield prediction from single and multiple lactation test days. The objective of this study was to compare different non-linear lactation curve models and to select the best fit model for evaluation of the Sirohi goat's milk production curve. Data retrieved fortnightly test day milk yield (FTDMY) in the various days (15, 30, 45, 60, 75, 90, 105, 120, 135 and 150) at 22.630 fortnightly test day milk yield of 2,263 Sirohi does in different lactations at All India Coordinated Research project area period from 2004 to 2016. Gamma, inverse quadratic polynomial, exponential, mixed log, and polynomial regression were evaluated to describe the lactation curve. The mean FTDMY increased from 0.811 ± 0.004 kg on Td₁ (15^th day of lactation) to 1.025 ± 0.005 kg on Td₃ (45^th day of lactation) and then decreased to 0.379 ± 0.001 kg on Td₁₀ (150^th day of lactation), with a coefficient of variation ranging from 20.40% to 28.68%. The polynomial regression function had the best adjusted R² value of 99.4% and the smallest root mean square error of 0.003 kg., with expected peak yield, persistency, and total milk yield were 1.03 kg, 60.8%, and 115.73%, respectively. Out of the five lactation curve models examined, the polynomial regression function produced an outstanding model for predicting fortnightly test day milk output in Sirohi goats, with a relatively strong R² and a low root mean square error (RMSE).

کلیدواژه‌ها

exponential؛ gamma؛ inverse quadratic polynomial؛ mixed log؛ polynomial re-gression

اصل مقاله

INTRODUCTION

Goats play an important role in livelihood and food security of small and marginal farmers of Rajasthan and are considered as “moving ATMs” for goat-keepers. These are considered as assurance for livelihood and survivability of “Ghumantu (migratory) and land-less livestock-keepers, especially shepherds”. The National Bureau of Animal Genetic Resources of India has thirty four recognized goat breeds (NBAGR, 2020). With 148.88 million goats, India ranks second within the world in terms of goat population, accounting for 27.80 percent of the country's total livestock population (FAOSTAT, 2019). Rajasthan with its 56.8 Million livestock population ranks second in the country and shares more than 10% livestock population of India. Rajasthan ranks first in country with 20.84 million populations of goats and 14% share of goat population from country (Rajasthan AHD, 2020) and the state has high genetic diversity amongst India’s goat population. The goat, a poor man's cow, provides milk and meat, which are important sources of animal protein. Goats produce about 3% of total milk in India, while they contribute 14.25 percent to meat production. (DADF Annual Report, 2017). Sirohi goats are a dual-purpose goat breed found primarily in the southern region of Rajasthan. They are well-known for their milk and meat production. According to Kapadiya et al. (2016) goat milk is considered as superior to cow and buffalo milk. It has a number of health benefits over cow’s milk, including improved digestion, increased alkalinity, and a lower s1-casein content, making it less allergenic. Goat milk is alkaline, unlike cow milk, which is acidic, making it ideal for those who suffer from acid reflux (Nazli, 2017). The lactation curve is outlined as a graph that shows the connection between milk yields and also the length of your time since biological process (Brody, 1964). Milk production generally peaks within the early stages of lactation then bit by bit declines (Leon-Velarde et al. 1995). It’s a valuable tool for genetic analysis and management selections involving time (Macciotta et al. 2011). Lactation knowledge allows for the prediction of total milk yield from single and multiple test days of lactation. The evaluation of lactation curve models is useful for monitoring individual yields for diet planning, early disease detection, and selecting superior animals to be parents in the next generation (Gipson and Grossman, 1989). A variety of empirical models have been developed to explain the lactation curve (Nelder, 1966; Wood, 1967; Wilmink 1987; Guo and Swalve, 1995; White et al. 1999).

 

MATERIALS AND METHODS

Data

The data were collected from All India Co-ordinated Research Project (AICRP) on Sirohi goat improvement, Livestock Research Station, Vallabhnagar, Udaipur, India. Data retrieved fortnightly test day milk yield (FTDMY) in the various days (15, 30, 45, 60, 75, 90, 105, 120, 135 and 150) at 22.630 FTDMY of 2.263 Sirohi does in different lactations during period from 2004 to 2016. The project area is located in Southern Rajasthan state and situated at 582 m above sea level on 24.67° N 74.00° E. which characterized by semi-arid climate and having annual normal rainfall of the State is 594.9 mm. out of which 75 to 95% of the rainfall mostly precipitates in the monsoon period i.e. from 1^st June to 30^th September. Similarly, the average temperature ranges from 10^C to 35^C in project area. Records pertaining to culling in the middle of lactation, abortion, still birth, or any other pathological causes affecting the lactation yield of the animals were considered abnormal, and thus such records were not included in the current study.

 

Housing, feeding, and lactation parameters

In the project area, Sirohi goats are raised in a semi-intensive system. Every day, goats grazed for six to eight hours on pasture. Goats are typically housed at night in Kacha floors that are covered by soil that has been coated with cow dung and are located at the farmer's house. Various types of trees, shrubs, and grasses can be found in the project area's pasture land at various times of the year. Available trees, shrubs and grasses different seasons as monsoon (Kair, Dhaman, Dudh, Patharchatta, Motha, Akra and Thur), winter (Neem, Motha, Akra, Keekar and Beri) and summer (Post harvest left over residue of Gram pea, Babul, Kair and Khejri) for Sirohi goat in southern Rajasthan. Vaccination and treatment services are provided to registered goat keepers in the project area by project staff and the Rajasthan animal husbandry department.

 

Estimation of lactation parameter

The data was used to evaluate the lactation curve parameters pertaining to five lactation curve function. Gamma function (GF) (Wood, 1967) (1).

Y_t= at^b e^-ct

Fitted in the log linear form:

logY= loga + blogt – ct

Where:

Y_t: average daily yield in the t^th fortnight.

a: initial milk yield, just after kidding.

b: inclining slope parameter up to peak yield.

c: declining slope parameter.

t: fortnightly test day.

e: base of natural logarithm (2.71828).

Inverse quadratic polynomial (IQP), (Nelder, 1966) (2).

Y^-1_t= a + bt^-1 + ct

Where:

Y_t: average daily yield in the t^th fortnight.

a: initial milk yield, just after kidding.

b: inclining slope parameter up to peak yield.

c: declining slope parameter.

t: fortnightly test day exponential function (EF), (Wilmink, 1987) (3).

Y_t= a + be^-0.7t + ct

Where:       

Y_t: average daily yield in the t^th fortnight of lactation.

a: initial milk yield, just after kidding.

b: inclining slope parameter up to peak yield.

c: declining slope parameter.

t: fortnightly test day.

Mixed log function (MLF), (Guo and Swale, 1995) (4).

Y_t= a + bt^½ + clogt + e_t

Where:

Y_t: average daily milk yield in the t^th test day of lactation.

a: initial milk yield just after kidding.

b: ascending slope parameter up to the peak yield.

c: descending slope parameter.

t: length of time since kidding.

e_t: residual error.

Polynomial regression function (PRF), (Ali and Schaeffer, 1987) (5).

Where:

Y_t: average milk yield in t^th fortnight of lactation.

 a: associated with peak yield.

b and c: associated with decreasing slope.

d: associated with the increasing slope, x= t/150.

e: base of natural logarithm (2.71828).

 

Fitting the models to lactation curve

The above-mentioned models were fitted to the Sirohi goat's FTDMY (kg) only after it had completed 150 days of milk yield (10 fortnightly) of lactation. The best model was chosen based on the highest adjusted coefficient of determination (R²) value and the lowest root mean square error (RMSE). The residuals were graphically plotted to determine the model's accuracy in fitting the lactation curves.

 

Estimated total milk yield

Total milk yield was estimated for the selected equations by the centering date method (CMD), also known as Fleischmann’s method (Ruiz et al. 2000). The general expression of the CDM method is:

Where:

ETMY: estimated total milk yield.

D₁: interval between kidding and first recording.

P_i: yield of the record I.

D_i: interval between the record i and the record (i+1) (i=1,...k).

15: days interval of milk recording in lactation period.

 

Persistency percentage

 

Persistency= 100 × TMY_LH/TMY_FH

Where:

TMY_LH: cumulative milk yield of last half of lactation curve.

TMY_FH: cumulative milk yield of first half of lactation curve.

 

Coefficient of determination (R2)

R² gives the percentage of variance of fortnightly yield explained by the model:

Where:

SSE: error sum of square.

SST: total sum of square.

Where:

N: no. of observations.

P: no. of parameter in the model.

 

Root mean square error (RMSE)

Root mean square error is a kind of generalized deviation.

Where:

n: number of observations.

y_i: actual values.

ỹ: values predicted by the regression model.

 

RESULTS AND DISCUSSION

A total of ten FTDMY records (15^th, 30^th, 45^th, 60^th, 75^th, 90^th, 105^th, 120^th, 135^th, and 150^th day) were collected at a 15^th day interval. The mean FTDMY increased from 0.811 ± 0.004 kg on Td₁ (15^th day of lactation) to a peak yield of 1.025 ± 0.005 kg on Td₃ (45^th day of lactation) and subsequently declined to 0.379 ± 0.001 kg on Td₁₀ (150^th day of lactation) and coefficient of variation was ranged from 20.40% to 28.68% (Table 1). The estimated lactation curve parameters and standard errors (Table 2), as well as the observed and predicted FTDMY (Figure 1 and 2).

 

Table 1 Descriptive statistics of fortnightly test day (FTD) milk yield in kg

The means within the same column with at least one common letter, do not have significant difference (P>0.05).

SDM: standard deviation of the mean; SEM: standard error of the means; CV: coefficient of variation.

 

Table 2 Estimates of the model parameters

 

GF: gamma function; IQP: inverse quadratic polynomial; EF: exponential function; MLF: mixed log function and PRF: polynomial regression function.

 

Figure 1 The observed and predicted FTDMYs from the various lactation curve functions

 

Figure 2 Residual errors between observed and predicted values from various lactation curve functions

 

Peak period, peak yield, persistency, and estimated total milk yield are presented, as well as predicted equations with R² and RMSE values for five different functions and correlation between observed and predicted milk yield (Tables 3 to 5). All models predicted the FTDMY with high degree accuracy (R²_adj) and the lowest RMSE. In the current study, the polynomial regression function produced the highest adjusted R² value of 99.4% and the lowest RMSR of 0.003 kg. The expected peak yield, persistency, and total milk yield were 1.03 kg, 60.8%, and 115.73%, respectively (Table 3). The error in FTDMY prediction using the polynomial regression function ranged from – 0.01 kg on the 30^th day to 0.03 kg on the 45^th day, with the expected peak yield (1.03 kg) observed on the 30^th test day of lactation (Table 4). The correlation between the observed and estimated results was higher (99.8 %) than for other functions (Table 5). Catillo et al. (2002) reported similar R² values (99%) in Italian water buffaloes and Sahoo et al. (2015) in Murrah buffaloes (R² value 99.8% and RMSE 0.003 kg). The gamma type function produced the second highest adjusted R² value of 98.8% and the lowest RMSR of 0.006 kg, with the projected peak yield occurring on the 45^th day of lactation's test day. The ascending phase and peak yield are not explained by gamma function. In Sirohi goats, this function explained a lower peak yield (0.99 kg) than the actual observed peak yield.

 

Table 3 Different lactation curve functions with parameters for prediction of fortnightly test days milk yield with goodness of fit

 

PP: peak period; PY: peak yield and TMY: total milk yield.

RMSE: root mean square error.

 

Table 4 Predicted fortnightly test days milk yield (FTDMY, kg) and error of different lactation curve functions

GF: gamma function; IQP: inverse quadratic polynomial; EF: exponential function; MLF: mixed log function and PRF: polynomial regression function.

 

Table 5 Correlations between the observed milk yield and the different non-linear model used to the lactation curve of Sirohi goats

GF: gamma function; IQP: inverse quadratic polynomial; EF: exponential function; MLF: mixed log function and PRF: polynomial regression function.

** Correlation is significant at the 0.01 level.

 

The correlation between the observed and estimated result was the second highest (99.6%) of the functions studied. According to the current findings, Akpa et al. (2011) observed an R² value of 98.3% in Alpine goats, Fernandez et al. (2002) reported a 98% R² value in Murciano-Granadina goats, and Waheed and Khan (2013) found an R² value of 98.2% in Beetal goats. Contrary to the current findings, Bilgin et al. (2010) found lower R² values for this function in the Awassi, Morkraman, and Tushin breeds of sheep, with 92.4%, 91.9%, and 86.2%, respectively, and 86.8% R² in Akkaraman ewes by Keskin and Dag (2006). In the Sirohi goat, the mixed log function produced the third highest adjusted coefficient of determination (97.6%) and the lowest RMSR (0.008 kg). The mixed log function projected a peak milk yield of 0.98 kg on the 30^th test day, which was marginally lower than the actual yield. Persistence (61.5%) and total milk yield (115.73%), on the other hand, were reported to be higher than observed. The error in FTDMY prediction using the mixed log function varied from −0.03 kg in the 15^th, 75^th, and 90^th days to 0.05 kg in the 45^th day. At the 45^th day, MLF had the largest prediction error in peak output. However, at the 15^th, 60^th, and 120^th days, the mixed log function slightly overestimated test day milk. The observed and expected milk yields are correlated. As a result, Sahoo et al. (2015) investigated the MLF in Murrah buffaloes, finding that the R2 and RMSE were both 98% and 0.09 kg, respectively. The inverse quadratic polynomial function produced (97.4%) adjusted R² and (0.009 kg) RMSE, with the maximum peak yield displayed (1.05 kg.). With a mixed log function, however, persistency (61.6%) and predicted total milk output (115.87%) were similar. The predicted error ranged from −0.06 kg in the 150^th day to 0.03 kg in the 90^th day. The observed and estimated milk yields were found to have a 99.0 % correlation. R² values (94% to 98%) in different parities of Italian water buffaloes were reported by Catillo et al. (2002). In this study, the exponential function was found to have the least fit for fortnightly test day milk yield, with the lowest adjusted R² (84.9%) and a greater RMSR (0.022 kg) in Sirohi goats. In comparison to observed and other functions on the 30^th day of lactation, the lowest peak yield (0.97 kg) was recorded on the 15^th day (Table 3). The expected inaccuracy varied from −0.16 kg on day 15 to 0.12 kg on day 45. In the 15^th day, the highest projected error of FTDMY was recorded. In the 15^th, 60^th, and 135^th days, the exponential function overestimated the FTDMY. Similarly, when compared to other functions in this investigation, the correlations between observed and predicted total milk yield were the lowest. R² values (97% to 98%) in different parities of Italian water buffaloes were reported by Catillo et al. (2002). On the other hand, Sahoo et al. (2015) found R² value (95%) and RMSE (0.14 kg) in Murrah buffalo.

 

CONCLUSION

Five mathematical functions for modeling the lactation curve in Sirohi goat were compared for accuracy of predicting milk yields from test day’s records. In the present findings, the result showed that the Ali and Schaeffer’s model was the best model to predict milk yield at AICRP project area of Sirohi goat, with a relatively strong adjusted coefficient of determination and a low RMSR, out of the five lactation curve models examined. The results also revealed that all of these models accurately predicted the lactation curve.

 

ACKNOWLEDGEMENT

The author gratefully acknowledges the support to Project In-charge of All India Co-ordinated Research Project (AICRP) on goat improvement, Livestock Research Station, Vallabhnagar, Udaipur, Rajasthan, India for providing data on Sirohi goat.

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