## 3 Results and Discussion
### Phase Space: Variability in EST by Transport Stage
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Stage1-Air**} & \multicolumn{2}{c}{**Stage2-Road**} & \multicolumn{2}{c}{**Stage3-Rest**} & \multicolumn{2}{c}{**Stage4-Road**} & \multicolumn{2}{c}{**Stage5-Road**} \\ \cline{2-11}  & **Area** (\({}^{\circ}\)**C\({}^{2}\)) & **C** (\({}^{\circ}\)**C) & **Area** (\({}^{\circ}\)**C\({}^{2}\)) & **C** (\({}^{\circ}\)**C) & **Area** (\({}^{\circ}\)**C\({}^{2}\)) & **C** (\({}^{\circ}\)**C) & **Area** (\({}^{\circ}\)**C\({}^{2}\)) & **C** (\({}^{\circ}\)**C) & **Area** (\({}^{\circ}\)**C\({}^{2}\)) & **C** (\({}^{\circ}\)**C) \\ \hline Pig 1 & 74.4 & 33.4 & 48.3 & 31.0 & 80.6 & 35.2 & 74.8 & 33.7 & 41.2 & 32.4 \\ Pig 2 & 89.0 & 34.4 & 22.2 & 35.6 & 41.7 & 35.7 & 25.3 & 35.5 & 29.8 & 34.2 \\ Pig 3 & 90.5 & 34.9 & 82.4 & 33.9 & 70.3 & 36.3 & 13.7 & 34.7 & 29.8 & 33.6 \\ Pig 4 & 88.7 & 34.4 & 62.6 & 35.4 & 32.4 & 36.4 & 27.4 & 35.9 & 37.1 & 35.7 \\ Pig 5 & 78.0 & 34.1 & 117.6 & 31.6 & 96.7 & 34.9 & 41.8 & 33.3 & 103.9 & 33.9 \\ Pig 6 & 90.8 & 34.4 & 64.1 & 31.1 & 58.3 & 35.4 & 48.4 & 30.2 & 49.0 & 31.8 \\ Pig 7 & 73.3 & 33.9 & 14.5 & 34.7 & 62.1 & 35.9 & 17.9 & 34.7 & 36.9 & 35.7 \\ Pig 8 & 141.7 & 33.5 & 78.6 & 34.1 & 61.6 & 35.3 & 36.7 & 32.0 & 51.7 & 33.5 \\ Pig 9 & 67.7 & 32.2 & 56.0 & 31.9 & 71.2 & 34.1 & 45.9 & 32.4 & 68.7 & 32.8 \\ Pig 10 & 57.5 & 35.4 & 13.1 & 34.8 & 48.1 & 35.6 & 13.1 & 35.4 & 15.5 & 31.6 \\ Pig 11 & 91.4 & 34.2 & 75.8 & 32.9 & 114.6 & 35.8 & 54.9 & 31.6 & 67.6 & 35.9 \\ Men & 85.7 & 34.1 & 57.7 & 33.4 & 67.1 & 35.5 & 36.4 & 33.6 & 48.3 & 33.7 \\ STD & 21.7 & 0.8 & 32.0 & 1.7 & 23.8 & 0.7 & 19.2 & 1.9 & 24.4 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Areas and centroids obtained using the phase space representation for each transport stage and pig (C = centroid temperature; STD = standard deviation). Figure 7: Phase space representation for all data (whole trip) of male pigs (black) and female pigs (red), (f = 5). To elucidate the reasons for the greater thermal variability during air travel, we have represented the phase space diagrams per animal during air travel and during one of the stages of road transport. From the representation of the complete time series in the phase space diagram, we identified different dynamics, some with a more homogeneous distribution and concentration of points in the whole area within the envelope, and others where the points are more dispersed. Figure 9 shows the phase space diagram corresponding with Stage1-Air (heterogeneous distribution of points) and Stage5-Road for all animals (homogeneous distribution of points, especially for Figs 1, 3, and 10); red dots are 75% of the points closest to the centroid. The spatial concentration of 75% of the dots in a very small area implies it is an attractor that all pigs tend toward. In the case of Stage1-Air, black dots (25% of the data furthest from the centroid) were more dispersed and further from the attractor. Thus, they can be interpreted as a representation of a specific and unique event, which caused an average increase in the area of 62% when shifting from considering 75% to 100% of the dots (Figure 9a). That event lasted 57 min, leading to a general decrease in EST by 8 \({}^{\circ}\)C with respect to the average value of the centroid (34.1 \({}^{\circ}\)C). We did not find a similar or generalized phenomenon (i.e., that affected all animals) in the rest of the transport stages. The same analysis carried out in the road transport stages caused an average increase in the area from 49.5% when going from considering 75% to 100% of the points (Figure 9b), showing that both the event number and its effect on the thermal variability was much higher during air transport compared with road transport. Previous work by other authors has shown that the visualization using phase spaces allows easy identification of events such as the opening of a door in cold rooms or when refrigeration equipment is turned on or off [27].