Isotope partitioning between cow milk and farm water: A tool for verification of milk provenance

Rationale The oxygen and hydrogen isotope compositions of the water component of the milk from nine Italian dairy farms were studied together with the farm water for one year. The aim was to verify the importance of farm water and seasonal temperature variation on milk isotope values and propose mathematical relations as new tools to identify the milk origin. Methods Milk was centrifuged to separate the solids and then distilled under vacuum to separate water. δ(18O/16O) and δ(2H/1H) analyses of the water molecules were carried out using a water equilibrator online with a mass spectrometer. For oxygen and hydrogen isotope determination, water was equilibrated with pure CO2 for 7.5 h and with pure H2 for 5 h, respectively. The isotope ratio value is indicated with δ (expressed on the VSMOW/SLAP scale) as defined by IUPAC. Results The average annual isotope value of milk at the different cattle sheds is mostly related to the farm water suggesting that the drinking water is the most important factor influencing the isotopic values of the milk water. The milk/water fractionation factor correlates with the milking time and, thus, the seasonal temperature is best described by a 4th order polynomial regression line. A two‐level check model was used to verify the milking provenance. Conclusions This study shows that it is essential to analyze both milk and farm water to indicate provenance. A two‐step verification tool, based on the difference between the measured and calculated δ(18O/16O)M values, and the difference between the calculated and estimated milk‐water fractionation factors, allowed the source determination of milk. Both conditions must be met if the milk is considered to be from the Parmigiano‐Reggiano production region. Although this approach was developed for this region, it can easily be tested and adapted to other dairy production areas.


| INTRODUCTION
Several empirical studies have demonstrated the utility of oxygen and hydrogen stable isotope measurements on milk for verifying its origin. [1][2][3][4][5][6][7][8][9][10][11][12][13] In fact, like many other natural products, milk retains its isotopic features acquired at the time of its production. The The verification of geographical origin is essential for particular local foodstuffs with Protected Designation of Origin (PDO) to protect their authenticity. The PDO designation of Parmigiano-Reggiano, the most famous region of cheese production, means that the milk used in its production must come from a defined region in the Po River plain and the northern side of the Apennine chain (Northern Italy). However, the remarkable price differences among cheeses makes it tempting for criminals to use fraudulent designation labels on products that do not correspond to the authentic production areas. In order to protect the consumer and assure honest competition on the market, it is desirable to develop objective and robust methods to verify the authenticity and origin of economically important products such as Parmigiano-Reggiano cheese. This paper investigates the isotopic signature of cow milk from this region concerning (i) farm water during the different periods of the year and (ii) local temperature, which influences evapotranspiration and animal's metabolism. The work describes a model for verifying the isotopic composition of milk characteristic of the area of production of the Parmigiano-Reggiano cheese.

| Selection of cattle sheds
Nine cattle sheds were randomly selected among the cattle sheds from the region of the Parmigiano-Reggiano cheese production. In addition, four sheds -Torrile, Villa Minozzo, Quattro Castella, and Viarolowere also sampled for model verification.

| Samples
Hydrogen and oxygen isotope determinations were carried out monthly from February 2018 to January 2019 on 108 samples of farm water and 108 samples of cow milk (average daily milk).
Samples of farm water (100 cm 3 in double-cap containers) were stored at 2 C and milk (50 mL in double-cap containers) at À20 C to avoid bacteria proliferation. The number of cattle per farm (≥40) is such that any influence on the milk isotopic composition linked to an individual animal (breed, time since to the last pregnancy, age, etc.) is taken into account. Milk was centrifuged (4000 rpm for 4 min) to separate the solids and distilled under vacuum to separate the water.

| Calculations and statistical analysis
The isotope fractionation between milk water (M) and farm water (W) was calculated using the following relationship: where α t is the isotope fractionation factor at the time t, while δ W,t and nicely describes the data distribution, but it does not generate a mathematical formula. In our case, the smoothing lines are very similar to the 4 th order polynomial regression lines: where A, B, C, D, and E are regression coefficients determined by fitting the curve to experimental data.

| RESULTS
Hydrogen and oxygen isotope data for the nine cattle sheds investigated are presented in Table S1 (supporting information).

| Oxygen and hydrogen isotopes in farm water (W)
The to À5.23‰ and À73.7‰ to À39.0‰, respectively, and the standard deviation is, in most cases, greater than the prediction uncertainty. were used to smooth the obtained data. The equation is reported ( Figure 3) without taking into account Castelnovo and Baiso: where the number of data used in the polynomial regression (n) = 84, coefficient of determination (R 2 ) = 0.30, and the standard error of the regression (s (yx)) = 0.92‰. This equation will be used later.  (Table S1,    This result is because when outdoors, evapotranspiration is greater, and the animals may drink evaporated water and eat grass with an elevated isotope ratio due to evapotranspiration. 24

| The isotopic fractionation factor between milk water and farm water and its dependence on the sampling time
The isotopic fractionation factor between milk water and farm water has been further evaluated using Equation 1.     T A B L E 2 (a) Data for new cattle sheds belonging to the area of production of the Parmigiano-Reggiano cheese; (b) data for cattle sheds that are declared by the farmers as belonging to the area of production of the Parmigiano-Reggiano cheese marked L1, L2, L3, and L4. The two-step criteria are also included  The heavy isotope enrichment of the milk is related to the isotope fractionation during water evaporation and CO 2 production.
During the summer, a dairy cow reacts to the high temperature by restoring its metabolism; the symptomatology will be characterized by an increase in body temperature by half a degree centigrade and an increased respiratory rate of over 80 beats per minute, directly affecting CO 2 production. This response increases the metabolic water production and, as this water is exhaled through the lungs, enhances the oxygen isotope fractionation. During this attempt to acclimatize and in full heat stress, a cow will reduce its milk production; a different production rate could directly modify the fractionation of oxygen in the udder between body and milk water. 10,28  (Table 2a).

| Two-step check to verify milk origin
Step one: first, the milking at time t was verified using the following condition:  (5) includes about 90% of the population data around the line (5) (Figure 3). Since the measured and calculated milk isotope values for the new cattle sheds agree with Equation 5, at the first level of investigation, the milk is compatible with the investigated area (Table 2a).
Step two: second, to check that the milk is compatible with the farm water, the following steps are performed: (a) the actual 18 α m,t value is obtained using the measured values for milk and farm water by Equation 1; (b) the obtained 18 α m,t value is then compared with 18 b α t , which is estimated for time t using Equation 6b.
The two values are in good agreement when the following relationship is valid: For the four new cattle sheds, the difference 18 α m,t À 18 b α t is always < 0.45‰ (Table 2a) In the next step we checked four samples, L1, L2, L3, and L4, declared by farmers to have originated from four locations of the area of production of Parmigiano-Reggiano (Table 2b). First, the isotopic values for the milk water were considered to check if the milk is compatible with the region. As presented in Table 2b all four samples L1, L2, L3, and L4 are compatible with the area.
Since the farm water was not available the isotope data from groundwater reported by Martinelli et al 22 Table 2b). It is possible that the origin declared by the farmers is suspicious.

| CONCLUSIONS
This study has investigated the relationship between the stable isotopic signatures of farm water and milk water as a tool for verifying if milk originates from the Parmigiano-Reggiano production region. It was shown that drinking water is the main factor influencing the isotope signature of the milk, but does not explain all of the observed variance. Other factors such as seasonal temperature variations that can induce a metabolic response in the animals can add to the observed isotopic variation in milk water.
Thus, to indicate provenance, it is essential to analyze both milk and farm water. If this is not possible, the isotopic composition of groundwater from the investigated region can be used in its place.
The study also found that the variation in δ( 18

PEER REVIEW
The peer review history for this article is available at https://publons. com/publon/10.1002/rcm.9160.

DATA AVAILABILITY STATEMENT
Data available in article supplementary material.