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Updated: Jan 12, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
Published on: January 19, 2019
Understanding ecological cascade in cyclic game systems by means of directed graphs
Ryoo Kyung Yang1, Seungmo Hong1, Suhyeon Kim1
1Department of Applied Mathematics, College of Applied Sciences, Kyung Hee University, Yongin 17104, Republic of Korea.
None:
Evolutionary game-based models hold a potential key to help interpret the evolution of systems based on the interaction of multispecies. In particular, in ecosystems with structures such as food webs, the extinction of one species through competition can lead to secondary extinctions, and such ecological cascades are common in cyclic game systems governed by the rock-paper-scissors metaphor. In this paper, we delve into ecological cascades in the evolution of cyclically competing populations by using directed graphs. By revisiting previous studies of cyclic game systems, we identify a common mathematical property in evolutionary directed graphs and predict evolution in terms of tournaments. We further compare a theoretical result with Monte Carlo simulations, which shows that the graph-based interpretation of ecological cascades is qualitatively consistent with numerical simulations. Ultimately, we may emphasize that the method based on directed graphs would be more practical for understanding the evolution of multispecies than numerical simulations.
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