Uncovering the underlying physical mechanisms of biological systems via quantification of landscape and flux

Xu Li^{1, †,}, Chu Xiakun¹, Yan Zhiqiang¹, Zheng Xiliang¹, Zhang Kun¹, Zhang Feng¹, Yan Han¹, Wu Wei¹, Wang Jin^{1, 2, ‡,}

(a)–(c) The population potential landscapeU((a) model of predation; (b) model of competition; (c) model of mutualism). (d)–(f) The intrinsic potential landscapeϕ₀((d) model of predation; (e) model of competition; (f) model of mutualism). On the top row, the flux velocity and the negative gradient of the population potential are denoted, respectively, by the purple arrows and black arrows. On the bottom row, the intrinsic flux velocity and the negative gradient of the intrinsic potential landscape are denoted, respectively, by the purple arrows and black arrows.^[22]