An observational study of growth rate and body weight variance partition for United Kingdom dairy calves from birth to 20 weeks of age

Graphical Abstract Summary: Sources of variation can be used to target resources to maximize potential intervention effect size. This research identified sources of variation in dairy calf birth weights and growth rates. Unexplained variance was partitioned proportionally to veterinary practice, farm, and calf levels (variance partition coefficient; VPC). At birth VPC was highest at the calf level, but this decreased with age. From 66 d of age onward, VPC was increasingly higher at the farm level. These trends are suggestive of the increasing influence of management and environment as calves age. This information can be used to inform strategies to investigate and optimize the efficiency of calf rearing systems.

F ollowing a long history of research (Heinrichs et al., 2017), attention has been paid to monitoring the productivity of youngstock rearing operations on UK dairy farms (Bazeley et al., 2016). Increasing calf growth rate can potentially lead to gains in first-lactation milk yield (Soberon and Van Amburgh, 2013). Other motivating factors likely include trends for fewer, increasingly specialized dairy farms, availability of precision farming technologies, and recognition of the scale of economic losses (Tozer and Heinrichs, 2001).
Target growth rates are based on the mean calf (Brickell et al., 2009;AHDB Dairy, 2018), yet the mean calf does not exist, and extreme variability between farms and between calves within farms has been noted (Brickell et al., 2009). Such targets are unlikely to be relevant and achievable for all calves on all farms because of generalizability limitations and unexplained variation. Farmspecific target setting has been exemplified by the benchmarking approach (Atkinson et al., 2017). However, arithmetic means give a biased measure of central tendency, and an improvement would be to use targets based on proportions of calves within a given weight range for their age. Proportional targets cannot be robustly extrapolated from frequentist analyses but could be informed by the posterior predictive distributions obtained from a Bayesian approach (Spiegelhalter et al., 2004).
Statistical models offer explanations for some variation in complex data through fixed effects defined by what is known. Remaining residual variation is due to unknown variables or random noise. For hierarchical data such as calves clustered within farms, the variance partition coefficient (VPC) describes the proportion of unexplained variance residing at each level of the hierarchy due to clustering (Goldstein et al., 2002). This indicates potential change though influencing variables acting at each level. The same principle is routinely applied in dairy management, where genetic gain is leveraged through targeting characteristics with relatively large genetic variance components in selective breeding decisions (Macedo et al., 2021). Similarly, information on sources of variation could be used to target resources for investigating calf management to influence production efficiency.
The aim of this research was to update reported estimates of birth weight and growth rate for UK Holstein-Friesian female dairy calves and to partition unexplained variance in calf weight up to 20 wk of age. Reporting is based on Strengthening the Reporting of Observational Studies in Epidemiology-Veterinary Extension (STROBE) statement guidelines (Sargeant et al., 2016).
Since at least 2014, a subscription-based online service has been available to support the recording and monitoring of calf weight and health on a national scale in the UK (Calf Tracker, Zoetis).
An observational study of growth rate and body weight variance partition for United Kingdom dairy calves from birth to 20 weeks of age S. C. Archer* Veterinary practices have accounts to access the service, allowing upload of individual calf data from client farms. Collection and recording of calf identity and weights took place according to farm-specific protocols. Calf Tracker data from June 5, 2014, to February 28, 2020, were made available by Zoetis. The database contained records from 74 UK veterinary practices, with 526 farms classified as dairy, 45,736 calves, and 106,411 weight recordings. Calves were Holstein-Friesian females (David Bartram, Zoetis; personal communication). Likely due to errors in data entry, there were extreme and implausible values for calf age; however, 92,298 recordings from calves aged 1 to 138 d were deemed reliable and retained. To selectively recruit calves with repeated weight measurements, data were excluded from farms with ≤12 mo of apparent monitoring activity based on dates of first and last recordings in the database. Weight measurements denoted as estimates were removed. Confirmed birth weights for 19,715 calves were included as weight measurements for age 0 d, with recording date aligned to date of birth. Weight recordings were restricted to >30 and ≤225 kg. The selected data set contained records from 28 veterinary practices servicing 139 farms with 19,708 calves aged up to 138 d, from which there were 59,588 recordings (Table 1). For included calves, the median number of weight measurements was 3 (interquartile range: 2-3; range: 1-17).
The data were initially explored using R (R Core Team, 2013). Subsequent modeling used R2MLwin (Zhang et al., 2016). The outcome of interest (y ijk ) was the test-day weight of the ith calf (kg), on the jth farm, and from the kth veterinary practice. A mixed model was fitted to the data and took the form where α = intercept value; X ijk = a matrix of exposure variables for polynomials of calf age in days; β = a vector of coefficients for X ijk ; v k = a random effect to adjust for clustering within veterinary practices, assumed to be normally distributed with mean 0 and variance σ v 2 ; u jk = a random effect to adjust for clustering within farms, assumed to be normally distributed with mean 0 and variance σ u 2 ; and e ijk = residual error, assumed to be normally distributed with mean 0 and variance σ e 2 . Calf age in days was forced into the model and investigated as polynomial terms. In this framework, β could be interpreted as a function of growth rate, and α could be interpreted as an estimate of birth weight. Month and year of measurement were investigated for inclusion as categorical terms. A plausible random slope for calf age was assessed for inclusion at the farm level. Parameters were initially estimated using iterative generalized least squares (Goldstein, 2003). Model fit was assessed by inspection of residuals for normality and by graphical comparison of predictions to raw data. To obtain robust credibility intervals for random effect variances, posterior predictive distributions for parameters were generated in a Bayesian framework (Zhang et al., 2016). Default noninformative prior distributions were used (Browne, 2015) for random effect variances as follows: Posterior predictive distributions for parameters were estimated from a sample of 10,000 Markov chain Monte Carlo simulations. To reduce autocorrelation, this was obtained by selecting every hundredth estimate in 1,000,000 Markov chain Monte Carlo simulations, following a burn-in of 100,000 simulations. Chain convergence was assessed by visual inspection to ensure that a stationary distribution had been reached and that chain length was consistent with estimates from the Raftery-Lewis diagnostic applied to variance parameters with probability of 0.95 that the 0.025 to 0.975 quantile would be accurate within 0.005. Effective sample size was recorded as a measure of autocorrelation (Browne, 2015). The final model was confirmed using deviance information criteria, where low values indicate a more parsimonious model (Spiegelhalter et al., 2002). Birth weight of the median calf on the median farm was 40 kg (interquartile range: 35-40 kg). At 20 wk of age, the median calf on the median farm was 136 kg (interquartile range: 117-159 kg). Between these time points, calf weight varied among calves, farms, and veterinary practices. Variability in estimates of calf weight increased with age, and sample size decreased as calves aged.
The final model included calf age as a quadratic term ( of interest defined in the aim and were excluded from the final model. The final model included a random slope for calf age at the farm level. Covariance between birth weight and growth rate was positive in 66% of simulations (Table 2), leading to a fanning pattern in growth curves (see graphical abstract). Variance partition coefficient estimates depended on calf age (Figure 1 This is the largest reported study of repeated weight measurements in dairy calves from birth to beyond weaning and the first study to partition variance in age-adjusted calf weights. Central tendency measures of birth weight and cumulative mean growth rate were consistent with previous reports (Brickell et al., 2009;Bazeley et al., 2016). In these studies, birth weight and growth rate in dairy calves have been estimated from smaller samples of UK farms and calves, yet variability in these parameters has been a notable finding (Brickell et al., 2009;Bazeley et al., 2016). Previously, the largest study was based on 5,273 Holstein heifers from 163 farms in Pennsylvania (Heinrichs and Hargrove, 1987), and in the United Kingdom a study of 509 calves on 19 dairy farms has informed industry recommendations (Brickell et al., 2009;AHDB Dairy, 2018). Brickell et al. (2009) estimated a cumulative mean daily growth rate of 0.77 kg/d (range: 0.45-1.13 kg/d) in calves up to 6 mo of age. Comparable mean daily growth rate on the median of 8 dairy farms over at least 730 d was 0.71 kg/d (range: 0.58-0.75 kg/d; Bazeley et al., 2016). On these 8 farms the relationship between calf weight and age also appeared to be quadratic, with growth rate progressively increasing with time from 0.29 kg/d (range: 0.00-0.52 kg/d) up to 30 d of age (Bazeley et al., 2016). Six of the 8 dairy farms had 348 calves with mean and median birth weight of 40 kg (range: 24-55 kg; Bazeley et al., 2016).
Variability in calf birth weight and growth rate estimates can be expected to decrease with increasing sample size. The current study therefore produced more precise estimates of mean birth weight (41 kg; BCI: 40-43 kg) and cumulative mean growth rate (0.73 kg/d; BCI: 0.70-0.75 kg/d), although different ages of calves were considered. The modeling approach adjusts for lack 250 Archer | Variance in calf body weight of independence between calves, meaning that estimates of central tendency apply to calves on the median farm serviced by the median veterinary practice. Coverage of cluster-specific means shows diversity between farms and veterinary practices. For the bottom 2.5% of farms serviced by the bottom 2.5% of veterinary practices, estimates of mean calf birth weight and cumulative mean growth rate were ≤34 kg (BCI: 31-36 kg) and ≤0.56 kg/d (BCI: 0.52-0.60 kg/d), respectively. For the top 2.5% of farms serviced by the top 2.5% of veterinary practices, estimates of mean calf birth weight and cumulative mean growth rate were ≥49 kg (BCI: 47-52 kg) and ≥1.00 kg/d (BCI: 0.96-1.04 kg/d), respectively. The 95% BCI reported are based on posterior predictive distributions of parameters, meaning that they can be applied directly as probability statements to inform decision making (Spiegelhalter et al., 2004) and used to develop farm-specific targets. For example, setting targets at the BCI lower bound would give a minimum target applicable to 97.5% of calves from a given percentile of farms. A large change in cumulative mean growth rate (equivalent to a farm in the bottom 2.5% moving to the top 2.5%) would require one or more interventions to increase cumulative calf growth rate by ≥0.44 kg/d. Such a change may be associated with an increase in mean first-lactation milk yield of 682 ± 280 kg (Soberon and Van Amburgh, 2013). The marginal value of any additional milk would be indicative of the potential intervention budget. Further research is needed to inform farm-specific budgets for appropriate interventions to increase the chance that changes are cost effective.
Mean calf growth rate varied between farms, such that sources of unexplained variation in weight were dependent on calf age. Influential farm-level differences could have been related to milk or colostrum feeding and environmental conditions in terms of hygiene and thermal comfort (Hyde et al., 2021). However, for neonatal calves, most unexplained variation in calf weight was at the calf level, relating to differences between calves within farms ( Figure 1). This could indicate variation in the application of management or environmental conditions over time. Missing explanatory variables could relate to genetic differences between calves, differences in dam characteristics such as parity, or differences in the viability of individual calves due to the effectiveness of passive transfer of immunity from colostrum, nutrition, and diseases such as diarrhea and pneumonia (Windeyer et al., 2014). Commercial information known to the database owners showed that calves were Holstein-Friesian females. It is possible that this assumption was unreliable in some cases, although favorable comparison of central tendencies for birth weights and growth rates with prior expectations suggests that any bias due to misclassification of breed and sex was inconsequential.
Compared with unknown variables acting at the calf level, any acting at the veterinary practice level were of lesser importance. This indicates that characteristics that could distinguish veterinary service providers are of limited importance in terms of calf birth weight and that the relative importance declines further as calves age. From 66 d of age, unexplained variation at the farm level exceeded that at the calf level. This could be due to increasing exposure to common environmental and management factors within farms that diminish the relative importance of phenotypic differences between calves over time. The development of optimal calf management strategies that realize genetic potential could be informed by research to identify reasons for differences in calf birth weight and growth rates among calves, farms, and veterinary practices throughout the rearing period. Results shown in Figure  1 can be applied to inform the allocation of resources for investigations. Studies in calves <66 d of age should prioritize factors underlying calf-level differences, such as differences in genotype, disease status, or failure of passive transfer. Studies in calves ≥66 d of age should prioritize factors underlying farm-level differences, such as differences in environment and management.
Results of this research are conditional on calves being eligible for weighing through survival. This could give an overly optimistic representation of calf production on the selected farms by being based on the best calves. Reasons for decreasing numbers of calves weighed with increasing age are unknown; however, calf mortality as a contributory factor (Brickell and Wathes, 2011;Hyde et al., 2020) should be considered before developing calf management strategies based on weight measurements alone.
Optimal calf-rearing strategies should aim to maximize lifetime productivity for the least cost. Heinrichs et al. (2017) reviewed a large body of research focused on developing growth standards for dairy heifers, ranging from small uncontrolled experiments to population studies. Accelerated growth during the rearing period to reduce costs has had mixed results in terms of first-lactation milk yield. High growth rates in the prepubertal period adversely influenced mammary development in some studies (Meyer et al., 2006) and were optimal at 0.80 kg/d in a meta-analysis of first-lactation milk yield (Zanton and Heinrichs, 2005). More than 99% of calves in this research remained <200 kg in weight, a value suggested to be an upper limit of the prepubertal period in Holsteins (Macdonald et al., 2005). Growth rates for calves on the median farm serviced by the median veterinary practice in this research approach this guideline. This ignores random effects due to farm, which have an increasing effect on calf growth rate as calves age. As growth rates varied between farms, there are opportunities to learn from a range of existing practices to optimize calf productivity.
This study was based on calves in a convenience sample of veterinary practices and farms. External validity has not been assessed. As such, mean birth weight and growth rate estimates should be extrapolated to the target population of UK dairy heifer calves with caution. This bias could lead to underestimation of unexplained variance, potentially increasing the relevance of this study.
In conclusion, mean birth weight and growth rate estimates were consistent with expectations. However, estimates varied substantially when random effects due to clustering of calves within farms and farms within veterinary practices were considered. In neonatal calves, most unexplained variance in weight was attributed to differences between calves within farms. Calf growth rate varied between farms, and difference between farms was the largest determinant of unexplained variance in calf weight from 66 d of age.
Understanding reasons for these differences should be the basis of research into optimal calf management strategies.
The author is grateful to Zoetis (Parsippany-Troy Hills, NJ) for providing access to the Calf Tracker data and for discussion of results. The University of Surrey granted ethical approval.
SCA was responsible for ideation, study design, data preparation, analysis, and reporting.
The author has no conflicts of interest.

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Archer | Variance in calf body weight