Dynamic optimization over infinite-time horizon: web-building strategy in an orb-weaving spider as a case study

Area of Science:

• Evolutionary Ecology
• Behavioral Ecology
• Mathematical Biology

Background:

• Dynamic state-dependent models are crucial in evolutionary ecology but typically use finite-time horizons.
• Infinite-time horizon models are more biologically relevant for state-dependent endpoints but lack general methods for biologists.
• Existing methods in economics and operational research are not directly applicable to biological systems.

Purpose of the Study:

• To present a general method and algorithm for solving infinite-time horizon problems in evolutionary ecology.
• To determine optimal strategies for organisms to reach target states quickly while minimizing mortality risk.
• To model and analyze web-building behavior in orb-weaving spiders to illustrate the method.

Main Methods:

• Development and description of a novel algorithm for infinite-time horizon dynamic state-dependent models.
• Application of the algorithm to model orb-weaving spider web-building behavior.
• Analysis of optimal strategies under varying conditions such as spider body weight and predation risk.

Main Results:

• The study demonstrates how to process and select optimal strategies over an infinite-time horizon.
• Spider web-building strategy is shown to vary with body weight and predation risk.
• Two key predictions: spiders decrease web size with increasing weight, and this decrease initiates earlier under higher predation risk.

Conclusions:

• The developed method provides a powerful tool for addressing complex evolutionary ecology questions with infinite-time horizons.
• Optimal foraging and life-history strategies can be elucidated using this approach, considering long-term survival and reproduction.
• The findings offer insights into the adaptive behavioral plasticity of orb-weaving spiders in response to environmental pressures.