The methods of mechanisms of evolutionary change are supported by evidence because evidence such as embryos, biochemical similarities, fossils, and comparitive anatomy show that there could be a close evolutionary relationship between organisms. For instance, organisms that are closely evolutionary may have homologous structures, such as a bird wing and a human hand. Or scientists at study embryos of different organisms and the similarities may tell you if they evoled from a common ancestor. The same thing goes for fossils. Fossils will show differences in shape and size and evidence of natural selection. Furthermore, the more similar the biochemical similarities, DNA and protein sequences, are the more closely related organisms could be. This is how the mechanisms of evolutionary change are supported by evidence. Hope this helps!