Searching on patch networks using correlated random walks: space usage and optimal foraging predictions using Markov...

Area of Science:

• Ecology
• Theoretical Biology
• Mathematical Biology

Background:

• Animal movement patterns are crucial for understanding foraging success and space utilization.
• Traditional methods like Monte Carlo simulations can be computationally intensive for analyzing complex movement strategies.
• Integrating random walk theory with foraging theory offers a powerful framework for ecological studies.

Purpose of the Study:

• To develop a novel representation of discrete correlated random walks using Markov chains.
• To explore the relationship between animal movement strategies, space utilization, and foraging success.
• To determine optimal movement strategies and home range sizes for central place foragers.

Main Methods:

• Representing a discrete correlated random walk as a Markov chain with displacements as states.
• Utilizing the theory of absorbing Markov chains for predictive analysis.
• Applying the method to a central place forager on a discretized hexagonal lattice.

Main Results:

• The Markov chain representation allows for direct predictions without simulations.
• Identified an optimal movement strategy involving mnemokinesis (a sinuosity regulating mechanism).
• The optimal strategy dictates the size of the optimal home range for the forager.

Conclusions:

• The novel Markov chain approach provides an efficient tool for analyzing animal movement and foraging.
• This framework can be applied to various movement spaces, including natural networks.
• The study successfully integrates random walk theory into foraging theory, offering new insights into animal behavior.