The rhizome concept proposed by Gilles Deleuze and Félix Guattari offers a novel perspective on the organization and interdependence of complex constellations of heterogeneous entities, their mapping and their ruptures. The emphasis of the present study is placed on the dynamics of contacts and communication among such entities that arise from experimentation, without any favored hierarchy or origin. When applied to biological evolution, the rhizome concept integrates all types of heterogeneity resulting from “symbiotic” relationships among living beings (or their genomic material), horizontal genetic transfer, recombination and mutation, and breaks away from the approach that gives rise to the phylogenetic tree of life. It has already been applied to describe the dynamics and evolution of RNA viruses. Thus, here we introduce a novel framework for the interpretation the viral quasispecies concept, which explains the evolution of RNA virus populations as the result of dynamic interconnections and multifaceted interdependence between highly heterogeneous viral sequences and its inherently heterogeneous host cells. The rhizome network perspective underlines even further the medical implications of the broad mutant spectra of viruses that are in constant flow, given the multiple pathways they have available for fitness loss and gain.