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Resurrection of Dormant Daphnia magna: Protocol and Applications

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Extinction of oscillating populations.

Naftali R Smith¹, Baruch Meerson¹

¹Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.

Physical Review. E

|April 15, 2016

Summary

This study models oscillating predator-prey populations facing extinction. Using a WKB approximation, it reveals how stochasticity drives extinction and how entropic barriers change near the Hopf bifurcation.

Area of Science:

Ecology
Mathematical Biology
Statistical Physics

Background:

Established populations often exhibit size oscillations, theoretically represented as limit cycles.
In isolated populations, intrinsic stochasticity can lead to extinction.
Previous WKB theories have addressed population extinction from fixed points.

Purpose of the Study:

To investigate the extinction dynamics of oscillating populations within a stochastic Rosenzweig-MacArthur predator-prey model.
To develop and apply a WKB approximation for analyzing extinction in these systems.
To examine the influence of the Hopf bifurcation on extinction barriers.

Main Methods:

Development of a WKB approximation to the master equation, using characteristic population size as the large parameter.

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Application of Floquet theory to the dynamics of an effective four-dimensional WKB Hamiltonian.

Evaluation of extinction rates and identification of most probable extinction pathways.

Main Results:

Quantification of extinction rates for oscillating populations.
Identification of the most probable paths to extinction from the limit cycle.
Demonstration of nonanalytic changes in entropic barriers to extinction at the Hopf bifurcation.
Analysis of subleading pre-exponential factors in the WKB approximation.

Conclusions:

The WKB approximation provides a powerful tool for studying stochastic extinction in oscillating populations.
Hopf bifurcations significantly alter extinction dynamics and entropic barriers.
Understanding these dynamics is crucial for predicting population persistence.