Moving-habitat models: A numerical approach.

Area of Science:

• Ecology
• Mathematical Biology
• Climate Change Science

Background:

• Global climate change necessitates species adaptation through movement to maintain thermal niches.
• Empirical data indicates that the speed of shifting temperature isoclines varies geographically and with elevation, potentially accelerating over time.

Purpose of the Study:

• To develop a mathematical framework for analyzing population dynamics in transient, moving habitats.
• To differentiate between populations at high and low risk of extinction under climate-induced habitat shifts.

Main Methods:

• Utilized a system of reaction-diffusion equations to model species persistence and distribution under varying habitat shifting speeds.
• Incorporated habitat-dependent movement and individual preferences, leading to density jumps across habitat types.
• Developed and validated a numerical finite difference scheme using a modified coordinate system to handle moving habitats and density discontinuities.

Main Results:

• Investigated diverse shifting-speed scenarios to understand population persistence mechanisms.
• Found that a strong preference for suitable habitat enhances population persistence at higher shifting speeds.
• Observed that this strong preference leads to smaller total population sizes at slower shifting speeds.

Conclusions:

• The developed mathematical tool provides insights into population resilience in dynamic environments.
• Habitat preference is a critical factor influencing species' ability to cope with climate-driven habitat shifts.
• Understanding these dynamics is crucial for predicting extinction risks in a changing world.