Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping.

Area of Science:

• Ecology
• Mathematical Biology
• Animal Behavior

Background:

• Animal movement is fundamentally influenced by cognitive processes like perception, learning, and memory.
• Distinguishing animal movement from physical particle motion necessitates incorporating these knowledge-based behaviors into models.
• Existing models often lack a comprehensive framework for integrating cognitive influences on movement.

Approach:

• This review synthesizes deterministic mathematical models, primarily nonlocal reaction-diffusion-advection equations, that incorporate cognitive influences.
• Mathematical guidelines are provided for assessing model rationality, aiding development, interpretation, and understanding model complexity.
• Available mathematical techniques and measures of success are presented to compare model predictions and outcomes.

Key Points:

• Cognition, including perception, learning, and memory, is essential for realistic animal movement modeling.
• Nonlocal reaction-diffusion-advection equations are a common framework for incorporating cognitive influences.
• Mathematical rules and comparison metrics are proposed to guide model development and interpretation.

Conclusions:

• Integrating cognitive processes into mathematical models offers a more accurate understanding of animal movement and space use.
• The review identifies numerous open mathematical and ecological challenges at the intersection of cognition, movement, and modeling.
• This work synthesizes current efforts and proposes future directions for advancing mechanistic animal movement modeling.