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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Published on: February 3, 2023

Persistence of structured populations in random environments.

Michel Benaïm¹, Sebastian J Schreiber

¹Institut de Mathématiques, Université de Neuchâtel, Switzerland.

Theoretical Population Biology

|April 11, 2009

Summary

Population persistence in fluctuating environments depends on the stochastic growth rate. A negative rate leads to extinction, while a positive rate ensures a stable population distribution, crucial for ecological dynamics.

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Area of Science:

Ecology
Mathematical Biology
Population Dynamics

Background:

Environmental fluctuations impact populations differently based on individual traits (size, age, location).
Understanding population dynamics requires integrating population structure, environmental variability, and density-dependent interactions.

Purpose of the Study:

To develop a general theory for population persistence in density-dependent matrix models within random environments.
To establish criteria for population persistence based on stochastic growth rates.

Main Methods:

Developed a general theory for persistence in density-dependent matrix models under environmental randomness.
Analyzed population dynamics for both compensating and overcompensating density dependence.
Presented methods for estimating stochastic growth rates.

Main Results:

For populations with compensating density dependence, persistence is dictated by the stochastic growth rate when the population is rare.
A negative stochastic growth rate predicts extinction (probability one); a positive rate predicts a unique positive stationary distribution.
Population abundance converges to this stationary distribution, with empirical measures aligning with it.

Conclusions:

The stochastic growth rate is a critical determinant of population persistence in random environments.
The theory provides a framework for analyzing persistence in various population structures (unstructured, spatially, stage-structured).
Spatially structured populations (e.g., coupled sink populations) can persist if local fitness varies temporally and is not strongly spatially correlated.