Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patch-level...

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• The Allee effect describes reduced per-capita growth at low population densities.
• Conspecific density-dependent emigration (DDE) is a key factor influencing population dynamics.
• Understanding DDE is crucial for predicting population persistence and spread.

Purpose of the Study:

• To model the influence of density-dependent emigration (DDE) on population dynamics under a weak Allee effect.
• To investigate how different forms of DDE affect the strength and consequences of Allee effects.
• To analyze the impact of DDE on population stability and spatial distribution within a habitat patch.

Main Methods:

• Mathematical modeling of a one-dimensional population patch with diffusion and a weak Allee effect growth rate.
• Incorporation of five distinct forms of density-dependent emigration (DDE).
• Analytical techniques including the method of subsuper solutions and time map analysis, complemented by numerical computations using Wolfram Mathematica.

Main Results:

• DDE with a positive slope was found to counteract Allee effects.
• DDE with a negative slope was found to enhance Allee effects.
• Complex population dynamics emerged, including multiple steady states with symmetric or asymmetric density profiles.

Conclusions:

• The form of density-dependent emigration significantly modulates Allee effect consequences.
• DDE can lead to complex population dynamics, including bistability and altered spatial distributions.
• Mathematical modeling provides valuable insights into the interplay between emigration, density dependence, and population viability.