Distributing Defenses: How Resource Defendability Shapes the Optimal Response to Risk

Area of Science:

• Ecology
• Evolutionary Biology
• Mathematical Biology

Background:

• Organisms often possess limited defensive resources that must be allocated among multiple assets.
• These assets can vary in value, cost of defense, and risk of attack, necessitating strategic allocation.
• Previous theories focused on resource defense, but defendability's role in defense allocation is less explored.

Purpose of the Study:

• To develop a general mathematical model for optimal defense allocation among heterogeneous assets.
• To investigate the influence of asset value, defendability, and risk of attack on defense strategies.
• To extend plant defense theory by incorporating the concept of defendability.

Main Methods:

• Development of a general mathematical model to predict optimal defense allocation.
• Analysis of how defendability, defined as the relationship between defensive investment and successful defense, impacts allocation.
• Consideration of two scenarios: 1) hard-to-defend assets cost more to defend, and 2) hard-to-defend assets have a lower chance of successful defense.

Main Results:

• When hard-to-defend assets are more costly to defend, more defenses are allocated to them, irrespective of risk.
• If hard-to-defend assets are less likely to be successfully defended, elevated risk leads to reduced defense allocation to these assets.
• This suggests that defendability, particularly the probability of successful defense, can significantly alter risk-sensitive defense strategies.

Conclusions:

• Defendability, defined by the functional relationship between investment and success, is crucial for understanding defense allocation.
• The optimal strategy for dividing defenses is sensitive to both the cost and the success rate of defending assets.
• This research offers a new perspective on how risk influences defensive strategies in systems with varying asset defendability, as seen in plants and ants.