A mathematical framework for optimal foraging of herbivores

Area of Science:

• Ecology
• Behavioral Ecology
• Mathematical Biology

Background:

• Optimal foraging theory typically assumes patchy food distribution for herbivores.
• This study relaxes the patchy distribution assumption for more realistic models.
• Herbivore foraging models often overlook arbitrary food distribution scenarios.

Purpose of the Study:

• To develop and analyze a novel optimal foraging model for herbivores (especially ungulates) with arbitrary food distribution.
• To investigate the role of food density thresholds in herbivore foraging decisions.
• To provide a biologically interpretable framework for understanding foraging behavior under varied food availability.

Main Methods:

• Developed a mathematical model where total foraging time is a variational expression.
• Incorporated constraints on total food intake and foraging path length.
• Analyzed the model to identify a critical threshold (lambda) for food acquisition.

Main Results:

• Proved the existence of a food acquisition threshold (lambda).
• Demonstrated that herbivores eat until food density reaches lambda or cease foraging if density is below lambda.
• Identified key relationships between model parameters and foraging behavior.

Conclusions:

• The established food acquisition threshold (lambda) offers a new perspective on herbivore foraging strategies.
• The model provides a more realistic representation of foraging behavior with arbitrary food distribution.
• Results have significant implications for understanding ungulate feeding ecology and resource management.