Non-equilibria in small metapopulations: comparing the deterministic Levins model with its stochastic counterpart

Area of Science:

• Ecology
• Population Dynamics
• Conservation Biology

Background:

• The classical Levins metapopulation model provides a deterministic framework for understanding population dynamics in fragmented habitats.
• Stochasticity plays a crucial role in small metapopulations, influencing extinction probabilities and timescales.
• Sudden environmental changes, such as altered patch numbers or dispersal rates, can disrupt metapopulation equilibrium.

Purpose of the Study:

• To investigate the stochastic analog of the Levins metapopulation model for small systems.
• To analyze the expected time to metapopulation extinction under sudden environmental perturbations.
• To compare the predictive power of deterministic model relaxation times with stochastic extinction times.

Main Methods:

• Examined a stochastic version of the Levins metapopulation model.
• Simulated sudden changes in patch number, colonization rates, and extinction rates.
• Calculated the expected time to metapopulation extinction.

Main Results:

• The expected metapopulation extinction time diverges from the relaxation time of the deterministic Levins model.
• Deterministic model relaxation times have limited predictive value for stochastic metapopulation behavior.
• For deterministically unviable systems, extinction time predictions remain qualitatively consistent.
• Improving remaining habitat quality to reduce local extinction rates is a more effective conservation strategy than habitat restoration or increasing dispersal.

Conclusions:

• Stochastic effects significantly alter metapopulation extinction dynamics compared to deterministic predictions.
• Conservation strategies should prioritize enhancing habitat quality to mitigate extinction risks.
• Management interventions should focus on reducing local extinction rates for greater effectiveness in preserving metapopulations.