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

Generalized Verhulst laws for population growth.

R Zwanzig

    Proceedings of the National Academy of Sciences of the United States of America
    |November 1, 1973
    PubMed
    Summary

    Population dynamics in complex ecosystems, modeled by Volterra-Lotka equations, exhibit hereditary effects and noise. Initial population levels significantly influence growth trajectories, leading to overshooting or precipitous decay before equilibrium is reached.

    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

    Two-state models of protein folding kinetics.

    Proceedings of the National Academy of Sciences of the United States of America·1997
    Same author

    Simple model of protein folding kinetics.

    Proceedings of the National Academy of Sciences of the United States of America·1995
    Same author

    Levinthal's paradox.

    Proceedings of the National Academy of Sciences of the United States of America·1992
    Same author

    Time dependent rate of diffusion-influenced ligand binding to receptors on cell surfaces.

    Biophysical journal·1991
    Same author

    Diffusion-controlled ligand binding to spheres partially covered by receptors: an effective medium treatment.

    Proceedings of the National Academy of Sciences of the United States of America·1990
    Same author

    Diffusion in a rough potential.

    Proceedings of the National Academy of Sciences of the United States of America·1988

    Area of Science:

    • Ecology
    • Population Dynamics
    • Theoretical Biology

    Background:

    • The Volterra-Lotka model describes predator-prey population dynamics.
    • Understanding single-species growth within a multi-species environment is crucial.
    • Hereditary effects and environmental interactions can alter population trajectories.

    Purpose of the Study:

    • To investigate single-species population growth and decay under Volterra-Lotka dynamics.
    • To incorporate hereditary effects and environmental interactions into population models.
    • To analyze population behavior relative to equilibrium levels.

    Main Methods:

    • Utilized a generalized Verhulst law derived from statistical mechanical theories of Brownian motion.
    • Modeled population dynamics with hereditary effects and an emergent "noise" source.
    • Numerically solved a special case with a damped exponential heredity kernel.

    Main Results:

    • Population growth near equilibrium follows a generalized Verhulst law with hereditary effects.
    • The model incorporates a "noise" source related to the heredity kernel.
    • Population trajectories show distinct overshooting or precipitous decay depending on initial conditions relative to equilibrium.

    Conclusions:

    • Hereditary effects and environmental noise significantly shape population dynamics.
    • Initial population density critically determines the approach to equilibrium.
    • The model provides insights into complex ecological interactions and population stability.

    Related Experiment Videos