Milk production and weather data
A total of 2.6 million test-day (TD) records for milk, fat, and protein yields from 170,439 Holstein cows raised in 1342 herds in Ontario, and 3.8 million records from 226,863 Holstein cows raised in 1962 herds located in Quebec, were provided by Lactanet. In Quebec and Ontario, the average size of herds is 76 and 95 cows, respectively, with mainly two types of barns — tie stall and free stall (
CDIC 2021a). The data collected spanned a 10 yr period (from 2010 to 2019) and included observations from the first three parities. Only herds with records in at least five years and only observations collected within the interval from 5 to 305 d in milk (DIM) were used for analyses. In each parity, cows were required to have a minimum of four records.
Meteorological data were obtained from Environment Climate Change Canada (ECCC) using the “weathercan” (
LaZerte and Albers 2018) package available in R (
R Core Team 2021). The data consisted of hourly measurements (i.e., 24 records per day) of ambient temperature (AT) and relative humidity (RH). Each day was divided into three periods (i.e., morning (5 am–11 pm), afternoon (12 pm–8 pm), and night (9 pm–4 am)), and weather stations were required to have a minimum of one reading per period in each day over the entire 11 yr period. A total of 30 and 37 weather stations in Ontario and Quebec were linked to more than one farm. Therefore, the nearest weather station was assigned to each farm based on their latitude and longitude using the “geosphere” (
Hijmans et al. 2019) package of R (
R Core Team 2021). Weather records were collected from a total of 33 and 43 weather stations located within a maximum distance of 20 km from each herd (average distance of 13.1 ± 5.2 km and 12.6 ± 4.6 km) in Ontario and Quebec, respectively.
Temperature–humidity index
Two alternatives of THI were used in this study: (1) THIavg, where daily average AT and daily average RH were used in the formula; (2) THImax, where maximum AT and minimum RH were used. These two alternate THI allowed fair comparisons with other studies that have assessed heat stress.
The THI formula currently used does not include wind speed and solar radiation, which may influence heat stress conditions experienced by cattle, especially if animals are kept outside (e.g., feedlot cattle;
Mader et al 2006;
Gaughan et al 2008). However, considering a predominantly housing system (i.e, tie or free-stall) and the lack of pasture access in Canada (
Beaver et al 2020), the influence of wind speed and solar radiation on heat stress conditions may be limited. Moreover, wind speed measurements from weather stations may not represent well the farm conditions as it has a greater dependency on local topography compared with temperature and humidity (
Dunn et al. 2014).
In general, THI values of 2 d prior to the TD record have been reported as having the greatest effect on reducing milk yield and feed intake (
West et al. 2003;
Spiers et al. 2004;
Bohmanova et al. 2008). Thus, considering the delayed effect of heat load on production traits, the value assigned to each test day, for both THI definitions (i.e., THI
avg and THI
max), was the average of the THI on the day of milk recording and the THI of two previous days (i.e., up to 48 h before milk recording). The total number of TD records per THI value by lactation, after merging the production data with the meteorological data, is shown in
Fig. 1.
Identification of heat stress threshold and effect on production
To identify the THI threshold in each parity at which milk, fat, and protein yields start to decline, the following steps were carried out: (1) a linear mixed model was fitted to adjust the phenotypes for known sources of environmental variation; (2) the adjusted phenotypes were plotted against the THI by lactation (first, second, or third) to provide visual information on the relationship between production and THI; and (3) a segmented polynomial was used to describe the shape of the curve describing the relationship between production and THI values, and the thresholds (i.e., breakpoints) for the polynomials were defined along the THI gradient.
In the first step, the analysis was performed for each trait (milk, fat, and protein yields) and each lactation (first, second, or third) using single-trait animal models using ASReml software (
Gilmour et al. 2015). The linear mixed model used can be described as follows:
where
yijklm is the
mth test-day record (milk yield in kg, fat and protein yields in g) of the
lth cow;
μ is the overall mean;
HYi is the effect of the
ith combination of herd and year of recording;
ADj is the jth combination of age at calving (eight classes for first lactation: = <24, 25, 26, 27, 28, 29, 30–31, >30 mo; six classes for the second lactation: = <36, 37, 38, 39–40, 41–42, >43 mo; and five classes for the third lactation: = <50, 51–52, 53–54, 55–56, >56 mo) and DIM (11 classes = 5–29, 30–60, 61–90, 91–120, 121–150, 151–180, 181–210, 211–240, 241–270, 271–300, 301–305 d);
Fk is the effect of
kth frequency of milking (
k = 1–3);
al is the random additive genetic effect of the l
th animal; and
eijklm is the residual term. Frequency of milking was included in the statistical model to account for the fact that animals that are milked more frequently tend to produce more milk. The residual term includes unknown sources of variation in
yijklm, such as THI, in which
, where
is the predicted phenotypic observation given by model [1]. Therefore, the residuals of model [1] are the phenotypic observations adjusted for the known fixed environmental effects (i.e., HY, AD, and F) and the random additive genetic effect of the animal.
Hereafter, the residual term of model [1] will be referred to as adjusted phenotype (
yadj), which was plotted against the THI to display the relationship between production and THI. Previous knowledge about THI thresholds for milk production (e.g.,
Bernabucci et al. 2014;
Carabaño et al. 2016) and visual inspection of the plot provided information on the most likely number and location of the breakpoints, i.e., where the pattern of milk, fat, and protein yields would change considering the THI gradient. Visual inspection and previous knowledge of the data to be fit have been used to determine the number and location of breakpoints for segmented polynomials (
Madár et al. 2003;
Misztal 2006;
Gorniak et al. 2014). A total of three, two, and one breakpoints were used for the segmented polynomials for milk, protein, and fat yield, respectively, to determine the THI thresholds for each trait and lactation.
Segmented polynomials describe a non-linear relationship between variables by connecting different functions through the breakpoints (
Rice 1969). Thus, with a prior determination of the number and regions of breakpoints and the adjusted phenotype from model [1], segmented polynomials allowed to find THI thresholds where production started to decrease. Segmented polynomials with different linear functions were fitted using the PROC REG procedure of the SAS software (version 9.2;
SAS 2011), and different breakpoint locations were tested. The general segmented polynomial model used in this study can be described as follows:
in which elements of
z are given by:
where yadj is the vector of adjusted phenotypes obtained from model [1]; α is the intercept; 1 is the vector of ones; β1 is the linear regression coefficient; x is the vector of THI values; γ1,…, γn are linear regression coefficients, which give the differences in the slopes in relation to the preceding linear segments; z1i,…,zni are covariates as defined above; and C1,…, Cn is the breakpoint values. The segmented polynomial model used for milk, protein, and fat yield had three, two, and one breakpoints, respectively. The final location of the breakpoints (i.e., THI value) was determined based on the adjusted coefficient of determination (R2) of the model and the statistical significance (P value) of the segments describing the change in the adjusted phenotypes. The linear regression coefficient for each breakpoint (γ) gives the rate of change in production, from which production loss can be estimated.
Economic loss associated with decreased milk production
A simplified estimation of economic loss (EL) associated with decreased fat and protein yield was calculated as follows:
where comp$ is the milk component price, which was calculated assuming the average prices paid to producers based on fat or protein yields (i.e., $8.28·kg
−1 for butterfat and $6.38·kg
−1 for protein yield) following the 2019–2020 Dairy Farmers of Ontario’s Annual Report (
Dairy Farmers of Ontario 2020), HS
days is the average number of days above the THI threshold per year,
γ is the average decline rate (converted to kg·unit
−1 of THI
max) estimated for the three parities and both provinces of either fat or protein yield, HS_THI is the average THI
max value above the THI threshold, and THI
threshold was set to THI
max = 58, based on the average of thresholds identified for fat and protein yields. A single THI threshold for fat and protein was assumed because the average THI threshold identified for each component across lactations did not differ considerably (<5 THI units). The EL for protein and fat yields was then multiplied by the number of milking dairy cows in Ontario and Quebec, and the resulted value summed up for the total EL.