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Fluctuations and correlations in lattice models for predator-prey interaction.
Mauro Mobilia1, Ivan T Georgiev, Uwe C Täuber
1Arnold Sommerfeld Center for Theoretical Physics and CeNS, Department of Physics, Ludwig-Maximilians-Universität München, D-80333 Munich, Germany. mauro.mobilia@physik.lmu.de
Summary
Spatial structure and noise disrupt predator-prey cycles, leading to a predator extinction threshold. This critical behavior aligns with directed percolation universality, challenging classical models.
Area of Science:
- Theoretical Ecology
- Statistical Physics
- Mathematical Biology
Background:
- Classical Lotka-Volterra models predict stable predator-prey cycles.
- Spatial structure and stochastic noise are often neglected in basic ecological models.
- Prey growth limitation can fundamentally alter population dynamics.
Purpose of the Study:
- To investigate the impact of spatial structure and stochastic noise on predator-prey dynamics.
- To determine the universality class of the predator extinction threshold.
- To explore the robustness of these dynamics with extended interaction ranges.
Main Methods:
- Development and analysis of a stochastic lattice predator-prey model.
- Inclusion of next-nearest-neighbor interactions in the predation process.
- Comparison of model results with mean-field theory predictions across different dimensions.
Main Results:
- Spatial structure and noise invalidate stable cycles, creating a predator extinction threshold.
- The extinction threshold belongs to the directed percolation universality class for 1 < d <= 4.
- Mean-field predictions are recovered only with rapid nearest-neighbor particle exchange.
Conclusions:
- The classical Lotka-Volterra picture is insufficient when spatial and stochastic effects are considered.
- Directed percolation universality governs predator extinction in this spatially extended predator-prey system.
- The model highlights the importance of interaction range and exchange rates in ecological dynamics.