In the post below we discussed what evolution really means. Evolution through either natural or artificial selection is an algorithm that is based on a tautological observation: the more likely an element is to survive and reproduce the more likely it is to pass on its heritable properties to its offspring. This is simply a logical truth — or at least a logical truth in any world in which there is reproduction and heritable mutation.
Not only is it a logical truth, it is a logical truth that is not derivable from the fundamental principles of physics. Hence it is another example of a truth of a "special science" that is not reducible to physics. (See my paper "Emergence Explained: Abstractions" for why this is important. I wish I had thought of this example when writing that paper!)
This is a nice example of a non-reductive truth because the truth of evolution-through-natural-selection is a consequence of the "axioms" that define a model (i.e., the level of abstraction) in which there is reproduction and heritable mutation. Once such a world is brought into existence (or in the terminology of "Emergence Explained," once such a level of abstraction is implemented) certain consequences follow, one of the most important of which is evolution through natural selection. In other words, evolution through natural selection is a property of (a truth about) the level of abstraction itself and not of any particular implementation of the level of abstraction. In that sense evolution through natural selection cannot be expressed in a traditional peel-the-onion reductionist manner.
Evolution through natural selection is also not reductive in a more traditional sense. A reductive explanation of a property typically decomposes the entity that exhibits that property into its components and then shows how the interactions of the components produce the property. The standard examples are chemical in which one shows how a chemical compound is created by combining, according to valence theory, the components that make up the compound.
In the case of evolution through natural selection, there is no isolatable entity (other than the biosphere itself, i.e., the entire level of abstraction) that exhibits evolution. Furthermore, the explanation of the evolutionary process is necessarily open rather than closed since it depends crucially on the environment to act as a selection mechanism. Thus, again, the peel-the-onion reductionist style approach to explanation doesn't work for evolution.
Evolution through natural selection is a phenomenon that exists in any level of abstraction that supports reproduction and heritable mutations. The mechanisms of reproduction and inheritance (DNA in the case of biology on this planet) are not relevant to the process as such. So again, there is no reductionist explanation. Evolution as a property of a level of abstraction is independent of the principles of the physics that implements the level of abstraction.