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Does increased stochasticity speed up extinction?

L H Alvarez1

  • 1Department of Economics, Turku School of Economics and Business Administration, Finland. luis.alvarez@tukkk.fi

Journal of Mathematical Biology
|February 2, 2002
PubMed
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Increased stochastic fluctuations, whether environmental or demographic, accelerate population extinction. Our findings confirm that greater randomness is detrimental to population growth and survival.

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.

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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.