Using conditional Kendall's tau estimation to assess interactions among variables in dairy-cattle systems

Context

Understanding how multiple factors interact in complex systems is an important issue. In particular, agricultural production systems are based on biological and ecological processes that are influenced by environmental and human factors, all of which interact. When evaluating such systems statistically, these multiple dependences and interactions make it more difficult to model system performances as a function of management practices and weather.

Objective

Our objective was to assess interactions among management practices, weather and system performances. We aimed in particular to identify subsets of farms whose correlations for given pairs of variables as a function of another variable deviated greatly from the traditional correlation between the variables (i.e., atypical farms).

Methods

We investigated a measure of dependence that assesses whether (and if so, how) the correlation between two variables varies as a function of a third one: conditional Kendall's tau. We applied this measure to a set of variables that described management practices (e.g., concentrated feed fed), weather (e.g., precipitation) and performances (e.g., milk production, enteric methane emissions) for dairy-cattle systems in France in 2013 and 2014 (2523 and 804 farms, respectively).

Results and conclusions

In 2013, the amount of digestible organic matter in the ration ingested per cow influenced the correlation between milk production per cow and enteric methane emissions per livestock unit. In particular, the correlation was negative for a set of atypical farms whose ingested digestible organic matter was $\approx$ 2050-$2900\mathrm{kg}.{\mathrm{cow}}^{-1}$. In addition, total annual precipitation in 2013 influenced the correlation between the amount of concentrated feed fed per cow and milk production per cow for farms surveyed in either year. In 2013 and 2014, the correlation began decreasing strongly beyond a certain threshold of precipitation (ca. 1400 and 1100 mm, respectively), which highlighted the need to adapt each farm's practices to its agricultural and weather context.

Significance

Application of conditional Kendall's tau identified interactions that caused the effectiveness of management practices to vary and how they did so.