Quality assessment of static aggregation compared to the temporal approach based on a pig trade network in Northern Germany

Abstract

Recent analyses of animal movement networks focused on the static aggregation of trade contacts over different time windows, which neglects the system's temporal variation. In terms of disease spread, ignoring the temporal dynamics can lead to an over- or underestimation of an outbreak's speed and extent. This becomes particularly evident, if the static aggregation allows for the existence of more paths compared to the number of time-respecting paths (i.e. paths in the right chronological order). Therefore, the aim of this study was to reveal differences between static and temporal representations of an animal trade network and to assess the quality of the static aggregation in comparison to the temporal counterpart. Contact data from a pig trade network (2006-2009) of a producer community in Northern Germany were analysed. The results show that a median value of 8.7 % (4.6-14.1%) of the nodes and 3.1% (1.6-5.5%) of the edges were active on a weekly resolution. No fluctuations in the activity patterns were obvious. Furthermore, 50% of the nodes already had one trade contact after approximately six months. For an accumulation window with increasing size (one day each), the accumulation rate, i.e. the relative increase in the number of nodes or edges, stayed relatively constant below 0.07% for the nodes and 0.12 % for the edges. The temporal distances had a much wider distribution than the topological distances. 84% of the temporal distances were smaller than 90 days. The maximum temporal distance was 1000 days, which corresponds to the temporal diameter of the present network. The median temporal correlation coefficient, which measures the probability for an edge to persist across two consecutive time steps, was 0.47, with a maximum value of 0.63 at the accumulation window of 88 days. The causal fidelity measures the fraction of the number of static paths which can also be taken in the temporal network. For the whole observation period relatively high values indicate that 67% of the time-respecting paths existed in both network representations. An increase to 0.87 (0.82-0.88) and 0.92 (0.80-0.98), respectively, could be observed for yearly and monthly aggregation windows. The results show that the investigated pig trade network in its static aggregation represents the temporal dynamics of the system sufficiently well. Therefore, the methodology for analysing static instead of dynamic networks can be used without losing too much information.

Keywords: Animal movement; Pig; Temporal network; Time-respecting path; Trade.