Validating statistical properties of resilience indicators derived from simulated longitudinal performance measures of farmed animals

Abstract

Resilience is commonly defined as the ability of an individual to be minimally affected or to quickly recover from a challenge. Improvement of animals’ resilience is a vital component of sustainable livestock production but has so far been hampered by the lack of established quantitative resilience measures. Several studies proposed that summary statistics of the deviations of an animal’s observed performance from its target performance trajectory (i.e., performance in the absence of challenge) may constitute suitable quantitative resilience indicators. However, these statistical indicators require further validation. The aim of this study was to obtain a better understanding of these resilience indicators in their ability to discriminate between different response types and their dependence on different response characteristics of animals, and data recording features. To this purpose, milk-yield trajectories of individual dairy cattle differing in resilience, without and when exposed to a short-term challenge, were simulated. Individuals were categorised into three broad response types (with individual variation within each type): Fully Resilient animals, which experience no systematic perturbation in milk yield after challenge, Non-Resilient animals whose milk yield permanently deviates from the target trajectory after challenge and Partially Resilient animals that experience temporary perturbations but recover. The following statistical resilience indicators previously suggested in the literature were validated with respect to their ability to discriminate between response types and their sensitivity to various response features and data characteristics: logarithm of mean of squares (LMS), logarithm of variance (LV), skewness (S), lag-1 autocorrelation (AC1), and area under the curve (AUC) of deviations. Furthermore, different methods for estimating unknown target trajectories were evaluated. All of the considered resilience indicators could distinguish between the Fully Resilient response type and either of the other two types when target trajectories were known or estimated using a parametric method. When the comparison was between Partially Resilient and Non-Resilient, only LMS, LV, and AUC could correctly rank the response types, provided that the observation period was at least twice as long as the perturbation period. Skewness was in general the least reliable indicator, although all indicators showed correct dependency on the amplitude and duration of the perturbations. In addition, all resilience indicators except for AC1 were robust to lower frequency of measurements. In general, parametric methods (quantile or repeated regression) combined with three resilience indicators (LMS, LV and AUC) were found the most reliable techniques for ranking animals in terms of their resilience.