论文标题
对非线性人口动态的普遍限制
Universal constraint on nonlinear population dynamics
论文作者
论文摘要
生态和进化过程表明，根据内部相互作用和环境变化，各种种群动态。尽管在预测生物学过程中至关重要，但发现这种非线性动态的一般关系仍然是一个挑战。在这里，我们对代表人口动态的一类广泛的非线性动力学系统得出了普遍的信息理论约束。约束被解释为对费舍尔自然选择基本定理的概括。此外，约束指示了分叉点周围临界放松速度的非平凡界限，我们认为这仅由分叉的类型普遍确定。我们的理论是针对表现出跨症状分叉的进化模型和流行病学模型的验证，以及经历极限周期振荡的生态模型。这项工作通过提供非线性系统的非平衡统计力学中的基本关系来预测信息理论中的生物动力学的方法。
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.
