# Clustering of the dynamics of milk lactose content throughout lactation and identification of variation factors

Auxane Hamon, Mathieu Arnal, Marie-Pierre Sanchez, Rachel Lefebvre, Laurent Meriaux, Sophie Lemosquet, Jocelyne Guinard-Flament

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## To cite this version:

Auxane Hamon, Mathieu Arnal, Marie-Pierre Sanchez, Rachel Lefebvre, Laurent Meriaux, et al. Clustering of the dynamics of milk lactose content throughout lactation and identification of variation factors. Journal of Dairy Science, inPress, 10.3168/jds.2025-27208. hal-05441091

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# Clustering of the dynamics of milk lactose content throughout lactation and identification of variation factors

Auxane Hamon,<fnref n="1" /> Ⓓ Mathieu Arnal,<fnref n="2" />,<fnref n="3" /> Ⓓ Marie-Pierre Sanchez,<fnref n="4" /> Ⓓ Rachel Lefebvre,<fnref n="4" /> Ⓓ Laurent Meriaux,<fnref n="5" />
Sophie Lemosquet,<fnref n="1" /> Ⓓ and Jocelyne Guinard-Flament<fnref n="1" />* Ⓓ

## ABSTRACT

Interest in milk lactose content (LC) has grown due to its potential as an indicator of udder health and metabolic disorders in dairy cattle. However, the variability of LC dynamics during lactation remains poorly described, and a better characterization of these dynamics could clarify our understanding of LC variations among cows, and potentially those due to udder health and metabolism-related variations. The aim of this study was to identify distinct patterns of LC dynamics and assess their environmental and genetic determinants, as well as their phenotypic and genetic associations with milk yield, Na, K, SCC, and their phenotypic associations with fat-to-protein ratio (FPR) and BHB. A total of 1,980,693 test-day records were analyzed from 183,150 Holstein cows in 2,239 herds across France. At least 2 records in the first 90 d and 4 records between 7 and 300 DIM were available for each cow, averaging 7.3 records per cow. Functional principal component analysis was used to describe LC dynamics throughout lactation. This approach involved smoothing the LC curves for each cow and then summarizing their overall shape using 3 principal components: average LC throughout lactation, LC slope and LC at mid lactation. Dynamics of LC were grouped into 6 clusters. Three clusters (3, 4, and 5) represented 86% of the data and shared similar dynamics with a flat trend after an initial rise in LC at early lactation and different average LC levels (cluster 3: 4.68%, cluster 4: 5.10%, cluster 5: 4.86%). Environmental and intrinsic animal factors explained 69% of the variability in average LC among clusters 3, 4, and 5, with cow parity and LC EBV identified as the main intrinsic contributors. The remaining clusters (1, 2, and 6) showed LC levels similar to

the mean of the dataset (LC: 4.88% ± 0.19%) until 150 DIM. Thereafter, 2 clusters displayed negative LC slopes (cluster 1: -0.13% and cluster 6: -0.07% per month of lactation) and one a positive slope (cluster 2: +0.05% per month). Fifteen percent of the variations in the LC slopes of clusters 1, 2, and 6 was explained by environmental factors, mainly calving season: winter calving was associated with clusters 1 and 6, and summer calving with cluster 2. The remaining unexplained negative slope variation from mid lactation onward appears to be related to distinct patterns characterized by higher FPR and milk BHB concentrations preceding the decline in LC, followed by increased SCC after 150 DIM. The lactose-based clusters also corresponded to distinct curves for milk sodium contents, and there were slight correlations for potassium levels, indicating different equilibria between the 3 main osmotic agents (lactose, sodium, and potassium), probably to maintain milk osmolarity. As a result, LC clustering uncovered meaningful physiological profiles: average LC levels were primarily driven by parity and genetics, whereas LC slope variations appeared to be more sensitive to environmental and health-related factors. These findings support the potential of LC dynamics, accessible via mid-infrared spectra, to serve as functional biomarkers for udder health and, potentially, of metabolic status.

**Key words:** lactose, lactation curve, genetic correlation, udder health, dairy cow

## INTRODUCTION

Interest in milk lactose content (LC) has increased in recent years, particularly because of its potential as an indicator of mammary gland health and metabolic disorders (Costa et al., 2019a; Hamon et al., 2024). Both disorders are common in dairy herds, and indicators such as SCC, fat-to-protein ratio (FPR), and BHB sometimes lack accuracy due to their temporal variability or external

<footnote n="1">¹PEGASE, Institut Agro, INRAE, 35042 Rennes, France</footnote>

<footnote n="2">²Institut de l'élevage, Idele, 31326 Castanet-Tolosan, France</footnote>

<footnote n="3">³GenPhySE, Université de Toulouse, INRAE, ENVT, 31326 Castanet-Tolosan, France</footnote>

<footnote n="4">⁴Université Paris-Saclay, INRAE, AgroParisTech, GABI, 78350 Jouy-en-Josas, France</footnote>

<footnote n="5">⁵Eilyps, 35740 Pacé, France</footnote>
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

factors (Nielsen et al., 2003; Ayadi et al., 2004; Jashari et al., 2016), highlighting the need for complementary indicators such as LC to improve diagnostic accuracy.

Most studies examining the effect of such disorders on LC were based on more or less frequent measurements at specific time points, often without properly accounting for the stage of lactation. However, LC varies during lactation. The LC curve most frequently described shows a rise at the start of lactation, followed by an almost flat course during the rest of lactation (Friggens et al., 2007; Haile-Mariam and Pryce, 2017). However, in some studies, the LC curve showed a decline from the peak to the end of lactation (Pollott, 2004; Miglior et al., 2006; Ptak et al., 2012). This suggests more or less pronounced variations in the evolution of LC during lactation, which cannot solely result from the modeling approach adopted by the authors (e.g., local regression vs. random regression with Legendre polynomials), but also reflect biological or environmental factors known to influence LC (Miglior et al., 2006; Haile-Mariam and Pryce, 2017; Gargiulo et al., 2025). These factors are numerous, being either intrinsic to the animals (genetics, parity, stage of lactation) or related to the environment (season, milking process, feeding practices), with reported variations in LC ranging between 0.6 and 4.8 percentage points of LC (Sneddon et al., 2015; Costa et al., 2019a; Gargiulo et al., 2025). These inconsistencies between LC curves across lactation may be attributed to differences in study populations, particularly in terms of genetic potential, the prevalence of health disorders, or herd-level management practices such as feeding practices or milking processes (Miglior et al., 2006; Friggens et al., 2007; Ptak et al., 2012).

Lactose content is a moderately heritable trait, with heritability estimates ranging from 0.17 to 0.53 (Miglior et al., 2006; Haile-Mariam and Pryce, 2017; Costa et al., 2019b). Genetic selection for animals with greater genetic merit can lead to an increase in LC (+0.16 percentage points; Sneddon et al., 2015), thus highlighting the presence of genetic variability within populations. This individual variability may contribute to different LC curves throughout lactation, potentially leading to distinct osmotic profiles. These profiles reflect the equilibrium between milk osmotic agents such as lactose, sodium (Na), and potassium (K), as previously observed when comparing parities in dairy cows without mammary gland inflammation (SCC <200,000 cells/mL) and under constant dietary conditions (Hamon et al., 2025). In commercial herd conditions, where health disorders such as udder inflammation or hyperketolactia are frequent and known to affect LC (Hamon et al., 2024), the osmotic equilibrium might be disrupted, leading to heterogeneous LC curves, some of which could reflect

underlying pathological conditions rather than physiological variations.

To our knowledge, no study to date has comprehensively described individual LC trajectories over the full course of lactation. We hypothesized that the variability in LC dynamics across individuals could partly be explained by environmental conditions (e.g., period of calving, milking process) and intrinsic animal factors such as genetic merit for LC or parity. We further assumed that these LC profiles would show consistent phenotypic and genetic associations with milk traits, including milk yield (MY), Na, K, SCC, FPR, and BHB, reflecting underlying physiological or pathological determinisms.

## MATERIALS AND METHODS

### Data Editing

The dataset was provided by the Eilyps consultancy firm (Pacé, France), which recorded milk data from dairy cows in Brittany, France, as part of a routine recording scheme. Milk LC, Na, K, fat, protein, and BHB contents were estimated using mid-infrared spectroscopy with a MilkoScan FT7 (Foss Electric A/S, Hillerød, Denmark). To ensure comparability between the laboratories involved, the instrument was routinely calibrated using standard samples. Regarding LC, laboratories updated the calibration measurements on 4 occasions: November 2, 2019; November 8, 2019; July 2, 2022, and December 27, 2022. To maintain consistency in LC testing across these periods, a linear model was applied to adjust the LC values. Somatic cell counts were determined by flow cytometry with a Fossomatic 7 DC (Foss Analytics). To achieve international harmonization, on April 1, 2021, French laboratories modified their standards for SCC analysis, which led to a 20% reduction in SCC values (Institut de l'Élevage, 2021). Consequently, SCC values recorded before this date were reduced by 20% to allow comparisons across all test-day records. Finally, to achieve normality and homogeneity of variance for genetic estimations, SCC was converted to SCS using the following transformation: $SCS = \log_2(\text{SCC}/100) + 3$. In addition to milk composition, associated MY data were also recorded, along with information on the milking process (conventional or automatic milking system [AMS]), age at first calving, calving date, number of artificial inseminations during the current lactation, and parity for each cow.

The original dataset contained 4,894,111 test-day records collected between January 2019 and December 2022. For our study, only records from Holstein cows between 7 and 300 DIM were selected, resulting in 3,218,911 test-day records. Abnormal values were defined as those deviating by more than 5 SD from the
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mean of each trait, calculated at each 20-day interval of DIM. Samples with abnormal or missing values for any of the traits considered in the study were excluded. Only cows with at least 2 test-day records during the first 90 DIM and a total of 4 test-day records per lactation were then retained, resulting in 4 to 13 test-day records per lactation. Based on these criteria, our final dataset consisted of 1,980,693 test-day records from 183,150 Holstein cows, representing 286,355 lactations across 2,239 herds. Descriptive statistics of number of herds, lactations, and average of MY and milk components are presented in Table 1. Among the 282,762 excluded lactations, the mean SCC (224,000 ± 697,000 cells/mL) was slightly higher than that of the retained ones (202,000 ± 642,000 cells/mL), and the mean FPR and BHB values during the first 50 days of lactation were similar between excluded (FPR = 1.35 ± 0.22; BHB = 0.10 ± 0.07 mmol/L) and retained cows (FPR = 1.35 ± 0.21; BHB = 0.09 ± 0.07 mmol/L). No culled cows were reported among the excluded lactations. These verifications indicate that the selection process did not introduce bias in the prevalence of udder or metabolic disorders.

## Genetic Parameters and Breeding Value Estimations

The relationship between LC dynamics throughout the lactation and individual genetic merit, variance and covariance components of LC, MY, SCS, Na, and K and individual EBV were estimated using WOMBAT software (Meyer, 2007) with single-trait and bivariate repeatability animal models. Because milk FPR and BHB are biologically relevant mainly in early lactation, unlike the other components that remain informative throughout the entire period, their inclusion would have required additional bivariate analyses restricted to early lactation. Therefore, the genetic evaluation was not performed for these traits. A total of 3 generations of ancestors were traced back, leading to a pedigree file of 335,523 individuals.

The general form of the model, in matrix notation, was as follows:

$$y = Xb + Za + Ww + e,$$

where y is the vector of phenotypic records for LC, MY, Na, K, and SCS; b is the vector of fixed effects concerning parity (4 classes: 1, 2, 3, and ≥4), calving month (12 classes: one class per month), milking process (manual vs. AMS), lactation stage (31 classes: one class from 7 to 10 DIM, then 10-day intervals from 11 to 301 DIM), and the combination of year (4 classes) and herd (2,239 classes); a is the vector of random additive genetic effects containing breeding values (EBVs) estimated for all the cows; w is the vector of random permanent environmen-

<table><caption>Table 1. Number of herds, lactations, test-day records, and descriptive statistics (mean ± SD) of milk yield and components by year and parity¹</caption><thead><tr><th rowspan="3">Item</th><th colspan="3">2019</th><th colspan="3">2020</th><th colspan="3">2021</th><th colspan="3">2022</th></tr><tr><th>P1</th><th>P2</th><th>P3</th><th>P1</th><th>P2</th><th>P3</th><th>P1</th><th>P2</th><th>P3</th><th>P1</th><th>P2</th><th>P3</th><th>P4+</th></tr><tr><th></th><th></th><th></th><th>P4+</th><th></th><th></th><th>P4+</th><th></th><th></th><th>P4+</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>Herd (n)</td><td>2,071</td><td>2,091</td><td>2,063</td><td>2,059</td><td>2,015</td><td>2,025</td><td>2,012</td><td>2,015</td><td>1,814</td><td>1,818</td><td>1,803</td><td>1,811</td><td>1,624</td><td>1,640</td><td>1,615</td><td>1,618</td></tr><tr><td>Lactations (n)</td><td>31,146</td><td>25,434</td><td>17,350</td><td>18,154</td><td>45,132</td><td>37,716</td><td>26,644</td><td>27,880</td><td>42,602</td><td>35,252</td><td>25,428</td><td>27,320</td><td>29,746</td><td>25,151</td><td>17,997</td><td>19,451</td></tr><tr><td>Test-day records (n)</td><td>150,210</td><td>119,614</td><td>79,479</td><td>81,000</td><td>183,815</td><td>151,411</td><td>106,200</td><td>110,086</td><td>184,930</td><td>150,015</td><td>106,728</td><td>113,347</td><td>143,539</td><td>121,082</td><td>86,230</td><td>93,007</td></tr><tr><td>Milk yield and components</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Milk yield (kg/d)</td><td>24.4</td><td>30</td><td>32</td><td>32.1</td><td>24.4</td><td>29.2</td><td>31.1</td><td>31</td><td>24.5</td><td>29.3</td><td>31.2</td><td>31.3</td><td>24.9</td><td>29.8</td><td>31.2</td><td>31.2</td></tr><tr><td>LC (%)</td><td>±5.4</td><td>±7.1</td><td>±7.8</td><td>±8.1</td><td>±5.4</td><td>±7.2</td><td>±7.8</td><td>±8.2</td><td>±5.4</td><td>±7.2</td><td>±7.8</td><td>±8.2</td><td>±5.4</td><td>±7.2</td><td>±7.9</td><td>±8.2</td></tr><tr><td></td><td>4.97</td><td>4.88</td><td>4.86</td><td>4.82</td><td>4.94</td><td>4.87</td><td>4.83</td><td>4.8</td><td>5</td><td>4.91</td><td>4.88</td><td>4.85</td><td>5.03</td><td>4.94</td><td>4.91</td><td>4.87</td></tr><tr><td>SCC (×1,000 cells/mL)</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td></tr><tr><td>Na (mg/kg)</td><td>138</td><td>166</td><td>237</td><td>333</td><td>132</td><td>170</td><td>238</td><td>344</td><td>124</td><td>154</td><td>222</td><td>326</td><td>128</td><td>170</td><td>239</td><td>362</td></tr><tr><td></td><td>±459</td><td>±569</td><td>±709</td><td>±873</td><td>±444</td><td>±569</td><td>±691</td><td>±884</td><td>±425</td><td>±539</td><td>±672</td><td>±869</td><td>±468</td><td>±580</td><td>±723</td><td>±944</td></tr><tr><td>K (mg/kg)</td><td>±37</td><td>±38</td><td>±36</td><td>±45</td><td>±36</td><td>±37</td><td>±41</td><td>±46</td><td>±35</td><td>±37</td><td>±40</td><td>±46</td><td>±35</td><td>±37</td><td>±40</td><td>±46</td></tr><tr><td></td><td>1,516</td><td>1,497</td><td>1,484</td><td>1,479</td><td>1,498</td><td>1,470</td><td>1,464</td><td>1,457</td><td>1,481</td><td>1,454</td><td>1,446</td><td>1,442</td><td>1,481</td><td>1,462</td><td>1,450</td><td>1,446</td></tr><tr><td>Fat/protein ratio</td><td>±82</td><td>±84</td><td>±84</td><td>±85</td><td>±81</td><td>±86</td><td>±86</td><td>±86</td><td>±82</td><td>±87</td><td>±86</td><td>±87</td><td>±84</td><td>±81</td><td>±85</td><td>±86</td></tr><tr><td>BHB (mmol/L)</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td><td>±0.2</td></tr><tr><td></td><td>0.09</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td><td>0.08</td></tr><tr><td></td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td><td>±0.1</td></tr></tbody><tfoot><tr><td colspan="16">¹Groups refer to cows in their first (P1), second (P2), third (P3), and fourth or greater (P4+) lactations.</td></tr></tfoot></table>
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tal effects; e is the vector of random residuals; and X, Z, and W are incidence matrices relating the corresponding effects to the dependent variable. Random effects were assumed to be normally distributed with zero means in both univariate and bivariate models. Total phenotypic variance was partitioned into additive genetic, permanent environmental, and residual components. Heritability (h²) was estimated as the proportion of phenotypic variance attributable to additive genetic effects as

$$h^2 = \frac{\sigma_a^2}{\sigma_a^2 + \sigma_e^2 + \sigma_r^2},$$

where σ_a² is the additive genetic variance, σ_e² is the permanent environmental variance and σ_r² is the random residual variance. Repeatability (t) was defined as the proportion of phenotypic variance explained jointly by additive genetic and permanent environmental effects as

$$t = \frac{\sigma_a^2 + \sigma_e^2}{\sigma_a^2 + \sigma_e^2 + \sigma_r^2}.$$

Genetic (or phenotypic) correlations (r) between 2 traits were calculated using the ratio of their covariance to the product of their SD, as follows:

$$r = \frac{cov_{1,2}}{\sqrt{\sigma_1^2 \cdot \sigma_2^2}}.$$

Where cov₁,₂ represents the additive genetic (or phenotypic) covariance between traits 1 and 2, and σ₁² and σ₂² are their respective additive genetic (or phenotypic) variances.

## Clustering of LC Curves

All statistical analyses involving clustering were performed using R software (version 4.3.2). The following steps were employed to analyze the dataset, as outlined by Arnal et al., (2018): (1) principal component analysis (PCA) on test-day records after data smoothing using the R package *fdapace* (Zhou et al., 2024), (2) a classification curve using the *rmixmod* R package (Langrognet et al., 2016), and finally, (3) an investigation into the relationships between environmental and cow-intrinsic factors using the *nlme* R package. To ensure reproducibility of the analyses, the R scripts used for the analyses are available as Supplemental File S1 (see Notes).

**Principal Component Analysis.** A PCA was applied to test-day milk lactose data for each lactation to first model individual LC curves and then to summarize their shapes through synthetic variables, namely the principal component scores (SPC). The dataset exhibited an unbalanced longitudinal structure, with between 4 and 13 test-day milk lactose per lactation. These test-day records were collected at different lactation stages depending on the cow, resulting in an irregular timing of observations across individuals. The smoothed mean LC curve of each lactation was initially calculated using linear Gaussian kernel regression between 51 equidistant support points, with all the measurements aggregated together. Subsequently, sample raw covariance was generated by aggregating all the raw covariance data per curve together. The off-diagonal of the sample raw covariance enabled estimation of the smoothed covariance. Finally, the estimated eigenfunctions, eigenvalues, and SPC were derived from eigen analyses conducted on the smoothed covariance matrix.

**Classification.** An unsupervised classification was applied to the principal components of the LC curves to identify groups of cows showing similar lactose dynamics. The aim was to describe the main patterns of inter-individual variability in LC trajectories across lactation. This tool is designed to fit a mixture model of multivariate components to a given dataset. The Bayesian information criterion (BIC) was also used to determine the optimal number of components, which was investigated across a range of 4 to 8 clusters.

To maximize log-likelihood and enhance robustness, a stochastic expectation-maximization algorithm was executed 100 times, each with 800 iterations on the initialization phase. This strategy was chosen because repeated trials consistently reproduced the same clusters and lactose curve shapes, confirming that the algorithm's parameterization was sufficient. Over the 183,150 cows, 76,962 cows were recorded over 2 or more lactations: 26,810 cows during their first and second lactations; 10,463 cows during their first, second, and third lactations; 10,197 cows during their second and third lactations; and 6,305 cows during their third and fourth lactations. The rest of the cows had nonconsecutive lactation recordings. The 10,463 cows with first, second, and third lactation records were selected to identify any trends in cluster changes between consecutive lactations using the *ggalluvial* R package.

## Relationships Between LC Clusters and Explanatory Factors

To identify factors underlying the clustering structure and to assess which proportion of the variance they
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

explained, a multiple linear regression analysis was performed. Cow-intrinsic factors (genetics, parity, calving month, age at first calving, number of artificial inseminations), environmental conditions (year), and milking processes were included as explanatory variables. Continuous variables such as the number of inseminations and EBV were categorized into tertiles based on their distribution. The global regression model was specified as follows:

$$PC_{ijklmnopq} = \mu + Y_i + Mo_j + Par_k + Mp_l + Ag_m + A_i_n + GMy_o + Glac_p + Gscs_q + Gna_r + GK_s + H_t + C_{u(t)} + \varepsilon_{ijklmnopqrs}$$

where $PC_{ijklmnopq}$ is the dependent variable SPC and $\mu$ is the mean component content when all fixed effects were set to the reference value (for categorical variables). The fixed effects tested were as follows: $Y_i$ is year (4 levels: 2019, 2020, 2021, 2022); $Mo_j$ is month of calving (12 levels: 1 = January, ..., 12 = December); $Par_k$ is parity (4 levels: 1, 2, 3, and $\ge$4); $Mp_l$ is milking process (2 levels: conventional or AMS); $Ag_m$ is age at first calving (3 levels: low = early = 18 to <21 mo, intermediate = 21 to <26 mo, late = 26–40 mo); $A_i_n$ is the number of inseminations (3 levels: low = <1, medium = 1–2, high = >2); $GMy_o$ is MY EBV (3 levels: low = < −0.35, medium = −0.35–0.95, high = >0.95); $Glac_p$ is LC EBV (3 levels: low = < −0.31, medium = −0.31–0.47, high = >0.71); $Gscs_q$ is SCS EBV (3 levels: low = < −0.36, medium = −0.36 to −0.04, high = > −0.04); $Gna_r$ is Na EBV (3 levels: low = < −9.94, medium = −9.94–3.04, high = >3.04); $GK_s$ is K EBV (3 levels: low = < −23.35, medium = −23.35 to 14.99, high = >14.99); $H_t$ ~ $N(0, \sigma_h^2)$ is the random effect of herd (n = 2,239); $C_{u(t)}$ ~ $N(0, \sigma_u^2)$ is the random effect of cow nested within herd (n = 182,031);

and $\varepsilon_{ijklmnopq} \sim N(0, \sigma^2)$ is the residual error, assumed to be normally distributed with constant variance. Multicollinearity among explanatory variables was assessed by calculating the variance inflation factor (VIF) for each predictor. As a general rule, a VIF value greater than 10 is considered indicative of problematic multicollinearity (Dórea et al., 2017). In our analysis, all VIF values were below 2.5, indicating a low and acceptable level of collinearity among predictors. Each factor of the global model was successively removed in order to study its relative effect comparing the $R^2$ of the model. Least square means were estimated using the *emmeans* R package. (Table 2).

## RESULTS

### Genetic Parameters and Breeding Value Estimations

Estimates of variance components, heritability, and repeatability for each trait are presented in Table 3. The traits showed moderate to high heritability, with the highest for LC and K (both $0.43 \pm 0.004$) and Na ($0.31 \pm 0.004$). Heritability was low for MY ($0.17 \pm 0.004$) and SCS ($0.10 \pm 0.003$). Repeatability values ranged from 0.40 for MY to 0.52 for LC. The coefficient of genetic variation ($CV_a$) was lowest for LC (2.21%), indicating limited genetic variation relative to the trait mean, whereas SCS exhibited a much higher genetic variation (25.54%). The genetic correlations shown in Table 4 revealed that LC was negatively correlated with Na (−0.82), K (−0.33), and SCS (−0.12). Milk yield exhibited positive genetic correlations with K (0.26) and SCS (0.26), whereas its correlation with LC was low (0.02). In addition, K was genetically correlated with SCS (0.22). At the phenotypic level, LC was negatively correlated with Na (−0.74), SCS (−0.66) and K (−0.22). Milk yield was positively correlated with K (0.28) and showed a slight

<table><caption>**Table 2.** Mean (± SD) of the first, second, and third principal components, the proportion of lactations, and the proportions of herds per cluster</caption><thead><tr><th rowspan="2">Cluster</th><th rowspan="2">PC1</th><th rowspan="2">PC2</th><th rowspan="2">PC3</th><th rowspan="2">Proportion of lactations<sup>2</sup> (%)</th><th rowspan="2">Proportion of herds<sup>3</sup> (%)</th><th colspan="4">Proportion of parities<sup>1</sup> (%)</th></tr><tr><th>P1</th><th>P2</th><th>P3</th><th>P4+</th></tr></thead><tbody><tr><td>1</td><td>-36.3 ± 25.2</td><td>17.7 ± 5.5</td><td>-3.8 ± 4.4</td><td>0.8</td><td>50.1</td><td>4</td><td>13</td><td>24</td><td>58</td></tr><tr><td>2</td><td>11.2 ± 18.1</td><td>-8.9 ± 3.6</td><td>2.2 ± 3.0</td><td>6.3</td><td>86.6</td><td>38</td><td>32</td><td>17</td><td>13</td></tr><tr><td>3</td><td>-32.7 ± 30.0</td><td>-3.0 ± 7.6</td><td>-1.1 ± 6.0</td><td>7.0</td><td>91.1</td><td>15</td><td>22</td><td>23</td><td>39</td></tr><tr><td>4</td><td>21.7 ± 14.5</td><td>3.0 ± 3.9</td><td>1.3 ± 2.7</td><td>32.5</td><td>97.2</td><td>55</td><td>23</td><td>13</td><td>10</td></tr><tr><td>5</td><td>-8.6 ± 14.4</td><td>-1.5 ± 3.7</td><td>-0.3 ± 2.6</td><td>46.4</td><td>99.0</td><td>23</td><td>31</td><td>22</td><td>23</td></tr><tr><td>6</td><td>-14.1 ± 18.1</td><td>9.2 ± 3.5</td><td>-1.7 ± 2.8</td><td>7.0</td><td>90.8</td><td>16</td><td>24</td><td>26</td><td>34</td></tr></tbody></table>

<footnote n="1">¹Proportion (%) of cows in their first (P1), second (P2), third (P3), and fourth or greater (P4+) lactation per cluster, relative to the total number of lactations (n = 286,355).</footnote>

<footnote n="2">²Proportion of lactations per cluster, relative to the total number of lactations (n = 286,355).</footnote>

<footnote n="3">³Proportion of herds per cluster, relative to the total number of herds (n = 2,239).</footnote>
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

<table><caption>**Table 3.** Additive genetic ($\sigma_a^2$), permanent environmental ($\sigma_e^2$), phenotypic ($\sigma_p^2$), and residual variances ($\sigma_r^2$); and heritability ($h^2$), repeatability ($t$), and coefficient of genetic variation ($CV_a$) of milk composition, SCS, and milk yield from univariate models</caption><thead><tr><th>Item</th><th>σ<sub>a</sub><sup>2</sup></th><th>σ<sub>e</sub><sup>2</sup></th><th>σ<sub>p</sub><sup>2</sup></th><th>σ<sub>r</sub><sup>2</sup></th><th>h<sup>2</sup></th><th>t</th><th>CV<sub>a</sub></th></tr></thead><tbody><tr><td>LC (%)</td><td>1.18</td><td>0.2592</td><td>2.7695</td><td>1.3312</td><td>0.426 (0.004)</td><td>0.520 (0.003)</td><td>2.21</td></tr><tr><td>Na (mg/L)</td><td>395.1</td><td>172.0</td><td>1,294.7</td><td>727.6</td><td>0.305 (0.004)</td><td>0.438 (0.002)</td><td>5.62</td></tr><tr><td>K (mg/L)</td><td>2,575.5</td><td>387.8</td><td>6,031.5</td><td>3,068.2</td><td>0.427 (0.004)</td><td>0.490 (0.003)</td><td>3.45</td></tr><tr><td>SCS</td><td>0.32</td><td>1.05</td><td>3.42</td><td>2.04</td><td>0.096 (0.003)</td><td>0.401 (0.003)</td><td>25.54</td></tr><tr><td>Milk yield (kg)</td><td>4.60</td><td>6.25</td><td>27.11</td><td>16.26</td><td>0.170 (0.004)</td><td>0.400 (0.003)</td><td>7.50</td></tr></tbody></table>

negative correlation with SCS (−0.14). Sodium was also positively correlated with SCS (0.32).

## Clustering of LC Curves

**Principal Component Analysis.** Principal component analysis explained 99.5% of the original variance across the first 3 principal components (PC), with 87.7%, 8.4%, and 3.3% for PC1, PC2, and PC3, respectively. Each principal component corresponded to a distinct characteristic of the LC curve during lactation, represented in Figure 1 by the smoothed LC curves of the extreme cows on each component (i.e., the 2,000 lowest and the 2,000 highest values of the corresponding PC). The first principal component (PC1) was an indicator of the overall level of LC throughout lactation: a low PC1 score corresponded to a low LC (4.53% ± 0.04%; mean ± SD) across the entire lactation period, whereas a high PC1 score indicated a high LC (5.30% ± 0.06%; mean ± SD). The second principal component reflected the LC slope related to the variation in LC between the peak and the end of lactation. A low PC2 score indicated a low initial LC (4.71% ± 0.04% during the first 100 DIM), increasing gradually by 0.05 percentage points per month until the end of lactation. In contrast, a high PC2 score corresponded to an initially elevated LC (5.01% ± 0.05% during the first 100 DIM), followed by a rapid decline of up to 0.12 percentage points per month of lactation. The third principal component (PC3) described the profile of the curve (concave or convex) at ~180 DIM: a low PC3 score corresponded to a concave curve with an average of 5.00% ± 0.04% between 150 and 200 DIM, whereas a high PC3 score was inverse with a LC averaging 4.64% ± 0.03%.

**Classification.** Hierarchical clustering on SPC was tested from 4 to 8 clusters. The BIC values obtained for 4, 5, 6, 7, and 8 clusters showed minimal variation: 5,915,412, 5,915,694, 5,915,987, 5,916,983, and 5,917,657, respectively. The 6-cluster model was chosen because it balanced size and distinct patterns. More clusters were not ideal, as the 7- and 8-cluster models contained 2 to 3 small clusters (<3% of lactations) whereas the 4- and 5-cluster models grouped together LC curves

that were clearly different. The 6-cluster model had only one small cluster (1.0% of lactations), the third-best BIC, and clearly distinct LC averages. The 286,355 lactations were distributed as follows: 0.8%, 6.3%, 7.0%, 32.5%, 46.4%, and 7.0% from clusters 1 to 6, respectively (Table 2). Almost all herds were represented across all clusters, with 83% of them containing cows from 5 or 6 different clusters. This indicated substantial intraherd variability in terms of LC dynamics, with within-herd cows exhibiting distinct lactation LC profiles. The mean and standard variation of the SPC of each component illustrated the LC curve characteristics for each cluster (Table 2). Mean scores were higher for PC1 than for PC2 and PC3 in all clusters, indicating that the primary distinction among clusters was the average level of LC over the whole lactation. The SD of SPC reflected intracluster variability in LC dynamics between individual lactations. Clusters 1 and 3, with the lowest proportion of lactations, had the largest standard variations for the 3 SPC.

The LC curves for the 6 clusters were estimated using the mean value calculated for each day between 7 and 300 DIM. For all milk traits, including LC, the daily means from 7 to 300 DIM were computed using records from 41 to 4,521 individuals per day and per lactose-based cluster, ensuring robust and representative lactation profiles (Figure 2A). Clusters 3, 4, and 5 exhibited a similar curve shape with a relatively stable LC over the lactation, after a rapid rise at the start of lactation (slope ranging from −0.01 to −0.02 percentage points per week) and different average LC values (lowest one for cluster 3; Figure 2A). In contrast, LC values in clusters 1, 2, and 6 did not remain stable after 150 DIM (Figure 2A).

<table><caption>**Table 4.** Estimates of genetic (below diagonal) and phenotypic (above diagonal) correlations with SEM for milk production traits from bivariate models</caption><thead><tr><th>Item</th><th>LC</th><th>Na</th><th>K</th><th>SCS</th><th>Milk yield</th></tr></thead><tbody><tr><td>LC</td><td></td><td><strong>-0.7400</strong></td><td><strong>-0.2217</strong></td><td><strong>-0.6607</strong></td><td>0.0810</td></tr><tr><td>Na</td><td><strong>-0.8197</strong></td><td></td><td>0.0443</td><td>0.3149</td><td>-0.1040</td></tr><tr><td>K</td><td><strong>-0.3289</strong></td><td>0.1805</td><td></td><td>-0.0405</td><td>0.2835</td></tr><tr><td>SCS</td><td>-0.1186</td><td>0.1840</td><td>0.2221</td><td></td><td>-0.1426</td></tr><tr><td>Milk yield</td><td>0.0201</td><td>0.1676</td><td>0.2585</td><td>0.2581</td><td></td></tr></tbody></table>
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Local linear regressions for lactose content with a minimum (dashed line) or maximum (continuous line) score for principal components 1, 2, and 3 (PC1, PC2, PC3).</figcaption></figure>

Specifically, LC decreased after 150 DIM in clusters 1 and 6, whereas it increased in cluster 2. This decline was steepest in cluster 1, as indicated by PC2 scores (cluster 1: −0.30, cluster 6: −0.16 in LC percentage points per week). This marked drop led to the lowest LC values at the end of lactation (cluster 1: 4.26% ± 0.20%, cluster 6: 4.60% ± 0.14%). In cluster 2, LC increased after 150 DIM, as illustrated by the lowest value on PC2 and the highest value on PC3 compared to the other clusters: milk LC increased by 0.11 percentage points per week up to 5.09% ± 0.13%, from 150 DIM until the end of lactation.

**Cows Over Several Lactations.** The 10,463 cows with first, second, and third lactation records were selected to identify any trends in cluster changes between consecutive lactations (Figure 3). We ensured that the distribution of cows across clusters in this sample accurately represented the entire dataset based on parity by comparing the repartition of individuals within clusters in the full dataset with that observed in the subset of cows recorded over 3 consecutive lactations. The width of each flow was proportional to the number of cows and highlighted the most common patterns. As in the full dataset, the majority of the 10,463 cows belonged to clusters 4 and 5. A total of 156 different combinations of clusters across the 3 consecutive lactations were identified. The most common cluster combinations corresponded to cows that remained in clusters 4 or 5 throughout their 3 lactations (11% and 19% of cows) or transitioned from cluster 4 in the first parity to cluster 5 in the second and third parities (11% of cows). The remaining combinations were less frequent, ranging from 0.009% to 7%, thus indicating the absence of a specific pattern.

## Milk Yield and Milk Component Curves Across Lactations

The curves for MY and milk components (Na, K, SCC, FPR, and BHB) were estimated for each lactose-

based cluster from 7 to 300 DIM in the same way as for LC values (at least 41 to 4,521 individuals per day and per lactose-based cluster). Their dynamic also differed across lactose-based clusters, with varying degrees of separation over the lactation. The MY of cows in cluster 4 with LC maintained at an elevated content across lactation displayed a lower peak and a higher lactation persistency over time (Figure 2B). By contrast, clusters 1 and 6 reached a more pronounced MY peak and then a sharper decline, particularly in cluster 1, which exhibited the lowest persistency. The MY curves for clusters 3 and 5 were similar to the overall mean curve. Cluster 2 displayed the lowest MY until ~150 DIM, where it reached the overall mean and maintained this value with the greatest persistency among all clusters. There were marked differences in Na values (Figure 2D) among the clusters. Sodium curves mirrored the LC profiles, but in the opposite direction. For example, in cluster 4, where LC was maintained at an elevated level across the lactation, the lowest Na levels were seen throughout lactation. Conversely, cluster 1, which was characterized by the sharpest decline in LC in mid lactation, displayed the largest increase in Na levels from mid to late lactation. Potassium (Figure 2E) exhibited a dynamic pattern similar to that of MY. In terms of clusters, the differences in K curves were less pronounced, and for some clusters, they were hardly distinguishable during certain stages of lactation. In the case of SCC (Figure 2C), the differences between clusters mainly concerned clusters 1, 3, and 6. Clusters 1 and 6 displayed markedly increasing SCC values after 150 DIM, particularly in cluster 1. Cluster 3 exhibited consistently higher SCC values compared to other clusters across all stages of lactation. Conversely, cows from clusters 2, 4, and 5, which maintained a higher LC throughout lactation, showed lower and more stable SCC curves. Regarding metabolic disorder indicators, differences were observed only for clusters 1, 3, and 6. Specifically, FPR values were higher during early lacta-
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Average lactose content (A), milk yield (B), SCC (C), sodium (D), potassium (E), fat-to-protein ratio (F), and BHB (G) curves per cluster and for all data across lactation (each point corresponds to the average lactose content of the cows at this time point).</figcaption></figure>

tion (<50 DIM) in these 3 clusters (Figure 2F) and milk BHB concentrations were higher in clusters 1 and 3 (Figure 2G) compared with the remaining clusters.

Relationships Between LC Clusters and Explanatory Factors

The relationships between LC clusters and both intrinsic animal factors (genetic merits, parity, age at first
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Distribution of cows across clusters for each parity, with flows representing the correspondence from one cluster to another (i.e. a flow corresponds to the same cow during 3 consecutive lactations).</figcaption></figure>

calving, and number of inseminations) and extrinsic factors (year of calving, milking process) were assessed based on the 3 PC by comparing the R² of the full model with that of models sequentially excluding each factor (Table 4). The global model displayed the highest R² and explained 69%, 15%, and 12% of the total variance in PC1, PC2, and PC3, respectively. For PC1, the lowest R² was observed for the model that did not fit the parity effect (R² = 0.518), closely followed by the model without the LC EBV effect (R² = 0.525), thus indicating that parity and LC EBV are the factors most strongly associated with PC1: cows with a lower parity or a higher LC EBV had the highest overall LC. For PC2 and PC3, the proportion of variation explained by environmental factors was low. Principal component 2 was associated with calving month (R² = 0.077) and year (R² = 0.113). Calving month and parity were both correlated with PC3, with the R² reduced to 0.052 and 0.097, respectively. Milk yield and SCC EBV, as well as the number of inseminations, were identified as the least related environmental factors for all 3 PC. (Table 5).

The relationships between environmental factors with the greatest effects on PC1 and PC2 are represented in Figure 4, where the effects of parity and LC EBV on PC1 can also be observed. Cows recorded in 2021 and 2022 had a higher average LC than those recorded in 2019. In addition, the year in which the test-day was conducted was associated with the LC slope, with cows recorded in 2021 and 2022 displaying a higher LC slope than those recorded in 2019 and 2020. Cows milked with

an automatic milking process displayed a higher average LC than those milked using a conventional system. Principal component 2 was primarily correlated with the calving month, with cows calving between August and September showing the lowest LC slope and those calving between February and March exhibiting highest slope. Overall, associations between LC curve descriptors and mineral EBV were weak. Sodium EBV showed a slight association with PC1, whereas potassium EBV showed slight associations with both PC1 and PC2. Cows with low K EBV values tended to have a slightly higher

<table><caption>**Table 5.** Coefficient of determination (R²) for the global model, where principal component scores for each of the 3 components are explained by all environmental factors, and for the global model progressively reduced by removing one environmental factor at a time</caption><thead><tr><th>Model</th><th>PC1</th><th>PC2</th><th>PC3</th></tr></thead><tbody><tr><td>Global model</td><td>0.692</td><td>0.145</td><td>0.116</td></tr><tr><td>Without parity</td><td><strong>0.536</strong></td><td>0.137</td><td><strong>0.101</strong></td></tr><tr><td>Without year</td><td>0.654</td><td><strong>0.112</strong></td><td>0.109</td></tr><tr><td>Without calving month</td><td>0.680</td><td><strong>0.078</strong></td><td><strong>0.053</strong></td></tr><tr><td>Without age at first calving</td><td>0.687</td><td>0.144</td><td>0.116</td></tr><tr><td>Without milking process</td><td>0.683</td><td>0.144</td><td>0.116</td></tr><tr><td>Without number of AI<fnref n="1" /></td><td>0.691</td><td>0.142</td><td>0.113</td></tr><tr><td>Without lactose EBV</td><td><strong>0.538</strong></td><td>0.143</td><td>0.116</td></tr><tr><td>Without MY EBV</td><td>0.691</td><td>0.142</td><td>0.114</td></tr><tr><td>Without SCC EBV</td><td>0.691</td><td>0.145</td><td>0.116</td></tr><tr><td>Without Na EBV</td><td>0.677</td><td>0.144</td><td>0.116</td></tr><tr><td>Without K EBV</td><td>0.687</td><td>0.143</td><td>0.116</td></tr></tbody></table>

<footnote n="1">¹AI = artificial insemination.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Least squares means on the first 2 principal components for the environmental factors most strongly associated with these components. Estimates of breeding values (EBV): L = low, M = medium, H = high. AMS = automatic milking system.</figcaption></figure>

overall LC and a lower LC slope than those with high K
EBV values.

DISCUSSION

The individual evolution of milk LC values across
lactation has been poorly studied, although evidence sug-
gests that distinct curve dynamics can be found within
large populations. These dynamics result from both in-
trinsic animal factors that include genetic merit for LC
and parity as well as extrinsic factors (year of calving,
milking process), while also being driven by physiologi-
cal and pathological factors that may contribute to the
emergence of specific LC patterns across lactation. In
this context, LC trajectories may reflect differences in
osmotic equilibrium between the main osmotic agents:
lactose, Na, and K. A previous study identified parity-
related differences in this equilibrium, with lower LC
values mainly being compensated by higher milk Na
levels in multiparous cows, along with temporal varia-
tions throughout lactation (Hamon et al., 2025). How-
ever, these findings were obtained under controlled ex-
perimental conditions with a constant diet and no udder
inflammation. In commercial farm settings, udder health
and metabolic challenges such as subclinical mastitis and
hyperketolactia (which are associated with alterations
in LC) are more prevalent (Hamon et al., 2024), so the
osmotic balance may be altered. This disruption could
partly explain the emergence of distinct LC curve pat-

terns, suggesting that pathological conditions may under-
lie some of the variability observed in lactose dynamics.
Consistent with this hypothesis, 6 distinct LC trajectories
were identified in the present study, with 2 predominant
patterns emerging: flat curves and curves characterized
by a marked decline or rise in LC during the second half
of lactation.

Clusters with a Similar Evolution and Only Differing
in Terms of Average Lactose Content

An LC curve characterized by an almost flat evolu-
tion following an initial increase early in lactation (as
described by Pollott, 2004; Miglior et al., 2006) was
expected and accounted for 86% of the total 286,352
lactations analyzed in this study (clusters 3, 4, and 5).
As the main osmotic agent, lactose induces an influx of
water into mammary epithelial cells that is proportional
to the amount of lactose synthesized. This explains the
relative stability of LC across lactation and its key role
in determining the volume of milk produced by cows
(Stinnakre et al., 1994; Miglior et al., 2006). Accord-
ingly, most animals recorded over several consecutive
lactations maintained a relatively flat LC evolution after
the peak and thus remained in clusters 4 and 5. What dif-
ferentiated these 3 curves and clusters was their average
LC throughout lactation, with cow-intrinsic factors and
environmental conditions together accounting for 69% of
this variability.
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

The primary explanatory factor, and the most well-
known, is the difference in LC between primiparous and
multiparous cows. Primiparous cows have higher LC
values than multiparous cows (+0.06 to +2.7 percentage
points; Miglior et al., 2006; Ptak et al., 2012; Haile-
Mariam and Pryce, 2017). In this study, we also observed
higher overall LC levels throughout lactation in primipa-
rous cows. Indeed, 55% of cows in cluster 4, with the
highest LC, were primiparous. Several hypotheses have
been advanced in the literature to explain the differences
in LC between parities: (1) the alteration of tight junction
permeability due to the gradual aging of tissue, cumula-
tive damage from repeated clinical or subclinical udder
inflammation, and mechanical stress on the epithelium
after repeated milkings for multiparous cows (Herve et
al., 2019; Costa et al., 2025); (2) differences in the syn-
thetic activity of the mammary gland between parities
(Miller et al., 2006); and (3) variations in the osmotic
balance between milk and blood depending on parity
(Hamon et al., 2025).

The second most influential explanatory factor, with an
effect nearly comparable to that of parity, was LC EBV.
Animals with high LC EBV displayed higher average LC
values, as seen in the cows from cluster 4. In this study, an
increase of 1 LC EBV point corresponded to a rise in LC
ranging from 0.21 to 0.27 percentage points in LC (aver-
age differences between clusters 3, 4, and 5). Sneddon et
al. (2015) had reported an increase of +0.16 percentage
points in LC among the 10% of cows with the best EBV.
The estimated heritability of LC (h² = 0.43) was among
the highest described in the literature for the Holstein
breed (h² = 0.25–0.43; Sneddon et al., 2015; Costa et
al., 2019b). The genetic variability of LC in the present
population was low (CVₐ = 2.21%) but slightly higher
than previously reported values (CVₐ = 1.95%–1.99%;
Costa et al., 2019b; Visentin et al., 2019). Nevertheless,
a substantial proportion of the phenotypic variability of
LC was attributable to genetics in the studied population.

The analysis of MY, Na, K, SCC, FPR, and BHB across
lactose-based clusters in this study enabled assessment
of the relevance of physiological mechanisms underlying
the remaining 32% of LC variability. In this case, MY
served as a proxy for the synthetic activity of the mam-
mary gland, and Na and K levels assessed the osmotic
balance, SCC reflected udder inflammation, FPR and
BHB indicated metabolic disorders. Globally, cluster 5
remained close to the overall average for all components,
cluster 4 (composed of 55% primiparous cows) showed a
typical primiparous MY curve, with a lower peak and bet-
ter persistency of lactation (Friggens et al., 1999; Hansen
et al., 2006), and cluster 3, mainly composed of multipa-
rous cows, had a peak close to the overall average but a
lower persistency. The osmotic equilibrium between the

3 main osmotic agents (LC, Na, and K) differed between the 3 flat LC curves (clusters 3, 4, and 5). Lactose and Na curves were consistently reversed in this study. The lower average LC observed in cluster 3 was associated with higher Na levels throughout lactation; conversely, the higher LC in cluster 4 corresponded to lower Na levels. This inverse relationship may partly reflect the parity proportion of these clusters, as clusters 3 and 4 were mostly composed of multiparous and primiparous cows, respectively. Previous findings had shown that lower LC levels in multiparous cows were primarily associated with an increase in Na levels in order to maintain the osmotic balance (Hamon et al., 2025). This compensatory relationship is further supported by the strong negative phenotypic (−0.74) and genetic (−0.82) correlations observed between these 2 osmotic agents, highlighting their coordinated role in the regulation of milk osmolarity. Given these strong correlations and the clearly differing Na values observed between lactose-based clusters, a strong relationship between Na EBV and these clusters was expected. However, although LC EBV clearly distinguished these 3 clusters, Na EBV showed no such association. This suggests that LC is largely genetically determined, whereas Na levels may adjust secondarily to variations in LC to maintain osmotic equilibrium, rather than being independently regulated. By contrast, the separation between clusters was much less pronounced for K, unlike Na, which displayed an opposite trend to LC. In cluster 3, the lower LC observed was associated not only with an increase in Na, but also with higher K levels during the first 100 DIM. In contrast, cluster 4, which had the highest LC level, showed lower K levels over the same period. These patterns indicated a distinct osmotic equilibrium between the 3 main osmotic agents in clusters 3 and 4, which again were differentiated by parity. This finding agrees with the results of a previous study, where K tended to be lower in primiparous cows than in multiparous cows (–63 mg/L) during the first 95 DIM (Hamon et al., 2025). Overall, these results highlight a coordinated adjustment of Na and K in response to LC level, with parity playing a central role in shaping these osmotic profiles.

Regarding SCC, cluster 3, which included 84.6% mul-
tiparous cows, showed higher levels than clusters 4 and
5 (423,000 vs. 126,000 and 209,000 cells/mL, respec-
tively), indicating a greater prevalence of udder inflam-
mation that may have contributed to its lower average
LC. It is well established that multiparous cows gener-
ally display higher SCC values than primiparous cows
(Harmon, 1994). In line with this, Costa et al. (2025) had
emphasized a lifelong and progressive decline in both LC
and MY, attributed to the epithelial damage caused by
mastitis and aging. Conversely, clusters 4 and 5, which
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

had higher average LC levels, displayed lower SCC val-
ues throughout lactation. Estimated breeding values for
SCS were not related to any LC curve characteristics (i.e.,
3 principal components) in the study, meaning cows were
not predisposed to higher SCC or an increased risk of
inflammation or the opposite. However, a strong pheno-
typic correlation was observed between LC and SCS (r =
-0.66), indicating that higher SCC levels are consistently
associated with lower LC values, regardless of the ani-
mal's genetic predisposition. Cluster 3 also appeared to
show a greater prevalence of metabolic disorders in early
lactation, as indicated by elevated milk BHB concentra-
tions and FPR values. This pattern could reflect intense
lipid mobilization leading to increased nonesterified
fatty acid (NEFA) release, which can exceed the liver's
oxidative capacity and result in ketone body production,
whereas the elevated FPR further supports the presence
of an energy deficit. Alternative explanations, such as
pronounced adipose tissue mobilization in over-condi-
tioned cows or rations that are deficient in glucogenic
precursors, cannot be excluded. Further investigations
are needed to clarify these mechanisms.

In addition, cows in cluster 3 were more frequently culled during or after the current lactation (33% in cluster 3 vs. 18% in cluster 4 and 25% in cluster 5), supporting the idea of a potentially higher prevalence of mastitis or metabolic disorders or an effect of advanced age, as this cluster included 39% of cows with 4 or more lactations. This interpretation aligns with the findings of Miglior et al. (2006), who reported that cows with lower LC values (<4.49%) had a 1.26-fold greater risk of being culled.

Clusters with Marked Changes in LC After the Peak

This study also identified LC curves that were atypical
when compared to those described in the literature, with
non-negligible positive or negative LC slopes from mid
lactation (150 DIM) onward. No studies in the literature
have reported this type of curve shape.

Although clusters 1, 2, and 6 represented small propor-
tions of the cows compared to the other clusters (1%,
6%, 7%), the number of animals remained substantial
given the large dataset (286,355 cows). Regarding cows
with multiple lactations in these 3 clusters, we were not
able to identify specific patterns of transitions between
clusters across consecutive lactations, meaning that we
could not predict whether a cow would belong to one
of these clusters in its next lactation. In this study, the
LC slope after 150 DIM was poorly explained by cow-
intrinsic factors, environmental conditions, and milking
process (12%–15%). Among these factors, the cow’s
calving month and the year of lactation emerged as the
main contributors to slope variations after the peak.

The relationship between calving period and LC is
complex to investigate, as it may reflect both a direct
influence of photoperiod on milk component yield and
the changes in feeding practices that typically accom-
pany seasonal transitions in dairy systems. Regarding the
photoperiod effect, increasing day length and light inten-
sity have concurrently been associated with higher LC
values by between 0.06 and 0.1 percentage points (Miller
et al., 1999; Lim et al., 2021). In this study, however,
the mid-lactation increase in LC observed in cluster 2
was unlikely to be related to photoperiod effects, as most
of the cows in this group calved from May to Septem-
ber and were thus generally exposed to decreasing day
lengths from mid lactation onward, or at most to the very
start of increasing photoperiods at the end of lactation.
Regarding clusters 1 and 6, which included cows that
predominantly calved from winter to early spring (Oct-
tober to April), the photoperiod may have contributed to
the patterns observed: a higher peak in MY during early
lactation, when day length was increasing, and a lower
persistency as day length decreased later in lactation.

The effects of calving season could also be linked to
changes in feeding practices that typically accompany
seasonal transitions in the Brittany region of France. The
mid-lactation rise in LC observed in cows in cluster 2
could be attributed to a transition from pasture-based
feeding to a TMR-based indoor diet. Conversely, in
clusters 1 and 6, the opposite transition, from an indoor
TMR-based diet in early lactation to subsequent pasture
feeding, could explain the decline in LC observed during
mid lactation. Indeed, higher LC levels were observed in
cows fed TMR or corn silage-based diets compared to
grazing or forage-based systems (+0.09 to +0.1 points;
Vicente et al., 2017; Gulati et al., 2018). Therefore, it
remains unclear whether the effect of calving season on
LC variations is driven by photoperiod, feeding, or a
combination of both, especially because calving month
alone accounts for only 9% of the variability of this
slope.

The high proportion of slope variation after 150 DIM that remains unexplained by cow-intrinsic factors and environmental conditions (85%–89%) can be explored through associations between milk traits and lactose-based cluster profiles. As suggested by altered lactation persistency and increased SCC, the negative LC slope after 150 DIM could be related to udder inflammation because of early or minor tissue remodeling or bacterial infection, or both (Dessauge et al., 2011; Antanaitis et al., 2021; Hamon et al., 2024). Some cows in clusters 1 and 6 were multiparous animals displaying pronounced milk peaks and thus substantial energy demands, which likely led to more pronounced negative energy balance and lipomobilization in early lactation, as reflected by higher
Hamon et al.: PROFILES OF LACTOSE CONTENT ACROSS LACTATION

FPR values in both clusters and increased milk BHB concentrations specifically in cluster 1. Such physiological intensity could make them more susceptible to health disorders as lactation progressed. Around mid lactation, signs of udder inflammation may emerge, potentially due to early tissue remodeling or bacterial infection, both suggested by the significant increase in SCC. This was particularly evident in cluster 1, where the decline in LC and the rise in SCC were most pronounced. This could contribute to a decline in MY from mid lactation through the end of the lactation period (Auldist et al., 1995). This hypothesis is supported by the fact that at the same time, Na levels rose while those of K slightly fell (only in cluster 1). These changes in osmotic balance are indicative of an altered permeability of mammary epithelial cells (Peaker, 1977; Summer et al., 2009). In fact, in the case of udder inflammation, and particularly of compromised mammary epithelial permeability, lactose may leak into the blood, leading to a reduction in its levels in milk (Peaker, 1977; Nguyen and Neville, 1998; Herve et al., 2019). The greater occurrence of metabolic disorders and udder health issues in clusters 1 and 6 was also supported by higher culling rates than in other clusters, except for cluster 3, where this was also observed (clusters 1, 3, and 6; 31%–46% vs. 16%–25% for other clusters; results not shown).

Perspectives on the Contribution of LC to Udder Health and Metabolic Status Assessment

The primary objective of this study was to determine whether distinct groups of cows could be identified based on the shape of their LC curves throughout lactation. Although the study was not specifically designed to assess LC as an indicator, the results nevertheless provide valuable insights into potential relevance for health disorder detection. Lactose content is relatively stable in milk and appears to be mainly determined by animal factors such as parity and genetic merit. Deviations from this baseline are therefore likely to be associated with health disorders. Furthermore, LC reflects different physiological mechanisms compared with other traits. Its combined use with routinely monitored indicators could provide complementary information. Unlike SCC, which primarily indicates inflammation, LC also captures changes in the integrity of the mammary epithelium, osmotic equilibrium, and udder synthetic activity, thereby providing information on earlier or more subtle impairments in gland function (Linzell, 1972; Shennan, 1990; Costa et al., 2019a). Regarding metabolic disorders, indicators such as BHB and FPR are mainly related to the cow's energy and lipid metabolism, through body reserve mobilization, incomplete oxidation of NEFA, and energy expenditure (Denis-Robichaud et al., 2014).

In a previous study investigating both udder health and metabolic status, we observed that the frequency of high SCC values was greater when milk BHB concentrations were also elevated, and that LC was lowest when both indicators were high (Hamon et al., 2024). Because these indicators are physiologically interconnected, their joint analysis will provide more integrated and reliable interpretations. For this reason, LC variations should always be interpreted together with other routinely used milk components, such as SCC for udder inflammation and BHB for metabolic disorders, in order to better understand and identify the origin of these variations.

CONCLUSIONS

The originality of this study lies in its description of LC variations throughout lactation and accounting for the genetic values of the animals for this trait. Most cows in the dataset displayed relatively flat LC curves after their peak lactation. However, some individuals displayed persistently lower LC throughout lactation or a decline in LC during mid lactation. This pattern seems to be linked to health disorders, particularly udder inflammation or metabolic disorders. Analyzing LC dynamically therefore appears to offer a useful way to identify cows that may present health issues, and combining LC with other milk components such as SCC, BHB, FPR, and Na and K when available, can enhance the understanding and interpretation of these variations. In situations where dynamic monitoring is not available, an individual reference value for LC could be estimated from parity and genetic merit, and any deviation from this expected level could suggest health disorders and merit further evaluation.

NOTES

The authors wish to acknowledge the company Eilyps for providing access to the data and for their valuable involvement in the development of this work. Supplemental material for this article is available at https://doi.org/10.5281/zenodo.15829339. ETHICS. The authors have not stated any conflicts of interest.

**Nonstandard abbreviations used:** AMS = automatic milking system; BIC = Bayesian information criterion; CV<sub>a</sub> = coefficient of genetic variation; FPR = fat-to-protein ratio; LC = lactose content; MY = milk yield; NEFA = nonesterified fatty acid; PC = principal component; PCA = principal component analysis; SPC = principal component score; VIF = variance inflation factor.
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ORCIDS

Auxane Hamon, https://orcid.org/0009-0003-1337-6031

Mathieu Arnal, https://orcid.org/0000-0002-2671-5026

Marie-Pierre Sanchez, https://orcid.org/0000-0002-1371-5342

Rachel Lefebvre, https://orcid.org/0000-0003-2313-9833

Sophie Lemosquet, https://orcid.org/0000-0002-1077-1285

Jocelyne Guinard-Flament https://orcid.org/0000-0001-5646-3774