Stochastic models in seed dispersals: random walks and birth-death processes

Area of Science:

• Ecology
• Mathematical Biology
• Statistical Physics

Background:

• Advanced seed tracking generates complex data, challenging traditional empirical and deterministic ecological models.
• Stochastic models, particularly those with Markovian properties, offer a flexible framework for analyzing natural phenomena in ecology.
• Current applications of stochastic models in seed dispersal studies are limited, indicating a need for broader adoption.

Purpose of the Study:

• To review and illustrate the application of three key stochastic models in seed dispersal research.
• To demonstrate the formulation of individual-based models for competing plant species using a nonlinear birth-death process (BDP).
• To show how symmetric and intermittent random walks can be used to formulate cover time models and their connection to the Gillespie algorithm.

Main Methods:

• Description of three stochastic models: birth-death process (BDP), 2D symmetric random walks, and intermittent random walks.
• Formulation of individual-based models for plant competition using nonlinear BDP.
• Application of random walks to develop cover time models and explore their approximation to Gumbel distribution.
• Demonstration of the formulation of these models using the Gillespie algorithm.

Main Results:

• The three reviewed stochastic models (BDP, symmetric random walks, intermittent walks) possess Markovian properties, enhancing their applicability.
• Individual-based models for two competing plant species were formulated using a nonlinear BDP.
• Cover time models were formulated using symmetric and intermittent random walks.
• The full cover time from symmetric random walks approximates the Gumbel distribution, similar to other search strategies.

Conclusions:

• Stochastic models provide a powerful and flexible approach to analyzing complex seed dispersal data, overcoming limitations of conventional methods.
• The application of BDP, random walks, and the Gillespie algorithm offers new avenues for modeling ecological processes like plant competition and seed removal.
• Further exploration of these stochastic models in seed dispersal can significantly advance our understanding of complex ecological systems and foraging behaviors.