Plasticity Decay and Attenuated Recovery (PDAR): A Hybrid Dynamical Model for the Historical Accessibility of Evolutionary Space

hidetomo maruta 

The evolutionary history of life is marked by a pronounced temporal asymmetry: an early, disproportionate generation of major morphological novelty, followed by extensive taxonomic diversification that does not appear to be accompanied by comparable expansion of morphological disparity. This paper develops a minimal hybrid dynamical model, termed Plasticity Decay and Attenuated Recovery (PDAR), that treats this asymmetry not as a static limit on evolution but as a consequence of a dynamic feedback between adaptation and the accessibility of future evolutionary states. Three state variables are introduced: accessible evolutionary potential P(t), selective/optimization state S(t), and accumulated structural and developmental constraint C(t). Continuous adaptive optimization is coupled to a monotonically accumulating constraint that lowers a state-dependent capacity bound K(C), while catastrophic events (e.g. mass extinctions) are represented as discrete impulses that release selection pressure without instantaneously erasing accumulated constraint. We derive conditions for forward invariance of the admissible state space, prove that unbounded constraint accumulation forces evolutionary potential toward zero in the limit, and show numerically that repeated catastrophic release combined with persistent constraint generates a characteristic attenuated sawtooth trajectory. The model yields falsifiable, quantitative predictions distinguishing it from established mechanisms such as ecological saturation, niche limitation, and extinction selectivity. A preliminary empirical assessment using three independent, publicly archived paleontological datasets finds heterogeneous post-extinction disparity responses rather than a uniform pattern, consistent with the model's rejection of a universal "extinction ⇒ expansion" rule, while the distinctive historically-conditioned attenuation mechanism itself remains to be directly tested.