Analyses of body weight patterns in growing pigs: a new view on body weight in pigs for frequent monitoring

Analyses o body weigh pa e ns in g owing pigs: a new iew on body weigh in pigs o equen moni o ing A. H. S yga 1† , K. A. Dolecheck 2 and A. R. K is ensen 1 1 Depa men o Ve e ina y and Animal Sciences, Uni e si y o Copenhagen, G ønnegå ds ej 2, DK-1870 F ede iksbe g C, Denma k; 2 Depa men o Animal and Food Sciences, Uni e si y o Ken ucky, Lexing on, KY 40546, USA (Recei ed 29 June 2016; Accep ed 24 May 2017) F equen BW moni o ing o g owing pigs can be use ul o iden i ying p oduc ion (e.g. eeding), heal h and wel a e p oblems. Howe e , in o de o cons uc a ool which will p ope ly ecognize abno mali ies in pigs’g ow h a p ecise desc ip ion o he g ow h p ocess should be used. In his s udy we p oposed a new model o pig g ow h accoun ing o daily fluc ua ions in BW. Body weigh measu emen s o 1710 pigs (865 gil s and 843 ba ows) o igina ing om fi e consecu i e ba ches om a Danish comme cial a m we e collec ed. Pigs we e inse ed in o a la ge pen (maximum capaci y =400) be ween No embe 2014 and Sep embe 2015. On a e age, each pig was obse ed o 42 days and weighed 3.6 imes a day when passing om he es ing o eeding a ea. Al oge he , 243,160 BW measu emen s we e eco ded. A mul ile el model o pig g ow h was cons uc ed and fi ed o a ailable da a. The BW o pigs was modeled as a quad a ic unc ion o ime. A diu nal pa e n was inco po a ed in o he model by a cosine wa e wi h known leng h (24 h). The model included pig e ec which was defined as a andom au o eg essi e p ocess wi h exponen ial co ela ion. Va iance o wi hin-pigs e o was assumed o inc ease wi h ime. Because only fi e ba ches we e obse ed, i was no possible o ob ain he andom e ec o ba ch. Howe e , in o de o accoun o he ba ch e ec he model included in e ac ions be ween ba ch and fixed pa ame e s: in e cep , ime, squa e alue o ime and cosine wa e. The gende e ec was no significan and was emo ed om he final model. Fo all ba ches, mo ning and a e noon peaks in he equency o isi s o he eeding a ea could be dis inguished. Acco ding o esul s, pigs we e ligh e in he mo ning and hea ie in he e ening (minimum BW was eached a ound 1000 h and maximum a ound 2200 h). Howe e , he exac ime o ob aining maximum and minimum BW du ing he day di e ed be ween ba ches. Pigs had access o na u al ligh and, he e o e, exis ing di e ences could be explained by a ying dayligh le el du ing obse a ions pe iods. Because he diu nal ampli ude o pig g ow h a ied be ween ba ches om 0.9 o 1.4 kg, BW moni o ing ools based on equen measu emen s should accoun o diu nal a ia ion in BW o pigs. This p oposed desc ip ion o g ow h will be buil in o a moni o ing ool (a dynamic linea model) and applied o a m da a in u u e s udies. Keywo ds: au oma ic g ow h moni o ing, BW, diu nal pa e n, pigs Implica ions Body weigh is a equen ly epo ed ai in biological s udies. Fo example, we wan o know how BW changes wi h age, du ing a disease o a e applying a he apy. Howe e , so a we ha e been neglec ing he ac ha BW can change also du ing a day. We showed ha BW o pigs du ing 1 day on a e age fluc ua es om 0.9 o e en 1.4 kg. These fluc ua ions a e highly s a is ically significan and should be included in ma hema ical models desc ibing g ow h. The knowledge on BW hy hm migh be use ul in designing expe imen s, in e p e ing esul s o de eloping moni o ing ools. In oduc ion I has been assumed ha he g ow h o pigs is well desc ibed. Fo pigs obse ed du ing sho ime in e als, g ow h has been defined simply by linea unc ions wi h he in e cep ep esen ing ini ial BW and he slope exp essing an inc ease in BW (To e al ., 2005). Fo pigs obse ed o e longe ime in e als, pe iods wi h as e and slowe g ow h a es ha e been exp essed in he o m o Gompe z unc ions (Niemi e al ., 2015). Such desc ip ion o g ow h is adequa e o adi ional BW moni o ing, which in ol es, o example, mo ing pigs om pens o a weighing c a e on a daily, weekly o mon hly bases. Mo e equen BW moni o ing can be use ul o p oduc ion moni o ing as well as iden i ying heal h † E-mail: [email p o ec ed] Animal , page 1 o 8 © The Animal Conso ium 2017. This is an Open Access a icle, dis ibu ed unde he e ms o he C ea i e Commons A ibu ion licence (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed e-use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. doi:10.1017/S1751731117001690 animal 1 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a and wel a e p oblems (Co nou and K is ensen, 2013). Howe e , o au oma ic g ow h moni o ing o be use ul, a mo e p ecise desc ip ion o g ow h migh be necessa y. In pa icula , diu nal g ow h pa e ns may be necessa y o accoun o when mul iple BW measu emen s a e aken wi hin 1 day. Män ysaa i and Män ysaa i (2015) sugges ed ha , in dai y ca le, BW a ies h oughou he day acco ding o udde , gu and bladde fill. Indeed, hey ound ha wice- daily BW measu emen s om 230 dai y ca le we e an a e age 7.3 kg lowe in he mo ning han in he a e noon. Because bo h measu emen s we e aken a e milking, a minimal e ec o udde fill was assumed. Ins ead, he diu nal influence was a ibu ed o he cows ea ing mo e du ing he day ime han du ing he nigh ime. Simila ly, mul iple ecen s udies using au oma ically collec ed da a ha e iden ified diu nal eeding pa e ns in pigs (Fe nández e al ., 2011; Hoy e al ., 2012; And e a e al ., 2016). Al hough i is in ui i e o hink BW o pigs migh also ollow a diu nal pa e n, no p e ious esea ch appea s o ha e e ified ha assump ion. This s udy is pa o la ge p ojec , aimed a designing a ool able o ale he a me abou de e io a ion in pigs’ g ow h. In o de o ale he a me o unexpec ed changes in g ow h, p ecise desc ip ion o g ow h on an hou ly basis has o be known. The main objec i e o his s udy was o desc ibe he ela ionship be ween he BW o pigs and ime exp essed in hou s and o e alua e he assump ion ha he BW o pigs ollows a diu nal cyclic pa e n. In he p esen ed s udy, he numbe o egis e ed isi s o he eeding a ea was also in es iga ed. F equencies o isi s o he eeding a ea we e compa ed wi h he ob ained diu nal ampli ude o pigs’g ow h. Ma e ial and me hods Da a om he he d The PigIT p ojec is a s a egic esea ch alliance ounded o imp o e wel a e and p oduc i i y in g owing pigs using ad anced in o ma ion and communica ion echnologies me hods (K is ensen and Jensen, 2015). The BW da a used in his s udy was collec ed on a comme cial he d o finishing pigs wi hin he PigIT p ojec . The he d included a finishe uni wi h ou la ge common pens, each wi h a maximum capa- ci y o 400 pigs. Each la ge common pen measu ed 14.0 m by 9.0 m and included a main a ea o es ing, wo eeding a eas wi h 18 eeding poin s each, and a slaugh e collec ion a ea. In his he d, he main a ea o each pen was sepa a ed om he eeding a ea and he slaugh e collec ion a ea by a weigh so ing sys em (Ag isys-Nedap, G oenlo, The Ne he - lands, g aphically illus a ed on Figu e 1). Each ime a pig wan ed o en e he eeding a ea i had o pass h ough he weighing sys em. When a pig en e ed he weighing sys em, he scale doo s closed, he pig was iden ified using an indi- idual elec onic ea ag, weigh was eco ded and hen he sys em di ec ed he pig o whiche e eeding a ea i was assigned (based on weigh ). A e eeding, pigs could exi he eeding a ea and en e he main a ea ia a one-way doo . Al e na i ely, once he pig eached slaugh e weigh i was au oma ically di ec ed in o he slaugh e collec ion a ea. Any sick pigs, when iden ified by he he d ca e ake , we e mo ed o a sec ion o sick animals. In he s udied a m all o he pigs o igina ed om a c oss- b ed dam (Land ace ×Yo kshi e) and a pu e b ed si e (Du oc), which is a common combina ion in Denma k. Pigs en e ed he la ge common pen finishe uni in mixed-sex g oups when hey eached ~30 kg. The sex o weighed pigs was iden ified using elec onic ea ags (gil s we e ma ked wi h e en numbe s while ba ows we e ma ked wi h odd numbe s). The pigs we e allowed a 5-week adap a ion pe iod o lea n he weigh so ing sys em. Du ing ha ime, all doo s be ween he main a ea and eeding a ea we e open. Following he adap ion pe iod, weigh was eco ded each ime each pig en e ed he eeding a ea un il slaugh e . In he case ha wo pigs en e ed he scale simul aneously, BW was no egis e ed. Fo each ba ch, BW da a we e egis e ed om he ime o u ning on scales un il he las pigs we e sen o slaugh e (example o all BW eco dings o Ba ch 1 is p esen ed in Figu e 2). All pigs we e ed ad libi um . Fo a de ailed desc ip ion o he eeding s a egy, see K ogsdahl (2015). In his s udy, BW measu emen s o pigs om Pen 1 (Ba ch 1, Ba ch 3, Ba ch 4, Ba ch 5) and Pen 2 (Ba ch 2) we e ob ained and analysed. Ba ches we e obse ed du ing di e en seasons. Ba ch 1 and 2 we e obse ed du ing win e , Ba ch 3 du ing sp ing, Ba ch 4 du ing summe and Ba ch 5 in au umn. A summa y o all BW da a used in his s udy is p esen ed in Table 1. Al oge he , 243,160 BW measu emen s we e collec ed om 1710 pigs. All collec ed eco ds we e used in he analyses. Pigs we e exposed o bo h na u al ligh (placing o doo s and windows ma ked in Figu e 1) and a ificial ligh (24-h lamp o e weighing scale). The a m had a combi-di use en ila ion sys em. Tempe a u e in he p oduc ion uni was Figu e 1 O e iew o he la ge common pen finishe uni ha da a was collec ed om o a s udy on daily changes in pig BW whe e (A) main a ea, (B) eeding a ea, (C) elie a ea, (D) so ing a ea, (E) weighing scale wi h 24-h lamp, (F) doo s and (G) windows ( om K ogsdahl 2015). S yga , Dolecheck and K is ensen 2 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a egula ed by he sp inkle s ha we e ins alled abo e he main, eeding and collec ing a ea and by he clima e com- pu e . Fu he desc ip ions o animals, labo and manage- men can be ound in K ogsdahl (2015). Time co ec ions In o de o p ope ly accoun o he diu nal pa e n in all ba ches, he ime o BW measu emen s was co ec ed o dayligh sa ing ime (DST). The DST indica o was ob ained using he app oach o G olemund and Wickham (2011), implemen ed in R. Time o each BW obse a ion was checked o DST changes. I BW was obse ed du ing cen al Eu opean summe ime, he ime o obse a ion was educed by 1 h. Due o he aining pe iod (when pigs we e passing h ough scales wi hou ha ing hei BW egis e ed) he fi s ini ial BW in o ma ion was ob ained a 29 days a e inse ion in he pen. The e o e, o his analysis, he ini ial obse a ion ime ( 0=0) was se a 696 h (29 days) a e inse ion. S a is ical analysis Me hods simila o S yga and K is ensen (2016) we e used o desc ibe he BW o pigs in he he d. The fixed pa o he model p esen ed by S yga and K is ensen (2016) was sup- plemen ed wi h fixed e ec s o he ampli ude and equency o a cosine wa e (used o accoun o he diu nal pa e n in daily BW). Due o he small numbe o obse ed ba ches (fi e consecu i e ba ches we e ollowed), i was no possible o es ima e he andom slope and in e cep o he ba ch e ec in he final model. Ins ead, he fi using gene alized leas squa es me hod was applied o ob ain a ep esen a ion o he BW o a pa icula pig a a gi en hou . Howe e , in o de o accoun o he a ia ion be ween ba ches, he final model was supple- men ed wi h in e ac ions be ween ba ches and he fixed elemen s o he model. In summa y, he ull model used in he analyses o BW o pig i in ba ch j o e ime was desc ibed as: yij =ðβ0+q0jÞ+ðβ1+q1jÞ +q2j 2+ðβ2+q3jÞcosðw Þ +ðβ3+q4jÞsinðw Þ+Aij +ϵij Aij N0;σ2 A  ;ϵij N0;σ2  ð1Þ in which β0;β1a e he fixed he d e ec s o in e cep and ime while β2and β3a e fixed e ec s o he cosine wa e, q0j;q1j;q2j;q3j;q4ja e he fixed e ec s o in e cep , ime, squa e alue o ime and cosine wa e assumed independen o di e en ba ches, Aij is a andom e ec o pig and ϵij is a andom esidual. Pa ame e s β2;β3;q3jand q4jde e mine he ampli ude and wis he leng h o he cosine wa e used o accoun o he diu nal pa e n in daily BW. He e, wis cons an , does no a y wi h pig o ba ch, and was calcula ed as w=2π=24 ( ep esen ing exac ly 1 day). In addi ion, a gende coe ficien was es ed. The P - alue o he gende coe ficien sugges ed no significan di e - ences be ween g ow h o gil s and ba ows ( P =0.52), and was he e o e emo ed om he final model. The model assumed ha he wi hin-ba ch e o s a e allowed o be he e oscedas ic. The ollowing models speci ying wi hin-g oup a iance we e es ed: fixed a iance, di e en a iances pe s a um, powe o co a ia e, expo- nen ial o co a ia e and cons an plus powe o co a ia e. The model which success ully desc ibed he wi hin-g oup a iance was cons an plus powe o co a ia e. This a iance model was gi en by he equa ion: σ2 A +σ2 =σ2 Aδ1+ jj δ2  2 +σ2δ1+ jj δ2  2(2) in which σ2 Ais he a iance in animal e ec , σ2is he a iance in measu emen e o , δ1and δ2a e cons an s o he a iance model es ima ed om da a. Since he BW da a consis ed o epea ed measu emen s on he same pigs, he pig e ec was assumed o be a fi s o de au o eg essi e p ocess wi h mean 0 and au oco ela ion ρso ha Aij =ρσ A =σA; 1  Aij; 1+ωij (3) in which ωij Nð0;ð1ρ2Þσ2 A Þ: The obse a ions o BW o pigs we e no equally spaced in ime. The e o e, simila o Pinhei o and Ba es (2000) we used con inuous- ime wi hin-g oup co ela ion models, which na u ally accommoda e he imbalance in he da a. Tes ed co ela ion models included: linea , a ional quad a ic, sphe ical, Gaussian and exponen ial. Simila o S yga and K is ensen (2016), he mos adequa e wi hin-g oup co ela- ion model o pig BW da a was ound when assuming ha he co ela ion be ween BW measu emen s o a single pig dec eases exponen ially wi h ime. Table 1 Summa y o da a om fi e ba ches used in a s udy o daily pig g ow h Inse ion No. o No. o To al no. o A e age no. o Ini ial mean Ini ial SD in Ba ch da e obse a ion days 1 Gil s Ba ows BW measu emen s obse a ion (pe pig/day) BW o pigs (kg) 2 BW o pigs (kg) 2 1 25.11.2014 60 166 164 54,322 3.55 57.5 9.9 2 08.12.2014 64 165 158 51,237 3.66 62.1 8.3 3 02.03.2015 58 178 173 43,130 3.61 61.6 9.9 4 08.06.2015 58 177 178 51,700 3.38 59.9 8.0 5 15.09.2015 35 3 179 170 42,771 3.77 55.0 9.7 1 Numbe o days om u ning on he scales un il he las eco ded deli e y o pigs om gi en pen o he slaugh e house. 2 Based on he fi s eco ded obse a ion. 3 The smalle numbe o obse a ions was due o an e o in sa ing da a in he da abase. Cyclic g ow h pa e n in pigs 3 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a Following he app oach o Pinhei o and Ba es (2000) he significance o e ms used in he fixed e ec model we e es ed by he condi ional F - es s in he single-a gumen o m o he ANOVA o fi ed models. The ANOVA me hod was also used o es he significance o he he e oscedas ic model. Spa ial co ela ion models we e compa ed based on in o ma ion c i e ia s a is ics (Akaike in o ma ion c i e ion and Bayesian in o ma ion c i e ion). Fo da a analyses and plo ing, he R s a is ical so wa e (R Co e Team, 2014) and nlme package (Pinhei o e al ., 2017) was used. Resul s To ge an o e iew o he collec ed da a, BW measu emen s om he fi e ba ches we e plo ed and examined. On a e age, each pig was obse ed o 42 days and had 3.6 egis e ed weigh s pe day. A bo h he daily and hou ly le el, inc easing a iance be ween pigs o e ime was e iden (Figu e 2) as p e iously iden ified by S yga and K is ensen (2016). In addi ion, a diu nal pa e n in hou ly BW measu emen s was iden ified as seen in Figu e 3. G ow h model wi h diu nal pa e n All pa ame e s desc ibing he BW o pigs om he s udied he d ( oge he wi h 95% confidence in e als and P - alues used o es ing he fixed e ec s o he model), ob ained om he model fi , a e summa ized in Table 2. Acco ding o he esul s, he lowes ini ial BW o pigs was iden ified in Ba ch 2 (51 kg) while he highes was iden ified in Ba ch 3 (60.5 kg). The he d daily gain was ~1.2 kg. The highes daily gain was ob ained o Ba ch 2 (a ound 1.3 kg/ day) whe eas he lowes was ob ained o Ba ch 5 (a ound 1.0 kg/day). Pigs we e ligh e in he mo ning ( he minimum o he equency wa e was ob ained a ound 1000 h) and hea ie in he e ening ( he maximum o he equency wa e was ob ained a ound 2200 h) (Figu e 4). Howe e , he exac ime o ob aining maximum and minimum BW du ing he day di e ed be ween ba ches. In his he d, daily a ia ion in BW o pigs was ~1.2 kg. The lowes daily ampli ude in BW o pigs was obse ed o Ba ch 5 (0.9 kg) whe eas he highes daily ampli ude in BW was ound o Ba ch 4 (1.4 kg). F equency o isi s o he eeding a ea In all o he ba ches, mo ning and a e noon peaks in he equency o isi s could be dis inguished. Howe e , o Ba ch 3 and Ba ch 4 he mo ning eeding peak was ea lie in he day han he o he obse ed ba ches (Figu e 5). Fo example, 4.9% o all egis a ions o Ba ch 3 we e aken be ween 0600 and 0659 h. Fo he same ba ch be ween 0900 and 0959 h he equency o obse a ions was 5.0%. Con a y, o Ba ch 1 he equency o obse a ions be ween 0600 and 0659 h was only 2.3%, while be ween 0900 and 0959 h he equency inc eased o 5.3%. Discussion Diu nal pa e n o pig g ow h In his s udy, he BW o pigs was modeled as a quad a ic unc ion o ime. A diu nal pa e n was inco po a ed in o he model by a cosine wa e wi h known leng h (24 h). In 1938, Baldwin and Kendeigh (1938) confi med he exis ence o daily hy hms in he BW o mul iple wild species o bi ds. They demons a ed ha BW a ia ion o he smalle passe ine species amoun o as much as 12% o he mean daily BW. Howe e , his a ied wi h di e ences in ai em- pe a u e, amoun o eeding and o he ac i i ies. Thei s udy iden ified ha all bi ds los BW a nigh and gained BW he ollowing day. The loss o BW du ing he nigh was explained by lowe ai empe a u e whe eas a g adual weigh inc ease du ing he day was due o ac i e eeding. Al hough he s udy on daily a ia ion in BW o wild bi ds con inued (see o example he e iew by Cla k (1979) o Macleod e al . (2005)), no much a en ion has been gi en o daily a ia ion in BW o a m animals. Daily measu emen s o a m animals a e ob iously a easie o ob ain han hose o wild li ing spe- cies. Howe e , especially o pigs, un il ecen imes i was no easy o collec equen in o ma ion on indi idual BW wi hou he need o handling animals, which was bo h ime consuming and expensi e. One migh suspec ha o ani- mals ha ha e cons an access o eed and a e kep in mo e o less cons an empe a u es he daily a ia ion in BW will Figu e 3 Body weigh measu emen s collec ed du ing he whole a ening pe iod o selec ed pigs om pen numbe 1. Figu e 2 Body weigh o all pigs om Ba ch 1. Each line ep esen s he BW o an indi idual pig. S yga , Dolecheck and K is ensen 4 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a be small. Howe e , ecen ly, Män ysaa i and Män ysaa i (2015) demons a ed clea diu nal changes in BW o No dic Red cows which had eed a ailable 24 h. In hei s udy, he a e age di e ence be ween mo ning and e ening BW o he cow was 7.3 kg. The au ho s a e no awa e o s udies ha ha e e alua ed he daily a ia ion in BW o pigs. Ou esul s showed ha he ampli ude o BW fluc ua ion was clea ly di e en be ween ba ches. I is in ui i e o sus- pec ha he numbe o isi s du ing he day could influence he ampli ude o BW fluc ua ions. Fo g owing–finishing pigs, eeding pa e ns changed wi h age om sho and equen meals o long and la ge ones (Bigelow and Houp , 1988; Fàb ega e al ., 2003). This was also seen in ou da a. Pigs in Ba ch no.5 we e obse ed o ~1 mon h only and isi ed he eeding a ea wi h he highes equency compa ed wi h pigs om o he ba ches which we e obse ed o e ~2 mon hs. Mo e equen isi s o he eeding a ea o pigs in Ba ch 5 esul ed in he lowes fluc ua ions in daily BW. On he con a y, pigs om Ba ch 4, wi h he lowes a e age numbe o weigh measu emen s we e cha ac e ized wi h he highes a ia ion in BW du ing a day. Nielsen e al . (1995) ound ha he g oup size in which pigs we e kep influenced eeding beha io a iables, wi h pigs kep in la ge g oups making ewe bu longe isi s o he eede compa ed wi h smalle g oups. In ou s udy, he ini ial size o he ba ches was simila . The size o he g oup Table 2 Pa ame e s used o desc ibe diu nal and pe iodic changes o BW o pigs in he examined he d du ing he a ening pe iod 1 Pa ame e 2 Symbol Value 95% confidence in e al P - alue He d fixed e ec o in e cep β056.38 ± 0.78 <0.01 He d fixed e ec o ime β14.90 ×10 −2 ± 1.24 ×10 −3 <0.01 He d fixed e ec o he cos wa e β257.70 ×10 −2 ± 1.43 ×10 −2 <0.01 He d fixed e ec o he sin wa e β3−25.92 ×10 −2 ± 1.44 ×10 −2 <0.01 In e cep ×Ba ch 2 q02 −5.22 ± 1.18 <0.01 In e cep ×Ba ch 3 q03 4.13 ± 1.09 <0.01 In e cep ×Ba ch 4 q04 1.94 ± 1.09 <0.01 In e cep ×Ba ch 5 q05 −2.53 ± 1.09 <0.01 Time ×Ba ch 2 q12 0.49 ×10 −2 ± 2.14 ×10 −3 <0.01 Time ×Ba ch 3 q13 −0.26 ×10 −2 ± 1.78 ×10 −3 <0.01 Time ×Ba ch 4 q14 −0.36 ×10 −2 ± 1.76 ×10 −3 <0.01 Time ×Ba ch 5 q15 −0.92 ×10 −2 ± 1.88 ×10 −3 <0.01 Quad a ic ime ×Ba ch 1 q21 −1.22 ×10 −6 ± 9.68 ×10 −7 0.01 Quad a ic ime ×Ba ch 2 q22 −5.43 ×10 −6 ± 1.16 ×10 −6 <0.01 Quad a ic ime ×Ba ch 3 q23 −6.88 ×10 −6 ± 1.13 ×10 −6 0.2 Quad a ic ime ×Ba ch 4 q24 −9.29 ×10 −8 ± 1.01 ×10 −6 0.8 Quad a ic ime ×Ba ch 5 q25 5.66 ×10 −6 ± 1.51 ×10 −6 <0.01 Cos wa e ×Ba ch 2 q32 −0.03 ± 2.18 ×10 −2 <0.01 Cos wa e ×Ba ch 3 q33 −0.36 ± 1.16 ×10 −2 <0.01 Cos wa e ×Ba ch 4 q34 −0.01 ± 2.06 ×10 −2 0.3 Cos wa e ×Ba ch 5 q35 −0.15 ± 2.05 ×10 −2 <0.01 Sin wa e ×Ba ch 2 q42 −0.02 ± 2.18 ×10 −2 0.06 Sin wa e ×Ba ch 3 q43 −0.30 ± 2.05 ×10 −2 <0.01 Sin wa e ×Ba ch 4 q44 −0.15 ± 2.03 ×10 −2 <0.01 Sin wa e ×Ba ch 5 q45 0.10 ± 2.10 ×10 −2 <0.01 E olu ion e o σ2 A04.60 ×10 −5 ± 2.29 ×10 −5 Obse a ional e o σ2 05.53 ×10 −7 ± 3.61 ×10 −8 Co ela ion 3 ρ 99.57 ×10 −2 ± 2.76 ×10 −4 Powe o a iance model δ 1 0.96 ± 0.03 Cons an o a iance model δ 2 1056.1 ± 242.29 1 BW o pig iin ba ch jo e ime was desc ibed using equa ion (1). 2 Es ima es o in e cep ×Ba ch 1, ime ×Ba ch 1, Cos wa e ×Ba ch 1 and Sin wa e ×Ba ch 1 we e equal o 0. 3 Assuming 24 h elapsed be ween measu emen s. Figu e 4 Diu nal fluc ua ions in he BW o pigs om each ba ch es ima ed om he de eloped model. Cyclic g ow h pa e n in pigs 5 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a was dec easing wi h ime as he ac ion o hea ies pigs was sen o slaugh e . As he same slaugh e s a egy was implemen ed o all ba ches, he g oup size was dec easing a he same pace o all ba ches. The e o e, di e ences in he numbe o isi s o he eeding a ea be ween ba ches could mos ly be a ibu ed o di e ences in age. The main ocus o his s udy was o desc ibe he g ow h o pigs on an hou ly basis. Howe e , u u e s udies on he ds using equen BW moni o ing o pigs in la ge pens could ocus on combing beha io al da a wi h BW measu emen s. Combining his in o ma ion would allow o s udy which ac o s (e.g. he ini ial BW o inse ed pigs, ini ial a ia ion in BW, e c.) influence he numbe o isi s o he eeding a ea as well as how he numbe o isi s o he eeding a ea influences g ow h a e in a la ge pen en i onmen . Obse ed pa e n o isi s o he eeding a ea D inking pa e ns a e closely co ela ed o eed consump ion (Bigelow and Houp , 1988). The e o e, no su p isingly, diu nal pa e ns including wo s able and dis inguished peaks we e iden ified in he d inking beha io o g owing pigs in he s udy by Madsen and K is ensen (2005). Those d inking peaks (mo ning and a e noon) desc ibed by Madsen and K is ensen (2005) coincide wi h he eeding ime and BW peaks ound in ou s udy. Bo h Hyun e al . (1997) and Young and Law ence (1994) iden ified a single eeding peak pe day in pigs ed ad libi um a ~0900 h. O he esea che s ha e iden ified wo eeding peaks pe day, one in he mo ning and one in he a e noon (Mon gome y e al ., 1978; Bigelow and Houp , 1988; De Hae and Me ks, 1992). Di e ences in he numbe o eeding peaks ha e been a ibu ed o he pho ope iod ha pigs a e exposed o (Feddes e al ., 1989) and he empe a u e in he a ening uni (Villag á e al ., 2007). In ou s udy, pigs had access o dayligh and o cons an a ificial ligh om a lamp ins alled abo e he scale (Figu e 1). Pigs in na u al condi ions a e ac i e upon dayligh (Cu is, 1937). Howe e , access o a ificial ligh could al e hei beha io . As epo ed by Lay e al . (1999), pigs wi h cons an access o ligh we e mo e ac i e be ween 1830 and 0630 h han pigs subjec ed o a 12h ligh –12 h da k cycle. To ou bes knowledge, he e a e no s udies ha epo ed pigs’ac i i y in a pen wi h dayligh access and a ificial ligh illumina ing he weighing scale in he pen. In Denma k, he a ailabili y o na u al ligh a ies acco ding o he season o he yea . Since ba ches we e obse ed du ing di e en seasons, di e en a ailabili y o dayligh clea ly influenced he equency o isi s o he eeding a ea. Fo example, pigs om Ba ch 3 we e much mo e ac i e a ound 0700hcompa edwi hpigs omBa ch1andBa ch2. Acco ding o Villag á e al . (2007) i he indoo empe a- u e is close o he he mo neu al zone (be ween 14°C and 24°C), pigs a e likely o de elop a na u al beha io wi h wo peaks o eed consump ion and ac i i y du ing he illumi- na ed pe iod. Howe e , Feddes e al . (1989) epo ed ha changes in empe a u e on he a m migh be su ficien o modi y eeding pa e ns o g owing pigs. They ound ha when he indoo empe a u e cycles be ween 26°C a 0530 h and 40°C a 1400 h, he diu nal eeding pa e n o pigs will be di e en compa ed o a scena io wi h cons an empe a- u e (33°C). They de e mined ha when empe a u e a ied, eed consump ion shi ed o he cooles pa o he he mal cycle. Mo eo e , he pe iod o highes eed in ake occu ed ea lie in he mo ning and la e a nigh han in he cons an Figu e 5 Pe cen age o o al isi s o he eeding a ea (BW measu emen s) in each ba ch depending on he hou o he day. S yga , Dolecheck and K is ensen 6 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a empe a u e ea men . Tempe a u e was no egis e ed in ou s udy he e o e he possible influence o empe a u e on he eeding pa e n could no be analysed. Gi en ha he a m had a sys em egula ing indoo empe a u e, big a ia ions du ing he p oduc ion cycle as epo ed in he abo e s udies we e unlikely. Fu u e applica ion o he model Diu nal a ia ion o BW in pigs can find applica ion in in o ming he a me o unexpec ed g ow h de e io a ion o whole ba ches o pigs o pa icula indi iduals. Un il ecen ly, ob ain- ing equen in o ma ion on BW in ol ed handling animals (mo ing hem o scales loca ed ou side o pens) he e o e, gaining p ecise knowledge on BW was di ficul and expensi e. Howe e , mo e and mo e a me s a e in es ing in p ecision li es ock echnologies, such as a weigh so ing sys em ins alled in la ge pens. In his sys em, in o ma ion on BW da a is collec ed on he a m when he pig is isi ing he eeding a ea. Body weigh is a equen ly epo ed ai in biological s udies. Fo example in pig p oduc ion, we wan o know how BW changes wi h age (Schinckel e al ., 2004), du ing a disease challenge o a e applying a he apy (S yga e al ., 2016). Howe e , so a diu nal BW a ia ion has been neglec ed. Acco ding o ou esul s, he di e ence be ween mo ning and e ening BW o a pig was significan . The e o e, any equen BW moni o ing ool aiming a de ec ing, o example, heal h o he d managemen p oblems should accoun o he diu nal a ia ion o BW in pigs. Mo eo e , any expe imen s in which BW is one o he esponse a iables should be conduc ed so ha BW is egis e ed only du ing a specific pa o he day. The model pa ame e s ob ained in his s udy will be used in a moni o ing ool (dynamic linea model (DLM)) based on equen BW obse a ions. Fo an example o he applica ion o a DLM o moni o ing g ow h o pigs, a e e ence o S yga and K is ensen (2016) is made. Acco ding o he ob ained esul s, pa ame e s desc ibing diu nal a ia ion in BW should be included. Mo eo e , he ob ained pa ame e s (e.g. he d fixed e ec s, obse a ional and e olu ion a iance as well as au oco ela ion) will be used o speci y a iance componen s and o se he ini ial dis ibu ion o he pa ame e ec o in he DLM. The season o he yea migh also influence he BW o pigs. In Polish condi ions, Kościński e al . (2009) ound ha he highes g ow h a e in pigs occu s be ween May and June. They also demons a ed ha he weigh o 6-mon h-old pigs plo ed by mon h o bi h ollows a cosine wa e wi h he highes BW occu ing in pigs bo n in Feb ua y and he lowes in pigs bo n in Augus . The e o e, season is ano he e ec ha should be conside ed o inclusion in he model o pig BW as mo e da a is collec ed. Conclusions In his pape we desc ibed a new model o pig g ow h applied o equen BW moni o ing. In he p oposed model, pig BW was desc ibed by he in e cep (ini ial BW), slope (a e age daily gain du ing a ening) and a pe iodic pa e n (diu nal fluc ua ions in BW). In he examined he d, he diu nal ampli ude o pig g ow h anged om 0.9 o 1.4 kg. The e o e, wi h mode n echnologies (such as au oma ic scaling sys ems), accoun ing o daily fluc ua ions in BW becomes necessa y. The p oposed ma hema ical model o g ow h will be buil in o a moni o ing ool (a DLM wi h Kalman fil e ) and applied o a m da a in u u e s udies. 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S yga , Dolecheck and K is ensen 8 h ps://www.camb idge.o g/co e/ e ms. h ps://doi.o g/10.1017/S1751731117001690 Downloaded om h ps://www.camb idge.o g/co e. IP add ess: 154.16.60.179, on 24 Jul 2017 a 12:32:13, subjec o he Camb idge Co e e ms o use, a ailable a