Effect of Heat Stress on Lactating Sows

Transcription

1 NCSU Statistics Department Consulting Project Effect of Heat Stress on Lactating Sows Client : Santa Mendoza Benavides, Department of Animal Science Consulting Team: Sihan Wu, Bo Ning Faculty Advisor: Dr.Bloomfield April Introduction The consulting project studies the effect of high ambient temperature and humidity on feed intake of lactating sows based on data collected from a commercial farm. In particular, the goal is to find the thresholds of temperature and humidity above which sows will be most stressed, and to study the behavior above such thresholds. 1

2 2 Background Seasonal variation in temperature has significant negative influences on reproductive performance of sows and subsequently profitability. Sows are sensitive to heat stress during the summer.they use reduction in feed intake as a mechanism to control body temperature (Williams, 1998). Past studies have shown that feed intake of sows reduce by 25% when housed at 3 C (Mullan, 1992). Overall, heat stress generates economic losses of $3 million per year (St-Pierre et al, 23). This project studies the effect of heat stress on feed intake of lactating sows in hope of innovating farm management to offset the negative effect caused by high ambient temperature. 3 Data Description The data was collected from a commercial farm in Oklahoma during summer and early fall of 213. It was originally used for another project to study the diet effect of fatty acid on lactating sows. In the study, 48 sows were randomly assigned to 1 diets during 21 days of lactation. The diets consists of 9 experimental diets with two fatty acid additives each at 3 levels, and a control diet without fatty acid additives. The daily feed intake of each sow was measured during lactation. Sows were divided into 21 groups based on their start dates of location. Those with similar start dates are arranged into the same group. Ambient temperature and humidity were recorded every 5 minutes for each group. Weight of each sow was recorded 1-2 days before farrow, at the begining and the end of the lactation. The sows in the study were on the first, third, fourth, or fifth parity. Parity stage is the number of litters sows delivered. Since sows with high parity in general have different physical characteristic from those with low parity, the second parity sows were purposedly excluded from the study to separate the low parity group from high parity 2

3 groups. To eliminate the effect of litter size, each sow was assigned 12 piglets. Before we fit the models, exploratory data analysis was performed to evaluate data. Some data with values out of physical bounds, such as humidity measurements exceeding 1%, are removed. From a summary plot of the maximum and minimum of daily temperature and humidity over the experiment period, we observe significant drops of both temoerature and humidity after day 33 of the calender year. This conincides with the time that farm adjusting room control facility in early fall. Thus we deleted the small portion of data after day Linear Mix Effect Model Using Summary Statistics Initially, it is hard to come up an idea to incorporate the 5 minutes observations of temperature and humidity into the model. To have a good understanding of the effects of temperature and humidity on feed intake, we fit linear mixed effect models using the summary statistics. The summary statistics being explored are daily minimum, daily average, and daily maximum of temperature and humidity. In the first model, only summary statistics of temperature are included. The farm where the data was collected is regulated by thermostats. When barn is hot during the day, the farm uses sprinkler and fans to cool down the environment and to pull the air out. The humidity decreases subsequently. This is an affordable strategy to comfort the sows during the summer. Figure 4.1 shows that ambient temperature and humidity are negatively correlated during the day, contrary to their positive correlation outdoor. Thus it is reasonable to explore temperature effect before studying its combined effect with humidity. Using AIC for stepwise selection of fixed effects, the best model including maximum 3

4 temperature, average temperature, and their interaction as fixed effects is y i j = β + β 1 AT j + β 2 HT j + β 3 AT j HT j + β 4 parity i j + β 5 W i + ns(lacday) + α i j + γ(α) i j + ɛ i j (4.1) where y i j is the response of feed intake for i th sow on j th day, AT j is the average temperature for j th day, HT j is the maximum temperature for j th day, W i is the weight of sow after farrow and before lactation. 1 For i th sow, ns(lacday) is the nature spline function 2 for lactation days with 8 degree of freedom, α i j is the random effect of group for i th sow on j th day, γ(α) i j is the random effect of sow ID nested in group for i th sow on j th day, ɛ i j N(,σ 2 ) is the random error for i th sow and j th day and the correlation of ɛ follows an AR(1) structure, where cor r (ɛ i j,ɛ i j ) = ρ j j, if i = i and j j, if i i The summary table of the model is in Table 4.1. In this model, LacDay is modeled as a natural cubic spline function with 8 degree of freedom. A natural cubic spline function is a piecewise cubic function passes through given points called knots, and with constraints that the first and second derivative are continuous at the knots. Since it is hard to incorporate all the features of lactation days using a single cubic function, we decide to break down lactation days into 8 stages, and model lacday as 8 segments of piecewise cubic function with 7 interior knots, which is a natural cubic spline function with 8 degree of freedom. From Table 4.1, parity is significant, which suggests low parity group is difference from high parity group. Weight 1 Among the three weights measured for sows, the weight before lactation is chosen for the model according to commercial practice. 2 The reason to apply nature spline function here is because lactation can not be modeled using a polynomial model to feedintake. 4

5 Value Std.Error t-value p-value (Intercept) average Temp high Temp average Temp * high Temp I (parity > 1) weight ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) Table 4.1: Model 1 summary of parameters is also significant, and has a negative relationship with feed intake. The high temperature is not significant and average temperature is at the edge of 95% significant level. In the next step, humidity is added into the model. Among different candidate models, the quadratic model with maximum temperature and average humidity gives the best explanation of variability of daily feed intake. This is consistent with a former study to evaluate the effects of climatic variables on feed intake of lactating sows (Bergsma and Hermesch, 212). The model is, y i j = β + β 1 HT j + β 2 HT 2 j + β 3AH j + β 4 AH 2 j + β 5 parity i j + β 5 W i + ns(lacday) + α i j + γ(α) i j + ɛ i j (4.2) where, HT j is the high temperature for j th day. Table 4.2 summarized the model that includes humidity. From the result, parity and weight both have similar interpretation as in Table 4.1. After humidity is added, high temperature and average humidity both are statistical significant. 5

6 Figure 4.1: Plot of average temperature and humidity over 24 hour period But it is interesting to find that temperature has negative effect on the feed intake in model 4.1 while it becomes positive in the model 4.2. It is hard to find a reasonable explanation between temperature and humidity. Actually, from Figure 4.1, by plotting the temperature and humidity during 24 hours, we find the curves are nonlinear. In order to find out the critical values of temperature and humidity that corresponds to maximum sow feed intake, we need to investigate a nonlinear estimation approach. 6

7 Value Std.Error t-value p-value (Intercept) poly(high Temp, 3) poly(high Temp, 3) poly(average Hum, 3) poly(average Hum, 3) I (parity > 1) weight ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) Table 4.2: Model 2 summary of parameters 5 Nonlinear Model using High Frequency Data 5.1 Incorporating High Frequency data Now that we have some basic understanding of how heat stress affect feed intake from the mixed effect model using summary statistics, we decide to incorporate the high frequency observations of temperature and humidity into the model. We hope to use an exploratory model to find the thresholds of temperature and humidity above which sows will be most stressed. Using the 24-hour observation, we can generate some relavent statistics. For example, a statistics measuring the instensity of temperture over the 24-hour period. s T 1t = T t where T t is the 5 minutes observation of temperature during 24 hour period. The integral 7

8 of s 1t is the area under the temperature curve. Since we do not have continuous data of the temperature, this can be approximated by the 5 minutes observations. There are 288 such observations over a 24 hour period. 288 T t dt T t 288 t=1 Given the temperature threshold T thresh, we can also generate a statistics to measure the intensity of exposure above temperature threshold. Let s T 2t = max(t t T thresh,) Then the integral max(t t T thresh,)dt is the intensity of exposure above temperature threshold. This is the area under the temperature curve and above the threshold line. The intergral can also be approximated by the 5 minutes observations. Similarly, we can generate information from the high frequency data of humidity given a humidity threshold. and s H1t = H t s H2t = max(h t H thresh,) 8

9 5.2 The Conditional Model To incorporate high frequency data, we consider a component S(T t, H t ) of temperature and humidity using the tensor product of (1, s T 1t, s T 2t ) (1, s H3t, s H4t ), such that β 1 S(T t, H t )dt = = I β 1 γ i s i (T t, H t )dt i=1 I β i i=1 = β 1 + β 5 s i (T t, H t )dt s T 1t dt + β 2 s T 1t s H1t dt + β 6 s T 2t dt + β 3 s T 1t s H2t dt + β 7 s H1t dt + β 4 s H2t dt s T 2t s H1t dt, (5.1) given the thresholds for temperature and humidity, we can fit a linear mixed effect model using integrated temperature and humidity stress as a predictor of feed intake, where y i j T thresh, H thresh = β + β 1 S(T t, H t )dt + β 2 parity i j + ns(lacday) + I parityi j >1 ns(lacday) (5.2) + β 3 W i + α i j + γ(α) i j + ɛ i j where T thresh and H thresh are thresholds for temperature and humidity. In the model, β 8 s T 2t s H2t dt was omitted based on AIC. 5.3 Optimal Threshold For fixed thresholds, the model continues to be linear in parameters. We can obtain the maximum likelihoods for the models given a range of temperature and humidity thresholds. Among all the possible models, the model with the optimized threshold gives the maximum profile likelihood. From sup T thresh A,H thresh B supl(β Y,T thresh, H thresh ) β 9

10 A = [2.,32.5] B = [47.3,9.8] where A and B are the ranges of observed temperature and humidity, we find the optimized thresholds to be T thresh = 28.6, H thresh = The Final Model using Optimized Threshold The final model using optimized threshold can be represented as an linear mixed effect model E(y i j T thresh = 28.6, H thresh = 71.12) = β + β 1 S(T t, H t )dt + β 2 I parityi j >1 + ns(lacday) + I parityi j >1 ns(lacday) + β 3 W i + α i j + γ(α) i j The summary of model parameters is listed in Table 5.1. All terms are significant except for s T 1t. By using this model, we can construct a heat stress index based on expected feed intake at different temperature and humidity, as shown in Figure 5.2. The contour plot shows that when temperature is above 28 C, sows become more stressed as humidity increases. They become most stressed when humidity is above 67%. The effect of humidity is more obvious when temperature is high. When temperature reaches 32 C, sows eat half as much when humidity is above 67% compared to when humidity is under 35%. Note that the contour plot is less accurate around the bondaries since we have fewer observations when temperature and humidity are extreme. Figure 5.3 presents the same result in a 3D plot, where z is the expected feed intake given temperature and humidity. 1

11 Value Std.Error t-value p-value (Intercept) BW I(parity > 1)TRUE ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) ns(lacday, 8) st st sh sh st1sh st1h st2h I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) I(parity > 1)TRUE:ns(LacDay, 8) Table 5.1: Model 3 summary of parameters 11

12 Figure 5.1: Coutour plot of expected feed intake under different temperature and humidity Figure 5.2: 3D plot of expected feed intake under different temperature and humidity 12

13 5.5 Summary From the linear models, we found that weight has negative effect on feed intake, and nature spline function fits well for lactation days. Also, we found there is a significant difference between low partiy and high parity groups. The disadvantage of these models is they cannot give the threshold values for temperature and humidity. The nonlinear model gives critical values for temperature and humidity. By using 5 minutes recording data over 24 hour period, the maximum profile likelihoods method yields critical values for temperature at 28.6 C and critical value of humidity at 71.12%. 6 Discussion The two linear mixed effect models using summary statistics of temperature and humidity gives an insight of how they affect feed intake. Although linear mixed effect models have been conventionally used in other studies, they cannot fulfill the objectives of finding the critial values. The model using high frequency data gives optimized thresholds for temperature and humidity, and reasonable explanation of heat stress impact using optimized thresholds. However, the maximum profile likelihood method does not give confidence intervals for the optimized thresholds. In addition, the exploratory model incoporates basis functions constructed based on intuitive understanding of the the project objectives. It is diffucult to validate such model given the lack of literatures on analysis of similar type of data. One possible but distinctive future approach we suggest is to use functional data analysis for the project. Functional data analysis gives information from curves and distributions. The plots of daily temperature and humidity, for instance, can be treated as functional data. This approach could be explored in the future. 13

14 References [1] Bergsma, R. and Hermesch, S., Exploring breeding opportunities for reduced thermal sensitivity of feed intake in the lactating sow. J. Animal Science, 9:85-98, 212 [2] Mullan, B.P., Brown, W. and Kerr, M., The response of the lactating sow to ambient temperature. Proceedings of the Nutrition Society of Australia, 17, 1992 [3] Pluske, J.R., Williams, I.H., Zak, L.J., Clowes, E.J., Cegielski, A.C. and Aherne, F.X., Feeding lactating primiparous sows to establish three divergent metabolic states: III. Milk production and pig growth. J. Animal Science, Vol. 76, No , April, 1998 [4] St-Pierre, N.R., Gobanov, B and Schnitkey, G., Economic losses from heat stress by US livestock industries. J. Dairy Sci., 86(Supplement): E52-E771, 23 14