Fig 1.
Two different patterns of higher-order species transfer between ports.
(b) Out of six ships, ship 1 and 2 follow the pattern in (a) left, and ship 4 and 5 follow the pattern in (a) right. Conventional first-order network ((c) left), where organisms have the same probability of being introduced to port E and F via port A. Higher-order network ((c) right) with a second-order dependency example in species transfer. Due to higher-order patterns in ship movements, organisms native to port C are more likely to get transferred to port F via ships traveling through port A and organisms native to port B are more likely to get transferred to port E via ships traveling through port A.
Fig 2.
A block diagram of the risk network construction.
The ecoregion data, environmental data, and the shipping data are used to compute the first-order (pairwise) NIS spread link between the shipping ports through each shipping introduction vector. The resulting probabilities along with the shipping trajectories are used for constructing the two SF-HONs, ballast SF-HON and biofouling SF-HON.
Table 1.
Comparison of basic properties of the four networks.
CC refers to the connected components of the graph.
Fig 3.
A heat-map of higher-order species flow resulting from ballast water (a) and biofouling (b) across major realms (a larger geographic scale that the ecoregion scale underlying other analyses).
The y-axis indicates target realms and the x-axis are the source realms (x-axis is shared). The risks are normalized to be in the range of [0, 1]. The inter-realm risk is overall higher in ballast SF-HON (a), while most high-risk connections in biofouling SF-HON are within the same realms (b). Eastern-Indo Pacific has the highest risk of NIS introduction to Temp Southern Africa in ballast SF-HON (a), while in biofouling SF-HON the highest target realm for Eastern-Indo Pacific is Central Indo-Pacific (b). Temperate Northern Atlantic has a significantly high risk of introduction to Eastern-Indo Pacific in biofouling SF-HON (b).
Fig 4.
The diverse higher-order clustering of shipping ports based on the ballast discharge risks (a) and higher-order clustering of biofouling risks (b).
The coloring of the ports indicates the port cluster. Ports which belong to multiple clusters through the higher-order patterns are shown as a pie chart with multiple colors. The pie chart size indicates the relative NIS spread risk for the port. The top ports with the highest risk are labeled by name.
Table 2.
Percentage of each ship type in the data for calculation of ballast and biofouling risk.
Percentage values for ship types with an overall higher NIS introduction risk (as identified in Fig 8) are marked as bold. We notice that most ship types with higher introduction risk (via ballast or biofouling) do not make a large portion of the records.
Fig 5.
Variation of number of higher-order nodes and average NIS spread risk for (a) ballast SF-HON and (b) biofouling SF-HON.
The average risk in both cases is normalized for easier comparison. In 2008 the average risk and number of higher-order nodes in ballast SF-HON drops, while they both increase in biofouling SF-HON.
Fig 6.
SF-HONs show significantly larger changes in both number of nodes (a) and edges (b) compared to SF-FONs.
Fig 7.
Validation results on the three data sets available.
Comparison of the SF-HONs versus SF-FONs and All-Paths models shows that SF-HONs have generally ballast SF-HON yields lower MSE (suggesting more accurate results) on the NAS and NEMESIS datasets, while biofouling SF-HON yields lower MSE (more accurate results) on the AquaNIS data.
Fig 8.
Box plots represent the NIS introduction risk for all voyages by different ship types for ballast water (a) and biofouling (b).
For ballast water, GWT and for biofouling, duration of stay at port display the same pattern as the NIS introduction risk.