Prediction of residual feed intake for first-lactation dairy cows using orthogonal polynomial random regression

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1 J. Dary Sc. 96 : /jds Amercan Dary Scence Assocaton, Predcton of resdual feed ntake for frst-lactaton dary cows usng orthogonal polynomal random regresson G. Manafazar,* T. McFadden,* L. Goonewardene,* E. Okne,* J. Basarab, P. L, and Z. Wang * 1 * Department of Agrcultural, Food and Nutrtonal Scence, Unversty of Alberta, Edmonton, Alberta, T6G2P, Canada Alberta Agrculture and Rural Development, Lacombe Research Centre, 6000 C & E Tral, Lacombe, Alberta, T4L 1W1, Canada Department of Statstcs and Actuaral Scence, Unversty of Waterloo, Waterloo, Ontaro, N2L 3G1, Canada ABSTRACT Resdual Feed Intake (RFI) s a measure of energy effcency. Developng an approprate model to predct expected energy ntake whle accountng for multfunctonal energy requrements of metabolc body weght (MBW), empty body weght (EBW), mlk producton energy requrements (MPER), and ther nonlnear lactaton profles, s the key to successful predcton of RFI n dary cattle. Indvdual daly actual energy ntake and monthly body weght of 281 frst-lactaton dary cows from 1 to d n mlk were recorded at the Dary Research and Technology Centre of the Unversty of Alberta (Edmonton, AB, Canada); ndvdual monthly mlk yeld and compostons were obtaned from the Dary Herd Improvement Program. Combnatons of dfferent orders (1 ) of fxed (F) and random (R) factors were ftted usng Legendre polynomal regresson to model the nonlnear lactaton profles of MBW, EBW, and MPER over 301 d. The F R 3, F R 3, and F R 2 (subscrpts ndcate the order ftted) models were selected, based on the combnaton of the log-lkelhood rato test and the Bayesan nformaton crteron, as the best predcton equatons for MBW, EBW, and MPER, respectvely. The selected models were used to predct daly ndvdual values for these trats. To consder the body reserve changes, the dfferences of predcted EBW between 2 consecutve days were consdered as the EBW change between these days. The smoothed total 301-d actual energy ntake was then lnearly regressed on the total 301-d predcted trats of MBW, EBW change, and MPER to obtan the frst-lactaton RFI (coeffcent of determnaton = 0.68). The mean of predcted daly average lactaton RFI was 0 and ranged from 6.8 to 8.64 Mcal of NE L/ d. Ffty-one percent of the anmals had an RFI value below the mean (effcent) and 49% of them had an RFI value above the mean (neffcent). These results ndcate that the frst-lactaton RFI can Receved January 8, Accepted August 21, Correspondng author: Zhquan.Wang@ualberta.ca 7991 be predcted from ts component trats wth a reasonable coeffcent of determnaton. The predcted RFI could be used n the dary breedng program to ncrease proftablty by selectng anmals that are genetcally superor n energy effcency based on RFI, or through routnely measured trats, whch are genetcally correlated wth RFI. Key words: dary cattle, feed effcency, random regresson model, resdual feed ntake INTRODUCTION Feed cost s the sngle-largest expense of dary producton (Vallmont et al., 2011) and has ncreased substantally over the last few years (Garca, 2009). Although t s a crucal factor n the proftablty of the dary ndustry, lttle attenton has been pad to mprove feed effcency through drect selecton on t (Lnn, 2006; Zaman et al., 2008). Ths s manly due to the dffcultes and costs assocated wth ndvdual feed ntake measurements (Kelly et al., 2010). In addton, the feed converson rato (FCR) and gross energy effcency (GEE), whch are the most common measures of feed utlzaton effcency, have 2 man problems. The FCR s the rato of nput (e.g., feed) to output (e.g., weght gan or mlk producton; Crews, 200). In the dary ndustry, GEE s defned as the energy n mlk dvded by the total energy ntake (Veerkamp and Emmans, 199). Frst, the energy ntake by dfferent anmals has dfferent partal effcences for mantenance, lactaton, and body tssue gan or loss, but FCR and GEE do not dstngush between them (Veerkamp and Emmans, 199). Second, these measures are well known to be phenotypcally and genetcally correlated wth measures of growth, producton, and mature sze (Crews, 200). Thus, selecton for mprovement of FCR and GEE would result n ncreased growth rate, mature sze, and consequently ncrease mantenance requrements (Crews, 200) n an unbalanced breedng goal. To overcome the aforementoned problems of effcency measures, an alternatve measure of energy effcency, resdual feed ntake (RFI), has been descrbed. Re-

2 7992 MANAFIAZAR ET AL. sdual feed ntake s the dfference between an anmal s actual energy ntake (AEI) and ts expected energy ntake (EEI) based on anmal s mantenance requrements and producton level, and s phenotypcally ndependent of producton trats (Koch et al., 1963); an alternatve defnton of RFI s feed ntake adjusted for body sze and producton level (mlk, proten, and fat yeld and changes n body fat composton). The effcent anmals, whch have low RFI values, consume less feed wthout compromsng the producton level. Meat-producng anmals use energy manly for mantenance and daly weght gan durng the growth perod. The relatonshp between energy ntake and producton s lnear n the testng perod of meat-producng anmals (Archer et al., 1999; Basarab et al., 2003). As a result, the evaluaton methods of ndvdual RFI for meat-producng anmals durng ther growth perod has been well studed n beef cattle, swne, and poultry usng lnear regresson models (Archer et al., 1999; Crews, 200). Unlke the meat-producng anmals, dary cows have multfunctonal energy requrements for mantenance, growth, pregnancy, and lactaton; furthermore, t s establshed that energy ntake and energy expendtures have nonlnear profles durng the lactaton perod n dary cattle, whereas ther ndvdual profles are dfferent among anmals (Coffey et al., 2001; Bewley and Schutz, 2008). Several studes have been conducted to predct RFI n early frst lactaton or the whole frst lactaton n dary cows, but they manly used a lnear regresson model (Van Arendonk et al., 1991; Svendsen et al., 1993; Zaman et al., 2008) and lmted records of ndvdual AEI (Van Arendonk et al., 1991; Coleman et al., 2010), or used a standard table of estmated requrement values such as those of the NRC (Svendsen et al., 1993; Zaman et al., 2008). The RFI obtaned from the above may not be very accurate, and worthy of further nvestgaton (Zaman et al., 2008). In addton, based on our awareness, no prevous research has used the daly actual measured feed ntake data, and they collected feed ntake data ether weekly or monthly n ther studes; therefore, ther feed ntake data collecton methods mght be too nsenstve to capture the dfference among anmals (Vallmont et al., 2011). Moreover, most of the prevous studes have not consdered the nonlnear profles of the component [metabolc BW (MBW), empty BW (EBW), and mlk producton energy requrements (MPER)] trats durng the lactaton perod. The objectve of ths research was to develop a modelng equaton to predct RFI n the frst-lactaton dary cow whle accountng for ts multfunctonal energy requrements and consderng the nonlnear lactaton profles of the component trats usng an orthogonal polynomal random regresson technque. Data Acquston MATERIALS AND METHODS Daly ndvdual feed ntake, monthly BW, mlk producton, and mlk composton of 281 frst-lactaton (1 DIM) dary cows from June 2007 to October 2012, were used n the analyss. These anmals were housed n a te-stall system at the Dary Research and Technology Center (DRTC) of the Unversty of Alberta (Edmonton, AB, Canada). The anmals receved 1 of the 3 (hgh-, md-, or low-energy dense raton) TMR accordng to ther mlk producton level. Indvdual offered feed weght n the mornng and refusal feed weght left on the next mornng were recorded daly. Offered feed was adjusted perodcally to keep the ndvdual refusal feed around 10% of the total feed offered. Feed compostons, ncludng mosture (%), CP (%), and NDF (%), were determned when the TMR ngredents changed, whereas detary DM (%) was measured monthly. Average DM of hgh-, md-, and lowenergy dense TMR over a -yr study were 2.12, 1.02, and 48.87%, respectvely, and ther net energy densty were 1.8, 1.72, and 1.6 Mcal/kg of DM, respectvely. The ndvdual mlk yeld and composton data were retreved from the offcal DHI Program, whch records mlk yeld and composton once every 2 to 36 d after calvng, but no earler than DIM. Therefore, mlk yeld and composton data were avalable from to DIM. In addton, repeated measurements of ndvdual BW and BCS of these hefers were measured at ther calvng and subsequently on ther DHI mlk samplng days durng ther lactaton. Body condton score was assessed on a 1 to scale wth 0.2 ntervals (Edmonson et al., 1989; NRC, 2001) by the same techncan over the study perod. All procedures of the study were revewed and approved by the Unversty of Alberta Anmal Care and Use Commttee. Data Edtng and Trat Dervatons Twenty cows were excluded from the analyss as they had less than 4 repeated mlk yeld and composton records, and 2 anmals were dsqualfed from the data set, as they had lower than 26 AEI observatons over 301 DIM. Two cows also were excluded from the data due to late age at frst calvng (972 and 1,17 d). In addton, 12, 48, and 487 records were removed from the BW, mlk yeld, and feed ntake data, respectvely, because they dd not fall wthn 3 standard devatons from the populaton mean on the test day. The remanng 1,837, 1,766, and 67,61 repeated records of BW, mlk yeld, and feed ntake data, respectvely, from 234 cows were used n the analyss.

3 NET FEED EFFICIENCY FOR DAIRY COWS 7993 Table 1. Descrptve statstcs for daly value of measured and derved trats (n = 234) Trat No. of records Mean SE Mnmum Maxmum Measured trat BW (kg) 1, BCS 1, Mlk (kg) 1, Fat (%) 1, Proten (%) 1, DMI (kg/d) 67, Age at frst calvng (d) Temperature and humdty ndex Derved trat Actual energy ntake (Mcal of NE L /d) 67, Metabolc BW (kg 0.7 ) 1, Mlk producton energy requrements (Mcal of 1, NE L /d) Empty BW (kg) 1, The daly AEI, MBW, MPER, and EBW for each anmal were derved from the recorded raw data usng the followng equatons: (1) Indvdual daly AEI (Mcal/d) = DMI ED,where DMI (kg/d) s an ndvdual daly DMI and ED (Mcal/ kg) s the net energy densty of the det; DMI was calculated as [offered feed (kg) refused (kg)] DM (%), where DM s the detary DM. (2) Metabolc BW (kg) = BW 0.7 (kg) (NRC, 2001). The analyss of BW records between to DIM were not adjusted for fetus growth weght because the energy requrements of fetus growth s neglgble n ths perod of pregnancy (NRC, 2001). (3) Mlk producton energy requrement was consdered as the energy contaned n the mlk produced, and t s equvalent to the sum of the heat of combuston of mlk fat, proten, and lactose. Heat of combuston of mlk fat, proten, and lactose were reported as 9.29,.71, and 3.9, respectvely. Mlk lactose content s less varable and s essentally constant at 4.8% of mlk (NRC, 2001). Because the DHI program does not record lactose, the MPER was calculated based on fat and proten content (NRC, 2001) and a constant value of lactose (4.8% 3.9) as MPER (Mcal/d) = {[ fat (%)] + [0.047 CP (%)] } mlk yeld. (4) Changes n BW of dary cows could be confounded wth many factors, ncludng water and gastrontestnal content (Bewley and Schutz, 2008), so t may not reflect true changes of tssue energy due to gut fll (NRC, 2001). Therefore, EBW was an adjusted BW for gut fll that could be representatve of true changes n body tssue weght (NRC, 2001). Empty BW, on average, was consdered to be 8% of lve BW n dary (NRC, 2001); however, n the current study, EBW was calculated usng the equatons provded by Coffey et al. (2001) to account for ndvdual gut fll at the test day, whch was a functon of DMI and the energy content of the det that each anmal consumed at the test day, as EBW (kg) = BW GF, wth GF (kg) = DMI [11 (7 MED/1)], where MED was the metabolzable energy densty (Mcal/kg) of the det and GF was gut fll. Descrptve statstcs of both measured and derved trats are gven n Table 1. Statstcal Modelng The predcton equaton of ndvdual lactaton RFI was developed n 2 steps: frst, we modeled the daly nonlnear profles of MBW, MPER, and EBW from ther respectve monthly measurements usng an orthogonal polynomal random regresson model (RRM). Second, we modeled the lactaton multfunctonal energy requrements of dary cows usng a multple lnear regresson. RRM Development for Indvdual MBW, MPER, and EBW. Random regresson modelng s a useful technque to model the longtudnal data for each anmal, and each anmal could have a predcted daly value for the trat under modelng (Coffey et al., 2001). An RRM can be modeled wth dfferent regresson approaches, and the Legendre polynomal random regresson model was used n ths study as follows: k1 k2 t t m m m m m= 0 m= 0 y F β P t λ P t ε = + ()+ ()+ where y t s a derved trat (MBW, EBW, and MPER) for anmal on day t, and F t represents fxed effects of the populaton used to defne contemporary groups. The fxed effects were combned month and year of measurement wth raton type of 238 levels, whch the anmal receved between 2 consecutve records; the temperature and humdty ndex (THI) at each test month wth a total of 6 levels; and the covarate of t,

4 7994 MANAFIAZAR ET AL. anmal s age at frst calvng devaton from the populaton mean (lnear and quadratc). Term β m s the fxed regresson coeffcent for a partcular contemporary group; λ m represents random regresson coeffcents assocated wth the anmal s addtve genetc effects plus ts permanent envronmental effects; P m (t) s the mth Legendre polynomal evaluated at tme t; the parameters k1 and k2 are the order of ftted fxed (1 ) and random (1 ) polynomals regresson, respectvely; and ε t s the resdual error assocated wth anmal at tme t. In ths study, 2 models orgnated from the combnatons of dfferent possble orders (1 ) of fxed (F) and random (R) factors were ftted usng Legendre polynomal regresson to model the nonlnear lactaton profles of MBW, EBW, and MPER. These models were denoted as F k1 R k2, where k1 and k2 were the order of the ftted fxed and random regresson varables, respectvely. For example, F R was a model wth both fxed and random varables wth order of. A predcton equaton out of the 2 ftted models was selected as the best predcton equaton for each trat based on log-lkelhood rato test (LRT) and Bayesan nformaton crteron (BIC; Tedesch, 2006). The LRT s a statstcal test used to compare the ft of 2 models, one of whch (reduced model) s a specal case of the other (full model). The BIC s a crteron for model selecton among a fnte set of models; t s based on lkelhood functon and consders a penalty term for the number of parameters n the model by whch a model wth smaller value s better. In the current study, the model wth both ffth fxed and random order (F R ) was consdered as a full model, and then the LRT value was calculated between pars of the full model and each of the other 24 reduced models as follows: LRT = 2log-lkelhood of full model 2log-lkelhood of reduced model. The calculated LRT value between the full model and each of the reduced models was compared wth a crtcal value to decde whether to reject the reduced model n favor of the full model. The crtcal values were determned based on degrees of freedom of change and sgnfcance level (P < 0.0) from ch-squared dstrbuton. Twenty-four LRT values were calculated and compared wth ther correspondng crtcal values for each trat to fnd the smplfed models that dd not sgnfcantly dffer from the F R model. If more than 1 model was not sgnfcantly dfferent from the full model, then the best model was determned based on the BIC among them and used to predct daly profles for each anmal from to DIM. The daly values were only predcted from to DIM for each trat (MBW, EBW, and MPER) because the frst 4 d of mlk (colostrum) producton records at each lactaton are not ncluded n the DHI recordng program. To consder the body reserve changes, the dfferences of predcted EBW between 2 consecutve days were consdered to be the EBW change (EBWC) between these days. The predcted daly values for each trat of each anmal were summed over 301 d to obtan the anmal s expected frst-lactaton value for that trat. Smoothng the daly actual feed ntake data usng predcted values from the developed predcton models s a way to reduce the error nose and capture the real pattern n the data. In the smoothng process, daly nose presumably due to error nose s reduced, and the ponts that are lower or hgher than the adjacent ponts wll be ncreased or decreased, whch leads to a smooth sgnal. To smooth daly AEI data, the best-predcton RRM wth ffth order of F and R effects was used to predct ndvdual daly AEI. Then, predcted AEI from to DIM for each anmal were also summed to obtan the ndvdual s 301-d AEI AEI and called smoothed total AEI. All of the statstcal procedures were performed usng PROC MIXED of SAS (SAS Insttute, 2003). Total Lactaton EEI and RFI Predcton. A multple lnear regresson model was used to predct the total lactaton ndvdual EEI value. The smoothed total 301-d AEI was lnearly regressed on total 301-d predcted trats of MBW, MPER, and EBWC to obtan the ndvdual s 301-d lactaton EEI and RFI as follows: AEI = β0 + β1 MBW + β2 MPER + β3ebwc + RFI. The 301-d frst-lactaton RFI for ndvdual anmal can be obtaned by subtractng the total 301-d expected energy expendtures from the smoothed total 301-d AEI of the th ndvdual as follows: RFI = AEI EEI = AEI β0 + β1mbw + β2mper + β3 EBWC. The daly average lactaton RFI for each ndvdual over 301 d can be obtaned by dvdng the total lactaton RFI by anmal s days n record.

5 NET FEED EFFICIENCY FOR DAIRY COWS 799 Fgure 1. Average actual energy ntake (Mcal of NE L /d) versus DIM. RESULTS Descrptve statstcs of measured and derved trats are gven n Table 1. The number of observatons per cow for measured (BW, BCS, mlk yeld, and composton) and derved (MBW, EBW, and MPER) trats over 301 d ranged from 4 to 11. However, the number of observatons per cow for AEI was 289, on average, and ranged from 26 to 301. The average of recorded daly AEI aganst DIM s shown n Fgure 1; the average daly derved and predcted MPER, EBW, and MBW are shown n Fgures 2, 3, and 4, respectvely. The peak of AEI occurred around 100 DIM (Fgure 1), whereas the peak of MPER occurred around 60 DIM (Fgure 2). Anmals began to lose ther body reserves to support ther mlk producton before the peak of AEI, and the nadr pont of EBW was around 60 DIM (Fgure 3). The LRT and BIC statstcs for all models that were not sgnfcantly dfferent from the full model by the LRT are presented n Table 2 for the 3 (MBW, EBW, and MPER) trats. The bold statstcs ndcate that the models were chosen based on BIC as the best predcton model for that trat. The models of F R 3, F R 3, and F R 2 were selected to predct the ndvdual s daly values for MBW, EBW, and MPER, respectvely. Scatter plots for the average daly predcted versus the average daly derved values of MPER, EBW, and MBW aganst DIM are shown n Fgures 2, 3, and 4, respectvely. It can be seen that the predcted values were matched well wth ther derved values for all 3 trats n ther respectve graphs. Fgure 2. Average daly derved ( ) and predcted ( ) mlk producton energy requrement (Mcal of NE L /d) versus DIM.

6 7996 MANAFIAZAR ET AL. Fgure 3. Average daly derved ( ) and predcted ( ) empty BW (kg) versus DIM. The developed EEI predcton equaton s gven below wth a coeffcent of determnaton of 0.68: EEI = 2, MBW MPER 11. EBWC, and the 301-d ndvdual lactaton RFI can be predcted as follows: RFI = AEI + 2, MBW MPER 11. EBWC. The mean of predcted daly average lactaton RFI was 0.0 and ranged from 6.8 to 8.64 Mcal of NE L /d (Fgure ). Ffty-one percent of the anmals had an RFI value below the mean (effcent) and 49% of them had a RFI value above the mean (neffcent). DISCUSSION Advantages of the Developed Model The objectve of ths study was to develop a predcton equaton to calculate lactaton RFI for dary cows durng ther whole frst-lactaton perod and to account for the anmals multfunctonal energy requrements. The developed predcton model also consdered the nonlnear lactaton profles of RFI component trats and used smoothed daly actual feed ntake data durng the whole lactaton perod. In ths research, measured AEI data was smoothed to remove the error nose n RFI predcton equaton. However, applyng measured AEI data n the RFI predcton equaton provded very smlar results to the smoothed AEI data. The correlaton between predcted RFI from measured AEI and Fgure 4. Average daly derved ( ) and predcted ( ) metabolc BW (kg 0.7 ) versus DIM.

7 NET FEED EFFICIENCY FOR DAIRY COWS 7997 Fgure. Average daly resdual feed ntake (RFI). Each bar ndcates daly RFI (Mcal of NE L /d) for each dary cow. ID = dentfcaton. smoothed AEI was Therefore, 289 repeated measurements of AEI over 301 d may be good enough to capture the real pattern of feed ntake n dary cattle, and smoothed data may be more useful to remove error nose when less-repeated data ponts over lactaton are recorded. Several prevous RFI predcton studes (Van Arendonk et al., 1991; Svendsen et al., 1993; Zaman et al., 2008; Coleman et al., 2010; Vallmont et al., 2011) for dary cattle n the lterature are summarzed n Table 3. Van Arendonk et al. (1991) predcted RFI n early lactaton (10 DIM) usng lnear regresson of average daly energy ntake on average daly MBW, average daly fat- and proten-corrected mlk, and average daly weght gan. In ths study, we used the actual daly feed ntake records from the entre lactaton to develop an RFI predcton equaton for the frst-lactaton dary cow (301 DIM) rather than early lactaton (10 DIM). Furthermore, Van Arendonk et al. (1991) used the average of BW gan over 77 d n the predcton model. Applyng an average of BW n early lactaton could gve a based result, as measurng BW around the nadr pont s mportant to ensure accurate apprasal of BW gan or loss. It s also well establshed that dary anmals lose ther energy reserves (BW and BCS) to support mlk producton n early lactaton and start to regan ther reserves after the energy ntake peak occurs (Coffey et al., 2001; Bewley and Schutz, 2008), whch s also supported by the results found n the current study (Fgure 3). For example, consder a cow that had 0.1 kg of weght loss n the frst 0 d n the test and 0.27 kg of weght gan for the rest of 27 d n the test (from 0 to 77 d n the test) n the study by Van Arendonk et al. (1991). The cow mght have zero average BW gan durng 77 d f her nadr pont occurred at the d 0. To accurately consder the body reserve changes, RFI may be predcted n a shorter tme, such as weekly; then, total lactaton RFI could be calculated to be the sum Table 2. Maxmum log-lkelhood, log-lkelhood rato test (LRT), and Bayesan nformaton crteron (BIC) values of dfferent models, whch were not sgnfcantly dfferent from the full model (F R ) 1 for metabolc BW (MBW), mlk producton energy requrements (MPER), and empty BW (EBW) 2 Model 3 df change Trat MBW MPER EBW Maxmum log-lkelhood LRT BIC Maxmum log-lkelhood LRT BIC Maxmum log-lkelhood LRT BIC F 4 R , ,870.0 F 4 R 3 7 4, ,842.8 F R 2 1 4, ,834.2 F R 3 11, , , , , ,128.6 F R 4 6, , , , , ,148.8 F R, , , , , , F = fxed factor and R = random factor, where the subscrpts ndcate the order ftted. 2 The selected model was based on maxmum log-lkelhood, LRT, and BIC values ndcated n bold. 3 The models were desgnated by F k1 R k2, where k1 and k2 are the order of fxed and random regresson, respectvely.

8 7998 MANAFIAZAR ET AL. of weekly predcted RFI over lactaton. In ths research, RFI component trats, ncludng EBWC, were summed over the lactaton perod to calculate total lactaton RFI (RFI Lactaton ). Moreover, we calculated ndvdual weekly RFI, and then the total ndvdual lactaton RFI was calculated by summng up the weekly RFI (RFI Weekly ) over lactaton. The 2 methods yelded very smlar results: the means (SD) of RFI Lactaton and RFI Weekly were 0.0 (2.42) and 0.0 (2.46), respectvely, and RFI obtaned from these 2 methods had a correlaton of Summng up the RFI component trats method s much easer computatonally and more applcable compared wth the weekly approach. Coleman et al. (2010) developed an RFI predcton equaton for frst-lactaton cows from 16 to 288 DIM n a pasture-based system (Table 3). They predcted RFI by regresson of estmated daly DMI on predcted daly energy expendtures (fat yeld, proten yeld, lactose yeld, MBW, BW change, and BCS) over 272 d. On one hand, Coleman et al. (2010) estmated ndvdual DMI by the n-alkane technque on 6 occasons from 16 to 288 DIM. The estmated observatons were then used to develop a predcton equaton based on a cubc splne regresson method to obtan an estmated daly DMI for each anmal over 272 d. On the other hand, they predcted DMI based on anmal energy expendtures (fat yeld, proten yeld, lactose yeld, MBW, BW change, and BCS). Then, they consdered ndvdual RFI as the dfference between daly estmated DMI from the cubc splne regresson data, wth predcted DMI based on anmal energy expendtures. However, RFI predcton s the dfference between daly actual DM or energy ntake, wth predcted DM or energy ntake based on anmal energy expendtures. Therefore, the man dfference between our study and that of Coleman et al. (2010) was that they used estmated daly DMI n ther study, whereas we used smoothed actual daly DMI measurements n the RFI predcton to subtract predcted DMI based on anmal energy expendtures. Wang et al. (2006) reported that accurate RFI test results requred at least 63-d observatons of actual daly DMI n a 90-d perod of a feed lot tral of RFI predcton for beef cattle. Although ther results may not drectly be applcable to dary cattle, at least ther results ndcate that an adequate number of DMI data measurements are requred to have an accurate RFI predcton, even wth lnear predcton n beef cattle. Coleman et al. (2010) had a lower number of daly actual DMI data than our study (6 vs. 289), so they mght suffer from loss of predcton accuracy. Two other studes (Svendsen et al., 1993; Zaman et al., 2008) predcted RFI for the frst 2 trmesters and the entre frst-lactaton perod (Table 3), respectvely. Both of these research teams used the table values of the standard NRC nutrent requrements to estmate energy expendtures nstead of usng actual ndvdual Table 3. Summary of avalable resdual feed ntake (RFI) predcton report n the lterature Item 1 Current study Vallmont et al. (2011) Coleman et al. (2010) Zaman et al. (2008) Svendsen et Van Arendonk et al. (1993) al. (1991) Breed Holsten Holsten Holsten Holsten Dual Holsten Rased system Te-stall Te-stall Pasture Te-stall Te-stall Te-stall n Test duraton Regresson approach to model energy snk profles NL 2 NL NL NP 3 NP L 4 Regresson approach to model relatonshp L; NL L L L L L between energy ntake and snks Recorded actual feed ntake/cow NP 44 R 2 of RFI predcton equaton 0.68 NP NP NP NP NP Components ncluded n expected energy ntake equaton MBW * * * * * MYC * * * * * * EBWC * BW * BCS * * * ADG * * * * RFI Mcal of NE L /d kg of DM/d Mcal/d MJ of ME/kg Mean 0.00 NP NP 64.2 Mnmum 6.8 NP NP 42.1 Maxmum 8.64 NP NP MBW = metabolc BW; MYC = mlk yeld and components; EBWC = empty BW change. 2 NL = nonlnear. 3 NP = not provded. 4 L = lnear. Components ncluded n the expected energy ntake equaton are ndcated by an astersk (*).

9 NET FEED EFFICIENCY FOR DAIRY COWS 7999 feed ntake measurements. Moreover, the standard requrements tables such as those of the NRC were prepared based on populaton averages and were not applcable to dentfy an effcent ndvdual. In the current study, both group mean effcency (the fxed effects) and the ndvdual devaton of effcency (the random effects) from the group mean were modeled and the latter allowed us to dentfy effcent anmals wthn the group. Model Development and Selecton Twenty-fve Legendre polynomal RRM were ftted for each of the energy expendture components (MBW, EBW, and MPER), and then LRT along wth the BIC were used to select the best predcton equaton for the energy expendtures. Random regresson modelng s a useful technque for analyzng longtudnal trats, such as feed ntake, mlk producton, and BCS (Schaeffer, 2004). It s a flexble model that allows regresson coeffcents to be dfferent among anmals, gvng each anmal a specfc model (Schaeffer and Dekkers, 1994). In an RRM, an average curve of a trat for all anmals n a partcular group s ftted as a fxed regresson, and devaton of each anmal from ths average curve s modeled usng random Legendre polynomals (Coffey et al., 2001; Schaeffer, 2004). Legendre polynomals have advantages of havng good convergence and lower correlatons between coeffcents, as the coeffcents are orthogonal compared wth an ordnary polynomal (Coffey et al., 2001; Schaeffer, 2004). The common statstcal crtera such as mean square of error, or coeffcent of determnaton were not useful for our model selecton because the numbers of parameters to be estmated were dfferent for all possble combnatons of the RRM. Therefore, we frst used LRT to test the profcency of reduced models compared wth the full model and then BIC was used to select the best model among the models that were as effcent as the full model. The prelmnary results of the tested fxed and random regresson orders of 1 to 10 for the trats showed that most of the orders greater than had a convergence problem. Therefore, possble orders (1 ) of F and R Legendre polynomal regresson models were tested to model the daly nonlnear lactaton profles of MBW, EBW, and MPER wth tme. For the 3 derved trats, a fxed regresson of order (F ) was selected, whereas random regresson of order 3 (R 3 ), 3 (R 3 ), and 2 (R 2 ) were selected for MBW, EBW, and MPER, respectvely, and were used to predct ther respectve daly values for each anmal. Several reports used Legendre polynomal RRM technque to model BW, energy balance, and mlk yeld wthn the frst-lactaton perod (Coffey et al., 2001; Banos et al., 200; Lu et al., 2006). They consdered a fxed regresson order of to model average records across all anmals for the tested trats. Random orders of and more were suggested to be used for modelng of energy balance, whch was a derved trat from BW and BCS (Banos et al., 200). It s noted that the random regresson model conssts of fxed and random parts. The random part of the model could be parttoned nto dfferent parts, ncludng anmal addtve and permanent envronmental effects (Coffey et al., 2001). If the random part dd not partton, t would be a combned effect of anmal addtve and permanent envronmental effects. Currently, a random order of 4 s beng used for both addtve and permanent effects n Canada for modelng of mlk yeld wthn the frst lactaton (Interbull, 2009). However, Lu et al. (2006) tested Legendre polynomal random orders of 3 to 8 to select the best order of ft for mlk yeld usng some statstcal crtera, ncludng LRT and BIC. They also compared the selected model wth the currently used model (order of 4 for both addtve and permanent random effects) n Canada and found that the random orders of and 7 were the best orders for addtve and permanent random effects, respectvely. Therefore, they concluded that the model used n the Canadan Holsten dary evaluaton was not the best, based on a sngle crteron, but was optmal when consderng all crtera ncludng LRT and BIC. However, n the current research, pedgree nformaton was not ncluded n the analyss, as we were nterested n predctng phenotypc RFI. Therefore, the anmal random effect was a combnaton of anmal addtve and permanent effects. Overall, the selected models n the current study were the best models that ftted the trats (Fgures 2, 3, and 4), and they were n lne wth comparable results n the lterature. EEI Equaton and RFI Calculaton The lnear and quadratc relatonshps between smoothed total AEI and total MBW, EBWC, and MPER were examned. The lnear RFI predcton equaton had a coeffcent of determnaton of The quadratc multple regresson adds just 2% to the coeffcent of determnaton n the lnear model, and none of the quadratc terms n the nonlnear predcton equaton were statstcally sgnfcant (P > 0.34). The coeffcent of determnaton determnes the percentage of the varaton of the dependent varable (AEI) that s explaned by ndependent varables (MBW, EBWC, and MPER). It s a good ndcator for comparng the dfferent RFI predcton modelng approaches. Ideally, we should compare the coeffcent of determnaton of our predcton equaton wth other avalable RFI

10 8000 MANAFIAZAR ET AL. predctons from the lterature. However, based on our awareness of publshed results, none of them provded a coeffcent of determnaton for ther RFI predcton equatons (Table 3). Therefore, we could not compare the coeffcent of determnaton drectly wth the predcton equatons n the prevous works n the lterature. Indvdual AEI and EEI, whch s predcted based on anmal mantenance and producton requrements, are necessary to calculate ndvdual RFI. The RFI calculaton method has been well establshed n beef cattle durng the growth perod. Generally, daly DMI and bweekly BW are recorded over 90 d n beef cattle durng ther growth perod. Then, lnear regresson of measured weght over tme s used to model the growth curve for each anmal and predct ts MBW and ADG (Basarab et al., 2003; Wang et al., 2006; Kelly et al., 2010). Basarab et al. (2003) used lnear regresson to model the growth curve of beef steers to predct the md-test BW and ADG of anmals durng the feedlot test perod and reported that all anmals had a growth curve wth a coeffcent of determnaton of more than 9%, ndcatng that the growth durng ths phase was lnear and the selecton of a lnear regresson model was an approprate approach. Consequently, expected DMI was calculated from lnear regresson of actual daly DMI on estmated MBW and ADG. As a result, the coeffcent of determnaton of RFI predcton equaton ranged from 0.72 to 0.82 n beef cattle (Basarab et al., 2003, 2007). However, energy requrements of dary cows are complcated and they need energy to produce mlk, grow, conceve, and brng ther calves to term whle mantanng themselves as bologcal enttes, stayng healthy, and keepng up wth general actvtes (Banos et al., 200). In dary cattle, the amount of energy ntake and that dspensed by an anmal determnes ts body energy state. Almost all lactatng anmals tend to lose ther body reserves to support lactogeness, especally n hgh mlk-producng cows (Coffey et al., 2001). Therefore, accountng for nonlnear lactaton profles for multfunctonal energy requrements of expected ndvdual energy ntake over DIM s the key success to obtan an accurate RFI predcton for dary cows. In the current study, the nonlnear lactaton profles of energy expendtures were accounted for by usng RRM and a summaton of ndvdual daly values over the trajectory. For multple requrements, the authors ntally consdered smoothed AEI as functons of total MBW, MPER, and BW over 301 d and accounted for 6% of varaton n AEI. Includng BCS n the ntal model produced an equaton wth a coeffcent of determnaton of about 0.8. However, after adjustng BW for gut fll and EBW, and then calculatng the EBWC and replacng wth BW and BCS, we provded a model that accounted for 68% of varaton n AEI. The prevous research teams n dary cattle dd not report coeffcents of determnaton for RFI calculaton; however, the acheved coeffcent of determnaton value for RFI predcton equaton was close to the lower range of beef studes (Basarab et al., 2003, 2007). In ths study, the mean of average daly lactaton RFI was 0.0 (SD = 2.42 Mcal of NE L /d; 1.33 kg of DM/d) and ranged from 6.8 to 8.64 Mcal of NE L /d ( 3.9 to 4.77 kg of DM/d). Other researchers also reported an average of zero for RFI n dary (Van Arendonk et al., 1991; Coleman et al., 2010), but no standard devaton was gven. The standard devaton of RFI estmaton n growng beef cattle was reported as almost 0.6 kg of DM/d and the range of RFI values has been reported from 2. to +2.2 kg of DM/d (Basarab et al., 2003; Wang et al., 2006; Kelly et al., 2010), wth an average of zero. CONCLUSIONS The F R 3, F R 3, and F R 2 RRM were selected as the best models to model the daly nonlnear profles and to predct ndvdual daly values of MBW, EBW, and MPER, respectvely. The results ndcated that the frst-lactaton RFI s predctable and could be used n the dary ndustry to ncrease proftablty by selectng anmals that are genetcally superor n energy effcency based on the predcted RFI wthout compromsng the producton level, through ndcator trats such as conformaton trats, marker-asssted selecton, and other genomc approaches. However, further nvestgatons are requred to develop a predcton equaton to calculate RFI across the lactaton. In addton, a need exsts to nvestgate the phenotypc and genetc correlatons between RFI and conformaton trats, fertlty, and lfetme proftablty, and to nvestgate ndcator trat(s) n an effort to ensure that the measurement of feed ntake and, consequently, RFI calculaton s more cost effectve. ACKNOWLEDGMENTS The authors are greatly thankful for the expermental support from the staff at the Dary Research and Technology Center (DRTC) of the Unversty of Alberta (Edmonton, AB, Canada), especally Reza Khorasan, the DRTC manager, and Harold Lehman, a senor DRTC techncan. The fnancal support from the Natural Scence and Engneerng Research Councl of Canada (NSERC, Ottawa, ON, Canada) s also greatly apprecated. REFERENCES Archer, J. A., E. C. Rchardson, R. M. Herd, and P. F. Arthur Potental for selecton to mprove effcency of feed use n beef cattle: A revew. Aust. J. Agrc. Res. 0:

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