Fig 1.
Flow chart of tabu search.
Fig 2.
A quantitative food web example with 6 species and 19 weighted links.
Virtual node v1 represents the external environment. The link from v1 to v2 with a green weight represents the energy flow that the food web receives from the external environment, and the links from v2, …, v7 pointing to v1 with yellow weights indicate energy flows from the food web into the external environment.
Fig 3.
Illustration of the tabu search-based food web disintegration strategy.
The blue row represents the current solution, X1, X2, X3, X4 represents the four different candidate solutions generated, and the right rectangle represents F(Xind). The red value is the optimal value of the objective function in one cycle, and its corresponding swap is noted as green.
Table 1.
Major characteristics of food webs used in the present research.
Fig 4.
Relationship between primary and cumulative extinction in 12 food webs in order of species richness.
ID, OD, SD, PD, EIG and TS represent the keystone species identification strategies based on in-degree, out-degree, sum of in-degree and out-degree, product of in-degree and out-degree, eigenvector, and tabu search, respectively. All algorithms were tested 10 times on each food web, and averages were taken as results.
Fig 5.
Mean SEA values(mean ± SEM) of each removal algorithm.
Table 2.
Secondary extinction area(SEA, t = 0.5).
Table 3.
Dunnett post hoc test results of secondary extinction area.
Fig 6.
Relationship between extinction threshold (t) and Robustness (R50) in 12 food webs in order of species richness.
The threshold t varied from 5% to 95% by 5%, and the robustness of each t is recorded for each removal approach. All algorithms were tested 10 times on each food web and averages were taken as results.
Fig 7.
Mean R50 values(mean ± SEM) of each removal algorithm(t = 0.5).
Table 4.
Dunnett post hoc test results of robustness.