## 3 Results
### Network Robustness Analysis  
We performed the plankton interaction network robustness analysis according to the network attack strategies and robustness evaluation schemes presented in Section 2.2. First, the number of different plankton types (1, 2, 3,..., _n_) by genus was set before starting the experiment. Then, attacks were carried out in certain proportions following different attack strategies. During network attacks, both the structure and characteristics of the network change. To assess the impacts of attacks on the network, we calculated the robustness evaluation indicators for the network at different attack degrees. Variations in the robustness evaluation indicators for the three networks under four attack strategies are shown through the curves in Figures 5-8, and changes in the robustness coefficients are displayed in Figure 5.  
In Figure 6, the evaluation indicators decrease rapidly under random vertex attacks for all three networks. Although the changes in the indicators differ across networks, their robustness is similar. This suggests that plankton communities can undergo dangerously rapid collapse when certain organisms disappear regardless of their community structure. Furthermore, the maximum connected component of all three networks decreases the most slowly, followed by the average vertex connectivity, while the network efficiency declines the fastest. This shows that even though the community remains structurally sound under random vertex attacks, its function is severely damaged. Figure 4: The correlation matrix of community \(c\) and the network \(c\) constructed based on the matrix. Figure 3: The correlation matrix of community \(b\) and the network \(b\) constructed based on the matrix. In Figure 7, the evaluation indicators perform better under random edge attacks for all three networks as compared to random vertex attacks. Networks \(a\) and \(c\) exhibit slow early stage declines, while network \(b\) is slightly less robust than networks \(a\) and \(c\); however, this difference is insignificant. These results suggest that random edge attacks have weaker destructive power than random vertex attacks. In the early attack stages, networks with more edges, such as \(a\) and \(c\), are less affected. This shows that plankton communities can resist natural disruptions well, especially highly interconnected communities such as \(a\) and \(c\). In Figure 8, the evaluation indicators decrease rapidly under vertex betweenness centrality attacks for all three networks, especially network \(b\). In network \(b\), when the vertex failure rate reaches 60%, the values of the average vertex connectivity and the network efficiency both drop to almost 0. At this point, the maximum connected component value is only about 10% of the original network. This shows that plankton communities can rapidly collapse under vertex betweenness centrality attacks, and that degradation of function is inevitable even if community biomass remains high. Figure 5: Changes in the robustness coefficient under different attack strategies. Figure 6: Changes in indicators under random vertex attack. In Figure 9, the evaluation indicators under edge betweenness centrality attacks perform better than under vertex betweenness centrality attacks for all three networks. The maximum connected components and the network efficiency of networks \(a\) and \(c\) exhibit show slow decreases, while network \(b\) decreases more rapidly, which is likely related to its having fewer edges. This suggests that more interspecies connections confer higher plankton community robustness. However, the intensity of damage under edge betweenness centrality attacks is greater compared to random edge attacks, despite both attack types targeting edges. This shows that deliberate attacks, whether on vertices or edges, consistently cause more damage than random failures. In Figure 5, the robustness coefficient intuitively expresses the overall network robustness under different attack strategies.