How to approach the resilience of livestock exposed to environmental challenges? Quantification of individual response and recovery by means of differential calculus

This work was originated from the need to study how animals individually react to environmental challenges. Common practical constraints in research protocols often lead to data collected at frequencies that are not high enough to capture the dynamics of animal responses. One approach to deal with that issue is to transform discrete empirical time series into continuous functions from which several descriptors can be extracted to characterise the response. A method for the extraction of smoothed functions from milk yield (MY) time series has been published before for dairy cows. This method was applied to detect challenges a posteriori. In this paper, we present an adaptation of this differential smoothing methodology, for the case when the environmental challenge is known a priori. This is advantageous because it allows for a more detailed characterisation of the response. Full description of the methodology is presented, where operations from differential calculus are applied to the smoothed functions to extract 23 descriptors that characterise the shape, dynamics and delay of individual responses to a single known challenge. We present examples of the application of the algorithm to individual time series of MY and plasma non-esterified fatty acid concentrations from suckling cows exposed to nutritional challenges that are known a priori. We propose a selection strategy for the smoothing coefficient (λ) based on the optimisation between noise reduction and output stability. If applied to groups of individuals that are sufficiently large, this methodology could provide information to help discriminating animals based on how they respond to the environmental challenges. This methodology may be used to develop decision-making tools for the selection of resilient individuals aiming at improving robustness and performance.