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Pollen limitation or mate search need not induce an Allee effect
J A Stewart-Cox1, N F Britton, M Mogie
1Department of Mathematical Sciences, University of Bath, BA2 7AY, United Kingdom. J.A.Stewart-Cox@maths.bath.ac.uk
Bulletin of Mathematical Biology
|July 7, 2005
Summary
Localizing reproduction and colonization processes can prevent the Allee effect in population models. This finding is crucial for understanding species invasions and population dynamics, especially in small, clumping populations.
Area of Science:
- Ecology
- Population Dynamics
- Mathematical Biology
Background:
- Traditional non-spatial population models often predict a critical depensation or Allee effect due to assumed diffuse distributions of individuals in small populations.
- This leads to limited contact rates and reduced reproduction, which may not accurately reflect natural scenarios like invasions where clumping occurs.
Purpose of the Study:
- To develop a more realistic population model that incorporates spatial processes like clumping.
- To investigate whether localizing reproduction and colonization can mitigate or eliminate the Allee effect.
Main Methods:
- Development of pair approximations for a probabilistic cellular automata model.
- Modeling independent pollination and seed setting processes (or mate search and reproduction) as either global or local.
Main Results:
- Global processes in the model recapture the Allee effect seen in non-spatial models.
- When both pollination and colonization processes are at least partially local, Allee effects can be avoided.
- Small populations become more clumped with local colonization and less wasteful of pollen with local pollination, resolving the Allee effect.
Conclusions:
- Spatial structure, specifically local pollination and colonization, is key to avoiding Allee effects in population dynamics.
- This spatially explicit modeling approach offers a more nuanced understanding of population persistence and invasion success.