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Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon.

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  • 1Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany. omrit1248@gmail.com.

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Summary

Adaptive bet-hedging models can be improved by considering extinction risk and finite time horizons. The log-optimal strategy emerges as a robust equilibrium for maximizing growth and minimizing risk.

Keywords:
Adaptive bet-hedgingExtinction riskFinite time horizonGame theoryGrowth-optimal portfolio theoryKelly gambling

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Area of Science:

  • Evolutionary biology
  • Mathematical modeling
  • Game theory

Background:

  • Adaptive bet-hedging models often use Kelly's optimal gambling theory to maximize long-term lineage growth rates.
  • Standard models may not fully capture evolutionary complexities like extinction risk in finite populations.

Purpose of the Study:

  • To propose an improved adaptive bet-hedging framework incorporating volatility minimization and finite time horizons.
  • To explore game-theoretic approaches for evolutionary strategies under extinction risk.

Main Methods:

  • Developed a model integrating volatility minimization and finite time horizons into growth maximization.
  • Applied game-theoretic competitive optimality to derive equilibrium solutions.
  • Analyzed fitness payoff functions and extinction risks.

Main Results:

  • The log-optimal strategy is identified as a unique pure strategy symmetric equilibrium.
  • This equilibrium is invariant to the evolutionary time horizon.
  • The strategy is robust even with low extinction risks.

Conclusions:

  • Departures from standard bet-hedging models are necessary for greater evolutionary realism.
  • Incorporating extinction risk and finite time horizons leads to a more nuanced understanding of optimal strategies.
  • The log-optimal strategy provides a stable and effective approach for evolutionary success under uncertainty.