Network visualizations and timelines
Figure 1 illustrates the three weighted agonistic interaction networks of weaned pigs, growing pigs and gilts aggregated over the whole observation period. Compared to the timelines in Figure 3, this implies an abstraction of the real fighting activities which can fluctuate within time. Especially the two network examples of growing pigs and gilts showed more agonistic interactions in the first six hours after rehousing and mixing. This information was lost in the aggregated networks (Blonder et al. 2012). However, due to the relative short observation period, the analysis of these aggregated networks give an insight into the formation and evolution of agonistic interactions directly after rehousing and mixing and enables therefore the comparison of different age levels.
Centrality parameters
Beside the unweighted centrality parameters, the weighted centrality parameters were analyzed in order to include the interaction frequencies of two specific opponents. Although other studies (Koene and Ipema 2014) stated that for small groups of animals with small datasets weighted social network analysis could probably be more powerful, the results of the present study showed high correlation coefficients between unweighted and weighted centrality parameters. Therefore, the further analysis focused on the unweighted centrality parameters. Whether the results of a weighted or an unweighted approach differ from each other, depends not exclusively on the group size, but also e.g. on the recorded interaction or the space allowance the animals have.
The results of the degree and the closeness centrality indicate that the weaned pigs fought more during the first two days after rehousing and mixing compared to growing pigs and gilts and could also reach their pen mates faster than the older age groups. Also, the number of different opponents was higher than in the older age groups, which can be derived from the results of the unweighted degree centrality. The relatively high values for both centrality parameters obtained in the flatdeck pens can be explained by the fact that nearly all animals in this age group fought against each other in the first two days after rehousing and mixing which led also to small distances between the single animals. In growing pigs and gilts, the number of fights decreased and a shift in the agonistic interactions towards specific animals could be observed. Therefore, lower values for the median closeness centrality but with a relatively high range could be obtained in these higher age levels. If agonistic interactions or other connections with a negative connotation are analyzed, it is necessary to consider that the outgoing centralities (e.g. out-degree and outgoing closeness centrality) measure the active behavior and the ingoing centralities (e.g. in-degree and ingoing closeness centrality) measure only the passive behavior. This is of particular importance when the social network structure of captive farm animals is analyzed. Here, the natural behavior of the animals is influenced by restrictions made by humans, e.g. limited space available and predetermined pen mates. For instance, a subordinate animal can avoid more easily an agonistic interaction in the wild, whereas in the artificial environment of a stable with limited space available only a low means of escape exists. Furthermore, the decrease in agonistic interactions with repeated rehousing and mixing situations can be explained as habituation effect (Coutellier et al. 2007). Alternatively, according to Hessing et al. (1993; 1994), the decrease could also represent a new coping strategy towards an unstable social structure in which the animals develop a preference for coping behaviors which are able to limit the energy costs and the number of injuries. As a result, a new stable social structure is established with fewer agonistic interactions (van Putten and Buré 1997). Due to the practical conditions, it has to be taken into account that the comparison between the different age levels could also be influenced by the different group sizes, by the available space (i.e. bigger pens with increasing age level) as well as by the increasing level of familiarity with higher age level. Marchant-Forde and Marchant-Forde (2005) stated that smaller group sizes in pigs do appear to have more post-mixing aggressions in comparison to larger group sizes. Other studies confirmed this statement (e.g. Nielsen et al. 1995; Andersen et al. 2004; Turner et al. 2001). However, also the pen size could be an explanation for this relation. The animals have in larger pens a greater distance available to avoid agonistic interactions, whereas in smaller pens they have to face them. Moreover, familiar pigs were engaged in fewer agonistic interactions than unfamiliar pigs (Puppe 1998). Also Arey and Franklin (1995) stated that the number of fights increased significantly with the number of unfamiliar animals. These findings could not be confirmed by Jensen and Yngvesson (1998) who did not find significant differences in the fighting behavior between unknown and already acquainted animals.
For the betweenness centrality low values and no significant differences between the three age levels could be obtained. This can be explained by the small group size and the limited space available. In larger groups, it is more likely that some animals form so-called bridges or cutpoints between different network components and as a consequence thereof these animals have a high betweenness centrality (Newman 2010).
Spearman rank correlations between the different calculated centrality parameters
In-degree – out-degree
For weaned pigs, a higher correlation coefficient between the in-degree and the out-degree centrality than for growing pigs and gilts could be obtained. This difference can be explained by the more stable rank order of growing pigs and gilts due to their increased familiarity and their experiences acquired from previous agonistic interactions. According to D’Eath (2004) and Otten et al. (1997), previous experiences of success or failure in aggressive interactions have long-lasting effects on the animals. Here, the previous dominance rank in particular had a prolonged effect on the rank position in later groups.
In the present study, correlation coefficients of 0.48 to 0.70 could be obtained between in-degree and out-degree. According to Szell et al. (2010), the correlations between the in-degree and the out-degree centrality in networks based on positive links are almost balanced with a correlation coefficient close to 1, whereas lower correlation coefficients in networks with negative links can be observed, such as in agonistic interaction networks. Although the correlation coefficients obtained are still relatively high for an agonistic interaction network, this finding can be explained by the fact that only the first two days after rehousing and mixing were analyzed in which the rank order of the animals had not been completely established. It is expected that a further decrease in the correlation coefficients can be observed after the stabilization of the rank order.
Degree, in-degree and out-degree – Betweenness
All correlation coefficients between the degree centralities and the betweenness centrality showed smaller values for weaned pigs than for growing pigs and gilts. This can be explained by the fact that the rehousing and mixing procedure after the farrowing stable is the first situation of this kind for the animals. Due to the fact that the animals were mixed and sorted by the smallest level of familiarity, they did not know each other from the previous pen and, therefore, all animals were involved in agonistic interactions in order to establish a stable rank order. As seen above, one explanation for these results could be that growing pigs and gilts specifically chose their opponents due to their experiences from previous agonistic interactions and also due to their confidence in their own fighting ability, indicating that they had learned to weigh up their chances of winning a fight.
Degree, in-degree and out-degree – Closeness, ingoing closeness and outgoing closeness
In weaned pigs, the correlation coefficients between the degree centralities and the closeness centralities showed higher values than for growing pigs and gilts. The higher values in weaned pigs can be explained by the first rehousing and mixing situation and the lack of experiences from previous agonistic interactions. They needed more agonistic interactions to establish a stable rank order. However, the values in growing pigs and gilts were also medium to high correlated. In small networks, one can say that the higher the degree centrality of a specific animal, the smaller is the distance of this animal to its pen mates, which is therefore correlated with the closeness centrality.
According to Krause et al. (2015), a primary advantage of social network analysis over other analytical methods is the ability to quantify indirect relationships or associations which allows for the detection of complex social structures. However, in the present study high correlation coefficients between the degree and the closeness centrality could be observed, indicating that this advantage only becomes apparent for moderate to large groups or otherwise if enough space is available to express for example evasive or avoidance behavior.
Spearman rank correlations of the centrality parameters between the different age levels
The relations between the centrality parameters over the observed age levels illustrate that only the consecutive age levels, i.e. weaned pigs to growing pigs and growing pigs to gilts, showed significant results. This indicates that experiences from previous rehousing and mixing situations significantly influence the behavior of the animals, which is in accordance with the findings described above that the animals gained confidence in the rank position already achieved (D’Eath 2004; Otten et al. 1997). Therefore, it is only possible to draw conclusions from one age level to the next, even though here only small correlation coefficients could be obtained.
For the correlations of the degree centrality over the different age levels, the out-degree centrality showed more stable results compared to the in-degree centrality. Similar results could be obtained for the outgoing closeness centrality. These findings can be explained by the fact that these centrality parameters are based on an active behavior, whereas the in-degree centrality depends on the aggression of the pen mates and the possibility to flee. The correlations of the betweenness centrality over the different age levels showed ambiguous results. Due to the small group size, the betweenness centrality only adopts relatively small values which can easily change with small changes in the network structure. Therefore, no clear trend could be observed.
Possible applications of social network analysis for management and welfare issues
According to Hinton et al. (2013), social network parameters could prove important in revealing potential causes of animal stress. For instance, with the help of centrality parameters, animals which show a disproportional amount of aggression or abnormal behavior, such as tail biting, as well as their victims can be detected. On this basis, it could be investigated how the network structure changes if some key individuals (i.e. with high centrality values) are removed from the group (e.g. Lusseau 2003). Depending on the chosen centrality parameter, the development of the agonistic interactions and the general stress level in the group could be compared and the appropriate parameter can be chosen to realize a maximum calming within the group. This approach would also reveal important insights in the relationship between the group members. Furthermore, the winner and the looser as well as the duration of an agonistic interaction should be included in the analysis. For example, a high out-degree centrality does not necessarily imply that it has also won the majority of the fights. Moreover, one cause for a high betweenness centrality may be the fact that the animals won a lot of fights and thus gained self-confidence in their own fighting ability. Therefore, they initiated fights with other individuals in the group. Another possibility for a high betweenness centrality may be that these animals lost agonistic interactions and reflected their frustration by an attack towards animals with a lower rank position. The analysis of this kind of associations could be used to identify key factors triggering harmful behavior.
Beside these relations between the animals, also resources, such as the access to feed or enrichment material, can be included in the network analysis as so-called multi-partite networks (Wasserman and Faust 1994). Previous studies showed that the supply of enrichment material reduced the number of aggression in the pen (Beattie et al. 1996; Schaefer et al. 1990) and that the feeding system had a large impact on the aggression among the animals (Hansen et al. 1982; Vargas et al. 1987). With this approach the questions could be answered why animals show aggressive behavior and if this behavior is correlated with a refused access to feed or enrichment material and therefore with an increased level of frustration.