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In complex adaptive systems (CASs), the relaxation based on intra-individual interactions and the adaptation based on sub-individual variations are two fundamental processes entangled to induce great complexity. We analyze the system evolution under multicellular homeostatic regulations coupled with various mutation strategies in computational tumorigenesis as a typical instance to clarify the coupling effect of relaxation and adaptation in CASs. Through visualizing the system dynamics on a synthesized fitness landscape which results from the superposition of the phase diagram and the individual fitness landscape, we entertain a simple theoretical framework that not only helps analyze our simulated multicellular dynamics but is potentially applicable to a broader class of problems in CASs where relaxation and adaptation intertwine. It is stressed that the nonadaptive relaxation process has the essential role in shaping the selective pressure of adaptation as well as in defining the final state of the evolution, whereas it is the rigidity of mutation strategy that determines the complexity of the dynamical process.

WHEN RELAXATION MEETS ADAPTATION IN COMPLEX ADAPTIVE SYSTEMS: A COMPUTATIONAL STUDY OF TUMORIGENESIS