Universal constraint on nonlinear population dynamics

Kyosuke Adachi

doi:10.1038/s42005-022-00912-4

2022-06-01

Kyosuke Adachi *

Ryosuke Iritani

Ryusuke Hamazaki

DOI：10.1038/s42005-022-00912-4

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摘要

En 中文

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. In evolutionary theory, Fisher's fundamental theorem of natural selection establishes a simple relation between the variance of the growth rate and the temporal increase in the average growth rate. Here, the authors extend the theorem based on statistical physics and information theory and show that the speed in dynamical systems describing nonlinear population dynamics is bounded by Fisher information with universal limit exponents only depending on the kind of bifurcation and not on the specific systems.

Keyword:

FUNDAMENTAL THEOREM

GENERIC INDICATORS

NATURAL-SELECTION

TIPPING POINT

RESILIENCE