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"Nested hierarchy" refers to the way taxonomic groups fit neatly and completely inside other taxonomic groups. For instance, all bats (order Chiroptera) are mammals. All mammals are vertebrates. Likewise, all whales (order Cetacea) are also mammals, and thus also vertebrates.
While it might seem that this arrangement is obvious and unavoidable, it is not. Taxonomic groups are defined by traits and it should be possible to mix traits from multiple defined groups. An example from classical mythology is the Pegasus, a creature with features defined as both mammal (produces milk like a horse) and bird (has feathers). Mammals and birds are both orders, so, if Pegasus existed, it would be a violation of the nested hierarchy, a creature that belonged to two separate groups. Likewise for satyrs (human torso, goats legs), jackalopes (rabbit body with an antelope head) and crocoducks (crocodile head, body of a duck).
It is not always possible to define a nested hierarchy for any arbitrarily selected set of items, though many creationists have used this as an out<ref>Camp, Ashby (2001) A Critique of Douglas Theobaldâ€™s "29 Evidences for Macroevolution", Part 1: â€œOne True Phylogenetic Treeâ€ </ref>. For instance, motor vehicles do not show conservation of traits to single taxonomic groups, no matter how you choose to define your taxonomy. Whether a car has air-conditioning is completely independent of whether it has power-steering, for example. Life, however, shows a clear nested hierarchy, at least with regards to multicellular organisms. An animal that produces milk (Mammals), will also have hair, have four limbs, be endothermic (warmblooded) plus possess many other characteristics. Why should this be? Why do no other animals or plants produce milk? Why do no mammals have four limbs plus a pair of wings, like the Pegasus or angels? This fits easily with the idea of common descent, but is not what would be expected from special creation (although it isn't completely at odds with creation either, as the creator(s) could create life in any configuration imaginable).
Evolution and the Nested Hierarchy
The most obvious and simplest explanation for the observed nested hierarchy of taxonomic categories is evolution. In fact, a nested hierarchy is the almost inevitable result of descent with modification, if no transfer of traits between branches of descent is possible. (See also Gene Transfer.)
Twin Nested Hierarchies
The two possible hierarchies, one formed by comparing morphology (the physical appearance of the organisms) and the other formed by comparing molecular data (genotype of the organisms), would be expected to be congruent if all life had originated via evolution from a common ancestor. While there are certainly discrepancies between the two nested hierarchies, the two trees certainly show an amazing degree of similarity.
Of course, based upon the fact that the genes of an organism determines the morphology of the organism, one may expect the two trees would share a certain degree of resemblance. However, the biochemical analyses can also look at things that have very little or no influence on morphology, such as non-functional DNA or the sequence of metabolic enzymes, and end up with the same results. Also, there is no reason to assume that similar morphology demands similar genetics, as convergent evolution of marsupials and eutherian mammals will attest. Creatures such as the marsupial mouse and the eutherian mouse look very similar, but they differ a great deal in their genetics and biochemistry. This is because there are many ways for DNA to encode for the same proteins or the same regulatory elements, thus resulting the same morphology with different genetics. Therefore while common design would not predict such a congruence between trees, common descent would. Thus, common descent is greatly corroborated by such congruence.