First-passage processes and the target-based accumulation of resources

Area of Science:

• Mathematical Biology
• Statistical Physics
• Theoretical Ecology

Background:

• Random search is prevalent in nature, from animal foraging to intracellular transport.
• Existing research often uses a searcher-centric view, focusing on first passage time (FTP).
• This study shifts to a target-centric perspective on resource accumulation.

Purpose of the Study:

• To analyze resource accumulation at targets considering multiple search-capture events and resource degradation.
• To apply queuing theory to derive expressions for resource distribution statistics.
• To investigate the Fano factor's dependence on degradation, delays, and geometry in various domains.

Main Methods:

• Utilized queuing theory to model resource accumulation and degradation.
• Applied the theory to diffusion in geometries like concentric spheres, wedges, and branching networks.
• Analyzed the Fano factor, a measure of statistical dispersion, in relation to model parameters.

Main Results:

• Derived general expressions for steady-state mean and variance of resource distributions.
• Demonstrated that the Fano factor can significantly deviate from Poisson statistics.
• Identified nonmonotonicity and crossover behavior in the Fano factor's dependence on parameters.

Conclusions:

• Resource accumulation statistics exhibit complex behavior beyond simple Poisson distributions.
• The Fano factor provides insights into higher-order statistics of resource accumulation.
• Model parameters, including degradation rates and geometric features, critically influence resource accumulation patterns.