Extinction dynamics of age-structured populations in a fluctuating environment

Area of Science:

• Population dynamics
• Ecological modeling
• Conservation biology

Background:

• Understanding population persistence is crucial for conservation.
• Vital rates (mortality, reproduction) often fluctuate due to environmental changes.
• Previous models may not fully capture extinction dynamics under fluctuating vital rates.

Purpose of the Study:

• To develop a model for density-independent population growth with fluctuating vital rates.
• To derive analytical formulas for extinction time distribution and cumulative extinction probability.
• To assess the accuracy of a diffusion approximation for population extinction.

Main Methods:

• Modeling population growth with stationary time series for mortality and reproductive rates.
• Utilizing a diffusion approximation for the logarithm of total population size.
• Deriving analytical formulas for extinction time and probability.

Main Results:

• Extinction time and probability depend on initial age distribution and diffusion parameters (mean mu, variance sigma^2).
• These parameters can be estimated from life history data and environmental fluctuation patterns.
• Conditional extinction time distribution is influenced by the magnitude, but not the sign, of mu.
• Diffusion approximation provides accurate extinction probability estimates for small to moderate environmental fluctuations.

Conclusions:

• The developed analytical framework accurately predicts population extinction risk.
• The model highlights the importance of initial population structure and environmental variability in extinction dynamics.
• This approach offers a valuable tool for conservation planning and risk assessment.