Modeling Interactions Within French Dairy-Cattle Systems Using R-Vines

Farms face multiple challenges, such as decreasing their environmental impacts without decreasing productivity or revenue too much. Farms emit several greenhouse gases, whose multiple sources are influenced by many interacting factors on the farms and in their environments, which make farms and their dynamics more difficult to understand. To assess specifically how these interactions influence farm performances, we investigated the ability of regular vine copulas, which are composed of a wide variety of bivariate copulas, to map multivariate complex dependence patterns. The method was applied to a dataset of management practices, emissions and productivity of 2347 French dairy farms. An initial assessment of all farms combined identified specific dependencies. In particular, methane emissions from manure management depended on milk production, since strategies for producing milk influence herd management, time spent inside the barn and manure management. A second assessment identified changes in the dependencies among variables as a function of farm productivity. In addition to describing interactions among descriptive variables of farms, this method characterizes their dependencies, even among their extreme values. The assessments demonstrated the utility of using regular vine copulas to model farms, whose variables are connected by chains of multiple reactions and interactions. Supplementary materials accompanying this paper appear online.