In Chile, milk production has increased by 556 million litres over the last two decades, reaching 2,230 million litres in 2024 (ODEPA, 2025), despite a notable 69% decrease in the number of dairy farms between 1997 and 2021 (Toro-Mujica and Vera-infanzón, Reference Toro-mujica and Vera-infanzón2024). This decrease in dairy farms is also being observed in other countries such as Canada, the United States and China (Tonet et al., Reference Tonet, Bánkuti, Damasceno, Da Silva Siqueira, Bouroullec and Loddi2023).
In parallel, the structure of the dairy sector has shifted. Currently, there are nearly 14,000 dairy farms in the country, with the majority (68%) operating in the southern regions. However, despite the overall reduction in the number of dairy farms, the category of large-scale operations has increased steadily by 144% for herd sizes between 500 and 1,000 cows, and by 556% for those with more than 1,000 dairy cows during the 1997–2021 period (Toro-Mujica and Vera-Infanzón, Reference Toro-mujica and Vera-infanzón2024).
Despite a reduction in dairy farms, the increased milk production has resulted from the intensification and increased production efficiency of dairy farm systems, where intensive farms operate using concentrates and maize silage as the main feed inputs, and animals are kept under partial or total confinement (Salazar et al., Reference Salazar, Dumont, Chadwick, Saldaña and Santana2007). This intensification is mostly observed in the central regions of Chile (regions V, RM, VI, VII and VIII) (Toro-Mujica and Vera-infanzón, Reference Toro-mujica and Vera-infanzón2024), where cows are housed in confined systems (Arias et al., Reference Arias, Heinsohn, Keim, Pinto and Bombal2025). According to Brito et al. (Reference Brito, Bedere, Douhard, Oliveira, Arnal, Peñagaricano, Schinckel, Baes and Miglior2021), the increase in milk production has been driven by improved productivity per cow, with more than 90% of high-yielding dairy cows globally belonging to specialized breeds: Holstein Friesian, Jersey and Brown Swiss. In Chile, Holstein Friesian cows are the predominant breed in specialized dairy systems (Toro-Mujica and Vera-Infanzón, Reference Toro-mujica and Vera-infanzón2024).
For Chilean dairy farmers, their income is primarily determined by the volume of liquid milk yield (MY) sold, and to a lesser extent by quality-related parameters such as fat content, protein content and somatic cell count (SCC). Therefore, one way to improve profitability is by increasing the amount of MY sold to dairy processors, as companies offer significant bonuses in their payment schemes. However, dairy farms in central Chile have limited space to expand their herd sizes due to land and environmental constraints. Another way to enhance profitability is by reducing costs, which can be achieved by distributing yields more evenly over the entire lactation period. Better lactation persistency is desirable because cows with improved persistency use forage more efficiently and experience less stress due to high peak production (Strucken et al., Reference Strucken, Laurenson and Brockmann2015; Cole et al., Reference Cole, Makanjuola, Rochus, Van Staaveren and Baes2023).
Traits such as MY, fat yield (FY), protein yield (PY) and persistency are influenced by various environmental and management factors, including parity, season, year, genetics, housing, feeding management, water and forage quality, milking frequency, gestation, endogenous annual rhythms and season of calving (Gengler, Reference Gengler1996; Catillo et al., Reference Catillo, Macciotta, Carretta and Cappio-borlino2002; Mellado et al., Reference Mellado, Antonio-chirino, Meza-herrera, Veliz, Arevalo, Mellado and De Santiago2011; Salfer et al., Reference Salfer, Dechow and Harvatine2019; Torshizi et al., Reference Torshizi, Mashhadi and Farhangfar2019; Cole et al., Reference Cole, Makanjuola, Rochus, Van Staaveren and Baes2023; Innes et al., Reference Innes, Pot, Seymour, France, Dijkstra, Doelman and Cant2024). Lactation persistency is described as the cow’s ability to maintain consistent MY over the lactation period – a trait positively associated with health and fertility (Cole et al., Reference Cole, Makanjuola, Rochus, Van Staaveren and Baes2023). Understanding the shape of lactation curves for milk production traits is crucial for decision-making in dairy farms at the population level (Macciotta et al., Reference Macciotta, Vicario and Cappio-borlino2005).
Quantifying MY, FY, PY, SCC and lactation persistency and the influence of non-genetic factors in intensive Chilean dairy systems is important, as most research has focused on the southern rather than the central regions (Smith et al., Reference Smith, Moreira and Latrille2002; Pérez et al., Reference Pérez, Anrique and González2007; Pérez, Reference Pérez2011) and/or is long-established (Melendez and Pinedo, Reference Melendez and Pinedo2007). An exception is the study by Guajardo et al. (Reference Guajardo, Velasco, Astudillo, Cáceres, Cea, Campos, Ocampo and Seminario2020), who reported fat and protein contents of 3.35% and 2.87%, respectively, but only in primiparous cows in a mixed production system (grazing ryegrass-white clover pasture supplemented with concentrate in summer and corn silage plus concentrate in winter), which is not representative of the central regions. On the other hand, the study by Melendez and Pinedo (Reference Melendez and Pinedo2007) analysed only MY and FY, omitting PY, SCC and persistency. In that study, MY ranged between 7,683 and 7,977 litres, and FY between 258 kg (3.36%) and 264.3 kg (3.31%). However, these metrics might no longer be representative of the current yield traits in central Chile. Therefore, the objective of this study was to characterize MY traits (MY, FY and PY), lactation persistency and somatic cell score (SCS) as an indicator of SCC throughout the entire lactation period in Holstein Friesian cows housed indoors in central Chile.
Materials and methods
Data
The present research is a retrospective observational longitudinal study conducted at the Experimental Station Julio Ortúzar Pereira, located in the Metropolitan Region of central Chile. The farm is operated by the AGRO UC Foundation of the Pontifical Catholic University. The farm operates under intensive, fully housed dairy production systems, with year-round calving. Cows are fed a balanced total mixed ration twice daily, formulated according to the recommendations of the National Academy of Sciences, Engineering and Medicine (NASEM, 2021), and have ad libitum access to water. To sustain production, cows received recombinant bovine somatotrophin (rbST) at 2-week intervals, in accordance with national regulations that permit its use in commercial dairy. Monthly herd-test records from 274 pure-breed American Holstein Friesian cows were used for analysis during the period January 2022 to April 2026. Records of daily MY, percentage of fat and protein, days in milk (DIM) and SCC were used. Daily FY and PY yield were calculated from daily MY by multiplying by their respective percentages. Herd test SCC was log2-transformed to SCS using the formula: 
${\text{SCS}} = {\log _2}({\text{SCC}})/100,000 + 3$ (Wiggans and Shook, Reference Wiggans and Shook1987). Lactation length was defined as the interval between calving and dry-off. For cows that did not reach an official dry-off – such as those sold or culled – the lactation was truncated at the last recorded test day. Initial data were restricted as follows: only cows with at least seven test-day observations were available for a given cow-lactation. Records between 5 and 400 DIM were considered. The first measurement had to occur early enough in lactation to provide a representative curve; therefore, cases in which the initial test day occurred later than 45 days after calving were removed. Lactations were only considered for cows in their first five parities. Lastly, records falling outside three standard deviations from the mean of each trait were discarded. The final data set included 3,021 herd-test records from 329 lactations from 206 individual cows.
Two categories were formed based on age at calving as an indicator of parity number, such as multiparous and primiparous. Further two categories were included based on season of calving (summer: calving between September and March; and winter: calving between April and August).
Lactation curves
To model test-day trajectories for milk, fat, protein and SCS, a random regression model incorporating fourth-order Legendre polynomials was fitted (Kirkpatrick et al., Reference Kirkpatrick, Lofsvold and Bulmer1990). Considering 
${Y_t}$as the level of production of a trait measured on day (t) of the lactation from calving, Legendre polynomials have become the function of choice for modelling lactation yields. Both Strabel et al. (Reference Strabel, Szyda, Ptak and Jamrozik2005) and Otwinowska-Mindur et al. (Reference Otwinowska-Mindur, Ptak, Jagusiak and Satoła2013) have indicated that fourth-order Legendre polynomials are the most suitable model for modelling lactation yields. In this study, a fourth-order Legendre polynomial was selected also because models with higher orders resulted in a covariance matrix that was not positive definite, indicating overparameterization or instability in the estimates.
The polynomial of fourth order, which describes a single observation, is defined as follows:
\begin{equation*}{Y_t} = {\alpha _0} \times {P_0} + {\alpha _1} \times {P_1} + {\alpha _2} \times {P_2} + {\alpha _3} \times {P_3} + {\alpha _4} \times {P_4},\end{equation*}where 
${\alpha _i}$are the regression coefficients to estimate, Pi are the functions of time (t) normalized to x which is standardized to an interval, defined as follows: 
$x = - 1 + 2\frac{{(t - {t_{{\text{min}}}})}}{{({t_{{\text{max}}}} - {t_{{\text{min}}}})}},$ where 
${t_{{\text{min}}}}$=5 days and 
${t_{{\text{max}}}}$=400 days, which means that herd-test records between 5 and 400 days were converted respectively to the interval −1 to +1 (Schaeffer, Reference Schaeffer2004).
According to Spiegel (Reference Spiegel1971), the first four Legendre polynomial’s functions of standardized unit of time 
$x$ and coefficients 
${\alpha _i}$ are calculated as follows: 
${P_0}\left( t \right) = 1$, 
${P_1}(t) = x$, 
${P_2}(t) = \frac{1}{2}(3{x^2} - 1)$, 
${P_3}(t) = \frac{1}{2}(5{x^3} - 3x)$ and 
$\,{{P}_4}({t} ) = \frac 1{8}(35{\mathrm{x}^4}-3{{0\mathrm{x}}^2}+3)$.
The model describes the average lactation curve using fixed coefficients and then allows each cow–lactation to adjust that curve through its own random coefficients. For a given cow–lactation i at day t, the predicted value is the sum of the population curve and the individual deviation associated with that animal. For the cow-lactation ‘i’ in DIM ‘t’, the equation is rewritten as follows:
\begin{equation*}
\begin{split}
{Y_{ti}} & = ({\beta _0}{P_0} + {\beta _1}{P_1} + {\beta _2}{P_2} + \cdots + {\beta _4}{P_4}) + {\alpha _{{0_i}}}{P_{{0_{\text{i}}}}} + {\alpha _{{1_i}}}{P_{{1_i}}}\\
&\quad + {\alpha _{{2_i}}}{P_{{2_i}}} + \cdots + {\alpha _{{4_i}}}{P_{{4_i}}} + {e_{ti}}
\end{split}
\end{equation*}where 
$\beta $ values are the fixed regression coefficients of the population, 
$\alpha $ values are the random regression coefficients for each combination cow-lactation and 
${e_{ti}}$ is the random error associated with each observation of day t and cow-lactation i. The SAS software package version 9.4 (SAS Institute Inc.) was used to model the lactation curves for MY, FY, PY and SCS.
Persistency
In this study, lactation persistency of each cow-lactation combination was calculated as follows: 
${\text{Persistency}}\;{\text{ = }}\;\frac{{{Y_{{\text{peak}}}}{\text{ - }}\;{Y_{{\text{end}}}}}}{{{t_{{\text{end}}}}{\text{ - }}{t_{{\text{peak}}}}}},$
where 
${Y_{{\text{peak}}}}$ is the yield at peak MY, 
${Y_{{\text{end}}}}$ is the yield at the end of lactation, 
${t_{{\text{peak}}}}$ is the time (in days) at peak yield, 
${t_{{\text{end}}}}$ is the time (in days) at the end of lactation.
This gives a measure in kg/day indicating how steadily MY declines after peak production; less negative values indicate improved persistency (Innes et al., Reference Innes, Pot, Seymour, France, Dijkstra, Doelman and Cant2024).
Statistical analysis
Accumulated yields for each cow-lactation combination were estimated using the polynomial equation as the sum from day 1 to actual lactation length. Average SCS, daily MY and fat and protein content (expressed as g/kg) were calculated as the mean of the estimated trait values derived from the orthogonal polynomial function. Then the following mixed linear model was used to obtain least-squares means and standard errors of the mean or each parameter of the lactation curve, persistency, predicted accumulated MY, FY and PY using PROC MIXED of SAS Version 9.4 (SAS Institute Inc.). An effect was considered significant when P was ≤0.05. The initial model included the fixed effect of parity (multiparous, primiparous), calving season (summer, winter), the interaction between parity and calving season, days to peak yield and age at first calving (in months) as covariates, and the individual cow as a random effect. For all the traits, except for FY, the inclusion of cow as a random effect or repeated subject was evaluated but failed to separate variance components (G-matrix not positive definite) or led to negative covariance estimates, and a non-significant null test (P > 0.05). Because most dairy cows contributed only one lactation and variance component estimation was unstable, a marginal model without random animal effects was adopted (McNeish and Bauer, Reference McNeish and Bauer2022). Also, the interaction between parity and calving season was removed because it was not significant (P > 0.05). Another mixed model for repeated measures was used to estimate least-squares means for average SCS, daily MY, and fat and protein content during lactation. The model included the fixed effect of the stage of lactation (SL1: ≤90; SL2: >90 and ≤180; SL3: >180 and ≤270; and SL4: >270 DIM), parity, calving season and their interaction as fixed effects, and the repeated effect of cow-lactation to account for repeated measures on the same cow in the lactation.
Results
Table 1 presents descriptive statistics for each trait considered in this study. Differences were observed by parity and calving season. Higher daily MY occurred in multiparous compared with primiparous cows in both summer (32.6 vs. 30.2 kg/day) and winter (34.3 vs. 31.6 kg/day). Daily fat content recorded in summer tended to be higher, whereas protein content remained relatively stable across groups. SCS was higher in multiparous cows, particularly in winter. From the 329 lactations recorded in 206 cows, a total of 228 and 101 lactations corresponded to multiparous and primiparous cows, respectively. On average, cows contributed 1.6 lactations, with most animals presenting two calvings (166; 50.5%), followed by one (104; 31.6%), three (51; 15.5%) and four (8; 2.4%) calvings per cow.
Mean, standard deviation (SD), maximum, minimum, median and interquartile range (IQR) for total lactation records of milk, fat, protein and somatic cell score by parity and calving season from January 2022 to April 2026
Table 1 Long description
Summary statistics are given for four traits: milk yield in kg, fat content in g per kg, protein content in g per kg, and somatic cell score, split by parity and calving season, with columns for number of herd test records, number of lactations, mean, SD, maximum, minimum, median, and IQR. For multiparous summer, number of herd test records is 1064 and lactations 118; milk yield mean 32.6, SD 9.3, maximum 59.0, minimum 7.0, median 34.0, IQR 26.0 to 38.0; fat mean 42.0, SD 9.5, maximum 73.2, minimum 11.8, median 41.3, IQR 35.4 to 47.8; protein mean 35.1, SD 3.5, maximum 45.1, minimum 24.3, median 35.0, IQR 32.8 to 37.6; somatic cell score mean 4.40, SD 2.2, maximum 9.64, minimum minus 0.84, median 4.36, IQR 2.65 to 6.09. For multiparous winter, herd test records 1036 and lactations 110; milk yield mean 34.3, SD 9.4, maximum 59.0, minimum 6.0, median 34.0, IQR 28.0 to 41.0; fat mean 39.6, SD 10.9, maximum 77.2, minimum 12.3, median 39.3, IQR 32.0 to 46.3; protein mean 34.8, SD 3.3, maximum 45.2, minimum 25.9, median 34.6, IQR 32.4 to 37.1; somatic cell score mean 4.72, SD 2.19, maximum 9.64, minimum minus 0.84, median 4.93, IQR 3.06 to 6.24. For primiparous summer, herd test records 689 and lactations 75; milk yield mean 30.2, SD 7.6, maximum 50.0, minimum 6.0, median 30.0, IQR 25.0 to 35.0; fat mean 42.0, SD 9.4, maximum 73.6, minimum 17.1, median 41.3, IQR 35.6 to 47.7; protein mean 34.5, SD 3.3, maximum 45.6, minimum 25.3, median 34.4, IQR 32.2 to 36.7; somatic cell score mean 3.38, SD 2.00, maximum 9.64, minimum minus 0.64, median 3.18, IQR 1.94 to 4.60. For primiparous winter, herd test records 232 and lactations 26; milk yield mean 31.6, SD 7.7, maximum 51.0, minimum 10.0, median 32.0, IQR 27.0 to 37.0; fat mean 42.0, SD 9.7, maximum 70.8, minimum 22.3, median 41.3, IQR 35.3 to 48.1; protein mean 34.8, SD 3.5, maximum 44.4, minimum 25.91, median 34.6, IQR 32.4 to 36.9; somatic cell score mean 3.18, SD 1.88, maximum 9.64, minimum minus 0.18, median 2.88, IQR 1.71 to 4.13.
Note: HT, herd test records; IQR, interquartile range, calculated as the difference between the 75th and 25th percentiles.
The predictive ability of the lactation curve methodology, calculated as the linear correlation (r) between observed and predicted values was medium–high for the MY and PY (MY: 0.79 ± 0.007; PY: 0.76 ± 0.008), medium for FY and fat content (FY: 0.69 ± 0.009; fat content: 0.64 ± 0.011) and above 0.80 for protein content and SCS (protein content: 0.83 ± 0.006; SCS: 0.85 ± 0.005).
Tables 2 and 3 present the estimated regression coefficients from the lactation curve models and the corresponding least-squares means for lactation length, accumulated total lactation yield of milk, fat and protein and lactation persistency of the milk. For total lactation of MY and FY, primiparous cows yielded similarly compared with multiparous cows, as shown by the least-squares means for both MY and FY (P > 0.05), but parity had a marginal effect on PY (P = 0.054). Meanwhile, cows calving in winter yielded significantly more accumulated MY than those calving in summer (difference 463 kg; P = 0.024), but this was not observed in FY (P = 0.695) and PY, which showed only a tendency (P = 0.074). Season of calving significantly affected persistency of MY (P = 0.050), whereas primiparous cows showed greater lactation persistency compared with multiparous cows. Neither age at first calving nor DIM had a significant effect on the traits studied, except a small but significant effect of DIM at peak of MY for persistency of the lactation (P < 0.0001).
Estimates of regression parameters (±standard error) for lactation length (days), total lactation milk, fat and protein yield (kg) and lactation persistency of the milk (kg/day)
Table 2 Long description
Regression estimates with standard errors and p values are given for lactation length in days, and milk, fat, and protein yield in kilograms, plus milk persistency. Intercepts are 330 plus or minus 22 for lactation length, 10,461 plus or minus 897 for milk yield, minus 0.0562 plus or minus 0.0121 for persistency, 399 plus or minus 39 for fat yield, and 348 plus or minus 32 for protein yield, each with p less than 0.0001. For parity, multiparous relative to primiparous reference has estimates of minus 10.1604 plus or minus 5.386 for lactation length with p 0.0601, 307 plus or minus 221 for milk yield with p 0.1649, minus 0.0136 plus or minus 0.0030 for persistency with p less than.0001, 12 plus or minus 10 for fat yield with p 0.2277, and 15 plus or minus 7 for protein yield with p 0.054. For calving season, summer relative to winter reference has estimates of minus 1.9258 plus or minus 4.9818 for lactation length with p 0.6993, minus 463 plus or minus 204 for milk yield with p 0.0240, 0.00552 plus or minus 0.0028 for persistency with p 0.0501, minus 4 plus or minus 9 for fat yield with p 0.6946, and minus 13 plus or minus 7 for protein yield with p 0.0742. Days in milk at peak has estimates of 0.0455 plus or minus 0.04156 for lactation length with p 0.2746, minus 2.5767 plus or minus 1.7036 for milk yield with p 0.1314, 0.0001 plus or minus 2.5 times 10 to the minus 5 for persistency with p less than.0001, 0.04967 plus or minus 0.05857 for fat yield with p 0.3970, and 0.0157 plus or minus 0.04943 for protein yield with p 0.7509. Age at first calving has estimates of minus 0.8309 plus or minus 0.8202 for lactation length with p 0.3118, 0.01634 plus or minus 33.7323 for milk yield with p 0.9996, 5.7 times 10 to the minus 5 plus or minus 0.0005 for persistency with p 0.9021, 0.2119 plus or minus 1.5392 for fat yield with p 0.8906, and minus 0.1921 plus or minus 1.1874 for protein yield with p 0.8716. Least square means with standard errors are also listed by class with number of lactations: multiparous has 228 lactations with 305 plus or minus 3 days, 10,248 plus or minus 116 kilograms milk, minus 0.0514 plus or minus 0.0017 persistency, 419 plus or minus 5 kilograms fat, and 354 plus or minus 4 kilograms protein; primiparous has 101 lactations with 316 plus or minus 5 days, 9,940 plus or minus 185 kilograms milk, minus 0.0378 plus or minus 0.0025 persistency, 406 plus or minus 8 kilograms fat, and 339 plus or minus 7 kilograms protein, with p values 0.0601, 0.1649, less than.0001, 0.2277, and 0.054 respectively. By calving season, summer has 193 lactations with 311 plus or minus 3 days, 9,862 plus or minus 128 kilograms milk, minus 0.0419 plus or minus 0.0018 persistency, 411 plus or minus 6 kilograms fat, and 341 plus or minus 5 kilograms protein; winter has 136 lactations with 309 plus or minus 5 days, 10,325 plus or minus 167 kilograms milk, minus 0.0474 plus or minus 0.0023 persistency, 414 plus or minus 7 kilograms fat, and 353 plus or minus 6 kilograms protein, with p values 0.6993, 0.0240, 0.0501, 0.6946, and 0.0742 respectively.
Note: AFC, age at first calving; DIM, days in milk; Ref, category used as reference in the regression analysis.
Number of lactations and least-squares means (± standard error) for lactation length (days), total lactation milk, fat and protein yield (kg) and lactation persistency of the milk (kg/day)
Table 3 Long description
Regression output lists estimates with standard errors and p values for intercept, parity number, calving season, and stage of lactation. Intercept estimate is 29.2675 plus or minus 0.6061, p value less than 0.0001. For parity number, multiparous has estimate minus 0.1502 plus or minus 0.5719 with p value less than 0.0001, and primiparous is the reference. For calving season, summer has estimate minus 1.4636 plus or minus 0.5263 with p value 0.0027, and winter is the reference. For stage of lactation, stage 1 estimate is 1.8770 plus or minus 0.5357 with p value 0.0005, stage 2 is 4.2853 plus or minus 0.5357 with p value less than 0.0001, stage 3 is 2.6801 plus or minus 0.5357 with p value less than 0.0001, and stage 4 is the reference. Least square means by stage of lactation show, for parity number, multiparous values of 35.4 plus or minus 0.30 at stage 1, 36.1 plus or minus 0.30 at stage 2, 31.8 plus or minus 0.30 at stage 3, and 28.4 plus or minus 0.31 at stage 4; primiparous values are 30.9 plus or minus 0.46, 33.0 plus or minus 0.46, 30.9 plus or minus 0.46, and 28.5 plus or minus 0.48 across stages 1 to 4. P values for the parity comparison by stage are less than 0.0001 at stages 1 and 2, 0.0972 at stage 3, and 0.7929 at stage 4. For calving season, summer values are 32.9 plus or minus 0.32 at stage 1, 34.1 plus or minus 0.32 at stage 2, 30.3 plus or minus 0.32 at stage 3, and 27.7 plus or minus 0.34 at stage 4; winter values are 33.4 plus or minus 0.41, 35.1 plus or minus 0.41, 32.4 plus or minus 0.41, and 29.2 plus or minus 0.43 across stages 1 to 4. P values for the season comparison by stage are 0.3116 at stage 1, 0.0310 at stage 2, less than 0.0001 at stage 3, and 0.0055 at stage 4.
Note: Persistency was calculated as (Yield_peak – Yield_end)/(Time_end – Time_peak).
Tables 4–11 present the estimates of regression parameters (a) and least-squares means (b) for daily MY, daily fat and protein content, and SCS by SL (90-day intervals). On contrary to accumulated lactation of MY, multiparous cows showed higher daily MY than primiparous cows in the first 180 days (SL1 and SL2, P < 0.05; Table 5), whereas no differences were observed in later stages. Furthermore, winter-calving cows had higher daily MY than summer-calving cows in SL2–SL4 (P < 0.05), indicating an interaction between calving season and SL (Table 5).
Estimates of the regression parameters (±standard error) for daily milk yield by stage of lactation (SL)
Table 4 Long description
Regression parameter estimates and least square means are reported for fat content in grams per kilogram, with standard errors and p values. In the regression section, the intercept is 40.0350 plus or minus 0.6292 with p value less than 0.0001. For parity number, multiparous has an estimate of minus 0.8489 plus or minus 0.5719 with p value 0.2155, and primiparous is listed as Ref. For calving season, summer has an estimate of 3.8804 plus or minus 0.5263 with p value less than 0.0001, and winter is Ref. For stage of lactation, stage 1 is 3.5650 plus or minus 0.5505 with p value 0.0005, stage 2 is minus 0.3455 plus or minus 0.5505 with p value less than 0.0001, stage 3 is minus 0.8892 plus or minus 0.5505 with p value less than 0.0001, and stage 4 is Ref. In the least square means section by stage of lactation columns labeled SL 1 through SL 4, multiparous values are 42.9 plus or minus 0.31, 39.5 plus or minus 0.31, 40.1 plus or minus 0.31, and 41.1 plus or minus 0.32, while primiparous values are 42.9 plus or minus 0.47, 40.3 plus or minus 0.47, 40.9 plus or minus 0.47, and 42.0 plus or minus 0.50. The parity p values by SL 1 through SL 4 are 0.9849, 0.1562, 0.1805, and 0.1531. For calving season, summer values across SL 1 through SL 4 are 42.3 plus or minus 0.34, 40.6 plus or minus 0.34, 42.2 plus or minus 0.34, and 43.5 plus or minus 0.36, and winter values are 43.6 plus or minus 0.43, 39.3 plus or minus 0.43, 38.8 plus or minus 0.43, and 39.6 plus or minus 0.44. The calving season p values by SL 1 through SL 4 are 0.0096, 0.0122, less than 0.0001, and less than 0.0001.
Note: Ref, category used as reference in the regression analysis.
Least-squares means (±standard error) for daily milk yield by stage of lactation (SL)
Table 5 Long description
Protein content is reported in grams per kilogram in two parts: regression parameter estimates with standard errors and p-values, and least square means with standard errors by stage of lactation labeled SL 1 through SL 4. Regression results list an intercept of 36.6816 plus or minus 0.2422 with p-value less than 0.0001. For parity number, multiparous has an estimate of minus 0.05449 plus or minus 0.2289 with p-value 0.2401, and primiparous is marked Ref. For calving season, summer has an estimate of 0.1078 plus or minus 0.2098 with p-value 0.0007, and winter is marked Ref. For stage of lactation, stage 1 is minus 3.8436 plus or minus 0.1999, stage 2 is minus 2.8942 plus or minus 0.1999, and stage 3 is minus 1.0974 plus or minus 0.1999, each with p-value less than 0.0001, and stage 4 is marked Ref. Least square means by parity number are, for multiparous: SL 1, 32.8 plus or minus 0.12; SL 2, 34.2 plus or minus 0.12; SL 3, 36.4 plus or minus 0.12; SL 4, 36.7 plus or minus 0.12; and for primiparous: SL 1, 32.8 plus or minus 0.18; SL 2, 33.8 plus or minus 0.18; SL 3, 35.8 plus or minus 0.18; SL 4, 36.7 plus or minus 0.19; with p-values 0.8720, 0.0643, 0.0076, and 0.8119 for SL 1 through SL 4. Least square means by calving season are, for summer: SL 1, 32.8 plus or minus 0.13; SL 2, 34.1 plus or minus 0.13; SL 3, 36.3 plus or minus 0.13; SL 4, 36.8 plus or minus 0.14; and for winter: SL 1, 32.8 plus or minus 0.17; SL 2, 34.0 plus or minus 0.17; SL 3, 35.9 plus or minus 0.17; SL 4, 36.7 plus or minus 0.17; with p-values 0.7385, 0.7397, 0.0391, and 0.6075 for SL 1 through SL 4.
Note: SL1, ≤90; SL2, >90 and ≤180, SL3, >180 and ≤270; and SL4, >270 days in milk.
Estimates of the regression parameters (±standard error) for fat content (g/kg) by stage of lactation (SL)
Table 6 Long description
Regression parameter estimates are listed with standard errors and p values for intercept, parity number, calving season, and stage of lactation. The intercept estimate is 4.0086 plus or minus 0.1415, with p value below 0.0001. For parity number, multiparous has an estimate of 0.9961 plus or minus 0.1937 with p value below 0.0001, and primiparous is the reference category. For calving season, summer has an estimate of minus 0.1816 plus or minus 0.1673 with p value 0.2778, and winter is the reference category. For stage of lactation, stage 1 is minus 0.9293 plus or minus 0.1038 with p value below 0.0001, stage 2 is minus 0.8110 plus or minus 0.1038 with p value 0.0007, stage 3 is minus 0.3520 plus or minus 0.1038 with p value 0.0007, and stage 4 is the reference category. Least square means for somatic cell score are given by class across columns labeled SL 1 through SL 4. For parity number, multiparous values are 4.04 plus or minus 0.10, 4.43 plus or minus 0.10, 4.48 plus or minus 0.10, and 4.91 plus or minus 0.11, while primiparous values are 3.02 plus or minus 0.16, 3.13 plus or minus 0.16, 3.58 plus or minus 0.16, and 3.39 plus or minus 0.16; the p value row under parity number is below 0.0001 for SL 1, SL 2, SL 3, and SL 4. For calving season, summer values are 3.46 plus or minus 0.11, 3.72 plus or minus 0.11, 4.10 plus or minus 0.11, and 4.33 plus or minus 0.11, while winter values are 3.59 plus or minus 0.14, 3.84 plus or minus 0.14, 4.25 plus or minus 0.14, and 4.51 plus or minus 0.14; the p value row under calving season is 0.4538 for SL 1, 0.4592 for SL 2, 0.3605 for SL 3, and 0.2778 for SL 4.
Note: Ref, category used as reference in the regression analysis.
Least-squares means (±standard error) for fat content (g/kg) by stage of lactation (SL)
Table 7 Long description
Summary statistics are reported for four traits: milk yield in kg, fat content in g per kg, protein content in g per kg, and somatic cell score, grouped by parity and calving season, with columns for No. of HT, No. of lactations, Mean, SD, Maximum, Minimum, Median, and IQR. Multiparous summer has 1064 HT and 118 lactations; milk yield mean 32.6, SD 9.3, maximum 59.0, minimum 7.0, median 34.0, IQR 26.0 to 38.0; fat mean 42.0, SD 9.5, maximum 73.2, minimum 11.8, median 41.3, IQR 35.4 to 47.8; protein mean 35.1, SD 3.5, maximum 45.1, minimum 24.3, median 35.0, IQR 32.8 to 37.6; somatic cell score mean 4.40, SD 2.2, maximum 9.64, minimum minus 0.84, median 4.36, IQR 2.65 to 6.09. Multiparous winter has 1036 HT and 110 lactations; milk yield mean 34.3, SD 9.4, maximum 59.0, minimum 6.0, median 34.0, IQR 28.0 to 41.0; fat mean 39.6, SD 10.9, maximum 77.2, minimum 12.3, median 39.3, IQR 32.0 to 46.3; protein mean 34.8, SD 3.3, maximum 45.2, minimum 25.9, median 34.6, IQR 32.4 to 37.1; somatic cell score mean 4.72, SD 2.19, maximum 9.64, minimum minus 0.84, median 4.93, IQR 3.06 to 6.24. Primiparous summer has 689 HT and 75 lactations; milk yield mean 30.2, SD 7.6, maximum 50.0, minimum 6.0, median 30.0, IQR 25.0 to 35.0; fat mean 42.0, SD 9.4, maximum 73.6, minimum 17.1, median 41.3, IQR 35.6 to 47.7; protein mean 34.5, SD 3.3, maximum 45.6, minimum 25.3, median 34.4, IQR 32.2 to 36.7; somatic cell score mean 3.38, SD 2.00, maximum 9.64, minimum minus 0.64, median 3.18, IQR 1.94 to 4.60. Primiparous winter has 232 HT and 26 lactations; milk yield mean 31.6, SD 7.7, maximum 51.0, minimum 10.0, median 32.0, IQR 27.0 to 37.0; fat mean 42.0, SD 9.7, maximum 70.8, minimum 22.3, median 41.3, IQR 35.3 to 48.1; protein mean 34.8, SD 3.5, maximum 44.4, minimum 25.91, median 34.6, IQR 32.4 to 36.9; somatic cell score mean 3.18, SD 1.88, maximum 9.64, minimum minus 0.18, median 2.88, IQR 1.71 to 4.13.
Note: SL1, ≤90; SL2, >90 and ≤180; SL3, >180 and ≤270; and SL4, >270 days in milk.
Estimates of the regression parameters (±standard error) for protein content (g/kg) by stage of lactation (SL)
Table 8 Long description
Regression estimates with standard errors and p values are reported for lactation length in days, milk yield, persistency, fat yield, and protein yield. Intercept estimates are 330 plus or minus 22 for lactation length, 10,461 plus or minus 897 for milk yield, minus 0.0562 plus or minus 0.0121 for persistency, 399 plus or minus 39 for fat yield, and 348 plus or minus 32 for protein yield, each with p value below 0.0001. For parity, primiparous is the reference; multiparous estimates are minus 10.1604 plus or minus 5.386 with p value 0.0601 for lactation length, 307 plus or minus 221 with p value 0.1649 for milk yield, minus 0.0136 plus or minus 0.0030 with p value below 0.0001 for persistency, 12 plus or minus 10 with p value 0.2277 for fat yield, and 15 plus or minus 7 with p value 0.054 for protein yield. For calving season, winter is the reference; summer estimates are minus 1.9258 plus or minus 4.9818 with p value 0.6993 for lactation length, minus 463 plus or minus 204 with p value 0.0240 for milk yield, 0.00552 plus or minus 0.0028 with p value 0.0501 for persistency, minus 4 plus or minus 9 with p value 0.6946 for fat yield, and minus 13 plus or minus 7 with p value 0.0742 for protein yield. For days in milk at peak, estimates are 0.0455 plus or minus 0.04156 with p value 0.2746 for lactation length, minus 2.5767 plus or minus 1.7036 with p value 0.1314 for milk yield, 0.0001 plus or minus 2.5 times 10 to the minus 5 with p value below 0.0001 for persistency, 0.04967 plus or minus 0.05857 with p value 0.3970 for fat yield, and 0.0157 plus or minus 0.04943 with p value 0.7509 for protein yield. For age at first calving, estimates are minus 0.8309 plus or minus 0.8202 with p value 0.3118 for lactation length, 0.01634 plus or minus 33.7323 with p value 0.9996 for milk yield, 5.7 times 10 to the minus 5 plus or minus 0.0005 with p value 0.9021 for persistency, 0.2119 plus or minus 1.5392 with p value 0.8906 for fat yield, and minus 0.1921 plus or minus 1.1874 with p value 0.8716 for protein yield.
Note: Ref, category used as reference in the regression analysis.
Least-squares means (±standard error) for protein content (g/kg) by stage of lactation (SL)
Table 9 Long description
Least squares means with standard errors are reported for lactation length in days, milk yield in kilograms, persistency in kilograms per day, fat yield in kilograms, and protein yield in kilograms, with counts of lactations, grouped by parity and calving season. For parity, multiparous has 228 lactations and primiparous has 101. Multiparous values are lactation length 305 plus or minus 3, milk yield 10,248 plus or minus 116, persistency minus 0.0514 plus or minus 0.0017, fat yield 419 plus or minus 5, and protein yield 354 plus or minus 4. Primiparous values are lactation length 316 plus or minus 5, milk yield 9,940 plus or minus 185, persistency minus 0.0378 plus or minus 0.0025, fat yield 406 plus or minus 8, and protein yield 339 plus or minus 7. Parity p values are 0.0601 for lactation length, 0.1649 for milk yield, less than 0.0001 for persistency, 0.2277 for fat yield, and 0.054 for protein yield. For calving season, summer has 193 lactations and winter has 136. Summer values are lactation length 311 plus or minus 3, milk yield 9,862 plus or minus 128, persistency minus 0.0419 plus or minus 0.0018, fat yield 411 plus or minus 6, and protein yield 341 plus or minus 5, while winter values are lactation length 309 plus or minus 5, milk yield 10,325 plus or minus 167, persistency minus 0.0474 plus or minus 0.0023, fat yield 414 plus or minus 7, and protein yield 353 plus or minus 6. Calving season p values are 0.6993 for lactation length, 0.0240 for milk yield, 0.0501 for persistency, 0.6946 for fat yield, and 0.0742 for protein yield.
Note: SL1, ≤90; SL2, >90 and ≤180; SL3, >180 and ≤270; and SL4, >270 days in milk.
Estimates of the regression parameters (±standard error) for somatic cell score by stage of lactation (SL)
Table 10 Long description
Regression parameter estimates for daily milk yield are listed with columns for, Estimate and, P value. Intercept is 29.2675 plus or minus 0.6061, with p value less than 0.0001. Under parity number, Multiparous is minus 0.1502 plus or minus 0.5719, with p value less than 0.0001, and Primiparous is marked, Ref. Under calving season, Summer is minus 1.4636 plus or minus 0.5263, with p value 0.0027, and Winter is marked, Ref. Under stage of lactation, stage 1 is 1.8770 plus or minus 0.5357 with p value 0.0005, stage 2 is 4.2853 plus or minus 0.5357 with p value less than 0.0001, stage 3 is 2.6801 plus or minus 0.5357 with p value less than 0.0001, and stage 4 is marked, Ref.
Note: Ref, category used as reference in the regression analysis.
Least-squares means (±standard error) for somatic cell score by stage of lactation (SL)
Table 11 Long description
Least squares means with standard errors are given for daily milk yield across four stage of lactation columns labeled SL1, SL2, SL3, and SL4, for parity number and calving season groups. For parity number, multiparous yields are 35.4 plus or minus 0.30 in SL1, 36.1 plus or minus 0.30 in SL2, 31.8 plus or minus 0.30 in SL3, and 28.4 plus or minus 0.31 in SL4. Primiparous yields are 30.9 plus or minus 0.46 in SL1, 33.0 plus or minus 0.46 in SL2, 30.9 plus or minus 0.46 in SL3, and 28.5 plus or minus 0.48 in SL4. The parity p-values by stage are under 0.0001 for SL1, under 0.0001 for SL2, 0.0972 for SL3, and 0.7929 for SL4. For calving season, summer yields are 32.9 plus or minus 0.32 in SL1, 34.1 plus or minus 0.32 in SL2, 30.3 plus or minus 0.32 in SL3, and 27.7 plus or minus 0.34 in SL4. Winter yields are 33.4 plus or minus 0.41 in SL1, 35.1 plus or minus 0.41 in SL2, 32.4 plus or minus 0.41 in SL3, and 29.2 plus or minus 0.43 in SL4. The calving season p-values by stage are 0.3116 for SL1, 0.0310 for SL2, under 0.0001 for SL3, and 0.0055 for SL4.
Note: SL1, ≤90; SL2, >90 and ≤180; SL3, >180 and ≤270; and SL4, >270 days in milk.
Regarding fat content, no differences were observed between primiparous and multiparous cows; however, calving season significantly affected this trait in summer-calving cows, showing higher values than winter-calving cows in SL2–SL4, while the opposite pattern was observed in SL1 (P < 0.05).
Parity had no effect on protein content except in SL3, where multiparous cows showed slightly higher values (P < 0.05), whereas calving season had a minimal effect, with differences observed only in SL3, where summer-calving cows had higher values than winter-calving cows (P < 0.05).
In general, there was a gradual and steady increase in SCS from the start to the end of lactation, but differences across the SL were only observed by parity, with values 25–45% greater in multiparous cows. This represents approximately a 1.0-to-1.5-unit difference in SCS, equivalent to about a 2.0- to 2.8-fold increase in SCC.
Discussion
This study is the first comprehensive description of milk production traits from a farm in central Chile in over 15 years. It describes factors that influence lactation curves of production traits in confined dairy cows, in contrast with Melendez and Pinedo (Reference Melendez and Pinedo2007), who aimed to determine the association between reproduction and production traits.
Parity
The literature indicates that in general, milk production traits tend to increase with parity, reaching their peak in parity number 3–4. This is due to (i) increasing size of the udder, which consequently increases the number of secretory cells with age, (ii) lower dry matter intake in younger cows, (iii) differences in tissue mobilization and (iv) a different endocrine background at calving in primiparous cows that limits nutrient partitioning into milk (Mellado et al., Reference Mellado, Antonio-chirino, Meza-herrera, Veliz, Arevalo, Mellado and De Santiago2011). For accumulated yields, previous studies in Holstein Friesian cows reported differences across parity ranging between 12% and 30% for MY (Mellado et al., Reference Mellado, Antonio-chirino, Meza-herrera, Veliz, Arevalo, Mellado and De Santiago2011; Pipino et al., Reference Pipino, Piccardi, Lembeye, López-villalobos and Vázquez2019; Innes et al., Reference Innes, Pot, Seymour, France, Dijkstra, Doelman and Cant2024), and between 9% and 12% for FY and PY, respectively (Pipino et al., Reference Pipino, Piccardi, Lembeye, López-villalobos and Vázquez2019).
Nevertheless, in this study, differences by parity were only observed in early-lactation (as daily MY) but not across the whole lactation. The literature indicates that production in multiparous cows generally declines more rapidly after peak of lactation, resulting in a progressive reduction in the difference in MY between parity groups as lactation advances (Innes et al., Reference Innes, Pot, Seymour, France, Dijkstra, Doelman and Cant2024; Busanello et al., Reference Busanello, Nogara and Zopollatto2025). In this study, on a daily basis, multiparous cows yielded an average of 3.8 kg of MY more than primiparous cows during the first 180 days, while in late-lactation, daily MY was similar between groups, suggesting that the similar accumulated MY between parities reported in Tables 2 and 3 might be explained by differences in lactation length across parities. On average, primiparous cows had 11 days longer lactation length than multiparous cows, although this difference only showed a tendency (P = 0.061). In agreement with this study, the effect of parity is not always consistent. For instance, for daily MY, there is evidence that no significant difference was observed in primiparous cows (Spolders et al., Reference Spolders, Meyer, Flachowsky and Coenen2004), whereas Siewert et al. (Reference Siewert, Salfer and Endres2019) observed parity-related differences only during early-lactation, although both studies were conducted in automatic milking systems. Those studies reported that visits to the automatic systems increased in primipara (2.3–2.9 visits per day), while remaining constant in multipara (around 2.5 visits per day) throughout lactation, consistent with the results presented in Tables 4 and 5.
The higher persistency observed in primiparous cows is consistent with other studies found in the literature (Yilmaz and Koc, Reference Yilmaz and Koc2013; Lembeye et al., Reference Lembeye, Lopez-villalobos, Burke and Davis2016; Innes et al., Reference Innes, Pot, Seymour, France, Dijkstra, Doelman and Cant2024) and is attributed to the lower degree of mammary gland development in primiparous cows.
Our study found higher values of persistency across parity compared with similar groups in the study of Innes et al. (Reference Innes, Pot, Seymour, France, Dijkstra, Doelman and Cant2024) who used the same formula (−0.0378 vs. −0.044 and −0.051 kg/day in primiparous cows, and −0.0514 and −0.0545 vs. −0.080 and −0.083 kg/day in multiparous cows). The observed improved persistency in this herd may be associated with management practices, including routine use of rbST, as was indicated by Mellado et al. (Reference Mellado, Antonio-chirino, Meza-herrera, Veliz, Arevalo, Mellado and De Santiago2011); although this study was not designed to assess this biological effect.
Calving season
Season of calving significantly affected total lactation of MY and persistency (Tables 2 and 3), but these higher yields were not reflected in higher values of accumulated lactation of FY and PY. Cows that calved in the coolest months of the year had higher MY compared with those that calved during the September–March period, suggesting that cows are particularly sensitive to heat stress during early- and mid-lactation. The literature is diverse regarding this effect. For instance, Catillo et al. (Reference Catillo, Macciotta, Carretta and Cappio-borlino2002) and Mellado et al. (Reference Mellado, Antonio-chirino, Meza-herrera, Veliz, Arevalo, Mellado and De Santiago2011) indicated that the sensitivity of the cows is likely due to difficulty in dissipating excess body heat during this period. Also, the increased MY observed in winter-calving cows align with high-amplitude annual rhythms reported in lower latitude regions of the United States (Salfer et al., Reference Salfer, Bartell, Dechow and Harvatine2020).
As shown in Tables 4 and 5, cows that calved in winter had higher daily MY than those that calved in summer from mid- to late-lactation (SL2–SL4). However, the opposite pattern was observed in fat and protein content, particularly for fat content, which increased as daily MY decreased. This is consistent with a dilution effect, whereby higher MY are associated with lower component concentration, resulting in no proportional increase in accumulated FY and PY. Most likely, the late-lactation period of cows calved in winter occurred during summer months. There is strong evidence that long-day stimulation increases daily MY (Dahl et al., Reference Dahl, Buchanan and Tucker2000; Lim et al., Reference Lim, Kim, Park, Ki and Kim2021), which may have contributed to a greater average daily MY observed in this group compared with their counterparts calved in summer. This explanation is plausible because milk component concentrations are stable across the seasons, following an annual cycle that peaks in mid-winter and reaches a nadir in summer, a trend that persists across herds (Salfer et al., Reference Salfer, Dechow and Harvatine2019).
Considering the greater accumulated MY in cows calved in winter, the fact that most milk is produced during the first months of the lactation, and the absence of any effect on SCS (which was similar across stages and calving seasons), the results of this study are particularly relevant since in Chile, dairy companies offer bonuses (approximately 10% of increment of the milk price) for milk produced during the winter months (April–August). Therefore, reproductive management strategies aiming to calve in late March to early April might be advisable to achieve more profitable lactation curves. In contrast with this study, Gengler (Reference Gengler1996) and Torshizi et al. (Reference Torshizi, Mashhadi and Farhangfar2019) summarized several studies of lactation persistency by calving season. Although evidence remains inconclusive, higher persistency is expected in cows that calve in late summer or early fall–winter.
There are several limitations to consider when interpreting the findings of this study. Because this was a retrospective observational study, the results should be interpreted as associations rather than causality. It is important to note that the data originated from a single intensive dairy farm located in central Chile, which may limit our ability to extrapolate the findings to other dairy farms, breeds and geographic regions. The major sources of variation were considered in the statistical models; however, unmeasured factors such as genetics, health status and environmental conditions may have contributed to the observed results. Therefore, the findings should be interpreted within the context of this specific dairy farm and used as a basis for generating hypotheses for future studies.
Conclusions
This study provides a comprehensive description of MY and related production traits (parity and calving season) in Holstein Friesian cows managed indoors in central Chile. Primiparous and multiparous cows exhibited similar total lactation of MY, FY and PY, but primiparous cows demonstrated greater persistency compared with multiparous cows. Winter calving was associated with higher MY without increasing SCS. These findings highlight the importance of considering parity and calving season when interpreting milk traits and designing management strategies in intensive dairy systems.
Author contributions
Conceptualization: F.L. Methodology: F.L. Formal analysis: F.L. Data curation: F.L. Writing original draft: F.L. Writing review and editing: F.L., M.D., G.S. All co-authors reviewed the final version and approved the manuscript before submission.
Declaration of interest
No conflict of interest is declared by any of the authors.
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