Calving is a key event on a dairy cattle farm and successful calvings are important to financial success of the farm. Calving complications lead to an increase in veterinary and labour costs and a decrease in revenue (loss of animals and/or reduced subsequent performance) [1–3]. Furthermore, difficult calvings compromise animal welfare and thereby consumer acceptability of dairy production systems .
In recent years, dairy cattle breeders have shown an increasing interest in selection for functional traits  and gradually the focus of selection is shifting from traits that increase profit towards traits that reduce costs . For example, easy parturition and calf viability are economically important traits but are not classical production traits. Since genetic selection could improve calving performance, it is important to include calving traits in genetic evaluations, although their implementation is not straightforward.
Calving ease (CE) and stillbirth (SB) are phenotypes that are generally scored on categorical or binary scales which make them sensitive to subjectivity, especially CE . Furthermore, heritabilities of these traits are generally low  and thus much data is needed to obtain sufficiently accurate estimates that have an impact on selection indices. But above all, calving trait phenotypes are affected by two separate components, the calf’s contribution (direct effect; e.g. arising from size, hormonal balance, weight) and the dam’s contribution (maternal effect; e.g. arising from pelvic measurements, ability to respond to parturition signalling), and this complicates statistical analysis [8–10]. In quantitative genetics, the objective is to separate additive genetic variances and co-variances from other sources of variance. The statistical model fitted for calving traits should therefore allow the separation and estimation of both direct and maternal effects but there is no consensus on which is the most accurate model to achieve this objective. Various statistical models have been reported throughout the years, each aimed at improving one aspect of their predictive ability. Consequently, many different statistical models are used in routine genetic evaluations to estimate genetic parameters for calving traits , while for production traits there is a greater consensus across countries . For CE, statistical models range from sire-maternal grandsire (S-MGS) models to animal models in univariate or multi-trait form that either allow a direct-maternal genetic covariance or fix this covariance to zero .
Overall, statistical models can account for direct and maternal effects in two ways i.e. animal models that fit calf and dam effects directly and S-MGS models that fit direct and maternal effects through the sire of the calf and dam, respectively . Each of these then has a family of implementation depending on how traits are defined and modelled e.g. univariately or multi-trait, which leads to the divergence in models seen today. The genetic covariance between direct and maternal effects plays a key role in the interpretation of estimated genetic parameters and the prediction of response to selection. For example, in the case of CE, this parameter represents the genetic relationship between the animals’ genetic predisposition for ease of being born and ease of giving birth.
This genetic covariance is however suggested to be sensitive to estimation bias [12–14]. Thus, estimates of direct-maternal genetic correlations reported for calving traits, which are often negative and of moderate to high magnitude, are questioned . Theories on the source of bias in estimates of direct-maternal genetic correlations range from ignored environmental covariances [14, 16, 17] to unaccounted contemporary groups [15, 18, 19]. Estimation of the direct-maternal covariance and remaining genetic components is said to be further improved by using a multi-trait model instead of a univariate model [20, 21]. Since CE and SB are highly correlated and show low heritabilities, it has been suggested that a multi-trait model that incorporates a highly heritable and correlated indicator trait such as birth weight, calf size and/or gestation length (GL), would lead to a more optimal analysis [20–22]. In addition to models incorporating indicator traits, it has also been proposed that the extension of univariate models to a multi-trait model between parities would be useful because of the potential genetic distinctiveness of calving traits in first and later parities. This implies that models fitting first and later parities as correlated traits are theoretically more correct than models that fit parity as a non-genetic effect [23–25].
However, given the high standard errors of the estimated maternal variances and direct-maternal covariances, it appears that statistical models used to analyse calving traits can still benefit from optimization. Previous studies on the estimation of genetic parameters for calving traits have been comparing models. However, in most cases, studies limit themselves to single comparisons, such as univariate versus multi trait models within either a sire or animal model framework [21, 24]. The objective of this study was to estimate the genetic parameters of calving traits for United Kingdom (UK) Holstein-Friesian cattle with a range of present-day statistical models for national genetic evaluations of calving traits. A comparison was made between S-MGS versus animal models and univariate versus multi-trait models between traits and parities.
GL was added to the multi-trait model to study any benefits of this indicator trait to the predictive ability of the model. Specific attention was given to the potential bias of the sensitive genetic correlation between direct and maternal effects and, lastly, a ‘total heritable variance’ for calving traits was estimated, combining direct and maternal variance components. This parameter was recently reported for the analysis of traits affected by indirect genetic effects  and is suggested to represent the total amount of total genetic variance available for response to selection. Its practical use for calving traits is discussed.