Genetic parameters for test-day milk yield in tropical Holstein Friesian cattle fitting a multiple-lactation random regression animal model

Sou h A ican Jou nal o Animal Science 2017, 47 (No. 3) URL: h p://www.sasas.co.za ISSN 0375-1589 (p in ), ISSN 2221-4062 (online) Publishe : Sou h A ican Socie y o Animal Science h p://dx.doi.o g/10.4314/sajas. 47i3.12 Gene ic pa ame e s o es -day milk yield in opical Hols ein F iesian ca le i ing a mul iple-lac a ion andom eg ession animal model S. Mese e 1# & E. Negussie2 1 Wolai a Sodo Uni e si y, College o Ag icul u e, P.O. Box 138, Wolai a Sodo, E hiopia 2 Biome ical Gene ics, Na u al Resou ces Ins i u e (LUKE), 31600 Jokioinen, Finland (Recei ed 12 Decembe 2016; Accep ed 29 Ma ch 2017; Fi s published online 26 Ap il 2017) Copy igh esides wi h he au ho s in e ms o he C ea i e Commons A ibu ion 4.0 Sou h A ican Licence. See: h p://c ea i ecommons.o g/licenses/by/4.0/za Condi ion o use: The use may copy, dis ibu e, ansmi and adap he wo k, bu mus ecognise he au ho s and he Sou h A ican Jou nal o Animal Science. ______________________________________________________________________________________ Abs ac Accu a e es ima es o gene ic pa ame e s a e essen ial o gene ic imp o emen o milk yield in dai y ca le and o se ing up b eeding p og ammes. Es ima es o gene ic pa ame e s om es -day models, pa icula ly o Hols ein F iesian ca le main ained in opical en i onmen s, a e scan in he li e a u e. The objec i e o his s udy was he e o e o es ima e gene ic pa ame e s o milk yield by i ing a mul iple- lac a ion andom eg ession animal model (RRM) based on da a om E hiopian Hols ein F iesian he ds. Da a we e used om he i s h ee lac a ions o cows ha cal ed be ween 1997 and 2013. The da a comp ised 13 421 es -day milk yield eco ds om 800 cows om wo la ge dai y he ds. Va iance componen s we e es ima ed using he a e age in o ma ion es ic ed maximum likelihood me hod i ing an RRM. He i abili y es ima es o i s , second, and hi d lac a ions anged om 0.20 o 0.26, 0.15 o 0.27, and 0.17 o 0.28, espec i ely. He i abili y es ima es anging om 0.15 o 0.28 indica e ha e ec i e gene ic imp o emen should be accompanied by a co esponding imp o emen o he p oduc ion en i onmen . Ac oss-lac a ion gene ic co ela ions be ween i s and second, second and hi d, and i s and hi d lac a ions, exp essed on a 305-day yield basis, we e 0.88, 0.83, and 0.70, espec i ely. These gene ic co ela ions, less han o equal o 0.88, indica e ha di e en lac a ions a e di e en ai s. Fo an accu a e e alua ion o he gene ic me i o animals o milk yield, lac a ions should be ea ed as di e en , bu co ela ed ai s in a mul iple-lac a ion analysis. ______________________________________________________________________________________ Keywo ds: Gene ic co ela ion, he i abili y, Legend e polynomial, es -day model # Co esponding au ho : [email p o ec ed] In oduc ion Mul iple obse a ions sco ed on a cow du ing lac a ion o m a classical example o longi udinal da a (Diggle e al., 1994). The cu en me hod o gene ic e alua ion uses se e al daily measu emen s, usually aken once a mon h ( es -day) on an indi idual cow epea edly o e he cou se o lac a ion (Fe ei a e al., 2002; Dzomba e al., 2010). Use o es -day da a would o e a p ac ical solu ion in de eloping coun ies, whe e he e is a lack o in as uc u e and esou ces o daily milk eco ding h oughou lac a ion (Ila sia e al., 2007; Geb eyohannes e al., 2012). Tes -day eco ds esul in ewe measu emen s o milk yield as opposed o daily eco ding, and hus educe he cos o milk eco ding comp omising he accu acy o animal e alua ion. This is pa ly because he co ela ion be ween es -day measu emen s o milk yield dec eases as ime be ween he measu emen s inc eases (Bilal & Khan, 2009). I also allows g ea e lexibili y in milk eco ding p og ammes (Schae e e al., 2000). A andom eg ession es -day model (TDM) is he me hod o choice o imp o e he quali y o animal e alua ion o longi udinal ai s, and has been implemen ed in many coun ies. In pa icula , mul iple- lac a ion TDM i ing andom eg ession is used o gene ic e alua ion o p oduc ion ai s in dai y ca le in a ious coun ies. The analysis o mul iple-lac a ion da a has shown ha gene ic co ela ions among lac a ions a e less han uni y (Zumbach e al., 2008), indica ing ha each lac a ion pe o mance is mo e o a sepa a e ai han has been app ecia ed (Powell & No man, 1981). Fu he mo e, eco ds o second and la e lac a ions p o ide mo e comple e in o ma ion on li e ime pe o mance han hose om i s lac a ion only (Powell & No man, 1981). Howe e , esul s om he de elopmen and applica ion o mul i- ai es -day animal e alua ions and he necessa y es ima es o gene ic pa ame e s o he a ious lac a ions o Hols ein F iesian ca le in opical en i onmen s a e pa icula ly scan y in scien i ic li e a u e. A i s s ep owa ds he possible applica ion o he mul iple-lac a ion TDM in E hiopia is o es ima e he gene ic pa ame e s o es - Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 353 day milk yields eco ds unde E hiopian condi ions. The e o e, he objec i es o his s udy we e o es ima e co a iance componen s and gene ic pa ame e s o milk yield i ing a andom eg ession es -day animal model using da a on he i s h ee lac a ions o Hols ein F iesian ca le om E hiopian he ds. Ma e ials and Me hods Fo his s udy, es -day da a we e used o he i s h ee lac a ions o Hols ein F iesian cows ha cal ed be ween 1997 and 2013. They comp ised 13 421 es -day milk yield eco ds be ween 5 and 305 days in milk (DIM) om 800 cows o wo he ds. Cows had o ha e es -day eco ds o he i s lac a ion o be included in he da ase . The numbe o es -day eco ds pe lac a ion anged om 8 o 10. Fi e age classes we e de ined in each lac a ion. These included cows less han 810, 811 o 990, 991 o 1170, 1171 o 1350 and abo e 1350 days old a i s cal ing; cows less han 1350, 1351 o 1530, 1531 o 1770, 1771 o 1980 and abo e 1980 days old a second cal ing; and cows less han 1800, 1801 o 2040, 2041 o 2280, 2281 o 2520 and abo e 2520 days a hei hi d cal ing. Cal ing mon hs we e assigned o one o h ee seasons, namely long-d y, sho - ainy and long-dai y seasons, co esponding wi h Oc obe o Feb ua y, Ma ch o May and June o Sep embe , espec i ely. The mul iple-lac a ion RRM included he i s h ee lac a ions as di e en ai s. The s a is ical model used o he analysis o he da a can be desc ibed as: ∑ ∑ ∑ Whe e: is he es -day eco d q o cow o made a DIMop o lac a ion is he ixed e ec o he d I is he ixed e ec o age a cal ing class k is he andom e ec o si e *cal ing yea in e ac ion l is he andom e ec s o he d es -day mon h n is andom addi i e gene ic e ec s is andom pe manen en i onmen al e ec s is he andom esidual e ec , , and a e eg essions o pheno ype on DIM o he j h season o cal ing, and he o h cow's andom addi i e gene ic and pe manen en i onmen al e ec s, espec i ely a e he co esponding m h coe icien s ha desc ibe he shape o he ixed eg ession lac a ion cu e. a e he co esponding second o de Legend e polynomial coe icien s ha desc ibe he shape o he andom eg ession lac a ion cu es. The ixed eg ession lac a ion cu e was modelled by a combina ion o Legend e polynomial and Wilmink unc ions as co- a iables: =0.7071, =1.2247* DIMop, =2.3717* DIMop2 - 0.7906, =4.6771*DIMop3 - 2.8062* DIMop and =exp-0.05DIMop Whe e: ep esen coe icien s o he hi d-o de o hogonal Legend e polynomial a DIM d plus he Wilmink unc ion (Wilmink, 1987), espec i ely. In he Wilmink unc ion, he exponen ial e m is gene ally ega ded as a cons an (Wilmink, 1987). In he p esen s udy, i was assumed o be -0.05. Legend e polynomials in combina ion wi h he Wilmink unc ion ha e been used by a ious au ho s (Lidaue e al., 2003; de Melo e al., 2007; Negussie e al., 2008; San os e al., 2013) in modeling he ixed lac a ion cu es o es -day milk yield in a ious b eeds o dai y cows. Va iance componen s we e es ima ed by a e age in o ma ion es ic ed maximum likelihood me hod using he DMU p og amme, a package o analysing mul i a ia e mixed models (Madsen & Jensen, 2013). Con e gence o solu ions was de e mined when he di e ence be ween he igh -hand side and le -hand side o he mixed model equa ion (MME) was less han 10-6. The esul ing es ima es o andom eg ession coe icien s we e hen used o calcula e a iance componen s and associa ed gene ic and pheno ypic pa ame e s. Fo each lac a ion, addi i e gene ic a iance (𝜎𝑎 ) o DIM 𝑑 was es ima ed as: 𝜎𝑎 (𝑑𝑖) 𝝓(𝑑𝑖)𝑮𝝓(𝑑𝑖) ′ Whe e G is he co a iance ma ix o he addi i e gene ic andom eg ession coe icien s, and 354 Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 𝑑 is DIM. Simila ly, he pe manen en i onmen al a iance (𝜎 𝑒 ) o DIM 𝑑 was es ima ed as: 𝜎 𝑒 (𝑑𝑖) 𝝓(𝑑𝑖)𝑷𝒆𝝓(𝑑𝑖) ′ Whe e: Pe is he co a iance ma ix o he pe manen en i onmen andom eg ession coe icien s, and 𝑑 is DIM. He i abili y o a pa icula DIM 𝑑 in lac a ion we e calcula ed by di iding he gene ic a iance 𝜎𝑎 (𝑑𝑖) by he sum o pe manen en i onmen al (𝜎 𝑒 (𝑑𝑖)) gene ic (𝜎𝑎 (𝑑𝑖)) and esidual (𝜎𝑒 ) a iances o a pa icula DIM 𝑑 . ĥ𝑑𝑖 𝜎𝑎 (𝑑𝑖) 𝜎 𝑒 (𝑑𝑖) 𝜎𝑎 (𝑑𝑖) 𝜎𝑒 The gene ic co ela ion be ween wo days in lac a ion 𝑑 and 𝑑 was calcula ed by di iding he addi i e gene ic co a iance be ween days 𝑑 and 𝑑 by he p oduc o he squa e oo o he gene ic a iances o days 𝑑 and 𝑑 . 𝑟𝑎(𝑑𝑖 𝑑𝑗) 𝝓(𝑑𝑖)𝑮𝝓(𝑑𝑗) ′ √𝝓(𝑑𝑖)𝑮𝝓(𝑑𝑖) ′.𝝓(𝑑𝑗)𝑮𝝓(𝑑𝑗) ′ Simila ly, he pheno ypic co ela ion was calcula ed by di iding he pheno ypic co a iance be ween days 𝑑 and 𝑑 , by he p oduc o squa e oo o pheno ypic a iances o day 𝑑 and 𝑑 . 𝑟𝒑(𝑑𝑖 𝑑𝑗) 𝝓(𝑑𝑖)𝑷𝝓(𝑑𝑗) ′ √𝝓(𝑑𝑖)𝑷𝝓(𝑑𝑖) ′.𝝓(𝑑𝑗)𝑷𝝓(𝑑𝑗) ′ Whe e: P is he co a iance ma ix o he pheno ypic eg ession coe icien s The gene ic and pheno ypic co ela ions be ween any wo lac a ions, o example 1 and 2 o he same DIM om mul iple-lac a ion RRM analyses, we e calcula ed by di iding he addi i e gene ic co a iance be ween days 𝑑 and 𝑑 by he p oduc o he squa e oo o he gene ic a iances o he days 𝑑 and 𝑑 . 𝑟𝑎(𝑑𝑖1 𝑑𝑖2) 𝝓(𝑑𝑖1)𝑮𝝓(𝑑𝑖2) ′ √𝝓(𝑑𝑖1)𝑮𝝓(𝑑𝑖1) ′.𝝓(𝑑𝑖2)𝑮𝝓(𝑑𝑖2) ′ 𝑟 (𝑑𝑖1 𝑑𝑖2) 𝝓(𝑑𝑖1)𝑷𝝓(𝑑𝑖2) ′ √𝝓(𝑑𝑖1)𝑷𝝓(𝑑𝑖1) ′.𝝓(𝑑𝑖2)𝑷𝝓(𝑑𝑖2) ′ Whe e: di1 and di2 a e DIM in lac a ion 1 and 2, espec i ely. G and P a e he co a iance ma ix o he addi i e gene ic and pheno ypic eg ession coe icien s om he mul iple-lac a ion analysis, espec i ely. Gene ic and pheno ypic co ela ions on a 305-day basis we e calcula ed as ollows: ∑𝝓(𝑑 ) 𝑑 . Whe e: is a ow ec o o o de quad a ic, wi h elemen s equal o he sum o e days 5 o 305. T =A⊗ Whe e: A is 3-by-3 iden i y ma ix. The gene ic co ela ions be ween any wo lac a ions, 𝑙 and 𝑙 o example, be ween lac a ion 1 and 2, o 305-day we e calcula ed by di iding he addi i e gene ic co a iance be ween 305-day 𝑙 and 𝑙 by he p oduc o he squa e oo o he gene ic a iances o he 305-day 𝑙 and 𝑙 . The same s eps we e ollowed o calcula e pheno ypic co ela ions. Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 355 𝑟𝑎( 1 2) 𝑻( 1)𝑮 𝑻( 2) ′ √𝑻( 1)𝑮 𝑻( 1) ′.𝑻( 2)𝑮 𝑻( 2) ′ Resul s The s uc u e o he da ase and pedig ee ile a e indica ed in Table 1. The a i ion in numbe o cows om he i s o hi d cal ing is consis en wi h he s uc u e o Hols ein he ds in E hiopia, whe e cows a ain, on a e age, 2.6 lac a ions (Table 1). The o e all means and s anda d de ia ions o es -day milk yields o i s , second, and hi d lac a ions we e 11.1 ± 3.9, 13.0 ± 4.7, and 13.9 ± 5.1 kg, espec i ely. The pheno ypic means and s anda d de ia ion o es -day milk yield along di e en DIM in he i s h ee lac a ions a e indica ed in Table 2. The pheno ypic end o es -day milk yield o all lac a ions showed a lowe milk yield a he beginning o lac a ion wi h peaks a 30 o 35 DIM. A e peak lac a ion, es -day milk yield showed a g adual bu consis en decline un il he end o he lac a ion pe iod. Table 1 Desc ip ion o es -day milk yield da ase s and s uc u e o he pedig ee ile om he i s h ee lac a ions in Hols ein F iesian cows Obse a ion Lac a ion Numbe I II III O e all Tes -day eco ds 6850 3996 2575 13421 Cows wi h eco ds 800 442 301 Animals in he pedig ee 1779 1779 1779 1779 Numbe o si es - - - 139 Numbe o dams - - - 617 Reco ds pe cow 8.5 9 8.6 - Cal ing age classes 5 5 5 15 Cal ing seasons classes 3 3 3 9 Cal ing yea 17 16 15 17 He d es -mon h classes 316 283 261 860 The esidual a iances es ima ed om mul iple-lac a ion analysis i ing a mul i- ai RRM model we e 2.33, 2.75 and 3.06 kg2 o i s , second and hi d lac a ions, espec i ely. In Figu es 1 and 2, es ima es o addi i e gene ic and pe manen en i onmen al a iances, espec i ely, a e shown o he es -day milk yield a a ious s ages du ing he i s h ee lac a ions. The es ima ed addi i e gene ic a iances om i s , second and hi d lac a ions anged om 1.29 o 2.00, 1.77 o 2.84 and 1.71 o 3.27 kg2, espec i ely. The es ima ed a iance o si e by cal ing yea in e ac ion om i s , second, and hi d lac a ions was 0.09, 0.22, and 0.47 kg2, espec i ely, and accoun s o a small po ion o he o al a iance. In all lac a ions, he addi i e gene ic a iances dec eased a he beginning o he lac a ion ajec o y and inc eased g adually owa ds he end. In pa icula , in he second and hi d lac a ions, highe a iances we e obse ed a he ex eme ends o he lac a ion pe iod. On he o he hand, in he i s lac a ion, a gen le decline in he es ima es o addi i e gene ic a iances was obse ed owa ds he end o he lac a ion. The highes addi i e gene ic a iances o i s lac a ion we e a he beginning o lac a ion and he o e all pa e n o he a iances along he lac a ion ajec o y was somewha consis en a e ea ly lac a ion. In gene al, he esul s showed ha es ima ed addi i e gene ic a iances o i s lac a ion we e lowe han hose o la e lac a ions. The hi d lac a ion had he highes es ima ed addi i e gene ic a iances compa ed wi h o he i s and second lac a ions. 356 Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 Table 2 Pheno ypic means and s anda d de ia ions (SD) o es -day milk yield (kg) in h ee lac a ions o Hols ein F iesian cows a selec ed days in milk DIM Lac a ion numbe I II III Mean SD Mean SD Mean SD 5 11.5 3.0 12.9 4.7 17.8 2.9 35 13.9 4.8 15.2 3.7 18.6 2.9 65 13.5 4.8 14.4 3.5 17.0 4.1 95 12.9 4.1 13.6 5.2 16.3 3.9 125 12.1 3.7 12.1 3.8 15.9 3.7 155 11.5 4.0 12.2 3.6 15.0 3.8 185 11.1 3.4 11.9 4.4 14.8 3.4 215 9.9 3.7 11.1 3.1 12.5 2.7 245 9.7 3.7 11.2 3.1 12.3 3.8 275 9.4 3.9 9.3 2.6 11.6 3.6 305 9.0 3.2 7.7 1.8 11.5 4.0 Figu e 1 Es ima es o addi i e gene ic a iances o milk yield a di e en s ages o lac a ion in he i s , second and hi d lac a ions o Hols ein F iesian cows o E hiopia Figu e 2 Es ima es o pe manen en i onmen al a iances o milk yield a di e en s ages o lac a ion in he i s , second and hi d lac a ions o Hols ein F iesian cows o E hiopia 1 1.5 2 2.5 3 3.5 535 65 95 125 155 185 215 245 275 305 Va ainces, kg2 Days in milk Fi s Second Thi d 0 2 4 6 8 10 535 65 95 125 155 185 215 245 275 305 Va iances, kg2 Days in milk Fi s Second Thi d Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 357 Du ing lac a ion, he es ima ed pe manen en i onmen al a iances anged om 1.98 o 5.08, 3.17 o 8.66, and 3.67 o 8.95 kg2 in he i s , second, and hi d lac a ions, espec i ely. The pe manen en i onmen al a iances o milk yield we e highe han he co esponding addi i e gene ic a iances in all h ee lac a ions. Simila o he addi i e gene ic a iances, he pe manen en i onmen al a iances showed a ma ked decline a he beginning o he lac a ion, we e lowe in mid lac a ion, and inc eased sligh ly owa ds he end o lac a ion in all h ee pa i ies. Fu he mo e, he es ima ed pe manen en i onmen al a iances showed an inc ease wi h inc ease in lac a ion numbe , as did he addi i e a iances. He i abili y es ima es o es -day milk yield om mul iple-lac a ion RRM analysis a e p esen ed in Figu e 3. O e all, he es ima ed he i abili ies o es -day milk yield anged om 0.15 o 0.28 ac oss lac a ion in he i s h ee lac a ions. Es ima ed he i abili ies o he i s , second, and hi d lac a ions anged om 0.20 o 0.26, 0.15 o 0.27, and 0.17 o 0.28, espec i ely. In gene al, he magni ude o he he i abili y es ima es was highe be ween DIM 230 and 260 compa ed wi h he beginning and end (ex emes) o lac a ion o all pa i ies. The di e ence in he i abili y es ima es be ween i s and second lac a ions was small o mos o he lac a ion, excep a he ex emes. The es ima es o he i abili y o he hi d lac a ion showed a ma ked decline in he ea ly s ages o lac a ion, wi h a sha p inc ease om DIM 65 o DIM 245, ollowed by a sligh decline he ea e . Figu e 3 Es ima es o he i abili y o milk yield a di e en s ages o lac a ion in i s , second and hi d lac a ions in Hols ein F iesian cows o E hiopia Gene ic co ela ions among es -day milk yields a he same DIM in he i s h ee lac a ions a e p esen ed in Table 3. The gene ic and pheno ypic co ela ions be ween lac a ions anged om 0.37 o 0.90 and 0.17 o 0.52, espec i ely, o he di e en s ages o lac a ion. Gene ic co ela ions be ween adjacen lac a ions such as i s and second o second and hi d we e highe han hose be ween i s and hi d lac a ions. Simila ly, pheno ypic co ela ions among es -day milk yields a he same DIM in he h ee lac a ions we e all posi i e and g ea e be ween consecu i e lac a ions han be ween he i s and hi d lac a ions. The es ima es o gene ic co ela ions calcula ed on 305-days basis be ween i s and second, i s and hi d and second and hi d lac a ions we e 0.88, 0.70 and 0.83, espec i ely. In addi ion, he es ima es o pheno ypic co ela ions on 305-days basis be ween i s and second, i s and hi d and second and hi d lac a ions we e 0.56, 0.51 and 0.61, espec i ely. Discussion In dai y cows, he le el o es -day milk yield di e ed no iceably be ween lac a ions. The esul s o his s udy in gene al showed ha he o e all mean es -day milk yield in i s lac a ion cows was lowe han ha o cows in la e lac a ions. P e ious s udies by Za adilo á e al. (2005) and Tijani e al. (2010) also epo ed ha he o e all means o milk yield inc eased wi h lac a ion numbe . The lowe milk p oduc ion du ing he i s compa ed wi h la e lac a ions could be explained because i s lac a ion cows we e s ill g owing, and nu ien s a e he e o e pa i ioned be ween g ow h and milk p oduc ion. In he p esen s udy, he o e all means o es -day milk yield o he i s h ee lac a ions we e lowe han hose epo ed by Za adilo á e al. (2005) o Hols ein cows (18.3, 21.8, and 23 kg o i s , second, and hi d lac a ions, espec i ely) in Czech and Tijani e al. (2010) o Hols ein cows (18.4, 19.8, and 20.9 kg o i s , second, and hi d lac a ions, espec i ely) in Mo occo. Simila ly, Cos a e al. (2008) and Bigna di e al. 0.10 0.15 0.20 0.25 0.30 535 65 95 125 155 185 215 245 275 305 He i abili y Days in milk Fi s Second Thi d 358 Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 (2011), wo king on B azil Hols ein, ca le epo ed highe i s lac a ion es -day milk yield o 22.53 and 27.45 kg, espec i ely, compa ed wi h he es ima es om he cu en s udy. Table 3 Es ima es o gene ic and pheno ypic co ela ions o es -day milk yield be ween i s and second (I- II), i s and hi d (I-III) and second and hi d (II-III) lac a ions om a mul iple-lac a ion andom eg ession es - day model in Hols ein F iesian cows o E hiopia DIM I-II I-III II-III Gene ic co ela ions 5 0.47 0.36 0.54 35 0.53 0.44 0.69 65 0.62 0.50 0.78 95 0.71 0.54 0.77 125 0.78 0.56 0.73 155 0.83 0.58 0.70 185 0.87 0.62 0.70 215 0.90 0.67 0.72 245 0.90 0.73 0.76 275 0.86 0.77 0.79 305 0.78 0.75 0.77 Pheno ypic co ela ions 5 0.30 0.17 0.37 35 0.37 0.28 0.43 65 0.42 0.36 0.47 95 0.45 0.41 0.49 125 0.47 0.43 0.50 155 0.49 0.43 0.51 185 0.50 0.44 0.52 215 0.52 0.45 0.52 245 0.52 0.46 0.51 275 0.49 0.47 0.47 305 0.42 0.46 0.38 A simila pheno ypic end o his s udy was epo ed o i s lac a ion es -day milk yield o Hols ein ca le by Shadpa a & Yazdanshenas (2005), Abdullahpou e al. (2010) and Boujenane & Hila (2012). An in e es ing obse a ion is ha in he E hiopian Hols ein F iesian, he peak o lac a ion was a ained a DIM 30, which was ea lie compa ed wi h ha o o he popula ions. Fo example, o Hols ein cows in B azil (San os e al., 2013) and Sahiwal cows in India (Dong e & Gandhi, 2014) he peak o lac a ion was a ained a a ound he eigh h and se en h weeks o lac a ion, espec i ely. The goal o selec ion in dai y ca le is o imp o e li e ime p oduc ion o cows, which implies ha aking he di e en lac a ions in o accoun (Beaumon , 1989) is essen ial o he es ima ion o gene ic pa ame e s and animal e alua ions. In mos opical coun ies, gene ic e alua ion o ca le includes di e en lac a ions as epea ed measu es o he same ai , he e o e assuming ha di e en lac a ions a e in luenced by he same se o genes (Geb eyohannes, 2012). Resul s om his s udy indica e ha lac a ions should be ega ded as di e en bu co ela ed ai s in gene ic e alua ions. In his s udy, esidual a iance showed an inc easing end wi h lac a ion numbe . A s eady ise in esidual a iance wi h inc ease in lac a ion numbe was epo ed by Tong e al. (1979), D ue e al. (2005) and Za adilo á e al. (2005) in dai y ca le and Zumbach e al. (2008) in dai y goa s. This s udy con i ms ha he e ogenei y in addi i e gene ic and pe manen en i onmen al a iances exis s o e lac a ions and ac oss DIM wi hin lac a ion. Se e al au ho s, including Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 359 Tong e al. (1979), Guo e al. (2002) and D ue e al. (2005), also epo ed ha in dai y ca le a iances inc eased wi h lac a ion numbe . Highe addi i e gene ic a iances obse ed a he ex eme ends o he second and hi d lac a ions in his s udy a e in line wi h hose o Za adilo á e al. (2005), who epo ed high gene ic a iances a he beginning and end o he i s h ee lac a ions in Czech Hols ein. On he con a y, Rekaya e al. (1999) in Spanish Hols ein F iesian, Pool e al. (2000) in Ne he lands Hols ein F iesian and D ue e al. (2003) in F ench Hols ein showed he highes gene ic a iance in mid lac a ion and lowe es ima es a he beginning and end o lac a ion. In his s udy, si e by cal ing yea in e ac ion was included in he andom pa s o he models mainly o accoun o he a ious g oups o si es used ac oss di e en yea g oups, which imp o ed he a iance s uc u e and led o as con e gence o solu ions. The gene ic a iance o milk yield is one indica o o he achie emen o gene ic imp o emen p og ammes in he coun y. Se e al s udies epo ed a ying ends o addi i e gene ic a iances ac oss he lac a ion pe iod. Fo ins ance, Za adilo á e al. (2005) in Czech Hols ein, Caccamo e al. (2008) in I alian dai y cows, and Mohammadi e al. (2014) in I anian Hols ein epo ed highe es ima es o addi i e gene ic a iances a he beginning and owa ds he end o he lac a ion. On he o he hand, El Fa o e al. (2008) in na i e B azilian Ca acu hei e s epo ed highe addi i e gene ic a iances a he beginning and a declining end a e wa ds. Flo es & an de We (2015) om hei wo k on da a om a bu alo popula ion epo ed highe es ima es o addi i e gene ic a iance in ea ly and du ing peak lac a ion. The highe pe manen en i onmen al a iance han ha o addi i e gene ic a iance, obse ed in his s udy, could be he limi ed da a used o a iance componen analysis. Excep a he ex emes o he lac a ion pe iods, he end o he es ima ed he i abili y was inc easing ac oss DIM in all pa i ies. Simila inc eases in he cou se o he he i abili y cu e in h ee lac a ions we e epo ed by Guo e al. (2002) in Danish Je sey and Za adilo á e al. (2005) in Czech Hols ein. The he i abili ies among lac a ions we e only sligh ly di e en om mid o end o lac a ion. The he i abili ies om hi d lac a ion we e highe han hose o he i s and second lac a ions o his pe iod, while no signi ican di e ences in he i abili y es ima es we e obse ed be ween he i s and second lac a ions. Simila indings ha e been epo ed om black and whi e ca le (S abel & Misz al, 1999) in Poland and Hols ein cows (Za adilo á e al., 2005) in Czech, indica ing ha he i abili y inc eased wi h inc ease in pa i y numbe . On he con a y, o he s udies epo ed ha es ima es o he i abili y o consecu i e lac a ions dec eased wi h inc ease in lac a ion numbe in Hols ein cows (Liu e al., 2000) in Ge many and Je sey cows (Guo e al., 2002) in Danish. One o he key poin s in dai y b eeding p og ammes is selec ion o young bulls, usually based on hei daugh e s’ pe o mance in i s lac a ion. Because longe i y, and hence pe o mance in la e lac a ions, is also o in e es o b eede s, he e ec i eness o selec ion schemes depends on he gene ic co ela ions be ween he i s and la e lac a ions (S abel & Jam ozik, 2006). I gene ic co ela ions be ween di e en lac a ions a e less han uni y, his implies ha di e en se o genes in luence es -day milk yields in di e en lac a ions. In his s udy, he gene ic and pheno ypic co ela ions be ween es -day eco ds depend on he s age o lac a ion and pa i y numbe . The gene ic and pheno ypic co ela ions calcula ed, based on bo h daily and an accumula ed 305-day basis be ween lac a ions we e highe o adjacen lac a ions ( i s and second, and second and hi d) han hose es ima ed be ween i s and hi d lac a ions. Simila ly, se e al au ho s ha e epo ed ha gene ic co ela ions o es -day milk yield be ween he i s and second lac a ions we e highe han he co ela ions be ween he i s and hi d lac a ions Czech Hols ein cows (Za adilo á e al., 2005), Polish black and whi e ca le (S abel & Jam ozik, 2006) and Mo occan Hols ein cows (Tijani e al., 2010). In his s udy, he gene ic co ela ions be ween lac a ions we e sligh ly highe han hose o o he s udies. Fo example, S abel e al. (2004) in Polish black and whi e ca le popula ion epo ed ha gene ic co ela ions be ween adjacen lac a ions we e 0.70 o milk yield, whe eas be ween i s and hi d lac a ions hey we e lowe (a ound 0.62). Simila ly, Za adilo á e al. (2005) in Czech Hols ein cows showed gene ic co ela ions o 0.77, 0.75 and 0.61 be ween i s and second, second and hi d, and i s and hi d lac a ions, espec i ely. In his s udy, he pa e ns o gene ic co ela ions showed an inc ease along DIM and a sligh decline owa ds he end o he lac a ions. Howe e , S abel & Jam ozik (2006) in Polish black and whi e ca le and Hols ein cows Tijani e al. (2010) in Mo occan Hols ein cows epo ed gene ic co ela ions ac oss lac a ions wi h smalles es ima es a he ex emes o lac a ion and highes in he middle o lac a ion. Conclusion Es ima es o gene ic pa ame e s a e essen ial o gene ic imp o emen o milk yield in dai y ca le and o se ing up sus ainable dai y b eeding p og ammes. Resul s om his s udy indica e ha he i abili y o milk p oduc ion anged om 0.15 o 0.30. This sugges s ha al hough he e is po en ial o gene ic imp o emen in milk yield o opical Hols ein F iesian, simul aneous imp o emen o he p oduc ion en i onmen is essen ial. Fu he mo e, esul s om he mul iple-lac a ion RRM analysis showed ha co ela ions among he i s h ee lac a ions on 305-d basis anged om 0.70 o 0.88. This indica es ha o accu a e e alua ion o 360 Mese e & Negussie, 2017. S. A . J. Anim. Sci. ol. 47 he gene ic me i o animals, he a ious lac a ions should be ea ed as di e en , bu co ela ed ai s in a mul iple-lac a ion analysis. Acknowledgmen s The au ho s would like o acknowledge he E hiopian Minis y o Ag icul u e, Na ional A i icial Insemina ion Cen e o p o iding he da a. The au ho s a e also g a e ul o he Biome ical Gene ics, Na u al Resou ces Ins i u e, Finland, o hei suppo in he da a analyses. Addis Ababa Uni e si y and Wolai a Sodo Uni e si y a e also acknowledged o hei inancial suppo . Au ho s’ Con ibu ions SM w o e he manusc ip , analysed he da a, and in e p e ed he esul s. EN pa icipa ed in he analysis and in e p e a ion o da a, d a ing and e ising he manusc ip . Con lic o In e es Decla a ion We wish o s a e ha he inancial sou ce and da a ma e ial used in his s udy a e duly acknowledged and ha he e a e no known con lic s o in e es associa ed wi h his pape . Re e ences Abdullahpou , R., Shah babak, M.M., Neja i-Ja a emi, A. & To shizi, R.V., 2010. Gene ic analysis o dai y milk, a and p o ein pe cen age o I anian i s lac a ion Hols ein ca le. Wo ld Appl. Sci. J. 10, 1042-1046. Beaumon , C., 1989. Res ic ed maximum likelihood es ima ion o gene ic pa ame e s o i s h ee lac a ions in he Mon bélia de dai y ca le b eed. Gene . Sel. E ol. 21, 493-506. Bigna di, A.B., El Fa o, L., To es Júnio , R.A.A., Ca doso, V.L., Machado, P.F. & Albuque que, L.G., 2011. 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