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## The Application of Recursive Mixed Models for Estimating Genetic and Phenotypic Relationships between Calving Difficulty and Lactation Curve Traits in Iranian Holsteins: A Comparison with Standard Mixed Models | ||

Iranian Journal of Applied Animal Science | ||

مقاله 6، دوره 8، شماره 4، زمستان 2018، صفحه 597-605
اصل مقاله (335.64 K)
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نوع مقاله: Research Articles | ||

نویسندگان | ||

M.S. Mokhtari ^{} ^{1}؛ M. Moradi Shahrbabak^{2}؛ A. Nejati Javaremi^{2}؛ G.J.M. Rosa^{3}
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^{1}Department of Animal Science, Faculty of Agriculture, University of Jiroft, Jiroft, Iran | ||

^{2}Department of Animal Science, University College of Agriculture and Natural Resources, University of Tehran, Karaj, Iran | ||

^{3}Department of Animal Science, University of Wisconsin-Madison, Madison, WI 53706, USA | ||

چکیده | ||

In the present study, records on 22872 first-parity Holsteins collected from 131 herds by the Animal Breeding and Improvement Center of Iran from 1995 to 2014 were considered to estimate genetic and phenotypic relationships between calving difficulty (CD) and the lactation curve traits, including initial milk yield (Ap), ascending (Bp) and descending (Cp) slope of the lactation curves, peak milk yield (Y_{m}), days to attain peak yield (T_{m}) and milk persistency (Pers) under recursive mixed models (RMMs) and standard mixed models (SMMs). Recursive mixed models (RMMs) were applied by fitting CD as a covariate for any of the studied lactation curve traits while considering genetic relationships between CD and these traits. The obtained results denoted a statistically significant non-zero magnitude of the causal relationships of CD with Ap and Bp, while the former influencing the latter. The causal effects of CD on Ap and were -0.351 kg and 0.005, respectively. Direct genetic correlations between CD and the studied traits under RMMs and standard mixed models (SMMs) were not statistically different from zero, except for the correlations of CD with T_{m}; indicating that genes associated with difficult births also increase peak days in milk. Comparison of both models by the deviance information criterion (DIC) demonstrated the plausibility of RMMs over SMMs for studying the relationships of CD with Ap and Bp while SMMs performed better for estimating the relationships of CD with Cp, Y_{m}, T_{m} and Pers. | ||

کلیدواژهها | ||

calving difficulty؛ lactation curve؛ recursive model؛ standard model | ||

اصل مقاله | ||

Structural equation models (SEMs) allow studying the causal relationships between phenotypes (Wright, 1934). These models were first introduced in genetics by Wright (1921). Calving is an important event on dairy farms, calving complications result in potential loss and/or impaired subsequent production and reproduction performance with implications on animal welfare, increased labor and veterinary costs with associated negative impact on revenue (Eaglen
The milk yield records initially analyzed included 989582 test-day records of 160243 cows collected from 131 herds of Iranian Holstein dairy cows from 1995 to 2014 by the Animal Breeding and Improvement Centre of Iran.Test-day records with first milk recording measured between 5 and 60 days of lactation period, consecutive sampling intervals of 25-35 days and with not greater than 305 dayslactation length were considered. Wood function is considered for describing lactation curve in the studied data set of first-parity Iranian Holsteins in the present study. Therefore, edited test-day milk yield records were used for calculating the lactation curve traits applying Wood function as below (Wood, 1967): y Where: t and y Ap: initial milk yield. Bp and Cp: ascending and descending slope of the lactation curves, respectively. Cows with atypical lactation curves i.e. with negative parameters Bpor Cp were discarded. Fitting wood function on the test day milk yield records was performed applying NLIN procedure and the Newton-Gauss method (SAS, 2004). Then individual cow lactation curve parameters including peak milk yield (Y Only single records from the artificial inseminations were kept, and all suspect records, including records with out-of-range values or records with missing information were removed. Age of the cow at the first calving was limited to the range from 20 to 38 months. Detailed information on the considered editing protocol for CD records have been presented by Mokhtari
For addressing the significant fixed effects to be fitted in the final models least squares analyses were carried out using the
Xb_{i} + Z _{h}h + _{i}Z _{s1}s + _{1}Z _{s2}s + _{2i}e_{i}Where: y b h s s e X, Z The matrix of structural coefficients (Λ) is a square one; off-diagonal elements were determined according to causal structures between the considered traits (Valente Implying that a recursive effect (represented by λ
Bayesian MCMC implementation was performed applying the THRGIBBS1F90 program of Misztal
The variances related to effects of sires of the calves and sires of the cows were transformed to the direct additive and maternal additive genetic (co)variances (Willham, 1972) as: Where: σ σ Additive genetic covariances between direct and maternal effects among each pair traits of i and j were computed according to Kriese Where: : covariance between direct additive genetic effects for traits i and j. : covariance between maternal additive genetic effects for traits i and j. : covariance between direct additive genetic effects of trait i and maternal additive genetic effects of trait j. : covariance between maternal additive genetic effects of trait i and direct additive genetic effects of trait j.
The phenotypic variance (σ In which, σ
The interpretation of parameters obtained under RMMs, the so-called system parameters in SEMs literature, is different from that of the analogous ones obtained under SMMs (Gianola and Sorensen, 2004). Therefore, further transformation is required to be able to compare (co)dispersion of random effects among two models fitted (i.e. RMMs and SMMs). Transformations for the estimated (co)variance matrices to the standard mixed model scale were carried out as: G The matrices G
Pedigree structure of the considered first-parity Holstein cows is presented in Table 1. After editing of CD records and elimination of cows with atypical lactation curves, cows with easy and/or difficult calving constituted 74.50% and 25.50% of total cows, respectively. Approximately, 24% of the cows were excluded because of atypical shape of lactation curve. By fitting wood function pearson's correlation coefficient between actual and the corresponding predicted milk records was obtained as 0.96, implying that lactation curve in the first parity Iranian Holsteins has been described properly by wood function. Wood is one of the most popular functions used for describing the lactation curve in dairy cows (Cilek and Keskin, 2008; Atashi
Ap: initial milk yield at the beginning of lactation; Bp: inclining slope of the lactation curve; Cp: declining slope of the lactation curve; Pers: milk persistency; Y SD: standard deviation.
Milk production started with an average value of 16.14 kg at the beginning of the lactation, increased with an average slope of 0.29 and reached average peak milk yield of 39.44 kg at an average time of 97 days after calving. After peak milk yield attained it decreased with an average slope of 0.003. Least squares means ± standard error for the studied lactation curve traits in cows with unassisted calving (CD=1) against cows with any type of assisted calving (CD>1) are presented in Table 3. Cows with difficult calving had significantly lower Ap and higher Bp than cows with easy calving (P<0.05). The value of Ap in difficult calving cows was significantly lower than the corresponding values in easy calving cows. While Bp in difficult calving cows was 0.03 higher than easy calving ones. In other words, dystocia significantly decreased initial milk yield and increased inclining slope of lactation curve in first-parity Iranian Holsteins. Atashi
Features of posterior means and posterior standard deviations (PSD) of the structural coefficients of CD on the studied lactation curve traits are presented in Table 4. CD is a categorical trait and analyzed applying threshold model. Therefore, the causal effects of CD on the other studied lactation-related traits were expressed on the liability scale. The estimated structural coefficients were significant only for Ap and Bp; highest posterior density (HPD) intervals did not include zero. It means that initial milk yield of first-parity Iranian Holstein cows and inclining slope of their lactation curve causally affected by calving difficulty. Posterior mean of recursive effect from CD on Ap was negative value of -0.351; implying that each 1-unit increase of liability for CD would decrease Ap by 0.351. Posterior mean of the recursive effects from CD on Bp was 0.005; suggesting that each 1-unit increase of liability for CD would increase Bp 0.005. The estimated causal effects of CD on Cp, Pers, T
Ap: initial milk yield at the beginning of lactation; Bp: inclining slope of the lactation curve; Cp: declining slope of the lactation curve; Pers: milk persistency; Y
CD: calving difficulty; Ap: initial milk yield at the beginning of lactation; Bp: inclining slope of the lactation curve; Cp: declining slope of the lactation curve; Pers: milk persistency; Y ** (P<0.01) and * (P<0.05). NS: non significant.
As structural coefficients measure recursiveness at the phenotypic level (Gianola and Sorensen, 2004) and are corrected for genetic effects it seems that they describe phenotypic relationships more accurately. In a previous study, Atashi
The DIC values for CD-Ap and CD-Bp under SMMs were higher than the corresponding values obtained under RMMs (Table 5), implying the plausibility of considering a cause-and-effect from CD on Ap and Bp. The lower DIC values for the RMMs are partly because of a lower penalty for model complexity in the DIC for RMMs (Bouwman
The posterior means and PSD for direct heritability of the studied lactation curve traits under SMMs and RMMs are presented in Table 6. It should be noted that parameters presented as under "RMMs" are pertaining to the standard equivalent. Similar estimates were obtained for direct heritability estimates of the studied lactation curve traits under both models. Heritability estimates for the studied traits were generally low; under both SMMs and RMMs, the lowest heritability was obtained for Bp (0.039 under SMM and 0.038 under RMM) and the highest one for Y
The posterior means and PSD for the direct genetic and phenotypic correlations of CD with the lactation curve traits under SMMs and RMMs are shown in Table 7.
CD: calving difficulty; Ap: initial milk yield at the beginning of lactation; Bp: inclining slope of the lactation curve; Cp: declining slope of the lactation curve; Pers: milk persistency; Y
Ap: initial milk yield at the beginning of lactation; Bp: inclining slope of the lactation curve; Cp: declining slope of the lactation curve; Pers: milk persistency; Y ** (P<0.01) and * (P<0.05).
CD: calving difficulty; Ap: initial milk yield at the beginning of lactation; Bp: inclining slope of the lactation curve; Cp: declining slope of the lactation curve; Pers: milk persistency; Y ** (P<0.01) and * (P<0.05). NS: non significant.
** (P<0.01) and * (P<0.05). NS: non significant.
In general, most of the direct genetic and phenotypic correlations between CD and the studied lactation curve traits were statistically non-significant (95% HPD intervals included zero). All the direct genetic correlations between CD and the studied lactation curve traits were statistically non-significant (95% HPD intervals included zero) except for CD-T
In Table 8, the posterior means and PSD for the contemporary group (herd-year-season of calving) and residual correlations between CD and the lactation curve traits under SMMs and RMMs are shown. All the estimated correlations between the contemporary group effects of CD with the lactation curve under both SMMs and RMMs were not statistically significant; 95% HPD intervals included zero. The estimated residual correlations for CD-Ap were significant, low and negative under both SMMs and RMMs (95% HPD intervals was not included zero). The residual correlations between CD and the other lactation curve traits were not significant under SMMs; 95% HPD intervals included zero. In other words, there are no correlations of CD with Bp, Cp, Pers, T
Causal effects of CD on the lactation curve traits in first-parity Iranian Holsteins were modeled applying recursive mixed models as a trait causally influences the subsequent lactation curve traits. After a difficult calving, the initial milk yield and inclining slope of lactation curve in first-parity Iranian Holstein cows were differently affected. Cows with calving difficulty have lower initial milk production but they recover by a quickly inclining slope of lactation curve (increasing production), and reaches the same peak milk production at the same time as cows without CD. Furthermore the milk persistency was identical in difficult and easy calving cows. In other words, a recovery and compensatory of cows with calving difficulty were observed. The existence of significant causal effects growing from CD on these traits indicated that inclusion of this trait in the genetic evaluation of Ap and Bp in first-parity Iranian Holsteins via RMMs is of importance. The application of the recursive model methodology gave clearance to distinguish between the effect of CD on Ap and Bp and the genetic relationship between CD and these two traits.
The contribution of Animal Breeding Center of Iran, especially Mr. M.B. Sayyad Nejad, for providing the required data set is greatly acknowledged. The work was supported by the University of Tehran. | ||

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