M C Codrea

S Højsgaard

N C Friggens

Differential smoothing of time-series measurements to identify disturbances in performance and quantify animal response characteristics: An example using milk yield profiles in dairy cows 1

Keywords: B-spline, feature extraction, phenotype, smoothing

ABSTRACT: Recent advances in on-farm technology now provide us with multiple time-series of reliably measured indicators of animal performance and status at the level of the individual. This paper presents a smoothing approach for extracting biologically meaningful features from such time series using bovine milk yield data as an example. The main goal of this study was to illustrate how the method can be used to detect production deviations, extract quantifiable features of the deviation profiles, and thus provide means to examine hypotheses concerning the nature of the deviations. The effectiveness of the method was assessed with complete lactation curves from 47 Holstein cows. Within their lactations, the cows were each subjected to 1 nutritional challenge for a period of 4 d (their standard diet: a maize silage-based total mixed ration was diluted with 60% wheat straw), which provoked a decline in the milk yield in all cows. The challenge was imposed between the same calendar days for all cows. Thus, the cows were at different stages of lactation: early (n = 14), mid (n = 15), and late (n = 18). Each milk-yield curve was decomposed into components that capture the short-term deviations of the cow such as the response to the nutritional challenge and describe the phenotypic potential yield function of that cow throughout its lactation. The difference between the 2 components gives a measure of the milk loss. In all, 480 deviations were detected from the complete lactations of 47 cows. The milk loss provoked by the feeding challenge (n = 47) was significantly related to the milk yield immediately before the challenge (r = 0.86, P < 0.01). The correlation between the rate of recovery and milk loss was (r = 0.94, P < 0.01). Further, there was no significant slope (P > 0.1) to the relationship between the ratio (rate of recovery/milk loss) and days from calving, indicating that the force of recovery was unaffected by stage of lactation. These results suggest that differential smoothing can be a useful tool for quantifying biological disturbances in animal performance and for extracting features that relate to the potential and robustness of an animal.

INTRODUCTION

Traditionally, in agricultural research, smoothing has been used largely to reduce the variability or noise in data so as to make it easier to detect differences between treatments (e.g., feeds or other systematic factors). In such situations, the aim of smoothing is to remove short-term disturbances from the data. Rather than using smoothing to eliminate disturbances, an alternative approach is to use smoothing to capture them. Disease episodes often cause short-term disturbances (e.g., a decrease in milk yield followed by a recovery; [START_REF] Fourichon | Effects of disease on milk production in the dairy cow: A review[END_REF]. Similarly, if an animal goes "off-feed," this will disturb production traits, although in this case, the disturbance can be of longer duration [START_REF] Bareille | Effects of health disorders on feed intake and milk production in dairy cows[END_REF]. Being able to identify and quantify the extent of these disturbances has been shown to be of value for health management [START_REF] Friggens | Estimating degree of mastitis from time-series measurements in milk: A test of a model based on lactate dehydrogenase measurements[END_REF]Kamphuis et al., 2008a).

The deviation and severity of an animal response to a disturbance (e.g., disease challenge, nutritional shortage) reflects, to some degree, the capacity of that animal to respond. As such, these responses contain biologically meaningful information. Thus, a method for quantifying the features of such data may provide quantitative information about the phenotype of the animal at a functional level. Using smoothing to identify disturbances implies decomposing the time series in question into the underlying long-term trend and deviations from it. The aims of this study are to examine the issues involved in decomposing time-series data to capture biologically meaningful features and to evaluate the ability of this approach to detect (known) disturbances in the time series of milk production. To this end, we have chosen a smoothing method that is an example of a functional form, which facilitates the extraction of features without compromising flexibility to fit different curve shapes. It is important to note that no assumption on the parameterization of the curve is needed.

MATERIALS AND METHODS

Experimental procedures involving animals were approved by the Danish Animal Experiments Inspectorate and complied with the Danish Ministry of Justice Law No. 382 (June 10, 1987) and Acts 739 (December 6, 1988) and333 (May 19, 1990) concerning animal experimentation and care of experimental animals.

Animals and Milking

In this study we analyzed the lactation curves from 47 Holstein cows from the resident herd at the Danish Cattle Research Centre (Tjele, Denmark). The cows were housed in a loose-housing environment with free stalls containing mats of hard rubber material and sawdust as bedding. Cows had free access to water and to an automatic milking system [Voluntary Milking System (VMS), DeLaval, Tumba, Sweden]. Because the cows visit the VMS on a voluntary basis, the milking intervals (the time interval between successive milking events) are variable. The minimum milking interval permitted by the VMS was 5 h. Cows that had not presented to the VMS in the previous 18 h were brought to the VMS for milking.

In all, 39,962 milkings were recorded from all lactations of the 47 cows with an average milking interval of 0.41 d (SD = 0.14 d). The milk yield per visit at the automatic milking system was converted to milk yield per day by dividing the measured milk yield by the milking interval, in days. Very short milking intervals, usually caused by premature removal of the milking set (i.e., those associated with incomplete preceding milkings), give rise to erroneously large yield values. Therefore, we adjusted the milking intervals shorter than 0.2 d to a value of 0.2 d. Similarly, very long milking intervals, usually caused by a cow being removed from the group for management reasons, can give rise to implausibly low yields, and we consequently set the maximum interval to 0.8 d. These adjustments affected 203 short-and 937 long-milking intervals. Within their lactations, the cows were each subjected to 1 nutritional challenge for a period of 4 d. During this period, their standard diet (a maize silage-based total mixed ration) was diluted with 60% wheat straw. The challenge was imposed between the same calendar days for all cows, and thus the challenge occurred at different stages of lactation: early (n = 14), mid (n = 15), and late (n = 18). All cows were healthy before and during the challenge trial. The complete lactations were used in this study and the effectiveness of the proposed method was particularly evaluated around the known challenge period. Other disease episodes, whether known or unknown, were not thoroughly investigated. The undisturbed phenotypic potential of each cow (i.e., the estimated milk yield if free from challenges) was the self-reference baseline for quantifying the deviations in yield.

Smoothing Method

We adopted the smoothing approach described, and termed functional data analysis, by [START_REF] Ramsay | Functional Data Analysis[END_REF].

Formally, the objective function

f c MY ( ) [ ] being mini- mized is f c y x t x t t MY j j L j N ( ) ( ) ( ) = -       + ∂       ∫ ∑ = 2 4 2 0 1 λ d [1] x t c t ( ) ( ), = ϕ
where y j are N observed raw values in the time-series interval [0, L], and x(t) is the smooth function constructed from the set of basis functions ϕ( ), t which are linearly combined with coefficients c. The scalar λ is a weighting term whose role is discussed in the following. We used B-spline basis functions, which can construct piece-wise polynomial functions joined at the knots (the points y j used in the fitting procedure). The roughness penalty, in this case the curvature of the second derivatives, is controlled by the scalar λ. When λ = 0, x(t) fits the data as well as is possible in terms of the squared error. As λ increases, more weight is put on the penalty term and thus the second derivative converges to a straight line (zero curvature). Therefore, different values for λ give different degrees of smoothing in both the function itself, as well as in its derivatives.

It is important to note that no a priori assumptions constrain the shape of the curve or the distance between knots. That is, the raw data need not be equidistantly sampled. Actually, it may be desirable to have more knots at regions with sharp changes, and only a few knots are required where the curve is rather flat, and thus, focus the smoothing to capture finer details in specific regions of interest. In this study, to imitate real-life situations, we did not use the information about the known challenge period for choosing knots. With the data described in functional form (basis functions, coefficients, and knots), the smooth curve can be estimated at any interior time point within the range of the data. This means that we can sample the curve with arbitrarily small resolution.

Having access to the derivatives of the function opens several possibilities: i) as they reflect rates of changes, they have intrinsic value in characterizing the dynamic behavior of the system under investigation; ii) deriva-tives provide means to find points of interest (landmarks) in the data (e.g., at peaks and troughs in the data, the first derivative is zero); and iii) landmarks can also be used to align and compare individual time profiles. Hence, several features can be extracted from the derivatives themselves, as well as from the timing and the amplitude of landmarks.

RESULTS

Differential Smoothing

By imposing different values of λ, which weights the roughness penalty, different degrees of smoothing can be readily obtained (Figure 1). Thus, it is possible to capture different aspects of the milk-yield curve. Using a small value of λ captures the finer details of the milkyield curve (e.g., λ = 100; Figure 1), which is useful for describing the short-term responses of the cow to, for example, infection or nutritional challenges. Using a larger value of λ provides a more stringent smoothing (e.g., λ = 10 8 ) that can reveal the long-term component of the yield curve (i.e., the natural changes in milk yield related to stage of lactation). The case with λ = 10 4 illustrates an intermediate profile.

To quantify the short-term disturbances (in this case, milk loss) the sudden decline in milk yield needs to be related to another quantity (e.g., the long-term curve). However, it is desirable to relate the loss with respect to what the cow would have produced when free from biological and technical disturbances. Such a baseline, termed here the "phenotypic potential yield curve," would provide more accurate measures of the biological response and requires that the general long-term smoothed curve is adjusted for these disturbances. The rationale in constructing such a function is as follows: i) there is a likelihood of a systematic bias in random error (e.g., milking machine errors are mostly low readings, mainly milk yields resulting from interrupted milkings), and ii) the majority of biological disturbances decrease milk yield. These 2 effects will create some degree of negative bias and an underestimate of the phenotypic potential curve, if ignored. Therefore, we need to positively offset the smoothed curve to obtain a curve that is representative of undisturbed phenotypic potential. A simple way of achieving this is by setting up asymmetric bounds for acceptable residuals, and then either exclude extreme values or downweight their contribution to the sum of squares. This can be done in several ways, and here we illustrate 2 such alternatives. An initial smoothing can indicate the data points that give large negative residuals (>1 SD of all the residuals across lactation), which can be discarded from a second smoothing. Such an offset curve, called here "residual filtered," is illustrated in Figure 2. A second example, using quantile regression [START_REF] Koenker | Quantile Regression[END_REF] with confidence limits of 90 and 60%, is shown in Figure 3. We call the resulting curve a quantile envelope. For the actual calculation of the quantiles we used Koenker's quantreg R package (http://cran.r-project. org/web/packages/quantreg/). We chose a nonparametric smoothing method with a penalty factor on the gradient, which gives piecewise linear fitted quantile functions. Thus, the quantile envelope is derived from piecewise estimates of the residual variation (data points above the 90% and below the 60% quantiles are excluded from the smoothing fit). In both offsetting strategies, the adjustment accounts for the inherent variability in the original measures.

Examples of offset curves representing undisturbed phenotypic potential and the much rougher curve that captures biological disturbances are shown in Figure 4 (top panel). In the subsequent analyses and results, we have chosen to use the quantile envelope method for deriving the undisturbed phenotypic potential because it is more internally consistent with the time-series approach as it accommodates the possibility of differences in residual variation at different times from calving.

For the purposes of the present paper, the choice of which method is used for off-setting the smooth fit to derive the undisturbed phenotypic potential is not important. What is important is to be clear that the choices of values for parameters such as λ, the number of knots in the fit, and the limits for the quantile regression were not based on a rigorous statistical optimization of parameters. Because the objective of this approach is to provide a biologically meaningful differential smoothing of the data, these parameters were chosen to best capture (i.e., fit by eye) the biological phenomena we wish to isolate. This "bio-logic" approach would be problematic if these parameters were adjusted for each individual curve being fitted because this would render invalid any comparison across cows. Thus, the same parameter values were used across all cows and, within the coefficients chosen, fitting was based on minimizing least squares and taking into account the distributions of residuals.

Feature Extraction: Quantifying Deviations and Deviation Profiles

In Figure 4, the middle and bottom panels are the first and the second derivatives of the rough curve (λ = Each deviation profile has a trough (T), which splits it into pre-and post-trough periods that correspond to response and recovery periods in milk yield. Two peaks (P pre and P post ) and 2 inflection points (I pre and I post ) can be detected on either side of T. The extreme values of the first and second derivatives of the smooth curve are denoted by (V min and V max ) and (A max , A minpre , and A minpost ), respectively. The timing features (Δt) are absolute time differences among the points of interest P pre , I pre , T, I post , and P post .

2,500). The derivatives can be useful features in their own right and also provide means to find relevant landmarks of the smooth curve. At peaks and troughs in the data, the first derivative is 0, and at inflection points (where the function changes concavity), the second derivative is 0. Figure 5 presents these features for 1 deviation profile (caused by the feed restriction imposed between 235 and 239 d from calving) in the smoothed milk yield curve shown in Figure 4. By detecting peaks and troughs, the deviation profile can be split into pre-and post-trough periods that correspond to response and recovery periods in milk yield. A panel of features that relate to aspects of the deviation profile of the cow can then be extracted. Examples of such features to quantify the loss, the timing of the response, and other aspects of the deviation profile are shown in Figure 5. The trough (T) is located where the first derivative values cross 0 from negative to positive. The pre-trough peak (P pre ) and the post-trough peak (P post ) are located where the first derivative values cross 0 from positive to negative. The pre-trough inflection point (I pre ) corresponds to the minimum value of the first derivative (V min ) and the post-trough inflection point (I post ) corresponds to the maximum of the first derivative (V max ). The extreme values of the second derivative are denoted by (A max , A minpre , and A minpost ), respectively. The milk yield loss (Q -T) is the difference between the milk level (T) and the corresponding potential level (Q) on the quantile envelope, which is a positively off-set smoothed curve that represents the undisturbed phenotypic potential yield.

In addition to the absolute levels of the features, their relative timing can also be powerful profile descriptors. Thus, we can construct timing features (Δt) as absolute time differences among the points of interest P pre , I pre , T, I post , and P post . For example, the response time Δt(P pre , T) can be calculated as the difference between the absolute time(P pre ) -time(T). Similarly, the recovery time can be quantified by Δt(T, P post ). Another example could be Δt(T, I post ), which measures how fast Figure 6. The relationships between the different deviation profile features (Figure 5) in a principal components analysis. Each deviation profile has a trough (T), which splits it into pre-and post-trough periods that correspond to response and recovery periods in milk yield. Two peaks (P pre and P post ) and 2 inflection points (I pre and I post ) can be detected on either side of T. The extreme values of the first and second derivatives of the smooth curve are denoted by (V min and V max ) and (A max , A minpre , and A minpost ), respectively. The milk yield loss (Q -T) is the difference between the milk level (T) and the corresponding potential level (Q) on the quantile envelope, which is a positively offset-smoothed curve that represents the undisturbed phenotypic potential yield. A clear grouping can be observed along the first principal component (PC1): the timing features (Δt), which are absolute time differences among the points of interest P pre , I pre , T, I post , and P post and are well separated from the absolute milk levels (P pre , I pre , T, Q, I post , and P post ) and from the derivative features (V min ,V max , A max , A minpre , and A minpost ). The later 2 groups are well distinguished in the second principal component (PC2). a cow can reach the maximum recovery rate (because V max is at I post ). The second derivative can also be used in a similar way to extract features from the rates of response (Figure 5). Table 1 gives a summary of the profile features of deviations in milk yield provoked by the nutritional challenge in the 47 cows. The absolute values of the rates of changes are shown (e.g., although V min is numerically negative, its absolute value denotes the rate of decrease, just like V max denotes the rate of increase).

Such a set of features can be seen as a panel of candidates for quantifying aspects of the ability of the cow to respond (i.e., her robustness; [START_REF] Friggens | Vers des définitions opérationnelles de la robustesse s'appuyant sur des faits biologiques: l'exemple de la nutrition[END_REF]. Considering the post-trough recovery period, one can use these features to ask questions about how different animals recover. For example, the ability of the animal to respond could be modeled using the analogy of a spring or elastic band where the larger the deviation, the stronger the force of recovery to the original state. This model would suppose a positive correlation between the size of the decline in milk yield (Q -T), and the rate of recovery, V max . In contrast, it has been argued that excessive rates of change in milk yield may be a physiological stress for the animal, and thus, animals may seek a constant rate of recovery independent of the size of the milk-yield loss. In this study, the correlation between V max and (Q -T) was r = 0.94 (P < 0.01). Further, there was no significant slope (P > 0.1) to the relationship between V max /(Q -T) and days from calving, indicating that the force of recovery was unaffected by stage of lactation. Thus, extracting response features provides a means to examine hypotheses concerning the nature of responses.

This approach can be further extended using multivariate statistical exploration of data to generate new hypotheses. For example, Figure 6 shows clear groups of features in a principal components analysis. Along the first principal component (PC1), the timing features Δt, which largely capture the shape of the deviation profiles, are clearly distinct from the absolute milk levels (P pre , I pre , T, Q, I post , and P post ) and from the derivative features (V min ,V max , A max , A minpre , and A minpost ). The latter 2 groups are well distinguished in the second principal component (PC2), and not surprisingly, (Q -T) is closer to the derivative than the absolute level features. By construction, (Q -T) is the instantaneous difference between the produced and the phenotypic potential yield curve. Therefore, we can conclude that the proposed estimation of the phenotypic potential yield is a suitable baseline for measuring disturbances.

Effectiveness of Quantifying Deviations

One test of the differential smoothing approach, and the choice of parameters values, is to examine the extent to which the deviations in milk yield provoked by the feeding challenge can be distinguished from other deviations in the roughly smoothed (λ = 2,500) milk yield curve. Figure 7 illustrates such deviations in the milk yield curves from 3 different cows with the off-feed challenge at different stages of lactation. The roughly smoothed curves clearly indicate the decline in milk yield during the challenge period for each cow, and also exhibit other deviations with unknown cause or unrelated to the off-feed experiment. In all, 480 deviations were detected from the complete lactations of the 47 cows. As can be seen in Figure 8, the size of the unplanned deviations was largely independent of the P pre . The average milk yield loss of these unplanned deviations was 2.73 kg•d -1 and the SD = 1.54 kg•d -1 . In contrast, the size of the deviations provoked by the feeding challenge was significantly related to P pre (r = 0.86, P < 0.01). The residual SD of these feeding challenge-provoked deviations was 1.24 kg•d -1 . Thus, with the parameter values indicated above, the differential smoothing method was clearly able to detect the feeding challenge-provoked deviations.

DISCUSSION

Smoothing has largely been used to reduce the variability or noise in data to make it easier to detect differences between treatments or other systematic factors by removing short-term disturbances from the data. Taking weekly averages of daily measures or using group averages are simple forms of smoothing, but far more complex methods, such as using random components in regressions on time (e.g., [START_REF] Ingvartsen | To what extent do variabilities in hormones, metabolites and energy intake explain variation in milk yield?[END_REF] or using Kalman filters [START_REF] Kalman | A new approach to linear filtering and prediction problems[END_REF], are becoming increasingly common.

In this study, we used smoothing to identify disturbances rather than eliminating them. We illustrated the approach on milk production records from a controlled "off-feed" experiment, and the results indicate that differential smoothing can be a useful tool for quantifying biological disturbances in animal performance. Further, biologically meaningful features can be extracted from the smoothed curves without the need for a priori assumptions about the shape of the lactation curve. As presented here, the method is particularly suited for off-line usage (when complete deviation profiles are available). It provides a means to quantify the consequences of disturbing factors, such as disease and feeding disturbances, as well as allowing hypotheses about the biological nature of the response to be explored. If the primary goal is to develop on-line monitoring systems to detect when the physiological balance of an animal is being disrupted and intervention by the farm manager may be needed, additional capabilities such as dynamic update of the time series and forecasting are required. Forecasting can be simple (e.g., based on the difference between the latest measure and a rolling baseline; [START_REF] Chagunda | A biological model for detecting individual cow mastitis risk based on lactate dehydrogenase: Model description[END_REF], or more complex (e.g., using nonparametric smoothing with latent factor models; [START_REF] Shen | On modeling and forecasting time series of smooth curves[END_REF], or using multivariate measures to quantify degree of infection [START_REF] Højsgaard | Quantifying degree of mastitis from common trends in a panel of indicators for mastitis in dairy cows[END_REF].

The amount of time and money that a farmer should invest in treating or preventing a disease will depend, in part, on the economic losses that disease causes (i.e., the size and duration of the production disturbance; [START_REF] Fourichon | Effect of disease on reproduction in the dairy cow: A meta-analysis[END_REF]. Further, if a method for quantifying the disturbance is developed using clinical disease cases, then it may be extended to identify subclinical cases, which are by definition more difficult to identify from classical symptoms alone [START_REF] Sloth | Potential for improving description of bovine udder health status by combined analysis of milk parameters[END_REF]. In this context, capturing disturbances (i.e., deviations from the underlying long-term trends) has been shown to provide early identification of onset of diseases, such as ketosis [START_REF] Nielsen | Predicting the risk of ketosis in dairy cows using on-line measurements of beta-hydroxybutyrate in milk: A biological model[END_REF] and mastitis [START_REF] Chagunda | A biological model for detecting individual cow mastitis risk based on lactate dehydrogenase: Model description[END_REF]Kamphuis et al., 2008b).

The approach of using the biological information in short-term disturbances has been greatly facilitated by the increasing availability of reliable, frequently measured, time-series data. It is now common for milk yield to be measured at every milking. Another example is the use of weigh platforms in milking systems that provide BW records 2 or more times a day. With this type Figure 8. Milk loss [defined as the difference between the milk level at the trough (T) of the deviation profile and the corresponding potential level (Q) on the quantile envelope, which is a positively offset-smoothed curve that represents the undisturbed phenotypic potential yield] vs. the milk yield at the preceding peak (P pre in Figure 5). Encircled cases are from the off-feed challenge experiment. The ■ is the first deviation in Figure 4 (at ~140 d from calving), which corresponds to a confirmed case of mastitis.

of technology and high measurement frequency, it becomes possible to distinguish biologically related disturbances from random measurement error.

Although demonstrated here using milk-yield data, the proposed approach is, in principle, generalizable to other biological time-series data. The increasing development of in-line measurement technology on the farm both affords the opportunity to develop such tools and presents the challenge of extracting the key information from such large quantities of data.

Figure 1 .

 1 Figure 1. An example of different degrees of smoothing applied to a lactation curve of milk-yield records. The different degrees of smoothing are obtained by imposing different weights on the roughness penalty term λ (see Eq. 1). Short-term disturbances in milk yield can be detected (λ = 100), as well as the general long-term trend (λ = 10 8 ; i.e., the natural changes in milk yield related to stage of lactation).

Figure 2 .

 2 Figure 2. The use of residual filtering to offset bias in the yield records. An initial smoothing can indicate the data points that give large negative residuals (encircled points), which can be discarded from a second smoothing. A slightly increased and smoother curve is found with the retained points.

Figure 3 .

 3 Figure3. The use of quantile regression to offset bias in the yield records. The resulting curve (λ = 10 6 ) represents undisturbed phenotypic potential when smoothing using data points within 60 and 90% quantiles.

Figure 4 .

 4 Figure 4. Top panel: an example of differential smoothing to obtain an offset curve representing undisturbed phenotypic potential (quantile envelope) and the much rougher curve (λ = 2,500), which captures biological disturbances. First and second derivatives of the rough curve can be estimated at any time point along the lactation curve. These are shown in the middle and bottom panels, respectively.

Figure 5 .

 5 Figure 5. Possible features for detecting and quantifying deviations in milk yield. Each deviation profile has a trough (T), which splits it into pre-and post-trough periods that correspond to response and recovery periods in milk yield. The trough occurs where the first derivative crosses 0 from negative to positive. Two peaks (P pre and P post ) can be located on either side of T where the first derivative crosses 0 from positive to negative. The pre-trough inflection point (I pre ) corresponds to the minimum value of the first derivative (V min ), and the post-trough inflection point (I post ) corresponds to the maximum of the first derivative (V max ). The extreme values of the second derivative of the smooth function are denoted by A max , A minpre , and A minpost , respectively. The potential level (Q) from the quantile envelope is an estimate of what the milk yield would have been in the absence of the challenge.

Figure 7 .

 7 Figure 7. Examples of milk yield curves from 3 cows with the off-feed challenge at different stages of lactation. The roughly smoothed curves clearly capture the decline in milk yield during the challenge period for each cow. Other deviations in milk yield can be observed throughout lactations.

Table 1 .

 1 Summary of the profile features of deviations in milk yield provoked by the nutritional challenge in cows (n = 47)

	Item 1	Mean	SD
	First derivative features, kg•d -2
	V min	0.98	0.45
	V max Second derivative features, kg•d -3	0.84	0.33
	A minpre	0.17	0.08
	A max	0.28	0.10
	A minpost	0.13	0.05
	Timing features, d
	Δt(I pre , P pre )	8.48	3.03
	Δt(T, P pre )	15.73	7.49
	Δt(T, I pre )	7.25	7.44
	Δt(I post , T)	5.62	1.33
	Δt(P post , I post )	11.80	7.43
	Δt(P post , T) Milk yield loss, 2 kg•d -1	17.43	7.84
	(Q -T)	7.52	2.38
	1

This study, which was part of the Biosens project, used data from the "On-line data to monitor health status of cows" project. The work was supported by the Danish Ministry of Food, Agriculture and Fisheries, the Danish Cattle Industry via Finance Committee Cattle (Copenhagen, Denmark), and the Faculty of Agricultural Sciences, Aarhus University (Aarhus, Denmark

).2 Corresponding author: marius.codrea@agrsci.dk Received December 2, 2010. Accepted

April 3, 2011.

at INRA Institut National de la Recherche Agronomique on September 28, 2011 jas.fass.org Downloaded from

Codrea et al. at INRA Institut National de la Recherche Agronomique on September 28, 2011 jas.fass.org Downloaded from

Milk yield loss (Q -T) = the difference between the milk level at trough (T) and the corresponding potential level (Q) on the quantile envelope, which is a positively offset-smoothed curve that represents the undisturbed phenotypic potential yield.


D Renaudeau

J L Gourdine

N R St-Pierre

A meta-analysis of the effects of high ambient temperature on growth performance of growing-finishing pigs

Keywords: feed intake, growing pig, growth, meta-analysis, temperature

High ambient temperature (T) is one of the most important climatic factors influencing pig performance. Increased T occurs sporadically during summer heat waves in temperate climates and year round in tropical climates. Results of published experiments assessing the effects of high T on pig performance are surprisingly variable. Thus, a meta-analysis was performed to aggregate our knowledge and attempt to explain differences in the results across studies on the effect of increased T on ADFI and ADG in growingfinishing pigs. Data for ADFI and ADG were extracted from 86 and 80 trials, respectively, from articles published in scientific journals indexed in PubMed, Science Direct, and from proceedings of scientific meetings through November 2009. Data on ADFI and ADG were analyzed using a linear mixed model that included the linear and the quadratic effects of T and BW, and their interactions as continuous, fixed effects variables, and the trial as a random effect factor (i.e., block). In ad-dition, the effects of housing type (2 levels: individual and group housing) and the year of publication (3 levels: 1970 to 1989, 1990 to 1999, and 2000 to 2009) on the intercept and the linear regression term for T (i.e., the slope) were also tested. Results showed that high T had a curvilinear effect on ADFI and ADG and that this effect was more pronounced in heavier pigs. Across T, ADFI was less when pigs were group-housed. The intercept and the regression coefficient (slope) for T were significantly affected by the year of publication. The effect of increased T was greater in more contemporary works, suggesting that modern genotypes could be more sensitive to heat stress than older genotypes of lesser growth potential. In conclusion, pig performance decreases at an accelerating rate as T is increased. The large between-study variability on the effects of high T on pig performance is partially explained by differences in pig BW and to a lesser extent by the year the study was published.

INTRODUCTION

According to Food and Agriculture Organization statistics, more than 50% of world pig production is currently occurring in tropical or subtropical regions [START_REF] Rosegrant | Global food projections to 2020: Emerging trends and alternative futures[END_REF]. Despite many challenges faced by the pig industry in these regions, it is expected that pig production in developing countries will sustain future growth [START_REF] Delgado | Livestock to 2020: The next food revolution. Vision initiative food, agriculture, and the environment[END_REF]. Heat stress is a major source of production losses in pig production. For example, the economic losses sustained by the US pork industry from heat stress were estimated at about $300 million per year [START_REF] St-Pierre | Economic losses from heat stress by US livestock industries[END_REF]. If the predictions of global climate change and the associated projected rise of ambient temperature (T) materialize (IPCC, 2007), the heat-stress-related problems in livestock production will increase in the future.

Because of their low capacity for dissipating body heat, pigs rely more on reducing metabolic heat production to maintain a constant body temperature in hot conditions than other domesticated species. The reduction in voluntary feed intake in heat-stressed pigs is considered as the main adaptation to reducing heat production. This reduced feed intake has a direct negative impact on growth performance. Many studies have been published on the effect of high T on the performance of pigs. In a qualitative review, Le Dividich et al. (1998) reported that change in feed consumption varied from 40 to 80 g/d per degree Celsius between 20 and 30°C. This large variability across studies could be explained by differences in animal characteristics (breed, BW, physiological status, sex), environmental conditions (housing, feed composition, management, sanitary status), other environmental factors (i.e., relative humidity) and experimental designs (number of pigs, number of temperature treatments, duration of exposure), or a combination of these variables. In practice, all these factors cannot be simultaneously studied within a single experiment. Thus, there is a need to summarize research findings across all the published studies to give a more accurate estimation of the magnitude of the effects of heat stress on pig performance over a large range of environmental and breeding situations.

The objectives of this study are to 1) quantitatively assess the effect of increased T on pig performance, and 2) identify factors modulating the magnitude of the identified response functions. The meta-analysis presented herein focuses entirely on growing-finishing pigs (i.e., greater than 10 kg of initial BW).

MATERIALS AND METHODS

Animal Care and Use Committee approval was not obtained for this study because no animals were used.

Database Description

A database containing data on animal and housing characteristics, dietary composition, ADFI, and ADG in growing-finishing pigs under thermal stress was compiled from 71 published papers in scientific journals indexed in PubMed, Science Direct, and from proceedings of scientific meetings that occurred before December 2009. To be included in the final database, studies had to meet the following criteria: 1) research methods (housing, feeding management) were adequately described, 2) growing-finishing pigs that had initial mean BW greater than 10 kg, 3) animals had free access to feed and water during the experiment, 4) experiments were conducted under controlled T conditions, 5) dietary CP was greater than 12%, 6) the duration of the experiment exceeded 7 d, and 7) at least 2 temperature treatments were used in the experiment. Forty-seven studies reporting 86 trials with 202 temperature treatment means met the criteria for ADFI. The corresponding values for ADG were 43 studies, 80 trials, and 182 temperature means. The main variables in the database regarding animal and housing characteristics, diet composition, and animal responses are reported in Table 1. The response (dependent) variables were ADFI (g/d or g/kg BW 0.60 per d), ADG (g/d), and feed conversion ratio (FCR, kilograms of feed/kilogram of BW gain). Values for all variables could not be determined for all observations. Therefore, the number of observations used for statistical analyses differed between response variables. In some instances, some records were incomplete or not reported uniformly, requiring calculation from the reported data. When a study did not report the outcome for all variables and when it was not possible to calculate a value from the reported data, missing values were considered as missing at random. When the ME content of a diet was not reported, it was estimated using the DE content of the diets, the ME/DE ratios calculated from INRA feed composition tables [START_REF] Sauvant | Tables de Composition et de Valeur Nutritive des Matières Premières Destinées aux Animaux d'élevage[END_REF], and the description of the feedstuffs used in the experimental diets.

Statistical Analyses

Data were analyzed according to [START_REF] St-Pierre | Invited review: Integrating quantitative findings from multiple studies using mixed model methodology[END_REF], which takes into account the random effect of the study and its possible interaction with fixed effect factors. The MIXED procedure (SAS Inst. Inc., Cary, NC) was used to solve the following base model:

Y ij = b 0 + b 1 T + b 2 T 2 + s i + a i T + e ij , [1]
where Y ij is the observed outcome for the dependent variable Y in the ith experiment at temperature level T, i = 1, ……n (n = 86 or 80, depending on the dependent variable), b 0 is the overall intercept, T is the ambient temperature (°C), b 1 and b 2 are the regression coefficients for T and T 2 (fixed effects), s i is the random effect of study (i.e., an intercept shift for each study), a i is the random interaction of study × T (i.e., a linear term shift for each study), and e ij is the residual error. In Eq.

[1], it is assumed that

s a e and s e i s 2 i a 2 ij e 2 i ij ≈ ≈ ≈ N N N ( , ), ( , ), ( , ), ( , )
.

0 0 0 0 σ σ σ Cov =
The random effects of the study on the quadratic regression coefficient of T (i.e., the study × T 2 interaction) was not included in the model because only 2 T levels were used in most of the published works (68%), thus leaving too few observations to estimate a variance component with reasonable accuracy.

Because the data were extracted from numerous published studies, each with their own experimental design, it was important to properly weigh the observations (the reported means) according to their relative precision (i.e., their SE). Therefore, observations were weighted by the number of animals in each trial to take into consideration the unequal residual variance among trials [START_REF] Sauvant | Meta-analyses of experimental data in animal nutrition[END_REF]). An unstructured variance covariance matrix (TYPE = UN in the MIXED procedure) was used to model the random intercepts and slopes, thus allowing for random covariance between slope and intercepts across the random studies [START_REF] St-Pierre | Invited review: Integrating quantitative findings from multiple studies using mixed model methodology[END_REF].

As previously reported [START_REF] Nienaber | Thermal environment effects of growing-finishing swine. I. Growth, feed intake and heat production[END_REF]Quiniou et al., 2000a), the effects of T on ADFI and ADG could be affected by the average BW during an experiment. Consequently, the basic model [1] was augmented as follows to account for the effect of BW on animal response to T:

Y ij = b 0 + b 1 T + b 2 T 2 + c 1 W + c 2 W 2 + c 3 TW + s i + a i T + e ij , [ 2
]
where W is the mean BW during the experiment (kg), and c 1 , c 2 , and c 3 are regression coefficients (fixed effects). Other continuous, independent variables were added to model [2] to assess their possible linear association with animal performance under thermal stress. Factors related to housing conditions (relative humidity, daily T range) and feed composition (diet ME and CP contents) were sequentially added and tested as linear fixed effect covariates in model [2].

Figure 1 shows the distribution of the studies according to their year of publication. Based on this distribution, observations were classified in 3 yr of publication groups: 1) before 1990 (n = 19), 2) between 1990 and 1999 (n = 14), and 3) after 2000 (n = 14). The effects of year of publication (3 levels), sex (5 levels: female, male, barrows, mixed of females and castrated males, and not reported), and housing conditions (2 levels: individual, and grouped housed) were added as fixed effects factors to model [2], as well as their interaction with T and T 2 . Terms were sequentially removed from the full model (i.e., model [2] with the addition of all continuous covariates, discrete independent variables, and their 2-way interactions with T and T 2 ) using the algorithm proposed by [START_REF] Oldick | Estimation of microbial nitrogen flow to the duodenum of cattle based on dry matter intake and diet composition[END_REF]. Goodness of fit was determined by the smallest root mean square error (RMSE) and the smallest value of the Bayesian information criterion. Model adequacy was assessed using plots of residuals (observed minus predicted) against predicted values of Y to test for linear prediction bias [START_REF] St-Pierre | Reassessment of biases in predicted nitrogen flows to the duodenum by NRC 2001[END_REF]. A correct graphical representation of statistical results in 2 dimensional plots from models of higher dimensional spaces due to the random effect of study requires that the observations on the dependent variables used in the plot be adjusted to take into account the random effect of the study [START_REF] St-Pierre | Invited review: Integrating quantitative findings from multiple studies using mixed model methodology[END_REF].

The quadratic effect of T was significant (P < 0.05) for all dependent variables studied, indicating a nonlinear effect of T on all dependent variables. The exact shape of the true, but unknown relationship is probably not a simple quadratic function. Physiological theory would indicate that the nonlinear relationship should consist of a plateau with a threshold change once T reaches a critical threshold temperature (CT, °C). Thus, a second analytical approach used a nonlinear model that included a CT. Under this model, ADFI [START_REF] Sauvant | Tables de Composition et de Valeur Nutritive des Matières Premières Destinées aux Animaux d'élevage[END_REF].

3 Pigs were individually housed in 32 of the 44 studies. 4 Expressed as a percentage of total observations collected, 41.6, 29.0, 11.6, and 1.1% of the observations were obtained from barrows, from a mix between barrows and females, from females, and from boars, respectively. For 17.3% of total observations, the sex type was not reported.

5 Average BW during the trial.

6 Calculated as ADFI/ADG, both expressed in kilograms per day. and ADG are assumed to remain nearly constant as T is increased as long as T < CT (Figure 2). To model the transition between the plateau when T < CT and the decline in ADFI and ADG when T > CT, a model adapted from [START_REF] Koops | Applications of a multiphasic growth function to body composition in pigs[END_REF] was used:

Y ij = a W b + e ij , [3]
where Y ij is the observed value of the dependent variable (ADFI or ADG) adjusted for the random effect of the study i (the empirical BLUP from the model [2]), b is the exponent relating W to Y, and W is the average BW during the trial, and e ij is the residual error, assumed approximately N(

). 0, e 2 σ In Eq. [3], the parameter a is itself a function of T and CT:

a = y 0 + v 1 s ln {1 + exp[(T -CT)/s]}, [4]
where y 0 is the value of a for T below the CT, v 1 is the linear component of the slope of the decline in Y when T > CT (g/d per °C), and s determines the smoothness of the transition around CT.

In the current study, s was fixed at 0.5, forcing a virtually instantaneous transition between the 2 parts of the function around CT. According to the model developed by [START_REF] Bruce | Models of heat production and critical temperature for growing pigs[END_REF], the relationship between CT and pig BW is not linear but semi-logarithmic. Consequently, we modeled the relationship between CT and BW using this equation:

CT = c + d ln(1 + W), [5]
where c is an intercept term (i.e., the value of CT when W = 0), and d is the marginal change of CT with respect to ln(1 + W). Parameters of the model expressed by [3], [4], and [5] were estimated using the NLIN procedure of SAS. The residual SD (g/d) and adjusted regression coefficients were calculated according to [START_REF] Gu | Growth, development, and carcass composition in five genotypes of swine[END_REF].

RESULTS AND DISCUSSION

Descriptive Statistics of the Data

Descriptive statistics for the data are reported in Table 1. An average of 18.4 pigs was used per trial, but there was a considerable variability in the number of pigs used across studies (range of 3 to 128 pigs/trial). The average daily ambient T ranged from 14 to 36°C, with a mean of 26.2°C across all studies. Trials averaged 45 d in length, with a minimal and a maximal value of 8 and 152 d, respectively. The average BW of pigs ranged from 14.0 to 101.5 kg, and the number of pigs per pen varied from 1 to 16. Average values across all trials for ADFI, ADG, and FCR were 1,837 g/d, 702 g/d, and 2.62 kg/kg, respectively.

Voluntary Feed Intake

Figure 3 shows a plot of the uncorrected ADFI vs. T. In this figure, the substantial variation in ADFI across studies is quite apparent. Parameters estimates, the SE, and the RMSE and the estimates of the covariance components for model [2] are reported in Table 2. The highly significant T 2 term provides conclusive evidence of a curvilinear relationship between ADFI and T. In contrast, NRC (1987) suggests that there is a linear relationship between ADFI and T. At W = 50, the function is maximized at T* = 20.2°C. Because most of the experimental observations were made between 20 and 32°C (Figure 3), this should not be interpreted as evidence that ADFI declines when T < T*. The residual plot showed no evidence of any prediction bias (linear or nonlinear) for model ADFI (Figure 4). Most residuals were less than |150| g/d, which is equivalent to about 8% of the mean ADFI. There was a strong relationship between adjusted and measured ADFI (adjusted R 2 = 0.98, Figure 5), indicating that observations within study are very predictable. The adjusted ADFI values are nothing else than the observed values corrected for the study effect. However, the random effects of trial [i.e., the variance due to trials on the intercept (σ s 2 = 181,012) and the linear effect of T (σ a 2 = 208)] were large and differed significantly from zero (P < 0.001). This implies that both parameters in the quadratic function (i.e., intercept and linear term for T) depend largely on specific factors within each study. In such case, this quantitative analysis has produced a model that is more accurate for explaining the observed ADFI within each study. However, predictions of future outcomes would not be very precise mainly because the actual realization of the future study is unknown [START_REF] Sauvant | Meta-analyses of experimental data in animal nutrition[END_REF]. In addition, one can suggest that important unidentified factors, others than those reported in published studies and accounted in the model, have a major impact on the relationship between ambient T and ADFI. In a descriptive review, Le Dividich et al. (1998) showed that high T negatively affects feed consumption in growing and finishing pigs and pointed out a large variability existed among studies regarding the range of decline in ADFI (40 to 80 g•d -1 •°C -1 between 20 and 30°C). As suggested by these authors, this high variability is explained by numerous factors including breed, BW, degree of fatness, diet composition, and T range. In addition, pre-experimental rearing conditions and their potential related effects on the animal response to heat stress during the experimental period could be an additional source of variation. Differences in the experimental protocol between studies (e.g., duration of acclimation period to temperature treatment before the experimental period) could also explain some of this variability [START_REF] Renaudeau | Effect of temperature level on thermal acclimation in large white growing pigs[END_REF]. Lastly, results of the present analysis indicate that the decline in ADFI associated with increased T is in fact greatly affected by the BW of the animals. For example, from the ADFI equation reported in Table 2, the decline in ADFI between 20 and 30°C would average 32 g•d -1 •°C -1 at a BW of 50 kg, and 78 g•d -1 •°C -1 at a BW of 100 kg. These figures are in fact in agreement with the range of values summarized by Le [START_REF] Le Dividich | Thermoregulation[END_REF].

As opposed to looking at the ADFI decline over a range of T as done in a descriptive review, the use of a function to represent the quantitative relationship between ADFI and T allows the estimation of the instantaneous rate of decline, the slope calculated as the partial derivative of the function with respect to T. This partial derivative represents the slope of the tangent line to the function (i.e., the instantaneous rate of decline in ADFI at a given T). For a 50-kg pig, values of the partial derivative at 25 and 30°C were -32.3 and -56.3 g•d -1 •°C -1 , respectively. In other words, the extent to which T affects the change in ADFI depends on the T, as found in prior research [START_REF] Nienaber | Thermal environment effects of growing-finishing swine. I. Growth, feed intake and heat production[END_REF]Quiniou et al., 2000c;[START_REF] Renaudeau | Effect of temperature level on thermal acclimation in large white growing pigs[END_REF]. Because the decline in ADFI is the most effective mechanism to decrease heat load [START_REF] Collin | Effect of high temperature on feeding behaviour and heat production in group-housed young pig[END_REF], the reduction in feed consumption of pigs under heat stress appears to be a key mechanism to maintain thermal equilibrium especially when ambient T increases noticeably above the upper limit of the thermoneutral zone. In our study, the linear term in the quadratic function varied significantly across studies (i.e., the significant study × T effect). This implies that the rate of decline in ADFI with T differed across studies. To illustrate this point, the 95% confidence interval for the slope of the tangent line can be calculated. From this calculation, there was a 0.95 probability that the instantaneous decline in ADFI at 25°C was between -35.5 and -30.1 g•d -1 •°C -1 , and between -58.5 and -54.1 g•d -1 •°C -1 at 30°C, respectively, for a 50-kg pig.

Under practical housing conditions and especially under tropical conditions where buildings are often semiopen, pigs are usually subjected to fluctuation in T throughout the day and across days. Consequently, the application of results collected in closely controlled and constant environment may be inappropriate when applied to variable T conditions. In fact, some evidences show that pigs are totally or partially capable of maintaining feed consumption when exposed to a cycling diurnal T challenge [START_REF] Morrison | Effect of diurnal air temperature cycles on growth and food conversion in pigs[END_REF]Quiniou et al., 2000b). In the present quantitative analysis, the daily range in ambient T did not explain sufficient variability to be retained in the model. However, this result may be explained by the insufficient number of trials in the database that used cyclic T (less than 16% of the total).

In pigs, feed intake is also influenced by other climatic factors including relative humidity (RH) and air renewal, but to a lesser extent than ambient T. Above 80% RH, the effects of heat stress on ADFI are magnified due to a decrease of the rate of evaporative heat loss [START_REF] Morrison | Effect of humidity on swine at high temperature[END_REF][START_REF] Granier | Effect of the humidity level of ambient air (temperature 28 deg C) on the growth performance of growing-finishing pigs[END_REF]. In the data set, RH was measured in only 42.6% of the studies, and in most instances (95.7%) the RH was below 80%. This explains why the effect of RH and its interaction with high ambient T was not significant in the present work. Clearly, further work is needed to quantify the effect of RH on pig performance under hot climate.

The quadratic equation modeled a smooth relationship between ADFI and T, without any break point temperature threshold. As pointed out earlier, the prevailing theory on the physiology of heat stress emphasizes a temperature threshold known as critical temperature. Accordingly, we used a near-plateau linear decline threshold model that allowed the determination of a critical threshold temperature. Parameter estimates and associated statistics for this nonlinear model are presented in Table 3. Based on the work of [START_REF] Collin | Effets de la température ambiante élevée sur le métabolisme énergétique du porcelet[END_REF], a plateau with quadratic decline model was fitted to account for the greater rate of ADFI decrease under very high T. The model [START_REF] Collin | Effets de la température ambiante élevée sur le métabolisme énergétique du porcelet[END_REF] is the variance estimate for the random intercept due to study;

σ a 2
is the estimated variance for the random linear term for T (i.e., the study × T interaction); σ s,a 2 is the covariance estimate between random intercept and slope.

3

The intercept was significantly affected by housing condition (individual vs. group housed; P < 0.01).

4

The intercept was significantly affected by the year of publication (1970 to 1989, 1990 to 1999, 2000 to 2009; P < 0.01).

5

The linear effect of T was affected by the year of publication (P < 0.01).

*Variance or covariance estimate was not significantly different from zero (P > 0.05).

This model, however, did not fit the data better than the simpler threshold and linear decrease model [3]. Its residual SD (183 g/d) was not different that of model [3]; nor was its estimate of CT [CT = 39.9 + 4.10 ln (1 + W)]. Therefore, we concluded that a plateau with linear decline model was sufficient to describe the ADFI response to T. The estimated exponent b relating ADFI to BW was 0.69 in model 3 (Table 3). This value is comparable with the value used by NRC when DE intake was related to BW in growing pigs kept in thermoneutral conditions (i.e., an exponent between 0.50 and 0.70). Based on our fitted model (Table 3) and for a 50-kg pig, ADFI remains approximately constant below 23.6°C and thereafter declines by 25 g•d -1 •°C -1 when T > 23.6°C (Figure 6). In grouped-housed growing pigs (70 kg of BW on average), ADFI decreased steadily by 95 g•d -1 •°C -1 above 25.5°C [START_REF] Huynh | Effects of increasing temperatures on physiological changes in pigs at different relative humidities[END_REF]. First, the discrepancy between both studies could be explained by difference in BW. However, in this later experiment, pigs were submitted to 9 successive T levels (from 16 to 32°C) for only 1 d without a previous acclimation period, which could explain the greater effect of T above CT on ADFI reported by these authors compared with our results. In fact, it has been shown that the reduction in ADFI during thermal acclimation occurs mainly within the first 2 to 3 d of exposure [START_REF] Renaudeau | Effect of temperature level on thermal acclimation in growing pigs estimated using a non-linear function[END_REF].

According to the results from the mixed model analysis (Table 2), the significant interaction between T and average W (P < 0.001) means that heavier pigs are more sensitive to high ambient T than lighter pigs. Based on the resulting equation, it is estimated that on average (i.e., across studies) the reduction in ADFI from 20 to 30°C are 9, 32, and 55 g•d -1 •°C -1 at 25, 50, and 75 kg of BW, respectively (Figure 5). Similar results were previously reported by Quiniou et al. (2000a). According to the results from the plateau and linear decline model (Table 3), CT for ADFI decreased as the BW increased following this relationship: CT = 40.9 -4.4 ln(1 + BW).

[6] Using Eq. [6], the threshold T at which ADFI begin to decline drops from 30.3 to 21.0°C between 10 and 90 kg of BW (Figure 7). These results are in agreement with a decrease of the upper limit of the thermal neutral zone with increasing pig BW [START_REF] Holmes | The influence of climatic variables on energy metabolism and associated aspects of productivity in the pig[END_REF]. The greater susceptibility of heavier pigs is mainly related to their increased metabolic rate at thermoneutrality in relation to their relatively high feed intake. In addition, heavy pigs have much smaller ratio of surface area to mass and a greater thermal insulation (increased subcutaneous tissue content) than young, light pigs [START_REF] Bruce | Models of heat production and critical temperature for growing pigs[END_REF]. Consequently, their ability to dissipate heat is theoretically less than that of piglets, which could partly explain their greater sensitivity to increased ambient T.

The housing conditions (individual vs. group) significantly affected the intercept of the mixed model for ADFI (-1,331 vs. -1,445 g/d). Therefore, across T, ADFI is less by an average of 114 g/d when pigs are group housed. This result can be attributed to differences in competition at the feeder [START_REF] Hyun | Effect of group size and feeder type on growth performance and feeding patterns in finishing pigs[END_REF]. However, housing conditions did not interact with the linear or quadratic terms associated with T. Thus, the intake difference between the 2 housing conditions does not appear to change with ambient T.

Growth Rate and Feed Conversion

Figure 8 shows a plot of the uncorrected ADG and FCR vs. T, with observations from a given trial connected by a common line. As for ADFI, the trial effect appears large for both ADG and FCR. Parameter estimates for the mixed model analysis of ADG and FCR are reported in Table 2. The variance components for study and study × T are relatively large for both dependent variables, indicating that many unknown and unaccounted for factors, specific to each study, remain to be identified. Residual plots for model predictions and the relationship between model predicted and experiment-adjusted ADG and FCR are shown in Figures 9 and10, respectively. According to Figure 9, there was no evidence for a prediction bias for ADG prediction (P > 0.05) even though 4 treatments means were overestimated (strongly negative residuals). However, there was an apparent positive slope bias for FCR prediction (P = 0.04), indicating that standard residuals tended to be positive at a high level of predicted 3. 3. FCR (Figure 9). Recall that model [2] was fitted using a weight on the observations equal to the number of pigs in each treatment mean. Algebraically, the method used in PROC MIXED guarantees that the sum of the weighted residuals is equal to zero (i.e., the average of the weighted residuals is equal to zero), and that the slope of the regression between the weighted residuals and the predicted values is also equal to zero [START_REF] St-Pierre | Reassessment of biases in predicted nitrogen flows to the duodenum by NRC 2001[END_REF]. Thus, the slight positive slope observed when regressing the standard residuals (as opposed to the weighted residuals) on the predicted values of FCR in Figure 9 only means that the weighting scheme used produced parameter estimates that were slightly, but significantly different than those that would be obtained if the observations had not been weighted.

The plot of predicted and observed ADG corrected for the trial effect vs. T suggests that the model fits the data set well except at the lower T (Figure 10). The RMSE for ADG and FCR predictions (217 g/d and 0.99 kg/kg, respectively) were high compared with the average ADG and FCR of the data set (707 g/d and 2.62 kg/kg, respectively; Table 2). As discussed for ADFI, these increased RMSE reflected an increased random variation induced by trial within study effect.

Based on the parameter estimates for the mixed model of ADG (Table 2), the estimated reduction in ADG for a 50-kg BW pig is about 18 g•d -1 •°C -1 when T is raised from 20 to 30°C. Under this range of T, FCR would remain nearly constant at a ratio of 2.70, indicating that the decreased ADG associated with heat stress is primarily a result of a decrease in feed intake. Therefore, the use of techniques that reduce the effect of heat stress on ADFI may be beneficial to maintaining growth performance under heat stress. At a very high T level, the FCR showed a slight increase (+0.2 kg/kg from 30 to 36°C), suggesting that pigs becomes less efficient in using feed for growth under severe heat stress conditions (Figure 10). It is unclear whether the marginal efficiency for growth is affected by severe heat stress as well.

In agreement with the effect of T on ADFI, the response of ADG to increased T was also curvilinear. At 25 and 30°C, the instantaneous rates of ADFI change were -10.9 and -24.6 g•d -1 •°C -1 , respectively, for a 50-kg-of-BW pig. The 95% confidence intervals were very narrow and ranged between -11.9 and -9.9 g•d -1 •°C -1 and between -25.6 and -23.5 g•d -1 •°C -1 at 25 and 30°C, respectively. Similarly, [START_REF] Nichols | Effect of temperature on performance and efficiency of finishing swine[END_REF], Nienaber and[START_REF] Nienaber | Performance of growing finishing swine in response to the thermal environment[END_REF][START_REF] Nienaber | Thermal environment effects of growing-finishing swine. I. Growth, feed intake and heat production[END_REF] reported that the extent to which high T affects growth performance depends on the T level.

Based on the parameter estimates for the mixed model (Table 2), the effect of increased T on ADG from 20 to 30°C is 2-fold greater at 75 than at 25 kg (25 vs. 11 g•d -1 •°C -1 ). According to the plateau and linear decline model for ADG, CT declines from 29.3°C at 10 kg of BW to 22.9°C at 90 kg (Figure 7). This matches the results obtained for ADFI and indicates that older, heavier pigs are more susceptible to high ambient T than young pigs. According to Figure 7, the CT values for ADG and ADFI are quite similar at BW less than 40 kg. Above this BW, the CT value for ADG becomes noticeably greater than for ADFI. In young pigs, the energy requirement for maximal growth usually exceeds the ad libitum-energy intake. Consequently, the reduced feed intake under heat stress has a direct negative effect on growth performance. In contrast, the greater energy consumption relative to requirements in heavier pigs explains the reduced CT for ADG than for ADFI in those pigs.

The intercept and the linear term for T in the equation for the mixed model of ADG (Table 2) The intercept, but not the linear term for T in the equation for the mixed model of FCR (Table 2), was affected by the year of publication. The effect of year of publication on the intercept of this equation was 4. 57, 4.32, and 4.06 for works published from 1960 to 1989, from 1990 to 1999, and from 2000 to 2009, respectively. Using a standard 50-kg pig housed at 20°C the mixed model equation indicates that the ADG was much greater and the FCR less in reports published from 2000 to 2009 than in those published from 1960 to 1989 (1,000 vs. 785 g/d and 2.0 vs. 2.4 kg/kg, respectively; P < 0.01). Intermediate values were found for studies published from 1990 to 1999 (885 g/d and 2.2 kg/kg, respectively). Between 20 and 30°C and at an average BW of 50 kg, the decline in ADG for each publication period was estimated at 12, 18, and 25 g•d -1 •°C -1 in works published from 1960 to 1989, 1990 to 1999, and from 2000 to 2009, respectively. The change in FCR from 20 to 30°C (+0.05 kg/kg) was similar across all years of publication. Even though many factors could be involved (e.g., difference in breeding conditions), the greater effect of increased T on growth performance in recent works could be explained by an improvement in the genetic potential for growth in pigs. In other words, genetic selection aimed at increasing the amount and efficiency of lean growth in pigs would lead to animals with a reduced capacity for coping with heat stress. [START_REF] Nienaber | Genetic and heat stress interaction effects on finishing swine[END_REF] observed that the threshold T at which heat stress affects performance is reduced in increased lean growth potential pigs compared with moderate growth genetic lines. This increased sensitivity of modern pigs to high ambient T is probably related to their greater metabolic heat production associated with greater production. In addition, according to [START_REF] Noblet | Metabolic utilization of energy and maintenance requirements in growing pigs: Effects of sex and genotype[END_REF], the maintenance requirements are also greater when synthetic line pigs are compared with conventional Large White pigs in connection to breed variations in fasting heat production due to change in weights of metabolically active body compartments such as viscera and lean mass.

In Table 2, dietary CP was found to affect the intercept of the equations relating ADG or FCR to ambient T (Eq. [3] and [4]); the linear term for T, however, was not affected by CP. An increase in dietary CP has a positive effect on ADG and feed efficiency. In most of the published studies assessing effects of CP level on performance under heat stress, the low CP diets were not supplemented with synthetic AA to meet the AA requirement for growth. This would explain why pigs fed reduced CP diets had poorer growth performance than those fed normal diets.

In conclusion, this analysis provides quantitative relationships between major performance variables and increased T. This study shows that factors other than those traditionally studied can interact with ambient T to affect performance. It is assumed that the animal sanitary status, climatic factors other than temperature, and animal performance before starting the experiment could explain the large variability observed for the effects of T among studies. Future work is needed to more precisely quantify the relative importance of these factors and to improve the accuracy of the model predicting the effect of increased T on growth performance of pigs. This may become even more important for pig production under tropical countries and in the context of potential climate change and mitigation strategies to reduce the associated impact on pig productivity.

Figure 1 .

 1 Figure 1. Histogram showing the frequency distribution of studies according to the year of publication.

Figure 2 .

 2 Figure 2. Graphical representation of the model used for the response of ADFI and ADG (Y) to ambient temperature change around a critical temperature point (CT, °C). y0 and v1 = the value of a below the CT; v1 = the linear component of the slope of the decline in Y above CT.

  is as follows: Y = a × W b , with a = y 0 (1 -s ln{1 + exp ((T -CT)/s)]}/(T -CT) + (y 0 + v 1 {T -CT} + v 2 {T -CT}²) × (s ln{1 + exp[(T -CT)/s)]}/{T -CT}).

Figure 3 .

 3 Figure 3. Effect of ambient temperature on ADFI in growingfinishing pigs (47 studies, 86 experiments, 3,714 pigs).

  Abbreviations and units: W, average BW (kg); FCR, feed conversion ratio (kg of ADFI/kg of ADG); T, ambient temperature (°C); CP (g/100 g); RMSE: root mean square error (i.e., the square root of the estimated residual variance of the model). 2 σ s 2

Figure 4 .

 4 Figure 4. Plot of residuals (observed -predicted) against predicted ADFI from the mixed model analysis. The line represents the regression of residuals on predicted ADFI [Y = -12.62 (13.85) + 0.0062 (0.0071) × predicted ADFI; R 2 = 0.003; P > 0.05].

Figure 5 .

 5 Figure 5. Average daily feed intake vs. model-predicted ADFI (solid line) in response to ambient temperature (solid line calculated from the Eq. [1] for an average BW of 50 kg).

Figure 6 .

 6 Figure 6. Effects of ambient temperature and pig BW on ADFI and ADG. The ADFI and ADG responses were calculated using the nonlinear models reported in Table3.

Figure 7 .

 7 Figure7. Effect of pig BW on the critical temperature for ADFI and BW. Responses were calculated using the nonlinear models reported in Table3.

Figure 8 .

 8 Figure 8. Effect of ambient temperature on ADG and feed conversion ratio (FCR = ADFI/ADG) in growing-finishing pigs (43 studies, 80 experiments, 3,609 pigs).

Figure 9 .

 9 Figure 9. Plot of residuals (observed minus predicted) against predicted ADG and feed conversion ratio (FCR = ADFI/ADG) from the mixed model analysis (Eq. [1]). The line represents the regression of residuals on predicted ADG [Y = -12.6 (7.5) + 0.017 (0.010) × predicted ADG; R 2 = 0.015; P > 0.05] or on predicted FCR [Y = -0.062 (0.034) + 0.026 (0.012) × predicted FCR; R 2 = 0.026; P = 0.04].

  were significantly influenced by the year of the study publication. The effect of year of publication on the intercept of this equation was -892, -786, and -489 g/d, for works published from 1960 to 1989, from 1990 to 1999, and from 2000 to 2009, respectively. The effect of year of publication on the linear term of the same equation was 72.2, 70.3, and 62.2 g•d -1 •°C -1 , for works published from 1960 to 1989, from 1990 to 1999, and from 2000 to 2009, respectively.

Figure 10 .

 10 Figure 10. Prediction of the ADG and feed conversion ratio (FCR = ADFI/ADG) vs. model-predicted ADG or FCR (solid lines) in response to ambient temperature (solid line calculated from Eq. [2] and [3] for an average BW of 50 kg).

Table 1 .

 1 Summary statistics for the data included in the data set

		No. of	No. of
	Item	studies	observations	Mean	SD	Minimum	Maximum
	No. of pigs/trial	47	202	18.4	18.7	3.0	128.0
	Climatic variable 1
	Average temperature, °C	47	202	26.2	5.6	14.0	36.0
	Daily range, °C	47	202	0.4	1.2	0.0	6.5
	Duration of exposure, d	47	202	45	29	8	152
	Relative humidity, %	47	113	63.3	14.0	30.0	95.0
	Feed composition
	CP, %	47	202	17.6	2.6	12.0	24.8
	ME, 2 MJ/kg	47	202	13.4	0.8	11.4	15.3
	Housing condition 3
	No. of pigs/pen	47	202	2.4	2.4	1.0	16.0
	Animal data 4
	BW, 5 kg	47	202	51.4	24.7	14.0	101.5
	ADFI, g/d	47	202	1,837	672	704	3,652
	ADFI, g/d per kg of BW 0.60	47	202	177	28	107	253
	BW gain, g/d	43	182	702	185	310	1,189
	Feed conversion ratio 6	43	182	2.62	0.73	1.47	4.91

1 In 35 of the 47 studies, temperature was maintained constant throughout the day and for the duration of the trial.

2

When dietary ME values were not reported, estimates were derived either from reported DE values or from diet description and feed composition table

Table 2 .

 2 Equations for polynomial regression of response of ADFI, ADG, and feed conversion ratio to ambient temperature and average pig BW 1

	Covariance component 2
		2	s
		σ
		RMSE
		P-value
	Parameter	SE
		Estimates
	Independent	variable
		Dependent variable

Corresponding author: david.renaudeau@antilles.inra.fr Received July

20, 2010. Accepted January 31, 2011.

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