Population dynamics in a time-varying environment with fat-tailed correlations.

Area of Science:

• Ecology
• Theoretical Biology
• Population Dynamics
• Environmental Science

Background:

• Temporal environmental noise (EN) is a critical factor influencing population and community dynamics.
• Traditional models often assume Markovian processes with exponential correlation time distributions (quenched or annealed regimes).
• Empirical evidence increasingly suggests fat-tailed decay in environmental correlation times, deviating from standard models.

Purpose of the Study:

• To investigate the ecological consequences of power-law correlated environmental noise on isolated and competing populations.
• To analyze the dynamics within the intermediate regime between quenched and annealed environmental noise.
• To characterize the extinction behavior of isolated populations under power-law correlated EN.

Main Methods:

• Theoretical modeling of population dynamics under power-law correlated environmental noise.
• Analysis of the intermediate regime between quenched and annealed dynamics.
• Investigation of extinction time scaling and dependence on spectral exponent for isolated populations.

Main Results:

• The intermediate regime between quenched and annealed dynamics can expand indefinitely under power-law correlated EN.
• Population dynamics in this intermediate region are dominated by infrequent but significant periods of stable environmental conditions.
• For isolated populations, extinction time exhibits power-law scaling with the logarithm of abundance and nonmonotonic dependence on the spectral exponent.

Conclusions:

• Power-law correlated environmental noise introduces novel dynamical behaviors not captured by traditional Markovian models.
• The identified intermediate regime highlights the importance of rare, long-lasting environmental states in ecological dynamics.
• Understanding these dynamics is crucial for predicting species persistence and evolutionary trajectories in fluctuating environments.