Does increased stochasticity speed up extinction?

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Population extinction is influenced by environmental and demographic stochasticity.
• Understanding the impact of increased randomness on extinction timing is crucial for conservation biology.

Purpose of the Study:

• To investigate how increased stochastic fluctuations affect population extinction dates.
• To determine if environmental or demographic stochasticity uniquely impacts extinction.
• To confirm the detrimental effect of stochasticity on population growth.

Main Methods:

• Modeling population density as a general linear diffusion process.
• Analyzing the properties of the minimal r-excessive mapping and moment generating function.
• Establishing conditions for convexity of these mathematical functions.

Main Results:

• Demonstrated that under specific conditions, increased stochastic fluctuations lead to a convex moment generating function.
• Showed that this convexity results in a unambiguously negative impact on the expected extinction date.
• Confirmed that increased stochasticity accelerates extinction regardless of its source (environmental or demographic).

Conclusions:

• Increased stochasticity, from any source, speeds up population extinction.
• Stochastic fluctuations are detrimental to population persistence and growth.
• The study provides mathematical confirmation of the negative effects of randomness in population dynamics.