Allee effects, invasion pinning, and species' borders

Area of Science:

• Ecology
• Mathematical Biology
• Biogeography

Background:

• Species geographic ranges are shaped by past invasions.
• Understanding invasion dynamics is key to explaining range formation.
• The Allee effect, a critical population density, influences invasion success.

Purpose of the Study:

• Investigate invasion models incorporating an Allee threshold.
• Analyze how Allee effects impact species invasion and range limits.
• Compare invasion dynamics in continuous versus patchy landscapes.

Main Methods:

• Utilized spatially continuous reaction-diffusion models.
• Employed spatially discrete coupled ordinary-differential-equation models.
• Derived conditions for invasion wave pinning in discrete models.

Main Results:

• The Allee effect can lead to invasion failure in both model types.
• Range limits due to propagation failure (pinning) are stable in patchy landscapes (discrete model).
• In continuous habitats, the zero velocity solution is unstable, suggesting limited persistence.

Conclusions:

• Allee effects can create stable range limits in patchy environments.
• Abrupt range limits may be caused by Allee effects, not solely competition or environmental barriers.
• The findings have implications for understanding spatially complex ecological dynamics and critical phenomena.