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Allee effects and population spread in patchy landscapes.

Gabriel Andreguetto Maciel¹, Frithjof Lutscher

¹a Instituto de Física Teórica, Universidade Estadual Paulista , São Paulo , SP 01140-070 , Brazil.

Journal of Biological Dynamics

|April 21, 2015

Summary

Alien species invasion dynamics were studied in heterogeneous environments with an Allee effect. Approximate spread speeds were derived and validated, showing landscape properties influence invasion rates.

Keywords:

35K57 92D25 Allee effects habitat heterogeneity homogenization individual movement behaviour invasions

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Area of Science:

Ecology
Mathematical Biology
Invasion Biology

Background:

Invasive alien species pose significant threats to biodiversity and ecosystem stability, causing substantial economic and environmental damage.
Understanding the spatial dynamics of invasions is crucial for predicting their spread and developing effective management strategies.
The Allee effect, a phenomenon where population growth rate decreases at low densities, can significantly impact invasion dynamics.

Purpose of the Study:

To investigate the spatial spread of invasive species in a heterogeneous environment incorporating a strong Allee effect.
To develop and validate mathematical models predicting invasion speed in complex landscapes.
To analyze the influence of landscape heterogeneity and demographic parameters on invasion dynamics.

Main Methods:

Utilized a reaction-diffusion model to simulate invasion dynamics.
Modeled the environment as periodically alternating favorable and unfavorable patches.
Employed homogenization techniques and established results for Allee effects in homogeneous landscapes to derive approximate spread speeds.
Validated derived expressions using numerical simulations.

Main Results:

Derived accurate approximate expressions for the spatial spread speed of invasive species.
Demonstrated that the derived expressions remain accurate even with significant landscape heterogeneity.
Quantified the dependence of spread rates on demographic parameters, movement behaviors, and landscape characteristics.

Conclusions:

The study provides accurate predictions for invasive species spread in heterogeneous environments with Allee effects.
Homogenization techniques are effective for modeling invasion dynamics beyond small-scale heterogeneity.
Landscape properties and species' demographic traits are critical determinants of invasion success and speed.