A nested hierarchy is any pattern of grouping where larger groups are divided into smaller groups, which are divided into smaller groups, etc. One group does not cut across another group. For example, the set of people who live in a particular county is a subset of those living in a particular state, and that is a subset of the people who live in a country (assuming geopolitical subdivisions are named like in many parts of the US). Everyone who lives in my county lives in North Carolina, and everyone who lives in North Carolina lives in the U.S. But the set of people who live near the ocean versus those who live far from the ocean cuts across those. People can be relatively near to or far from the ocean and be in the same state or country. That’s a non-nested hierarchy.
Biological classification follows a nested hierarchy. All known life fits into either Bacteria, Archaea, or Eukaryota. In turn, we can recognize kingdoms within each of those domains, and phyla (or divisions) within the kingdoms, and classes in the phyla, and so on down. The general pattern is obvious to anyone, and it was formally developed in Linnaeus’ classification in the mid-1700’s, well before any major evolutionary ideas became popular.
Evolution produces a generally nested hierarchy. If species A and B split from each other, and then A splits into C and D and B splits into E and F, this will make C and D more similar to each other, and E and F more similar to each other. Lateral gene transfer and incomplete lineage sorting do occur, but for eukaryotes those are generally relatively minor components of the genome. Human designers, on the other hand, tend to take pieces from various sources. Although you could trace the origin of a current Ford model through the company history, a modern Ford has a significant input from the computer industry, among other sources, and does not simply derive from a long line of tweaking a Model T.
Assessing evolutionary connections requires an overall consideration of features. Both convergent and parallel evolution should happen if evolution is occurring. Identifying whether a feature evolved convergently or in parallel, versus indicating actual close relationship, requires several considerations. (Incidentally, these are often not well-explained in general biology textbooks). What function does the feature have? If it is specifically useful, the feature is likely to be developed convergently, but key details will often be quite different. For example, tuna, squids, requiem sharks, ichthyosaurs, dolphins, and submarines all have similarly streamlined shapes -anything moving quickly through water needs that. But there are major differences in the structure and use of the fins and flippers - the streamlined shape is convergent. On the other hand, all except the submarine share a large set of biochemical and developmental similarities that are not necessary for their lifestyle. Those similarities are most simply explained by descent from a common ancestor. Bat, bird, pterosaur, and insect wings have similar external shape - they are all wings and have to be shaped appropriately for flight. But their internal structures are different. The insect wing, made from a chitinous exoskeleton, is totally different from the other three. All of the others have bones built of apatite, with a generally similar basic structure to them. This reflects their all being vertebrates, descended from an ancestor with bones. They also have similar sets of bones in the wings - we can recognize a humerus, radius, ulna, carpals, metacarpals, and phalanges. These reflect all three being descended from an ancestor with front limbs having a particular set of bones. But the bird, bat, and pterosaur use those bones very differently to build the wing, showing that the wing itself evolved separately in the three groups. Birds have long feathers sticking off the back of the arm, and the hand is quite reduced. Bat wings are mostly hand. Pterosaurs have one long finger supporting the front of the wing, with stiff rods providing support within the wing. They also incorporate the hind legs into the wing. Conversely, all birds have similar structure to their wings. We don’t find hawks with wings that are more like bats and robins with wings that are more like pterosaurs. All birds have similar wing types. This follows a nested hierarchy. A bat could keep warm with contour feathers or with fur - there is no functional requirement for bats to not have feathers, and a designer working like a human engineer might well make such a mix. But we do not see such mixing in nature.
