Application of different models to the lactation curves of unimproved Awassi ewes in Turkey
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1 Souh African Journal of Animal Science 005, 35 (4) 38 Applicaion of differen s o he lacaion curves of unimproved Awassi ewes in Turkey B. Dag 1#, I. Keskin 1 and F. Mikailsoy 1 Deparmen of Animal Science, Faculy of Agriculure, Selcuk Universiy, 4031, Konya, Turkey Deparmen of Soil Science, Faculy of Agriculure, Selcuk Universiy, 4031, Konya, Turkey Absrac The objecive of his sudy was o invesigae he use of four differen mahemaical funcions (Wood, Inverse Polynomial, Quadraic and Cubic s) for describing he lacaion curve of unimproved Awassi ewes. Daa were colleced from 136 ewes from he same flock raised on he Sae Farm of Gözlü in he Konya Province of Turkey. The differences in esimaed oal milk yields beween he s were no saisically significan. All s were adequae in describing oal milk yield, hough oal milk yield esimaed using he Cubic was very close o oal milk yield calculaed by he Fleischmann mehod. Age effecs on parameers were no significan. The Inverse Polynomial overesimaed he peak yield significanly. Esimaed peak yields of he Wood and Cubic were similar while ha obained from he Quadraic was significanly lower han ha of he oher s. Day of peak yield esimaed by he s varied beween 10. and 56.4 days. The differences beween days of peak yield esimaed using he differen s were significan. R values of he s ranged from 0.74 o The Cubic gave he bes R value. The lowes mean square predicion error was found using he Cubic. Correlaion coefficiens beween oal milk yield calculaed by he Fleischmann mehod and esimaed oal milk yield from he oher s ranged from o The highes correlaion coefficien was found for he Cubic. As a resul, he Cubic showed he bes fi o he daa colleced from unimproved Awassi ewes and allowed a suiable descripion of he shape of he lacaion curve. Keywords: Unimproved Awassi, sheep, ewes, lacaion curve, milk yield, mahemaical # Corresponding auhor. bdag@selcuk.edu.r Inroducion Appropriae s for describing lacaion curves provide useful informaion for breeding programs and managemen pracices, especially for culling and in assessing he nuriional and healh saus of animals. In order o assess plausible forms of lacaion curves, milk yield records colleced hroughou he whole lacaion are required (Chang e al., 001). Empirical algebraic s offer summaries of longiudinal milk yield paerns hroughou lacaion, from which cumulaive curves can be esimaed (Ruiz e al., 000). These s allow oal milk yield predicion from parial or incomplee daa, and hey can be used in ling sudies for analysing changes in milk yield caused by environmenal facors (Goodall & Spreavak, 1985; Moran & Gnanasakhy, 1989). Animals wih he poenial for a high milk yield can be idenified by using his informaion before he lacaion has been compleed. Furhermore, lacaion curves can be used o esablish a suiable ime o end he lacaion (Chang e al., 001). Several mahemaical s have been developed o describe lacaion curves (Wood, 1967; Neal & Thornley, 1983; Grosmann & Koops, 1988; Moran & Gnanasakhy, 1989; Rook e al., 1993; Dijksra e al., 1997; Cappio-Borlino e al., 1997; Pollo, 1999; 000). The Wood has been used in mos lacaion curve sudies, because i includes he basic feaures of lacaion curves wih only hree parameers a, b and c which allow he calculaion of average producion, maximum producion and day of maximum producion, respecively. This has made he Wood he mos widely used funcion for he descripion of lacaion curves. Mos of he alernaive s are also based on he Wood (Cobby & Le Du, 1978; Wilmink, 1987; Papajcsik & Bodero, 1988). However, empirical mahemaical s have been proposed o describe he regular shape of he lacaion curve in dairy cows and dairy sheep (Torres- Hernandez & Hohenboken, 1980; Cappio-Borlino e al., 1989; Cappio-Borlino e al., 1995; Groenewald e al., 1995). Aemps o fi hese s o decayed curves resuled in parameer esimaes ha fell ou of he range of biological significance (Cappio-Borlino e al., 1997).
2 Souh African Journal of Animal Science 005, 35 (4) 39 The Awassi is he mos numerous and widespread ype of sheep in souhwes Asia. I is he ypical sheep breed of Syria, Lebanon, Jordan and Israel. The Awassi is also disribued hroughou souheas Turkey. I is very hardy and hrives well under poor feeding and exreme climaic condiions. Husbandry is ypically exensive. Animals are kep in simple sheep sheds during winer when hey are fed on sraw. In some flocks animals receive some hay and a limied amoun of concenraes for a shor period before and afer lambing. The lacaion period is 6-7 monhs. The average oal milk yield (TMY) is abou kg for unimproved Awassi ewes while he TMY of improved Awassi ewes is ca kg. Body weighs of ewes and rams range from 45 o 50 kg and 60 o 70 kg, respecively. Average greasy fleece weigh is abou kg. Saple lengh and wool fineness are cm and 3-35 µ, respecively (Kaymakçı, 004). The Awassi has a brown face and legs wih he fleece varying in colour from brown o whie. The unimproved Awassi sheep has a big fa-ail. The objecive of his paper was o invesigae he use of a range of mahemaical funcions for describing he lacaion curve of unimproved Awassi ewes in Turkey. Maerials and Mehods Daa were colleced from 136 unimproved Awassi ewes from a flock kep a he Sae Farm of Gözlü in he Konya province (38 o 7'N, 3 o 'E and 930 m above sea level) of Turkey. Ewes were classified ino six age groups of (n = 16), 3 (n = 13), 4 (n = 9), 5 (n = 3), 6 (n = 15) and 7 (n = 31) years of age. Age a firs lambing was ca. 4 monhs. All ewes lambed in March. They were hand-milked wice daily and he firs milk es was performed wihin he firs monh afer lambing (mean = 5.3 days, s.d. = 3.1) in an aemp o describe he peak yield. All lambs suckled heir dams freely unil firs milk recordings. They were hen kep on a residual suckling regimen unil 75 days of age, when hey were weaned compleely from milk. During he residual suckling period, lambs joined heir dams afer morning and evening milking for residue suckling for a period of 30 minues a a ime. The lacaing ewes were grazed from April o December and were kep and fed indoors hroughou he winer. Milk yield was recorded fornighly and TMY hrough he lacaion was calculaed by using he Fleischmann mehod: TMY y + (( y + y )/ ( )) where TMY is oal milk yield; is yield a firs milk = 1 1 i i+ 1 i+ 1 i recording; 1 is inerval beween lambing and firs recording; yi is yield of he record i and i is inerval beween record i and record ( i + 1), ( i = 1,..., k) (Ruiz e al., 000). Four differen mahemaical s were used o describe he lacaion curve: he Wood (Wood, 1967), he Inverse Polynomial, he Quadraic and he Cubic. b ( c ) b b The Wood : Y() = a e and peak yield for his is: Ymax = a( b / c) e which occurs a ime b / c ; Y = / a + b + c. In his equaion peak yield is: Y max = 1/ b + ac The Inverse Polynomial : () ( ) and he ime a peak yield: = a / c ; The Quadraic : Y () = a + b + c Y max ( b / c) + c( b / c). Peak yield for his is: = a + b, ime a peak yield: = b / c ; The Cubic : Y max = a + b Y = a + b + c + () d 3. Peak yield for his is: ( c c 3bd / 3d) + c( c c 3bd / 3d) + d( c c 3bd / 3d) 3 ime a peak yield: = c c 3bd / 3d where is he milk yield a day x from lambing, e is he base of naural logarihm, a, b, c and d are he Y () parameers which characerize he shape of he curve and which were esimaed from a nonlinear regression analysis using he Miniab program (Miniab, 1995). The parameers obained were used o calculae he prediced yields in he original equaions above. Residuals, defined as he absolue values of he difference beween he prediced yield and he real daa of daily milk yield were calculaed and hen he mean square predicion error (MSPE) for each lacaion curve fied, was calculaed and averaged for each. y 1,
3 Souh African Journal of Animal Science 005, 35 (4) 40 The main crieria used o compare s were he relaive size of he MSPE. Models resuling in smaller MSPE were considered o be superior, because less residual variaion remained in he daa and residuals were more randomly disribued (Papajcsik & Bodero, 1988). Furhermore, coefficiens of deerminaion (R ) adjused by he number of parameers in each and correlaion coefficiens beween TMY calculaed by he Fleischmann mehod and esimaed TMY from he s, were calculaed. Resuls and Discussion Toal milk yields calculaed by he Fleischmann mehod and esimaed TMY from he s in each age group are shown in Table 1. Milk producion was no affeced by age. The Wood and Inverse Polynomial s underesimaed TMY, bu he Quadraic slighly overesimaed TMY. Esimaed TMY according o he Cubic was very close o TMY calculaed by he Fleischmann mehod. However, differences beween s were no saisically significan. I can be said ha he s were adequae for describing TMY. Porolano e al. (1996) repored ha he Wood underesimaed he oal lacaion milk producion in Comissana sheep. Pollo & Goowine (000) repored ha some nonlinear funcions fied he daa beer han Wood s. On he oher hand, i has been repored ha he Wood equaion is no suiable for dairy sheep under grazing condiions in which environmenal effecs influence milk yields (Cara e al., 1995; Ruiz e al., 000). Table 1 Esimaed oal milk yields (TMY in kg) of unimproved Awassi ewes a differen ages (as year) using he differen s Ages TMY Wood Quadraic Inverse Cubic n (years) (Fleischmann) Polynomial ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 5.77 Overall ± ± ± ± ±.46 The parameers of he s and heir comparison for he goodness of fi saisics o describe he lacaion curves of unimproved Awassi ewes are given in Table. Age effecs on parameers were no significan. The differences beween peak yields prediced by he s, excep for he difference beween he Wood and Cubic s, were significan (P < 0.01). The Inverse Polynomial overesimaed peak yield. Peak yields according o he Wood and Cubic s were similar. The Quadraic s peak yields were significanly lower han hose of he oher s. Day of peak yield averaged across age groups for he s, ranged from 10. o 56.4 days. The differences beween days of peak yield esimaed from he s were significan (P < 0.01). The Inverse Polynomial and he Wood esimaed he day of peak yield earlier han he oher s. Pollo & Goowine (000) repored he day of peak yield as 7 days for ypical lacaion curves of improved Awassi ewes. Daily milk yields of ewes raised under exensive sysems such as encounered in his sudy depend on grazing condiions. Peak yields may be delayed by unsuiable grazing condiions. Pasure in he sudy region is bes in May wih respec o grazing capaciy. Therefore, he peak yields of ewes in he sudy were especially noiceable a ha ime. The R values of he s ranged from 0.74 o The Cubic gave he highes R value followed by he Wood. The differences beween R values of he s were significan (P < 0.01) excep for he difference beween he Quadraic and he Inverse Polynomial s. Ruiz e al. (000) deermined he R values of six mahemaical s ranging from 0.93 o 0.97 and hey suggesed a nonlinear variable decay for describing he lacaion curve of Laxa sheep. However, Porolano e al. (1996) and Franci e al. (1999) repored lower R values for he Wood compared o his sudy.
4 Souh African Journal of Animal Science 005, 35 (4) 41 The differences beween MSPE values of he s were significan (P < 0.01) excep for he differences beween he Wood and he Quadraic s (Table ). The bes MSPE value was found using he Cubic and he Inverse Polynomial provided he wors MSPE value. Similarly, Ruiz e al. (000) repored ha he Inverse Polynomial gave he wors MSPE value. On he oher hand, he Inverse Polynomial has only been recognized as a good descripion for lacaions commencing in he summer monhs in dairy cale and for hose cows beginning a low milk yields and reaching peak earlier han average. On he oher hand, Pollo & Goowine (000) repored ha he Moran funcion ( a b c ( Y ) () ) d / = e always gave he lowes MSPE. Table Mean values and sandard errors for he parameers of s and comparison for he goodness of fi saisics o describe he lacaion curves of unimproved Awassi ewes Models Wood Quadraic Inverse Polynomial Cubic Ages a ± s a b ± s b Parameers c ± s c d ± s d Peak yield (ml) Day of peak yield R MSPE ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Overall 0.44 ± ± ± a 5.36 a a 0.04 a 0.51 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Overall ± ± ± b b 0.74 b a 1.57 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Overall ± ± ± c 10.3 c b 0.16 b ± ± ± * ± ± ± * ± ± ± * ± ± ± * ± ± ± * ± ± ± * Overall ± ± ± * a 45.1 d c 0.00 c a, b, c The means wihin columns wih differen superscrip are significanly differen a P < 0.01 MSPE - mean square predicion error Correlaion coefficien beween TMY calculaed by he Fleischmann mehod and esimaed TMY from he s for age groups, are given in Table 3. All correlaion coefficiens were significan (P < 0.01). Esimaed TMY from he Cubic gave he highes correlaion coefficien (0.998) wih TMY calculaed by he Fleischmann mehod. These correlaion coefficiens can be used as a measure for deermining he goodness of fi of s.
5 Souh African Journal of Animal Science 005, 35 (4) 4 Table 3 Correlaion coefficien beween oal milk yield calculaed by he Fleischmann mehod and esimaed oal milk yield from he s * Ages Wood Model Quadraic Model Inverse Polynomial Model Cubic Model Overall * All correlaion coefficiens are significan (P < 0.01) Conclusion The Cubic showed he bes fi o he daa colleced from unimproved Awassi ewes and allowed a suiable descripion of he shape of he lacaion curve. Toal milk yield esimaed by he Cubic was similar o he esimaion made by he Fleischmann mehod. Age effecs on TMY and parameers were no significan. Acknowledgmens This research was funded in par by a gran from he Universiy of Selcuk (BAP), Konya, Turkey. References Cappio-Borlino, A., Maccioa, N.P.P. & Pulina, G., The shape of Sarda ewe lacaion curve analyzed by a Comparmenal. Lives. Prod. Sci. 51, Cappio-Borlino, A., Pulina, G. & Rossi, G., A non-linear modificaion of Wood s equaion fied o lacaion curves of Sardinian dairy ewes. Small Rumin. Res. 18, Cappio-Borlino, A., Pulina, G., Cannas, A. & Rossi, G., The curve of lacaion of Sardinian sheep adaped o one funcion of range ype. Zoo. Nur. Anim. 15, Cara, A., Sonna, S.R. & Casu, S., Esimaing lacaion curves and seasonal effecs for milk, fa and proein in Sarda dairy sheep wih a es day. Lives. Prod. Sci. 44, Chang, Y.M., Rekaya, R. Gionala, D. & Thomas, D.L., 001. Geneic variaion of lacaion curves in dairy sheep: A Bayesian analysis of Wood s funcion. Lives. Prod. Sci. 71, Cobby, J.M. & Le Du, Y.L.P., On fiing curves o lacaion daa. Anim. Prod. 6, Dijksra, J., France, J., Dhonoa, M.S., Maas, J.A., Hanigan, M.D., Rook, A.J. & Beever, D.E., A o describe growh paerns of he mammary gland during pregnancy and lacaion. J. Dairy Sci. 60, Franci, O., Pugliese, C., Acciaioli, A., Parisi, G. & Lucifero, M., Applicaion of wo s o lacaion curves of Masese ewes. Small Rumin. Res. 31, Goodal, E.A. & Spreavak, D., A Bayesian esimaion of he lacaion curve of a dairy cow. Anim. Prod. 40, Groenewald, P.C.N., Ferreira, A.V., Van der Merwe, H.J. & Slippers, S.C., A mahemaical for describing and predicing he lacaion curve of Merino ewes. Anim. Sci. 61, Grossman, M. & Koops, W.J., Muliphasic analysis of lacaion curves in dairy cale. J. Dairy Sci. 71, Kaymakçı, M., 004. Sheep Breeding Manual. TİGEM, 004- (in Turkish). Miniab, Miniab reference manual, Release 10 Xra. Miniab Inc. Sae Coll., PA 16801, USA. Moran, S.V. & Gnanasakhy, A., A new approach o he mahemaical formulaion of lacaion curves. Anim. Prod. 49, Neal, H.D. & Thornley, J.H.M., The lacaion curve in cale: a mahemaical of he mammary gland. J. Agric. Sci., Camb. 101,
6 Souh African Journal of Animal Science 005, 35 (4) 43 Papajcsik, I.A. & Bodero, J., Modelling lacaion curves of Friesian cows in a subropical climae. Anim. Prod. 47, Pollo, G.E., Describing he lacaion of dairy animals. Proc. Br. Soc. Anim. Sci. p. 197 (Absr.). Pollo, G.E., 000. A biological approach o lacaion curve analyses for milk yield. J. Dairy Sci. 83, Pollo, G.E. & Goowine, E., 000. Appropriae mahemaical s for describing he complee lacaion of dairy sheep. Anim. Sci. 71, Porolano, B., Spaafora, F., Bono, G., Margioa, S. Todoro. M., Oroleva, V. & Leo, G., Applicaion of he Wood o lacaion curves of Comissana sheep. Small Rumin. Res. 4, Rook, A.J., France, J. & Dhonoa, M.S., On he mahemaical descripion of lacaion curves. J. Agric. Sci., Camb. 11, Ruiz, R., Oregui, L.M. & Herrero, M., 000. Comparison of s for describing he lacaion curve of Laxa sheep and an analysis of facors affecing milk yield. J. Dairy Sci. 83, Torres-Hernandez, G. & Hohenboken, W.D., Biomeric properies of lacaions in ewes raising single or win lambs. Anim. Prod. 30, Wilmink, J.B.M., Adjusmen of es day milk, fa and proein yield for age, season and sage of lacaion. Lives. Prod. Sci. 16, Wood, P.D.P., Algebraic of lacaion curve in cale. Naure 16,
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