The potential of kernel density estimation for modelling relations among dairy farm characteristics

Agricultural systems are generally characterised by many dependent variables that represent their management practices and performances. Parametric approaches are usually used to explore data collected from farms and relations among variables. However, these approaches are generally limited by strong assumptions about the shape of the model that relates variables to each other, which can induce bias in studies. To address these limitations, we investigated the potential of non-parametric kernel density estimators to help explore relations among variables that characterise farms (e.g., forage and milk production, greenhouse gas (GHG) emissions), which have the advantage of requiring no assumptions about the shape of these relations. Multivariate kernel density estimation analyses the probability that the values of two or more variables will simultaneously fall within a given range for each variable. The practical utility of this approach was shown by identifying subsets of a population of 96 dairy farms in 2013 in Normandy, France, that had forage production, milk production and GHG emissions that most other farms in the same population were likely to have. Several farms outside of the highest density regions, but which lay with the same range of grass or maize production, were able to produce 28% or 27% more milk per cow, respectively (or emit 21% or 9% less GHGs per livestock unit, respectively) each year than farms inside these regions. Characteristics of these farms that increase milk production (e.g., higher maize silage production, more often with majority-Holstein herds) or decrease GHG emissions per livestock unit (e.g., lower maize silage production, more often with majority-Normande herds) were identified. Kernel density estimation can be useful for selecting farms with particularly high or low production or environmental performances in a sample of farms as a function of multiple characteristics.