Impacts of Tempo and Mode of Environmental Fluctuations on Population Growth: Slow- and Fast-Limit Approximations of Lyapunov Exponents for Periodic and Random Environments

by Pierre Monmarché, Sebastian J. Schreiber and Édouard Strickler

This work derives analytical approximations for how environmental fluctuation frequency affects population growth in structured populations experiencing periodic or random switching between environmental states. Key findings: (1) In slow-switching limits, periodic and random fluctuations have equivalent effects on growth rates, but differ significantly in fast-switching limits. (2) Applications to metapopulation models show that slower environmental switching promotes persistence, with random environments allowing higher switching frequencies for persistence than periodic ones. The results demonstrate that both tempo (frequency) and mode of environmental fluctuations critically influence population dynamics. 

Population growth rates in a fluctuating two-patch environment. Both tempo (slow vs. fast) and mode (random vs. periodic) can determine persistence.