Citation
Optimal foraging, the marginal value theorem
TL;DR
Organisms should leave patches when marginal return equals environmental average return
Charnov's marginal value theorem is the foundational mathematical framework for the entire chapter. It formalizes when organisms should leave a resource patch: when marginal gain equals average gain across the environment. This principle directly translates to business decisions about when to exit customers, markets, or products.
The theorem's counter-intuitive insight - leave while food remains - challenges the common business instinct to maximize extraction from current opportunities. Charnov's work provides the mathematical proof that optimizing across environment beats optimizing within patches.
Key Findings from Charnov (1976)
- Organisms should leave patches when marginal return equals environmental average return
- Optimal departure occurs before resources are exhausted
- Travel time between patches affects optimal residence time
- The theorem can be graphically solved using tangent lines to gain curves