The spatial-temporal pattern of RMT network stability in the estuarine phytoplankton community

Ecosystem stability is a central focus in ecological research. Despite the proliferation of stability measurement indices in recent years, they tend to have specific conditions and do not provide a widely applicable network index for measuring stability. In this research, we established an indicator to assess network stability, and compared the network stability features in estuarine phytoplankton networks from a temporal and spatial perspective. Based on microscopic examination, we acquired phytoplankton community data of 15 sampling points at three hydrological periods in the Bohai Bay. In addition, we analyzed the spatial pattern of phytoplankton biodiversity in the estuary of Bohai Bay by using α-diversity indices (e.g. Shannon, Simpson and Evenness). Then, we developed an optimized co-occurrence network using Random Matrix Theory (RMT). We also selected 12 topological indices to describe the attributes of networks. According to the eigenvector centrality algorithm, we built an indicator of Key Nodes Concentration (K), and also compared the Geodesic Efficiency (E) to verify the network stability. Our findings reveal distinct spatial and temporal patterns: the Shannon and Chao indices peaked at different locations across hydrological periods. The highest Shannon index was at F14(Yellow River old course) in the normal-flow period, while it was at F4(Shahe River estuary) in the high-flow period. Additionally from the aspect of topological indices, we can see the distribution in the low-flow period is the most uniform (degree = 0.076, betweenness centrality = 0.224) and the average degree in the high-flow period was significantly higher than that in the normal-flow period and the low-flow period. The calculation results show that the network's stability is highest during the high-flow period, with K = 0.406 and E = 0.332, and both K and E values decrease across the three periods. And 73.3 % of the esturary were more stable during the common-flow period. This research (a) provides a fundamental network-based topological indices for quantifying network stability.; (b) improving a co-occurrence network establishment approach by using RMT theory; (c) reveals the spatial-temporal variability of estuarine ecological networks. These findings provide a scientific foundation for the management and conservation of phytoplankton ecological networks in Bohai Bay.