The impact of time-weighted historical payoffs on evolution dynamics of strategies

Evolutionary game theory often oversimplifies fitness by equating it with immediate payoffs. This approach neglects biological realities, such as historical payoffs, resource storage, and metabolic transformation. This study addresses this gap by proposing a novel time-weighted fitness framework. This framework integrates these processes through a three-level structure: resource acquisition, cumulative fitness, and instantaneous fitness. This framework incorporates a maximum storable resource amount and three time-weighted modes (equal, decreasing, increasing) to simulate diverse life-history strategies. Analytical and numerical results reveal that time-weighted resource metabolism generates evolutionary dynamics inaccessible to the classical model. Decreasing time-weighting prioritizes early resource gains. This mode can induce persistent oscillations in strategy frequencies and strong path dependence, which aligns with capital breeding strategies. Increasing time-weighting, which amplifies recent resource gains, intensifies selection pressure over time, corresponding to terminal sprint strategies like pre-dormancy hyperphagia. When resources saturate, all dynamics revert to classical forms, signaling a strategic shift from capital accumulation to income competition. This work unifies historical contingency with instantaneous selection. It offers a mechanistic theory for interpreting diverse ecological patterns, from population cycles to life-history transitions.