Phylogenetic trees of individual genes of prokaryotes (archaea and bacteria) generally have different topologies, largely owing to extensive horizontal gene transfer (HGT), suggesting that the Tree of Life (TOL) should be replaced by a "net of life" as the paradigm of prokaryote evolution. However, trees remain the natural representation of the histories of individual genes given the fundamentally bifurcating process of gene replication. Therefore, although no single tree can fully represent the evolution of prokaryote genomes, the complete picture of evolution will necessarily combine trees and nets. A quantitative measure of the signals of tree and net evolution is derived from an analysis of all quartets of species in all trees of the "Forest of Life" (FOL), which consists of approximately 7,000 phylogenetic trees for prokaryote genes including approximately 100 nearly universal trees (NUTs). Although diverse routes of net-like evolution collectively dominate the FOL, the pattern of tree-like evolution that reflects the consistent topologies of the NUTs is the most prominent coherent trend. We show that the contributions of tree-like and net-like evolutionary processes substantially differ across bacterial and archaeal lineages and between functional classes of genes. Evolutionary simulations indicate that the central tree-like signal cannot be realistically explained by a self-reinforcing pattern of biased HGT.