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Compartment model of strategy-dependent time delays in replicator dynamics

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Fic,  Malgorzata
IMPRS for Evolutionary Biology, Max Planck Institute for Evolutionary Biology, Max Planck Society;
External Organizations;
Research Group Theoretical Models of Eco-Evolutionary Dynamics (Gokhale), Department Theoretical Biology (Traulsen), Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Gokhale,  Chaitanya S.       
Department Theoretical Biology (Traulsen), Max Planck Institute for Evolutionary Biology, Max Planck Society;
External Organizations;
Research Group Theoretical Models of Eco-Evolutionary Dynamics (Gokhale), Department Theoretical Biology (Traulsen), Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Fic, M., Bastian, F., Miękisz, J., & Gokhale, C. S. (submitted). Compartment model of strategy-dependent time delays in replicator dynamics.


Cite as: https://hdl.handle.net/21.11116/0000-000F-DD23-1
Abstract
Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems and leads to models that are challenging to analyse and computationally expensive to solve. In this work, we propose an intermediate solution to resolve the issue in the framework of evolutionary game theory. Our compartment-based model includes time delays while remaining relatively simple and straightforward to analyse. We show that this model yields qualitatively comparable results with models incorporating explicit delays. Particularly, we focus on the case of delays between parents' interaction and an offspring joining the population, with the magnitude of the delay depending on the parents' strategy. We analyse Stag-Hunt, Snowdrift, and the Prisoner's Dilemma game and show that strategy-dependent delays are detrimental to affected strategies. Additionally, we present how including delays may change the effective games played in the population, subsequently emphasising the importance of considering the studied systems' temporal aspects to model them accurately.