Estimation of Parameter Distributions in a Model of Magnesium Dynamics in Cows to Predict the Risk of Tetany in Dairy Herds

The onset of tetany, when dairy cattle have insufficient magnesium, has a huge impact both economically and on animal welfare. We have previously adapted a model of magnesium dynamics in sheep (Robson et al. 1997) for use with dairy cattle as an aid to understanding aspects of magnesium metabolism which influence the risk of animals contracting tetany (Bell et al. 2005). To estimate this risk in a dairy herd, we carried out Monte-Carlo simulations in which model parameters for individual animals in the herd were varied randomly according to their statistical distributions (McKinnon et al. 2003). In this approach the choice of parameter distributions can significantly influence the risk estimates. In some cases the distributions are available from the literature, but in other cases they must be obtained using some sort of parameter refinement process to estimate the parameter distributions from measured data corresponding to a model output (Figure 1).