非线性种群动力学的泛约束
Universal constraint on nonlinear population dynamics
摘要：
生态和进化过程显示出各种种群动态，取决于内部相互作用和环境变化。虽然在预测生物过程中至关重要，但发现这种非线性动力学的一般关系仍然是一个挑战。在这里，我们推导出一个普遍的信息理论约束的一类广泛的非线性动力系统表示为人口动态。这个限制被解释为费雪自然选择基本定理的推广。此外，约束表明非平凡的边界临界松弛的速度在分歧点，我们认为是普遍确定的分歧的类型。我们的理论得到验证的进化模型和流行病模型，其中表现出跨临界分岔，以及生态模型，其中经历极限环振荡。这一工作通过提供非线性系统的非平衡统计力学的基本关系，为用信息论预测生物动力学铺平了道路。
英文摘要：
Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics has remained a challenge. Here, we derive a universal information-theoretical constraint on a broad class of nonlinear dynamical systems represented as population dynamics. The constraint is interpreted as a generalization of Fisher's fundamental theorem of natural selection. Furthermore, the constraint indicates nontrivial bounds for the speed of critical relaxation around bifurcation points, which we argue are universally determined only by the type of bifurcation. Our theory is verified for an evolutionary model and an epidemiological model, which exhibit the transcritical bifurcation, as well as for an ecological model, which undergoes limit-cycle oscillation. This work paves a way to predict biological dynamics in light of information theory, by providing fundamental relations in nonequilibrium statistical mechanics of nonlinear systems.
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