Final answer:
The theory of evolution by natural selection was the key discovery that transformed our understanding of phylogeny, which was further advanced through DNA sequencing and cladistics.
Step-by-step explanation:
The discovery that profoundly changed the way we look at phylogeny for all species was the theory of evolution by natural selection. This theory, developed by Charles Darwin, provided a systematic explanation for the diversity and relatedness of life forms on Earth, including insights into fossils and biological adaptation. Subsequently, advancements like DNA sequencing and the development of cladistics further refined our understanding of phylogenetic relationships. DNA sequencing allows the comparison of genes across extant and extinct species to reveal evolutionary relationships, while cladistics uses morphologic and molecular data to construct phylogenetic trees and trace the evolutionary pathways of life.