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## Archivos de medicina veterinaria

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*versión impresa* ISSN 0301-732X

### Arch. med. vet. vol.43 no.2 Valdivia 2011

#### http://dx.doi.org/10.4067/S0301-732X2011000200007

*Arch Med Vet *43, 145-153 (2011)

**ORIGINAL ARTICLE**

**Environmental factors affecting lactation curve parameters in the United Kingdom's commercial dairy herds**

**Factores ambientales que determinan los parámetros de la curva de lactación usando un modelo biológico en rebaños lecheros comerciales en el Reino Unido**

**B Albarrán-Portillo**

^{a*}

**, GE Pollott**

^{b}

^{a} Centro Universitario UAEM Temascaltepec, Universidad Autónoma del Estado de México, México.

^{b }Royal Veterinary College, Royal College Street, London, UK.

* Carretera Toluca-Tejupilco Km 67.5, Estado de México, C.P.51300; __bapbap24@yahoo.com.mx__.

**SUMMARY**

The purpose of this study was to investigate the environmental factors affecting lactation curve parameters derived from a biological model. The biological approach to lactation curve fitted 2 logistic curves to mimic the initial increase in milk secretory cell numbers in early lactation, and the progression of apoptosis in late lactation. Records from 182,987 Holstein-Friesian cows were analysed. Main factors such as cow, herd and lactation number accounted for 74% of the total sum of squares (P < 0.001). The average age at first calving was 28 months; which had a significant effect on all curve parameters. Increments of age at first calving from 20 to 40 months, were associated with linear increments in total milk yield, and calculated total milk yield. Parameters from the increasing phase of lactation such as maximum secretion potential, growing midpoint from start of lactation to peak yield, and peak yield, were highly correlated amongst themselves (> 0.60). Curve parameters, maximum secretion potential and peak yield were highly correlated indicating that these two parameters are practically the same. Additionally, high estimates of maximum secretion potential and peak yield resulted in high total milk yield. The early day of peak had an adverse effect over persistency of lactation given by the high correlation between day of peak and persistency (0.64). Cow, herd, lactation number and age at first calving were the most determining factors on the lactation curve of first calving and multiparous dairy cows.

* Key words: *biological model, dairy cow, environmental factors, lactation curve.

**RESUMEN**

El objetivo del trabajo fue determinar los factores ambientales que determinan los parámetros de la curva de lactación utilizando un modelo biológico de ajuste de curva. El modelo propuesto ajusta dos curvas logísticas que simulan el incremento inicial en el número de células secretoras de leche en la lactación temprana, y la progresión de la apoptosis en la lactación tardía. Se analizaron lactaciones de 182.987 vacas Holstein-Friesian. Los factores vaca, rebaño y número de lactación explican el 74% de la suma total de cuadrados (P < 0,001). La edad promedio a primer parto fue de 28 meses, teniendo un efecto significativo sobre la mayoría de los parámetros de la curva. Incrementos en la edad a primer de parto (20-40 meses) fueron asociados con incrementos lineales en los rendimientos totales de leche. Los parámetros tasa máxima de secreción y máximo de lactación estuvieron altamente correlacionados entre sí, indicando que son virtualmente los mismos. Adicionalmente, altos valores de estos dos parámetros indican altos rendimientos totales de leche. El día del máximo de lactación se correlacionó negativamente (0,64) con persistencia de la lactación. Los factores vaca, rebaño número de lactación y edad a primer parto fueron los factores más determinantes sobre los parámetros de la curva de lactación de vacas de primera lactancia así como de lactaciones múltiples.

* Palabras clave: *modelo biológico, vaca lechera, factores ambientales, curva de lactación.

**INTRODUCTION**

Several empirical models have been used to fit the lactation curve accounting for factors affecting milk yields (Masselin *et al *1987). The incomplete gamma function proposed by Wood (1967), has been extensively used to fit lactation curves. This model accounts for the main parameters of the lactation curve such as: milk yield at the start of lactation, rate of increase to peak yield, and persistency of lactation. Most recently, other methods such as random regression models (Schaeffer and Dekkers 1994), and spline models (White *et al *1999, Misztal 2006), have been used with good results. However, the parameters resulting from these models do not reflect the biological processes of lactation in its parameters (Pollott 2000).

Pollott (2000) developed a model which produces parameters with a biological explanation of lactation curve. This biological model accounts for mammary parenchyma cell proliferation, their differentiation into secretory cells and depletion of cell population due to programmed cell death (apoptosis) (figure 1). These processes have been reported extensively by Knight and Wilde (1987, 1993), Wilde and Knight (1988, 1989) and Wilde *et al *(1997).

Pollott's model produce three biological base parameters: Maximum secretion potential (MS), which is a function of the total number of parenchyma cells, and the maximum secretion rate (kg/cell per day); the relative growth rate in cell numbers from parturition to peak yield; and the relative death rate in cell numbers from mid to the end of lactation. In this way the model provides parameters with a biological meaning, covering those parameters by Wood's model, complementing in this way, parameters that describe the shape of the lactation curve.

The biological model consists of seven parameters which under commercial milk records schemes (monthly records) it is not possible to use, since some lactations contain as few as 4 records, causing an over parameterization in case of use this model. That is why a reduced version of Pollott's model with two or three parameters have been developed, and were compare with some widely used models such as Wood, the model of Grossman and Koops (1988), and Morant and Gnanasakthy (1989), using dairy sheep and dairy cow lactations, with monthly records. In both cases, the results showed that the reduced version of the biological model with two and three parameters, produced residual mean squares that are smaller or similar when comapred to the other models (Pollott and Gootwine 2000).

Albarrán-Portillo and Pollott (2008) used the biological two-parameter model, using commercial monthly records with as little as 4 test-day records, in order to estimate the genetic factors affecting lactation curve parameters from commercial dairy herds, proving the genetic relationship among output parameters from the biological model. They concluded that biological parameter maximum secretion potential (MS), and proportional reduction in cell numbers (DR), did not show a high genetic correlation among them, making them subjected to selection. The parameter MS, and its genetic correlated parameters like peak yield, implies higher milk yields, where as lower values of DR, implies more persistent lactations, that results in higher total milk yields.

Milk production, apart from the genetic merit of the cow, is affected by several environmental factors that must be considered in order to estimate accurately total milk yields. Such factors are herd, year and season of calving, lactation number, and age at first calving among some others (Lee *et al *1995, Brotherstone *et al *2004).

The aim of this research was to use a two-parameter biological model to fit lactation curves of dairy cows from commercial herds, with the purpose of determining the environmental factors affecting lactation curve parameters.

**MATERIAL AND METHODS**

**DATA**

The data used in this research came from a large database provided by National Milk Records Ltd. (Chippenham, UK), from commercial dairy herds in the United Kingdom. Lactations were composed by monthly records, and to be used in this analysis they were edited as follows: lactations with first test day recorded after d 80 of lactation were deleted, as were lactations with < 4 test-day records (TD). Cows younger or older than 20 months of age at first calving were deleted. Lactations were grouped according to lactation number; eight groups were formed. Lactation group number eight was composed by lactations ≥8.

The final database included 392,954 lactations from 182,987 cows from 431 dairy herds that remain in the database. Number of test-day records per lactation ranged from 4 to 15, with an average of 10 TD per lactation.>

**MODEL**

Lactations curves were fitted using the 2-parameter multiplicative model (Model 1). This model is an alternative to the original 7-parameters multiplicative model (Pollott 2000), and was used for the first time by Pollott and Gootwine (2000), who would have had the difficulty of fitting a model with 7 parameters to farm recorded monthly test-day records.

The 2-parameter model was:

> |

where M* _{t} *= Milk yield on

*t*day of lactation; MS = the maximum secretion potential of lactation;

*z*= [(1-0.9999999)/0.9999999]; and DR = the relative decline in cell numbers as lactation progresses (Pollott and Gootwine 2000, Pollott and Gootwine 2001). Basically, the model comprised 2 logistic curves (figure 1). The first curve accounted for the increase in cell numbers during early lactation as a function of time. Specifically, the first part of the equation estimated MS as the maximum secretion rate of milk as the product of the average secretion rate per cell (Sa), and the number of differentiated parenchyma cells (NDPC). The second logistic curve determined the down slope of the lactation (after peak yield) due to the relative death rate of cells as a function of time, the proportional reduction in cell numbers (PR) as lactation progresses (Pollott 2000).

Curves were fitted to each of the 392,954 lactations using the 2-parameter biological model with an iterative nonlinear curve fitting procedure (NLIN) in SAS (SAS Institute 1999). The iterative process was initiated using preliminary estimates of the parameters [e.g., MS = 0.1 to 85 (bounds 0 MS < 85) and DR = 0.000001 to 0.1 (bounds -1 < DR < 1)]. The best fit of the model with respect to a particular lactation was obtained when the differences between the residual sums of squares in successive iterations was <10^{-6} (Albarran-Portillo and Pollott 2008).

**CURVE PARAMETERS**

The outcome parameters from the model MS and DR, were complemented with calculated values of the lactation curve such as growing midpoint from the start of lactation to peak yield (GM), peak yield (PY), day of peak (DP), persistency (PS) which was estimated at the midpoint between peak yield and the end of lactation, observed total milk yield (TMY) and calculated total milk yield (CTMY) (Pollott 2000). Total milk yield was the lactation milk yield calculated from the original test-day records using the test-interval method of Sargent *et al *(1968).

**STATISTICAL ANALYSIS OF LACTATION PARAMETERS**

Lactations were analysed using Model 2 in order to determinate the environmental factors that affect lactation curve traits. The model was fitted to the 8 lactation parameters shown in table 1, using GLM procedure (SAS 1989).

where μ = overall least square mean, C* _{i} *= Cow (

*i*=1 to 182,987) H

*= herd*

_{j}*j*(

*j*= 1 to 431), and YR

*= calving year*

_{k}*k*(

*k*= 1994 to 2003), and S

*= season of calving (*

_{l}*l*= spring to winter), and LNO

*= lactation number*

_{m}*m*(

*m*= 1 to ≥ 8), and

*e*represents the random error term. Due to the large number of levels of factor cow, it was absorbed from the analysis using the Absorb statement in GLM procedure, in order to reduce time and computing memory resources, since there are no interactions between cow and the main factors (SAS 1989). Least square means were computed for each of the factors in the model, except for the factor absorbed.

_{ijkl}The ANOVA analysis results used Type III sums of squares, and least square means were computed for each of the factors in the model.

**AGE AT FIRST CALVING**

In order to determine the effect of age at first calving (AFC) on milk production first, second and third lactations were selected from the main data set to be analyzed. The characteristics of each lactation were: record of date of birth and date of calving, cows younger than 20 months and older than 40 months at first calving were excluded from the analysis. Model 2 was fitted to first, second and third lactation records (119,580, 74,986 and 18,498 lactations, respectively). Afterward, lactation number (LNO), was omitted from the model and instead AFC and AFC^{2 }were included as covariates. The reason to include AFC^{2} in the analysis was due to the fact that AFC has a curvilinear effect on lactation traits (Pollott 2004).

**CORRELATION ANALYSIS**

Correlation analyses were carried out between the eight lactation curve parameters, fitting Model 2 to all traits using the MANOVA option in GLM procedure in SAS (1989).

**RESULTS**