**4. Quantitative genetic analyses of individual reaction norm**

the exposure of dairy goats to moderate HS conditions (THI = 79) decreased milk yield in Alpine but not in Nubian goats. Differences in the genetic potential for adaptive traits and also

**Figure 2.** Graph of daily kg of milk yield (DMY) and g of fat plus protein yield (DFPY) as a function of THI for Murciano‐

**3. Physiological and metabolic response to heat stress under controlled** 

Animals respond to HS reducing feed intake to decrease metabolic heat production and launching heat dissipation mechanisms like increased perspiration and respiratory rate. The combined effect of lower dry matter intake (DMI) and higher energy expenses to maintain body temperature may provoke a negative energy balance and a deficit of nutrients with negative effects on production and reproduction, as well as on the animal health status. In dairy cattle, only 40% of the reduction of milk yield has been proved to be due to a lower feed intake [32, 33]. Heat stress is accompanied by metabolic changes that are also responsible for the decrease in production. In dairy goats maintained in climatic chambers to generate a

for production might explain these differences.

Granadina (MG) and Payoya (PY) goats (from Ref. [29]).

**conditions**

332 Goat Science

The current approach to the quantitative genetic analysis of the response of milk traits to HS uses frequently random regression models based on the concept of norm of reaction: the different phenotypic expressions of a gene in different environments [48]. The magnitude of the change in the value of a given trait from one environmental condition to another measures the plasticity of an individual for a given trait and it is also a measure of the genotype by environment interaction. According to their norm of reaction, animals can be classified as stable or robust for a certain trait if the value of that trait remains constant through the range of values of the environmental variable and unstable or plastic if the value of the trait changes.

These models include two types of quantitative variables: the test‐day values of milk traits (yield, contents of fat, protein or any other milk component) registered periodically to each animal in each farm and the values of a certain climatic variable (most frequently THI) registered in meteorological stations located the closest the possible to the farm. Misztal [49] and Ravagnolo et al. [50] were the first to apply this methodology for the estimation of the genetic components of the response to HS in dairy cattle. The model proposed by Misztal presented the test‐day milk yield as a function of the THI with an independent term or intercept, standing for general genetic component of the trait, and a random coefficient or slope, representing the specific response of daily milk yield to a unit increase in the THI, which can be considered a measure of the susceptibility to HS. This model has been later modified including an individual threshold value of the climatic index considered, below which the animal is in a comfort state with no effects of HS. This threshold is different for each animal [51, 52].

The general form used in these works for the estimation of the variance components is a random regression model including the combination of herd and date of recording of the trait, the combination of age and parity number, the number of kids born, and a fixed function of the covariables of the THI trajectory (modelled with a Legendre polynomial) as fixed effects, and the additive genetic function of the animal with milk records and their parents without data, the permanent environmental function of the animal with milk records through the THI trajectory (modelled with Legendre polynomials) and the residual (with homogeneous variance) as random effects. With the variance components estimated in these analyses, it was

), genetic correlations (*r*

(*i* and *j*) of the trajectory of the THI values and the EBV for any animal with milk records or

The main results obtained are similar in the four studied breeds and they can be summarised

**1.** In general, the genetic variances for the intercepts (defining the overall genetic value for the trait that does not change with the heat load) of the functions of responses of milk traits to THI were much higher than those of their slopes (specific HS tolerance). The genetic covariances between intercepts and slopes were negative, indicating that high‐yielding animals are less tolerant to HS. The covariances between the intercepts and the slopes for

**2.** Heritability estimates varied through the scale of values of THI, as can be seen in **Figure 3**. The pattern is very similar in all four breeds; therefore, only the estimates of *h*<sup>2</sup>

**3.** Genetic correlations between adjacent points in the THI scale are high (over 0.90), whereas these values are low between distant THI points, reaching values below 0.80 which is the threshold value proposed by Robertson [54] as indicative of a significant genotype by environment interaction (G×E). This implies that the genetic potential for production under hot and cold conditions is ruled by at least partially different genetic backgrounds. The ratio between the variances of the slopes and the intercepts indicates the magnitude of this inter-

tory in Malagueña and Payoya breeds. Permanent environmental correlations (*r*p) between

correlations is an indicator of the persistence of the expression of the performance of the animal through the THI conditions. Differences between the four studied breeds were observed to this respect, PY being the breed with a better ability to adapt to stress conditions. This breed is raised under a semi‐extensive production system and its average milk yield is lower than that of the other breeds which are raised under more intensive conditions. **4.** The EBVs are not constant throughout the range of values of THI, as can be seen in **Figure 5**, which represents the evolution through the scale of values of THI of EBVs of the 100 animals of Murciano‐Granadina breed with the highest EBVs at THI = 31 (a value corresponding to HS conditions) and the 100 animals with the lowest EBVs at the same THI. Three types of responses to THI were observed: non‐tolerant animals, with their EBV decreasing as THI increases; robust, with EBV independent of THI and tolerant, with EBV increasing

*a ij*

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) throughout the THI trajec-

. The pattern of these

in Mur-

2

the permanent environmental effects were also negative.

ciano‐Granadina and Payoya goats are presented in **Table 2**.

action. **Figure 4** presents the values of genetic correlations (*r*<sup>g</sup>

pairs of points in the THI scale showed a similar pattern to those of *r*<sup>g</sup>

possible to compute the heritability (*hi*

as follows:

as THI increases.

without milk records if it is in the pedigree.

Quantitative genetic analyses of the response of milk traits to HS in small ruminants are scarce, as opposed to those in dairy cattle. The first study carried out in small ruminants presented the results of a study on dairy sheep in the Mediterranean region [4], showing similar results to those observed in dairy cattle. The first application to the study of the effects of HS on milk traits in goats was performed in the region of Andalusia, in South Spain, in a native dairy breed (Payoya) raised under semi‐extensive conditions [53]. A modified version of Finocciaro's THI and the selection criterion of the breeding programme of the breed (protein plus fat yield) were used as climatic variable and as quantitative trait, respectively. Genetic variation for the response to the increasing values of THI was found, with some animals showing a stable genetic response through the range of values of THI and others showing a significant reduction of their breeding value for the trait under HS conditions.

Later studies went deeper into the analysis of the response of milk traits to HS in other native Spanish breeds: Murciano‐Granadina, Malagueña, Florida and Payoya (**Table 1**). A real comfort zone under a given THI value cannot be observed, but a smooth increase of the level of production up to 20–30 units of THI and a negative slope afterwards as a consequence of HS was found. The estimated average loss of fat plus protein yield as an effect of HS ranged between 1.9 and 3.1% [21]. It is easy to understand the importance of the economic loss in a region in which the animals might be under HS condition an average of 140 days per year. Menéndez‐Buxadera et al. [21, 29] described the change of the components of the genetic variation, the heritability (*h*<sup>2</sup> ) and the estimated breeding values (EBVs) throughout the scale of values of the THI.


**Table 1.** General statistics of the data used in the heat stress studies of native Spanish breeds of goats (from Refs. [22, 29]).

The general form used in these works for the estimation of the variance components is a random regression model including the combination of herd and date of recording of the trait, the combination of age and parity number, the number of kids born, and a fixed function of the covariables of the THI trajectory (modelled with a Legendre polynomial) as fixed effects, and the additive genetic function of the animal with milk records and their parents without data, the permanent environmental function of the animal with milk records through the THI trajectory (modelled with Legendre polynomials) and the residual (with homogeneous variance) as random effects. With the variance components estimated in these analyses, it was possible to compute the heritability (*hi* 2 ), genetic correlations (*r a ij* ) for each trait and for all points (*i* and *j*) of the trajectory of the THI values and the EBV for any animal with milk records or without milk records if it is in the pedigree.

These models include two types of quantitative variables: the test‐day values of milk traits (yield, contents of fat, protein or any other milk component) registered periodically to each animal in each farm and the values of a certain climatic variable (most frequently THI) registered in meteorological stations located the closest the possible to the farm. Misztal [49] and Ravagnolo et al. [50] were the first to apply this methodology for the estimation of the genetic components of the response to HS in dairy cattle. The model proposed by Misztal presented the test‐day milk yield as a function of the THI with an independent term or intercept, standing for general genetic component of the trait, and a random coefficient or slope, representing the specific response of daily milk yield to a unit increase in the THI, which can be considered a measure of the susceptibility to HS. This model has been later modified including an individual threshold value of the climatic index considered, below which the animal is in a

comfort state with no effects of HS. This threshold is different for each animal [51, 52].

significant reduction of their breeding value for the trait under HS conditions.

tion, the heritability (*h*<sup>2</sup>

values of the THI.

334 Goat Science

Quantitative genetic analyses of the response of milk traits to HS in small ruminants are scarce, as opposed to those in dairy cattle. The first study carried out in small ruminants presented the results of a study on dairy sheep in the Mediterranean region [4], showing similar results to those observed in dairy cattle. The first application to the study of the effects of HS on milk traits in goats was performed in the region of Andalusia, in South Spain, in a native dairy breed (Payoya) raised under semi‐extensive conditions [53]. A modified version of Finocciaro's THI and the selection criterion of the breeding programme of the breed (protein plus fat yield) were used as climatic variable and as quantitative trait, respectively. Genetic variation for the response to the increasing values of THI was found, with some animals showing a stable genetic response through the range of values of THI and others showing a

Later studies went deeper into the analysis of the response of milk traits to HS in other native Spanish breeds: Murciano‐Granadina, Malagueña, Florida and Payoya (**Table 1**). A real comfort zone under a given THI value cannot be observed, but a smooth increase of the level of production up to 20–30 units of THI and a negative slope afterwards as a consequence of HS was found. The estimated average loss of fat plus protein yield as an effect of HS ranged between 1.9 and 3.1% [21]. It is easy to understand the importance of the economic loss in a region in which the animals might be under HS condition an average of 140 days per year. Menéndez‐Buxadera et al. [21, 29] described the change of the components of the genetic varia-

Years 2000 – 2006 2006 – 2012 2006 – 2012 2002 – 2007 No. of milk records 63,640 160,067 129,450 81,625 No. of animals in pedigree 6037 14,089 12,268 9917 No. of herds 20 17 20 18

Average daily milk yield (kg) 2.06 ± 0.93 2.01 ± 0.96 2.30 ± 1.10 1.89 ± 0.83 Average daily fat + protein yield (g) 176.4 ± 80.48 191.60 ± 82.13 189.20 ± 83.2 161.6 ± 71.0

**Table 1.** General statistics of the data used in the heat stress studies of native Spanish breeds of goats (from Refs. [22, 29]).

) and the estimated breeding values (EBVs) throughout the scale of

**Murciano‐Granadina Malagueña Florida Payoya**

The main results obtained are similar in the four studied breeds and they can be summarised as follows:


**Figure 3.** Change of the estimates of *h*<sup>2</sup> along the scale of values of THI in Malagueña and Payoya breeds (from Ref. [22]).

**Figure 4.** Genetic correlations of daily fat plus protein yields at THI = 7 and the same trait at all other values of THI in

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337

**Figure 5.** Evolution through the scale of THI values of the EBVs of the 100 animals of Murciano‐Granadina breed with

the highest EBV at THI = 30 and the 100 animals with the lowest EBV at the same THI (from Ref. [55]).

Florida and Malagueña goats (from Ref. [22]).

As a consequence of the differences in the estimates obtained for the variance components and the EBVs along the scale of THI values, any of the studied milk traits cannot be treated as the same trait throughout this scale. This is particularly important in respect to the estimation of breeding values, because the conventional methods of estimation are ignoring these differences and estimating these values at a fixed THI value; therefore, not tolerant animals might be selected. This genetic variability for the response to climatic conditions can be used to select the most adequate animals (tolerant or robust) to cope with future climate changes.


**Table 2.** Range of heritability (*h*<sup>2</sup> ) values of daily milk yield (DMY) and daily fat plus protein yield (DFPY) in the comfort and stress thermic zones and genetic correlation (*r*<sup>g</sup> ) between zones in Murciano‐Granadina and Payoya goats (from Ref. [29]).

**Figure 4.** Genetic correlations of daily fat plus protein yields at THI = 7 and the same trait at all other values of THI in Florida and Malagueña goats (from Ref. [22]).

As a consequence of the differences in the estimates obtained for the variance components and the EBVs along the scale of THI values, any of the studied milk traits cannot be treated as the same trait throughout this scale. This is particularly important in respect to the estimation of breeding values, because the conventional methods of estimation are ignoring these differences and estimating these values at a fixed THI value; therefore, not tolerant animals might be selected. This genetic variability for the response to climatic conditions can be used to select the most adequate animals (tolerant or robust) to cope with future climate changes.

 **comfort** *r***<sup>g</sup>**

DMY 0.27–0.30 0.69–0.85 0.22–0.28 DFPY 0.21–0.23 0.71–0.85 0.20–0.22

DMY 0.21–0.22 0.71–0.90 0.22–0.24 DFPY 0.19–0.20 0.72–0.91 0.20–0.21

along the scale of values of THI in Malagueña and Payoya breeds (from Ref. [22]).

 **between zones** *h***<sup>2</sup>**

) values of daily milk yield (DMY) and daily fat plus protein yield (DFPY) in the comfort

) between zones in Murciano‐Granadina and Payoya goats (from

 **stress**

**Figure 3.** Change of the estimates of *h*<sup>2</sup>

**Murciano‐Granadina**

**Table 2.** Range of heritability (*h*<sup>2</sup>

and stress thermic zones and genetic correlation (*r*<sup>g</sup>

**Payoya**

336 Goat Science

Ref. [29]).

*h***2**

**Figure 5.** Evolution through the scale of THI values of the EBVs of the 100 animals of Murciano‐Granadina breed with the highest EBV at THI = 30 and the 100 animals with the lowest EBV at the same THI (from Ref. [55]).
