Trait X is fitter than trait Y in a population of organisms if those organisms have other biological traits T and live in an environment that has properties E. The theory of natural selection is filled with statements of this form.

Evolutionary biologists often appeal to parsimony when they seek to explain why organisms "match" with respect to a given trait. For example, why do almost all the organisms that are alive today on our planet use the same genetic code? If they share a common ancestor, the code could have evolved just once and then been inherited from the most recent common ancestor that present organisms share. On the other hand, if organisms in different species share no common ancestors, the code must have evolved repeatedly.

Darwin repeatedly used the hypothesis of common ancestry as a platform on which to build his various ideas about testing hypotheses concerning natural selection. He also argued that adaptive similarities provide little or no evidence for common ancestry. Although this second claim needs to be fine-tuned, Darwin was right that ample evidence for common ancestry can exist even if none of the characteristics we observe were caused to evolve by natural selection.

Evolutionary game theory was originally developed as an alternative to the hypothesis of group selection; now it is clear that game theory models postulate group selection, even if they do not use the g-word.

The rabid opposition to group selection has now considerably subsided. In the process, the conceptual structure of evolutionary theory has become clearer, as have the relationships that connect different theoretical approaches.

The more evolutionary theory gets called an atheistic theory, the greater the risk that it will lose its place in public school biology courses in the United States. If the theory is thought of in this way, one should not be surprised if a judge at some point decides that teaching evolutionary theory violates the Constitutional principle of neutrality with respect to religion.

The upshot is that most philosophers of biology now hold that biological properties supervene on physical properties (where supervenience is taken to include some kind of "in virtue of" relation), and that fitness and other biological properties are not identical with physical properties.