Livestock Research for Rural Development 30 (6) 2018 | Guide for preparation of papers | LRRD Newsletter | Citation of this paper |
Performance data of Sahiwal cows born between 1972 and 2004 with milk records between 1976 and 2008 were analysed to estimate genetic parameters for longevity in Sahiwal cattle in Kenya. Measures of longevity related to productive life were: time between birth and last milking record in months (Long_1), time between first calving and last milking record in months (Long_2), number of lactations initiated (Long_3), total number of days in lactation over all lactations (Long_4) and total milk yield over all lactations (kg) (Long_5). Measures of longevity related to survival (Long_6) were defined as survival from birth to 44, 56, 80, 92, 104 and 128 months; or survival from first calving (Long_7) to 12, 36, 60, 84 and 96 months. Longevity measures related to productive life were analysed using linear models while those related to survival were analysed via threshold models. Heritability estimates for measures of longevity related to productive life were low, and ranged from 0.038±0.032 to 0.097± 0.04. Estimates of heritability for longevity measures related to survival were higher and ranged from 0.084±0.053 to 0.119±0.035. However, survival from first calving to predefined ages had higher heritability estimated (0.09 to 0.12) compared to survival from birth (0.084 to 0.104). Estimates of heritability obtained using threshold models (survival measures) were higher than those estimated using linear models (productive life measures). Heritability estimates for survival measures were higher in the later periods and were higher for Long_7_than Long_6. Long_7 had highest additive genetic variance and heritability estimate, and should therefore should be used for genetic evaluation of longevity in Sahiwal cattle in Kenya. This study has also provided part of genetic and phenotypic parameters to enable inclusion of longevity in the breeding objective for the Sahiwal cattle improvement programme.
Keywords: linear models, Kenya, productive life, sahiwal, survival, threshold models
Although milk production is considered as the single most important trait in dairy farming, cattle breeding programmes are changing their breeding objectives to include longevity, type and functional traits (Banga et al 2013; 2014), so that cows can meet the challenges of high milk production. Longevity or the age at which a cow leaves the breeding herd is a trait of great economic importance in dairy and beef cattle breeding (Banga et al 2013). Productive longevity can also be described as the number of calvings per female (Varonaet al2012).
Direct selection for longevity has resulted in improved health and fitness (Garcia et al 2015) and even milk production of cows (Kern et al 2014). Therefore breeding for longevity is considered to have ethical and economic benefits since it results in favorable response in profitability of beef and dairy cattle enterprises (Garcia et al 2015). In beef and dairy cattle, longevity plays a considerable role in the farm economy by increasing the profit realised per cow and enables greater response to selection because fewer animals exit the herd due to involuntary culling (Logrotta et al 2010; Garcia et al 2015); a situation that provides greater selection intensity among females, and surplus heifers for sale (Banga et al 2013), contributing to the profitability is dairy and beef enterprises.
Longevity can be described variously as length of productive life, lifetime milk production, herdlife, total number of lactations and survival from birth or first calving to a certain age (Vacek et al 2006; Varona et al 2012). The inclusion of longevity in the breeding objective is hampered because the trait is lowly heritable (Caetano et al., 2012; Kern et al 2014; Van Pelt et al 2015) and the delay in availability of phenotypic information (Lagrota et al 2010), which may lead to increase in generation interval (de Mello et al 2014). This is so when parameters for survival to a certain age are estimated via a linear model (Cruickshank et al 2002, Tsurata et al 2005; Daliri et al 2008). Higher estimates of heritability for survival have been reported when using threshold models (Ahlman et al 2011; Kern et al 2014). Higher heritability estimates can lead to higher rates of genetic gains for longevity in selection programmes. The objective of this study was to estimate variance components, genetic and phenotypic parameters for longevity for the Sahiwal breed in Kenya using linear and threshold models.
Performance data of Sahiwal cows born between 1972 and 2004 obtained from the National Sahiwal Stud at Kenya Agricultural and Livestock Research organization (KALRO), Naivasha,. Production and reproduction data i.e. date of birth date of first calving, date of last milking, milk yield by parity for each cow were collected. Longevity was defined as related to productive life or survival.
Table 1. Data structure use for analysis of measures of longevity for the Sahiwal cattle in Kenya |
||
Measure of longevity |
No. of animals with records |
Number of sires |
Long1 |
2524 |
303 |
Long2 |
1991 |
302 |
Long3 |
2707 |
317 |
Long4 |
2707 |
317 |
Long5 |
1990 |
303 |
Long6_44 |
1887 |
209 |
Long6_56 |
1806 |
201 |
Long6_80 |
1623 |
178 |
Long6_92 |
1433 |
163 |
Long6_104 |
1292 |
145 |
Long6_128 |
1012 |
138 |
Long7_12 |
1507 |
169 |
Long7_36 |
1411 |
153 |
Long7_60 |
1121 |
122 |
Long7_84 |
915 |
106 |
Long7_96 |
862 |
96 |
Longevity was defined as time between birth and last milking record in months (Long1), time between first calving and last milking record in months (Long2), number of lactations initiated (Long3), and total number of days in lactation over all lactations (Long4), total milk yield over all lactations (kg) (Long5) or survival from birth to 44 months (Long6_44), 56 months (Long6_56), 80 months (Long6_80), 92 months (Long6_92), 104 months (Long6_104), and 128 months (Long6_128) or survival from first calving as survival from for 12 months (Long7_12), 36 (Long7_36), 60 (Long7_60), 84 (long7_84) and 96 months (Long7_96) from first calving |
Measures of longevity related to productive life were time between birth and last milking record in months (Long1), time between first calving and last milking record in months (Long2), number of lactations initiated (Long3), and total number of days in lactation over all lactations (Long4), total milk yield over all lactations (kg) (Long5).
Measures of longevity related to survival were defined as survival from birth to 44 months (Long6_44), 56 months (Long6_56), 80 months (Long6_80), 92 months (Long6_92), 104 months (Long6_104), and 128 months (Long6_128). An alternative measure was survival from first calving as survival from for 12 months (Long7_12), 36 (Long7_36), 60 (Long7_60), 84 (long7_84) and 96 months (Long7_96) from first calving. The data structure in terms of number of cows, sires and dams of cows and contemporary groups for measures of longevity are shown in Table 1. Measures of longevity related to survival were recorded as 1 for a cow that remained in the herd and 0 for those that were not in the herd at a particular age. Cows that were still alive at the time of analysis were excluded.
Measures of longevity related to productive life were defined alternatively as length of productive life or functional longevity (months), total milk yield over all lactations (kg), number of lactations initiated, time between birth and last milking record in months, time between first calving and last milking record in months and total number of days in lactation over all lactations (Kern et al 2014). Variance components, genetic and phenotypic parameters for longevity were estimated using a linear model using the expectation maximization method in WOMBAT (Meyer 2007) using a convergence criterion of 10^{-9}. The analysis was restarted at each convergence and the values obtained in the previous convergence used as initial values for the new analysis until there occurred no change at the 4^{th} decimal value of -2Log Likelihood in successive runs. The statistical model was:
y = Xβ + Z + e
where y, β, a and e are vectors of observation for longevity measures, fixed effects (contemporary group, first lactation milky yield class and age class at first calving), random additive genetic effects and random residual effects, respectively. X and Z are incidence matrices linking fixed and random additive genetic effects to observations.
For survival traits an additional threshold effect was fitted. Assumptions for random additive genetic effects and threshold model were:
where ;
where ;
where G, R, A, I are matrices of additive genetic, residual, kinship coefficient and identity variances, respectively; σ^{2}_{a} and are σ^{2}_{e} additive genetic and residual variances, respectively;IW is the inverted Wishart distribution;u_{a},S_{a}, andu_{e} and S_{e} are priori values and degrees of freedom for direct additive genetic and residual variances, respectively.
Longevity measured as survival from birth or first calving analysed as threshold traits assumed to have an underlying continuous distribution. The threshold model relates survival to a given age in a categorical scale with a normal underlying continuous scale, U. The underlying continuous scale, U was assumed to have a normal distribution:
where θ=(b’,a’) is a vector of parameters location with b=fixed effects (as defined from a frequentist point of view) and a=random additive effects; W and I are known incidence and identity matrix, respectively, and =residual variance. The prior distributions for residual and direct additive genetic effects were assumed to follow multivariate normal distributions as follows:
respectively, where A is the numerator relation matrix; σ^{2}_{a,} σ^{2}_{a} and I are additive genetic variance, residual variance and identity matrix, respectively. The linkage between the categorical and continuous scales can be established unequivocally based on the contribution of probability of an observation belonging to the first category being proportional to:
where y_{v} is the response variable to the V^{th} observation, assuming values of 0 or 1 for an observation in first or second category, respectively;t and U_{v}_{ }are the threshold value and value underlying variable, respectively; ϕ is the cumulative distribution function of a normal standard variable andw_{’y} is an incidence column vector linking θ to the V^{th} observation.
Variance components for survival measures were estimated via Bayesian inference using THRGIBBS1F90 (Misztal et al 2002). Outputs from this software were used to obtain a posteriori estimates using POSTGIBBSF90 (Misztal et al 2002). Convergence of all Bayesian analyses were verified using the R program using Geweke’s (1992) and Heidelberger and Welch (1983) diagnostics, from the Bayesian Output Analysis Program – BOA (Smith 2005).
Sahiwal cows produced 3425.5 ±1534.2 kg of milk throughout an average productive life of 2.73 ± 1.44 lactations. The number of lactations initiated (Long3) ranged from 1 to 11. The average days in milk during productive life were 1172.7±703.7 days and ranged from 960 to 6246 days. The period of time that cows remained in the herd from birth (Long1) or from first calving (Long2) to last day in milk was 2231.1±887.8 days and 1172.7±703.7 days, respectively (Table 2).
Table 2. Means, standard deviations, minimum and maximum for longevity measures related to productive life for Sahiwal cattle in Kenya |
||||
Measure |
Mean |
Standard deviation |
Minimum |
Maximum |
Long1 |
2231.1 |
887.8 |
960.0 |
6246.0 |
Long2 |
1172.7 |
703.7 |
226.0 |
4720.0 |
Long3 |
2.7 |
1.44 |
1.0 |
11.0 |
Long4 |
738.0 |
428.4 |
10.0 |
3147.0 |
Long5 |
3425.5 |
1534.2 |
10.0 |
11616.0 |
Longevity was defined as time between birth and last milking record in months (Long1), time between first calving and last milking record in months (Long2), number of lactations initiated (Long3), and total number of days in lactation over all lactations (Long4), total milk yield over all lactations (kg) (Long5) |
Estimates of components of additive genetic and residual variances for measures of longevity related to productive life are shown in Table 3. Additive genetic variances were lower than residual variances for all measures of longevity related to productive life (Table 3). The values of additive genetic variance ranged from 0.058 (Long3) to 366033 (Long5). Heritability estimates for measures of longevity related to productive life were low, with the highest being 0.097± 0.04 (Long5).
Table 3. Estimates of additive genetic variance ( ), residual ( ) and heritability estimates (h^{2}) for measures of productive life for the Sahiwal cattle in Kenya |
|||||
Parameter |
Long1 |
Long2 |
Long3 |
Long4 |
Long5 |
σ^{2}_{a} |
25208.9 |
24740.5 |
0.0589 |
8820.0 |
366033 |
σ^{2}_{e} |
296090 |
318344 |
1.505 |
118783 |
3397910 |
h^{2} |
0.078 ±0.038 |
0.072±0.027 |
0.038±0.032 |
0.069±0.034 |
0.097±0.037 |
Longevity was defined as
time between birth and last milking record in
months (Long1), time between first
calving and last milking record in months (Long2), |
For measures of survival from birth, there was a decrease of 31.5% and 42.8% in the survival rate between birth to 36 months ((Long6_36) to 72 months (Long6_72) and from calving to 44 months and 96 months. Survival rates up to 12, 24 and 54 months from first calving were similar to measures of survival from birth. The reduction in survival for both measures of survival to different ages indicates reduced ability of cows to persist in the herd due to voluntary or involuntary culling. Measures of estimated mean, median and mode of variance components and heritability were all similar, indicating that the posterior distributions of these parameters were more or less symmetric (Tables 4 and 5). Heritability estimates for measures of survival from birth ranged from 0.084 (Long6_44) to 0.104 (long6_128), and were lower than those estimated those estimated from first calving (Table 5).
Table 4. Posterior descriptive estimates for additive genetic variance (σ^{2}_{a}), residual (σ^{2}_{e}) and heritability estimates for measures of survival from birth for the Sahiwal cattle in Kenya |
||||||
Parameter |
Mean ±sd |
Mode |
Median |
Min |
Max |
IC- 95% |
Long6_44 |
||||||
σ^{2}_{a} |
0.092±0.071 |
0.113 |
0.082 |
0.010 |
0.162 |
0.010 to 0.153 |
σ^{2}_{e} |
1.007±0.032 |
0.955 |
1.008 |
0.902 |
1.116 |
0.902 to 1.039 |
h^{2} |
0.084±0.053 |
0.105 |
0.075 |
0.011 |
0.126 |
0.011 to 0.128 |
Long6_56 |
||||||
σ^{2}_{a} |
0.094±0.076 |
0.081 |
0.072 |
0.009 |
0.182 |
0.054 to 0.170 |
σ^{2}_{e} |
1.017±0.036 |
0.979 |
1.006 |
0.905 |
1.110 |
0.892 to 1.053 |
h^{2} |
0.085±0.058 |
0.076 |
0.067 |
0.010 |
0.141 |
0.057 to 0.139 |
Long6_80 |
||||||
σ^{2}_{a} |
0.112±0.061 |
0.092 |
0.093 |
0.010 |
0.183 |
0.010 to 0.182 |
σ^{2}_{e} |
1.014±0.043 |
1.009 |
1.004 |
0.900 |
1.111 |
0.904 to 1.104 |
h^{2} |
0.100±0.041 |
0.084 |
0.085 |
0.011 |
0.142 |
0.012 to 0.142 |
Long6_92 |
||||||
σ^{2}_{a} |
0.114±0.063 |
0.111 |
0.110 |
0.038 |
0.162 |
0.013 to 0.182 |
σ^{2}_{e} |
1.004±0.049 |
1.005 |
1.003 |
0.897 |
1.111 |
0.913 to 1.125 |
h^{2} |
0.102±0.042 |
0.099 |
0.099 |
0.040 |
0.127 |
0.014 to 0.139 |
Long6_104 |
||||||
σ^{2}_{a} |
0.127±0.075 |
0.192 |
0.117 |
0.010 |
0.219 |
0.010 to 0.269 |
σ^{2}_{e} |
1.105±0.054 |
1.009 |
1.004 |
0.904 |
1.104 |
0.901 to 1.511 |
h^{2} |
0.103±0.056 |
0.160 |
0.105 |
0.011 |
0.165 |
0.012 to 0.151 |
Long6_128 |
||||||
σ^{2}_{a} |
0.116±0.081 |
0.121 |
0.106 |
0.001 |
0.193 |
0.013 to 0.176 |
σ^{2}_{e} |
1.007±0.064 |
0.996 |
1.001 |
0.907 |
1.107 |
0.920 to 1.117 |
h^{2} |
0.104±0.057 |
0.108 |
0.094 |
0.001 |
0.148 |
0.014 to 0.136 |
Longevity was defined as survival from birth to 44 months (Long6_44), 56 months (Long6_56), 80 months (Long6_80), 92 months (Long6_92), 104 months (Long6_104), and 128 months (Long6_128) . |
Additive genetic variances for survival measures from first calving increased from twelve months after first calving (long7_12) to 96 months after fist calving (long7_96). Heritability estimates ranged from 0.090 (long7_12) to 0.119 (long7_96). Heritability estimates for longevity measured as survival from birth or first calving to last day in milk (Table 3 and 4) were generally low compared to those related to productive life (Table 3).
Table 5. Posterior descriptive estimates for additive genetic variance (σ^{2}_{a}), residual (σ^{2}_{e}) and heritability estimates (h^{2}) for measures of survival from first calving for the Sahiwal cattle in Kenya |
||||||
Parameter |
Mean SD |
Mode |
Median |
Min |
Max |
IC- 95% |
Long7_12 |
||||||
σ^{2}_{a} |
0.099±0.006 |
0.071 |
0.076 |
0.007 |
0.110 |
0.016 to 0.098 |
σ^{2}_{e} |
0.997±0.057 |
1.002 |
0.997 |
0.912 |
1.102 |
0.898 to 1.097 |
h^{2} |
0.090±0.044 |
0.066 |
0.070 |
0.008 |
0.085 |
0.018 to 0.082 |
Long7_36 |
||||||
σ^{2}_{a} |
0.108±0.007 |
0.061 |
0.069 |
0.007 |
0.097 |
0.018 to 0.103 |
σ^{2}_{e} |
0.999± 0.051 |
0.977 |
0.990 |
0.906 |
1.098 |
0.898 to 1.099 |
h^{2} |
0.097±0.053 |
0.059 |
0.065 |
0.008 |
0.081 |
0.020 to 0.085 |
Long7_60 |
||||||
σ^{2}_{a} |
0.115±0.071 |
0.061 |
0.091 |
0.008 |
0.109 |
0.028 to 0.110 |
σ^{2}_{e} |
1.005±0.054 |
1.012 |
1.009 |
0.895 |
1.097 |
0.900 to 1.110 |
h^{2} |
0.103±0.043 |
0.057 |
0.083 |
0.008 |
0.090 |
0.030 to 0.090 |
Long7_84 |
||||||
σ^{2}_{a} |
0.117±0.007 |
0.071 |
0.081 |
0.007 |
0.110 |
0.024 to 0.163 |
σ^{2}_{e} |
1.005 ±0.052 |
1.000 |
1.003 |
0.905 |
1.095 |
0.904 to 1.106 |
h^{2} |
0.104±0.046 |
0.066 |
0.075 |
0.008 |
0.092 |
0.026 to 0.128 |
Long7_96 |
||||||
σ^{2}_{a} |
0.140±0.007 |
0.095 |
0.096 |
0.015 |
0.156 |
0.022 to .169 |
σ^{2}_{e} |
1.008±0.056 |
0.994 |
1.004 |
0.908 |
1.113 |
0.901 to 1.115 |
h^{2} |
0.119±0.035 |
0.087 |
0.088 |
0.016 |
0.123 |
0.023 to 0.132 |
Key: Longevity was defined as survival from first calving as survival from for 12 months (Long7_12), 36 (Long7_36), 60 (Long7_60), 84 (long7_84) and 96 months (Long7_96) from first calving |
The number of cycles, burn-in and number of Markov chains chosen for the current analyses were sufficient to attain convergence of all posterior distributions of the parameters for survival measures, presenting values greater than 0.05% of the Geweke’s test. The highest heritability was estimated for total milk yield over all lactations (Long5).
In most cattle breeding programmes, milk production is the single most important trait. However, cattle breeding programmes are changing their breeding objectives to include longevity and type and functional traits (Banga et al 2013; 2014), so that cows can meet the challenges of high milk production.
The average observed age from birth and calving to last day in milk of 74.4 months and 39.1 months, respectively reported in the current study were longer that 57.2 and 30.1 months, respectively, reported by Nilforooshan and Edriss (2004) for Iranian Holsteins. Kern et al. (2014) reported estimated of 60.1 and 33.5 months for Brazilian Holsteins. However, the estimates reported in the current study were similar to those reported for Simmental dairy cows of 72 and 47.5 months (Javanovac and Raguz 2011). The average number of lactations initiated of 2.7 was similar to estimates of 2.7 and 2.8 for Brazilian and United States Holsteins, respectively (Tsurata et al 2005; Kern et al 2014). A higher estimate of 3.4 was reported for Simmental dairy cows (Strapak et al 2011). The diversity of measures of survival as herdlife or productive life could be attributed to genetic and environmental differences between the populations. Lifetime milk production, total lactation length and age from calving to last day in milk cover an animal productivity and can be used as an indicator of the efficiency of a production system since they include reproductive and productive information. The proportion of animals retained for long in a herd can be achieved decreased incidences of involuntary or voluntary culling (Forabosco et al 2009). Increase in the proportion of longer lived animals in a herd is accompanied by increased milk production and lowered risk of involuntary culling, leading to increased herd profitability.
The number of cows that failed to survive to a pre-determined period as measured by survival measures amplifies the challenges associated with maintaining better producing cows. Such cows are likely to have feet, udder and or reproductive problems, leading to involuntary culling (Queiroz et al 2007). Measures of longevity related to herd life and survival as used in the current study are alternative measures. Each measure has its advantages and can be used for selection. Considerations in terms of merit include the period required to obtain the necessary information and whether the partial information provided by survival measures is sufficient (Vollema et al 2000). Since information is obtained before an animal dies, survival measures to a specified age provides an opportunity to reduce generation interval and faster rate of genetic gain for longevity (Galeazzi et al 2010).
All measures of longevity used in the current study were associated with high estimates of residual variances and low estimates of additive genetic variance hence the low estimates of heritability. The heritability estimates found in the current study of 0.04 to 0.119 were within the range reported for different cattle populations across the world. Heritability estimates cattle populations in temperate climatic conditions ranged from 0.02 to 0.10 (Vollema and Groen 1996; Tsurata et al 2005) while in tropical conditions the range was 0.06 to 0.18 (Kern et al 2014; M’hamdi et al 2014). Low heritability estimates for measures of longevity could be partly attributed to exclusion of censored records. When records are not censored, survival analyses yields slightly lower heritability estimates for longevity (Forabosco et al 2006) possibly due to loss of genetic variation because of exclusion of censored records.
Survival from birth had lower heritability estimates (0.08 to 0.10) compared to survival from first calving (0.09 to 0.12). A similar trend was reported for Holstein cows in Brazil (Kern et al 2014). This could be attributed to the fact that the two measures deal with different periods in a cow’s life and that all survival from first calving is adjusted for first lactation milk yield. Heritability estimates for survival measures increased with increasing period for survival, indicating a decreasing influence of the environment as a cow matures. A similar trend has been reported in previous studies for different dairy cattle populations (Vollema and Groen, 1996; Ahlman et al 2011; Kern et al 2014).
The benefits arising from direct selection for longevity include improved health and fitness (Garcia et al 2015) as well as milk production of cows (Kern et al 2014). Longevity is influenced by culling decisions, whether voluntary or involuntary. An increase in longevity of cows due to decreased involuntary culling contributes to reduced replacement costs and greater selection intensity for milk yield. This results in greater genetic gains due to increased chances of voluntary culling (Logrotta et al 2010; Garcia et al 2015). Lower replacement rates also lead to surplus heifers for sale (Banga et al 2013), contributing to profitability of cattle enterprises. Breeding for longevity is therefore considered to have ethical and economic benefits since it results in favorable response in profitability of beef and dairy cattle enterprises (Garcia et al 2015). In the current study measures of longevity related to survival to predetermined ages had higher heritability estimates and could therefore be used as selection criteria for longevity.
Estimates of heritability for longevity measures (life time milk yield, total lactation length, number of lactations initiated, age from birth or first calving to last day in milk) obtained using linear models were lower compared to those estimated using threshold models (survival from birth or first calving to specified ages). A similar trend was reported by Kern et al (2014) for Brazilian Holsteins. The estimates of heritability were also similar to those reported in the current study. The highest heritability estimates for survival measures were found for survival either from birth or first calving to the last age specified, similar to reports by Kern et al (2014) for Brazilian Holsteins. These measures of longevity, analysed using threshold models, have been reported to have higher heritability estimated compared to linear models (Sousa et al 2000; Ahlman et al 2011; Kern et al 2014). Linear models yield lower estimates compared to survival models partly due to inclusion of censored records and time-dependent variables (Ducrocq et al 1988; Forabosco et al 2006) as the environmental conditions affecting cow survival changes over time. Estimates of heritability using threshold models in the current study were similar to those found using similar models in Brazilian and Swiss Holsteins (Alman et al 2011; Kern et al 2014).
The inclusion of longevity in the breeding objective is hampered because the trait is lowly heritable (Van Pelt et al 2015; Kern et al 2014) and the delay in availability of phenotypic information (Lagrota et al 2010), which may lead to increase in generation interval (de Mello et al 2014). However, as demonstrated in the current study and other studies, (Vacek et al 2006; Varona et al 2012; Kern et al 2014), survival traits analysed using threshold models yield higher heritability estimates for longevity. Inclusion of such traits can lead to higher rates of genetic gains for longevity in selection programmes. Direct selection for longevity should nevertheless be compared with indirect selection on correlated traits expressed early in a cow’s life because such traits have higher heritability (Daliri et al 2008). Indirect selection in such a scenario would also lead to faster genetic gain for longevity.
Ahlman T, Berglund B, Rydhmer L and Strandberg E 2011 Culling reasons in organic and conventional dairy herds and genotype by environment interaction for longevity. Journal of Dairy Science 94: 1568-1575. https://www.ncbi.nlm.nih.gov/pubmed/21338822
Banga C, Neser F and Garrick D 2013 Derivation of economic values of longevity for inclusion in the breeding objectives for South African dairy cattle. International Conference on Agriculture and Biotechnology, IACSIT Press, Singapore DOI: 10.7763/IPCBEE. 2013. V60. 14. http://www.ipcbee.com/vol60/014-ICABT2013-T3022.pdf
Banga C, Neser F and Garrick D 2014 Breeding objectives for Holstein cattle in South Africa South African Journal of Animal Science 2014, 44 ( 3):199-214. http://www.scielo.org.za/scielo.php?script=sci_abstract&pid=S0375-15892014000300001&lng=en&nrm=iso
Caetano S L, Rosa G J M, Savegnago R P, Ramos S B, Bezerra L A F, Lôbo R B, de Paz C C P and Munari D P 2012 Characterization of the variable cow’s age at last calving as a measurement of longevity by using the Kaplan–Meier estimator and the Cox model. Animal 7: 540-546. https://www.cambridge.org/core/journals/animal/article/
Cruickshank J, Weigel K A, Dentine M R and Kirkpatrick B W 2002 Indirect prediction of herd life in Guernsey dairy cattle. Journal of Dairy Science 85: 1307-1313. https://www.journalofdairyscience.org/article/S0022-0302(02)74195-7/pdf
Daliri Z, Hafezian S H, Shad Parvar A and Rahimi G 2008 Genetic relationships among longevity, milk production and linear type traits in Iranian Holstein Cattle. Journal of Animal and Veterinary Advances 7: 512-515. https://www.medwelljournals.com/abstract/?doi=javaa.2008.512.51
de Mello F, Kern E L and Bretas A 2014 Longevity in dairy cattle. Journal of Advances in Dairy Research 2: 126. doi:10.4172/2329-888X.1000126. https://www.omicsonline.org/open-access/longevity-in-dairy-cattle-2329-888X-1000126.pdf
Ducrocq V, Quaas R L, Pollak E J and Casella G 1988 Length of productive life of dairy cows. 2. Variance component estimation and sire evaluation. Journal of Dairy Science 71: 3071-3079. https://www.journalofdairyscience.org/article/S0022-0302(88)79907-5
Forabosco F, Bozzi R, Filippini F, Boettcher P, Van Arendonk J A M and Bijma P 2006 Linear model vs. survival analysis for genetic evaluation of sires for longevity in Chianina beef cattle. Livestock Science 101: 191-198. https://www.sciencedirect.com/journal/livestock-science/vol/101
Forabosco F, Jakobsen J H and Fikse W F 2009 International genetic evaluation for direct longevity in dairy bulls. Journal of Dairy Science 92: 2338-2347. https://www.sciencedirect.com/journal/journal-of-dairy-science/vol/92/issue/5
Galeazzi P M, Mercadante M E Z, Silva J A IIV, Aspilcueta-Borquis R R, Camargo G M F and Tonhati H 2010 Genetic parameters for stayability in Murrah buffaloes. Journal of Dairy Research 77: 252-256. https://www.cambridge.org/core/journals/journal-of-dairy-research/article.
Garcia J, Anderson D P, Herring A D and Riley D G 2015 Economic Analysis of Selecting for Cow Longevity. A Selected Paper prepared for presentation at the Southern Agricultural Economics Association’s 2015 Annual Meeting, Atlanta, Georgia, January 31-February 3, 2015. http://www.saea.org/wp-content/uploads/2014/12/prog2015.pdf
Geweke J 1992 Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo JM, Berger JO, Dawid AP, Smit AFM (eds.) Bayesian statistics. 4. Proceedings of the 4^{th} Valencia international meeting held in Peńíscola, Spain, April 15-20, 1991, New York, NJ, USA, 169-193. https://pdfs.semanticscholar.org/2e86/50b01dd557ffb15113c795536ea7c6ab1088.pdf
Jovanovac S and Raguž N 2011 Analysis of the Relationships between type traits and longevity in Croatian Simmental cattle using survival analysis. Agriculturae Conspectus Scientificus 76, 249-253. https://acs.agr.hr/acs/index.php/acs/article/view/661
Kern E D, Cobuci J A, Costa C N, Neto J B, Campos G S and McManus C M 2014 Genetic parameters for longevity measures in Brazilian Holstein cattle using linear and threshold models. Archiv Tierzucht 57(33): 1-12. https://www.arch-anim-breed.net/57/33/2014/aab-57-33-2014.pdf
Lagrotta M R, Euclydes R F, Verneque R S, Santana Júnior M L, Pereira R J and Torres R A 2010 Relationship between morphological traits and milk yield in Gir breed cows. Pesquia Agropecuária Brasileira 45, 423-429. http://www.scielo.br/pdf/pab/v45n4/a11v45n4.pdf
Meyer K 2007 WOMBAT - A tool for mixed model analyses in quantitative genetics by Restricted Maximum Likelihood (REML). Journal of Zheijang University Science. B8: 815-821. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.452.6670&rep=rep1&type=pdf
M'hamdi, N, Aloulou R, Bouallegue M, Brar S K and Hamouda M B 2010 Study on functional longevity of Tunisian Holstein dairy cattle using a Weibull proportional hazard model. Livestock Science 132: 173-176.
Misztal I, Tsuruta S, Strabel T, Auvray B, Druet T, Lee D H 2002 BLUPF90 and related programs (BGF90). Proceedings of the 7^{th} World Congress on Genetics Applied to Livestock Production 19–23 August 2002, Montpellier, France. Communication 28-07. http://nce.ads.uga.edu/wiki/lib/exe/fetch.php?media=28-07.pdf
Nilforooshan M A and Edriss M A 2004 Effect of age at first calving on some productive and longevity traits in Iranian Holsteins of the Isfahan Province. Journal of Dairy Science 87: 2130-2135
Queiroz S A, Figueiredo G, Silva J A IIV, Espasandin A C, Meirelles S L and Oliveira J A 2007 Estimates of genetic parameters of stayability in Caracu cattle. Revistas Brasileira de Zootecnia 36: 1316-1323. http://www.scielo.br/pdf/rbz/v36n5/13.pdf
Smith B J 2005 Bayesian output analysis program (BOA) Version 1.1 user’s manual. Iowa State University, Iowa City, IA, USA. Available at: http://www.public-health.uiowa.edu/boa/BOA.pdf.
Sousa W H, Pereira C S, Bergmann J A G and Silva F L R 2000 Estimates of variance components and genetic parameters for reproductive traits by means of linear and threshold models]. Revistas Brasileira de Zootecnia 29: 2237-2247. http://www.scielo.br/pdf/rbz/v36n5/13.pdf
Strapák P, Juhás P and Strapáková E 2011 The relationship between the length of productive life and the body conformation traits in cows. Journal of Central European Agriculture 12: 239-254. https://jcea.agr.hr/en/issues/article/905
Tsuruta S, Misztal I and Lawlor T J 2005 Changing definition of productive life in US Holsteins: Effect on Genetic Correlations. Journal of Dairy Science 1156-1165
Vacek M, Štípková M, Nemcová E and Bouška J 2006 Relationships between conformation traits and longevity of Holstein cows in the Czech Republic. Czech Journal of Animal Science 51: 327-333. https://www.agriculturejournals.cz/publicFiles/52306.pdf
Vollema A R and Groen A F 1996 Genetic parameters of longevity traits of an upgrading population of dairy cattle. Journal of Dairy Science 79, 2261-2267.
Vollema A R, Van Der Beek S, Harbers A G F and De Jong G 2000 Genetic evaluation for longevity of Dutch dairy bulls. Journal of Dairy Science 83: 2629-2639. https://www.journalofdairyscience.org/article/S0022-0302(00)75156-3/pdf
Received 23 February 2018; Accepted 3 May 2018; Published 1 June 2018