An energetic nonlinearity connects molecular mechanics to evolutionary robustness and adaptation

Biological actuators – from myosin motors to muscles – follow Hill’s model where a dimensionless parameter α captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic α^*=3.85 ± 2.32 across natural muscles and showed that α^* optimizes a power-efficiency tradeoff, potentially explaining its prevalence in nature. However, those results reflected short-term actuation tasks whereas phenotypic distributions in α emerge over evolutionary timescales. Here, we use numerical simulations of self-propelled agents to explore how nonlinear actomyosin actuation (parameterized by α) shapes population dynamics. Agents of different α compete for resources and reproduce with slight mutations. The relative resource availability S drives populations in α toward distinct behaviors: under abundance or scarcity, specialized α survive. However, with competition, populations evolve toward distributions centered around the characteristic α^* observed in nature. Further, we show that the evolution rate δ governs a balance between adaptability and robustness: large δ generates instability and extinction, small δ prevents adaptation, while intermediate δ enables long-term adaptation while remaining robust to short-term noise. Our results suggest that nonlinear actomyosin actuation provides a general understanding of energy management in actomyosin systems across timescales, from task-specific to evolutionary timescales.