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Climate Change and Integrodifference Equations in a Stochastic Environment.
Juliette Bouhours1, Mark A Lewis2,3
1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G2G1, Canada. bouhours@ualberta.ca.
Bulletin of Mathematical Biology
|September 21, 2016
Summary
Climate change forces species migration. This study shows that variability in habitat shifts and population growth rates negatively impacts species persistence, decreasing survival thresholds and increasing extinction risk.
Area of Science:
- Ecology
- Climate Change Biology
- Mathematical Biology
Background:
- Climate change causes habitat shifts, necessitating species migration for survival.
- Previous models assumed deterministic rates for habitat shifts and population growth.
- Variability and uncertainty in these rates are critical but often overlooked factors.
Purpose of the Study:
- To analyze population persistence under uncertain and variable climate-driven habitat shifts.
- To develop a threshold criterion for population persistence considering stochastic environmental changes.
- To quantify the impact of variability in habitat shift rates and population growth on species survival.
Main Methods:
- Utilized a stochastic integrodifference equation model for shifting habitats.
- Derived a metric for asymptotic growth rate from the linearized operator.
- Connected the persistence metric to eigenvalue problems for integral operators.
Main Results:
- Variability in yearly shifts and growth rates significantly reduces the threshold for population persistence.
- Identified a critical habitat shifting speed above which populations face extinction.
- Numerical simulations with butterfly populations confirmed decreased persistence with increased variance.
Conclusions:
- Environmental change rate variability poses a significant threat to species persistence.
- Clear bounds for environmental change rates are established for species survival.
- Understanding stochasticity is crucial for predicting species' responses to climate change.
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