Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

On the path to extinction.

Peter Jagers1, Fima C Klebaner, Serik Sagitov

  • 1Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden. jagers@chalmers.se

Proceedings of the National Academy of Sciences of the United States of America
|April 5, 2007
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Fast, bioluminescent blinks attract group members of the nocturnal flashlight fish Anomalops katoptron (Bleeker, 1856).

Frontiers in zoology·2025
Same author

Correlation between bioluminescent blinks and swimming behavior in the splitfin flashlight fish Anomalops katoptron.

BMC ecology and evolution·2024
Same author

New observations of fluorescent organisms in the Banda Sea and in the Red Sea.

PloS one·2024
Same author

Diversity and function of fluorescent molecules in marine animals.

Biological reviews of the Cambridge Philosophical Society·2024
Same author

Counting unique molecular identifiers in sequencing using a multi-type branching process with immigration.

Journal of theoretical biology·2022
Same author

Amendment to: populations in environments with a soft carrying capacity are eventually extinct.

Journal of mathematical biology·2021
Same journal

Tau protein as a regulator of mitochondrial function and dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

A scalable, dividing cell model for the robust propagation and quantification of human sporadic Creutzfeldt-Jakob disease prions.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Epigenetic regulation of mesenchymal BMP signaling directs postnatal organ innervation.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Single-shot wide-field biochemical imaging at 1 kHz frame rate.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Morphogenesis and topological evolution of a frustrated nematic liquid crystal under confinement.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

B cell-intrinsic CXCR3 drives efficient generation of ectopic pulmonary germinal center responses to influenza A virus infection.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

This study reveals predictable patterns in population extinction, showing that extinction time scales with the logarithm of population size. Population size during extinction follows a power law, approaching a Gumbel distribution.

Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Stochastic Processes

Background:

  • Population extinction is a critical phenomenon.
  • Intrinsic extinction occurs when reproduction rates are insufficient for replacement.
  • Subcritical branching processes model populations with expected progeny less than one.

Purpose of the Study:

  • To uncover fundamental patterns in intrinsic population extinction.
  • To mathematically describe the time to extinction (T) and population size at intermediate stages (uT).
  • To analyze the behavior of subcritical populations starting from a large initial size (x).

Main Methods:

  • Analysis of subcritical branching processes.
  • Asymptotic behavior analysis for large initial populations (x).

Related Experiment Videos

  • Application of extreme value distributions and Gumbel distribution.

    • Main Results:

    • Time to extinction (T) scales as log(x)/r, where r is the Malthusian parameter.
    • Population size at time uT scales as x^(u-1) for large x.
    • The population size distribution partway to extinction converges to a process involving constants and a Gumbel random variable.

    Conclusions:

    • Predictable mathematical patterns govern intrinsic population extinction.
    • The study provides a precise description of extinction dynamics over time.
    • Findings are applicable to understanding population decline in various biological systems.