Virus pandemics have significantly impacted human welfare and development. Understanding the true molecular evolution of viruses is critical for preventing future pandemics and developing the next-generation drugs and vaccines. Unfortunately, viruses exhibiting constant genomic substitution rates (GSRs) despite increasing vaccinations and human infections (SARS-CoV-2) and viruses under seemingly extreme conservation (ZIKV) paints a confusing picture of viral evolution, and the main evolutionary theories (Selectionist Theory, Kimura’s Neutral Theory) cannot explain their molecular evolution. Here, we developed a first-principle model, c/u, to characterize reproductive fitness changes in viruses based on variations in the nucleotide/codon mutation rate (c) with respect to the global genomic mutation rate (u). c/u is nucleotide-centric, since phenotypic changes in proteins are reflected by genotypic changes in genes. c/u can assign selection types to coding regions (virus function) and non-coding untranslated regions (UTRs, virus gene regulation). Additionally, c/u can handle conserved sites (c/u=0) and sites with few mutations under false positive selection (c/u\u3c\u3c\u3e\u3e1). The constant GSRs of SARS-CoV-2 and ZIKV are seemingly under effective neutral selection (c/u=1), indicating no advantageous/disadvantageous fitness change. Yet, the L-shaped probability distribution of c/u for a NT site indicates high sequence conservation, with higher c/u values being increasingly uncommon. Varying nucleotide and segment substitution rates were observed in both viruses, indicating a mixture of advantageous selection (c/u\u3e1) and purifying selection (c/
