The last of Liouville’s theorems treated in this monograph arises in accordance with classical mechanics. It is an integrability of the Hamilton system under the transformation of sympletic variables. The geometric structure hidden behind it is a suggestion to understand the principle of relaxation of singularities, caused by the skew-symmetric interaction of species and also the symmetry achieved by the action–reaction law in the duality between particle density and field distributions. The first section is a summary. In the second section we observe this fact of singularity cancellation in classical mechanics to reach the notion of a Poisson manifold. In the third section we confirm that the relaxation of the singularity, in the models of multi-species in mathematical biology, emerges from this Poisson structure, particularly in dissipative Lotka–Volterra systems. Motivated by this observation, we treat the reaction–diffusion systems with super-critical growth rate in the fourth section. The fifth section is devoted to the quantized blowup mechanism realized in the 2D Smoluchowski–Poisson equation at three levels of time scale; stationary, in finite time, and in infinite time. This model is a simplified system of chemotaxis, but is concerned, rather more, with the motion of the mean field of many point vorticities in relaxation time, that is, from quasi-equilibrium to equilibrium. This physical background is the origin of recursive hierarchy observed in this model, realized as a collapse and sub-collapse dynamics controlled by a Hamiltonian. There Liouville’s theory of transformation acts as a basic tool. In the final section we turn to a problem in mathematical oncology, the chemotactic paradox. We thus conclude this chapter with a fusion of Liouville’s theory in several areas, that is, the method of Lagrange coordinates and classification of entire solutions, which results in quantized blowup mechanism, duality between field and particle, recursive hierarchy, nonlinear spectral mechanics, space homogenization of isolated systems, emergence from reaction network, and cancellation of singularities in multi-component systems.