Social network analysis and the implications for Pontocaspian biodiversity conservation in Romania and Ukraine: A comparative study

Analysis Social network analysis. For readability, we provide the full SNA methodology and term definitions in S1 Text. We translated the collected interviews into an adjacency matrix, a square matrix reporting weights (strength) of all the relational ties (see S1 Dataset). We consid- ered only confirmed information sharing links i.e. relational links described by both stakehold- ers involved. Unconfirmed links (16% of all the reported relationships) were considered unreliable and were omitted from the study. Tie-strength values of confirmed relationships between pairs of stakeholders did not always match. In case of bi-directional relationship, tie values were left as reported by the stakeholders. In case of unidirectional confirmed links, we selected the lowest and therefore most conservative tie values. Two institutions could not be interviewed resulting in some missing network data. We imputed the missing data using the imputation-by-reconstruction method [48]. We visualized the sociogram using the CRAN R package ’igraph’ [49]. The basic network statistics including number of actors and relational ties, graph density and centralization index were calculated using the CRAN R package ‘igraph’ [49]. The mean shortest distance was calculated using the CRAN R package ‘tnet’ [50] because the ‘igraph’ package does not take edge weights into account when measuring the shortest distance. We used frequency of contact as a measure of strength of the relationship and defined strong rela- tionships as the weights �3 on a scale ranging from no contact to very frequent contact (S1

Appendix). Centrality of individual nodes was calculated using degree centrality and betweenness cen- trality values. We calculated node-level statistics using the CRAN R package ‘tnet’ [50] which considers tie weights and corrects for the number of intermediary nodes. Central stakeholders were regarded as those with centrality scores higher than, or equal to the third quartile thresh- old values [28, 47, 51]. Brokerage was measured by combining quantitative and qualitative approaches. Brokers are nodes which are between other nodes in a network and have the power to control the flow of information [39, 52, 53]. Quantitatively, brokerage was measured through betweenness cen- trality and Burt’s constraint metrics [39, 52]. Qualitatively, we examined the network narra- tives and extracted evidence that stakeholders are actually engaging in brokering behavior, such as mobilization of information, deliberation between different types of stakeholders and mediating between working groups to address conservation issues [54]. Here, we regarded stakeholders as brokers when they had high betweenness scores, low Burt’s constraint values, and were engaged in brokering behavior. We used only the strong ties (� 3) to calculate betweenness centrality and Burt’s constraint metrics as these reflect regular contacts. We cal- culated Burt’s constraint utilizing CRAN R package ‘igraph’ [49]. Finally, we used a null-model test to identify the presence of ‘network homophily’ in the network. ‘Network homophily’ is the selective linking between actors based on specific attri-

butes, in our case the category of stakeholder institutes [55]. With a null-model test, we tested whether densities within and between stakeholder groups (defined by the stakeholder cate- gory) were significantly higher or lower than random expectation. Qualitative analysis. We used the ‘inductive approach’ for qualitative analysis, so the themes (recurrent unifying concepts or statements about the content/subject of the inquiry) of interaction and perceived sufficiency of interaction were determined based on the collected data and not on prior knowledge or assumptions [56, 57]. The themes were established from the collected interviews based on repetitions [58]. We used a ‘constant comparison’ method to refine the dimensions of established themes and to identify the new themes [59]. We then counted the identified themes and determined their relative importance based on the order of PLOS ONE Social network analysis and the implications for Pontocaspian biodiversity conservation in Romania and Ukraine PLOS ONE | https://doi.org/10.1371/journal.pone.0221833 October 23, 2020 6 / 20