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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Comprehensive phase diagram for logistic populations in fluctuating environment.

Yitzhak Yahalom1, Bnaya Steinmetz1, Nadav M Shnerb1

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E
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Summary

This study analyzes population dynamics, considering both internal random birth-death events and external environmental changes. It identifies three distinct phases influencing extinction times and their relationship with population size and carrying capacity.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Population dynamics are modeled as birth-death processes influenced by environmental factors and density.
  • Deterministic models like logistic growth exhibit a transcritical bifurcation, separating extinction and active phases.

Purpose of the Study:

  • To comprehensively analyze population dynamics phases under demographic and environmental stochasticity.
  • To investigate the relationship between extinction time, population size, and carrying capacity.

Main Methods:

  • Analysis of a birth-death process model incorporating endogenous demographic noise and environmental stochasticity.
  • Detailed study of three identified population phases and their transitions.

Main Results:

  • Identified three distinct population phases: inactive, power-law, and exponential.
  • Characterized mean time to extinction (T) in each phase: independent of carrying capacity (N) in the inactive phase, scaling as T∼N^{q} in the power-law phase, and T∼exp(αN) in the exponential phase.
  • Identified breakdown of continuum approximation within the power-law phase and analyzed changes in decline modes.

Conclusions:

  • The study provides a detailed understanding of population dynamics phases and extinction behaviors.
  • Findings are applicable to analyzing ecological time series and informing conservation management strategies.