Stochasticity-induced stabilization in ecology and evolution: a new synthesis.

Area of Science:

• Ecology
• Population Dynamics
• Theoretical Biology

Background:

• Random environmental variation is known to stabilize competitor coexistence.
• Previous analyses focused on log abundances and mean logarithmic growth rates, but these metrics do not fully capture invasion probabilities or extinction times.
• These metrics can decrease as the mean logarithmic growth rate increases, indicating limitations in prior approaches.

Purpose of the Study:

• To synthesize stochasticity-induced stabilization (SIS) phenomena.
• To develop a new theoretical framework based on the ratio of expected arithmetic growth to its variance.
• To clarify relationships between life-history strategies and SIS.

Main Methods:

• Developed a theoretical framework using the ratio of expected arithmetic growth to its variance.
• Applied the diffusion approximation to derive explicit formulas for invasion probabilities and persistence times.
• Reviewed and explained diverse examples from population genetics, microbiology, and ecology.

Main Results:

• Invasion probabilities and persistence times become single-valued, monotonic functions of the growth rate to variance ratio under diffusion approximation.
• The new framework unifies various SIS phenomena, including the storage effect in the lottery model.
• Clarified the influence of life-history strategies on SIS and analyzed extinction dynamics when SIS fails.

Conclusions:

• The ratio of expected arithmetic growth to its variance provides a transparent and unified theoretical framework for understanding stochasticity-induced stabilization.
• This framework offers a more robust understanding of species coexistence and persistence compared to previous methods.
• The study highlights the importance of considering growth rate variance in ecological and evolutionary dynamics.