When we talk about naturalistic evolution, were talking about the claim that the diversity of life is the result of undirected, natural processes. In principle, one could come up with any number of possible naturalistic explanations for that diversity. How do you assess all those possible explanations?
We dont really have toat least not at this point in the FAQ. The question were concerned about here is not whether we can rule out every conceivable naturalistic theory, but whether scientists have shown that biological systems evolved naturalistically. That limits the field to proposals that are alleged to be well supported by evidence. Proposals that are merely possible, plausible or suggestive are irrelevant.
The main contender for a supposedly well supported theory, of course, is Darwins theory of evolution.
Darwins theory has been cogently summarized by the late Harvard paleontologist and science historian, Stephen Jay Gould. According to Gould, Darwins theory consisted of three basic facts and one inference. The facts are: First, that all organisms produce more offspring than can possibly survive; second, that all organisms within a species vary, one from the other; third, that at least some of this variation is inherited by offspring.
From these facts, said Gould, we easily infer the process of natural selection. Those organisms that inherit the more favorable variations will be better adapted to their local environment. This makes them better able to pass these variations to the next generation. Over successive generations, the proportion of those with favorable variations will growuntil they comprise virtually the whole population
Contemporary Darwinism (also called neo-Darwinism) adds to Darwins original theory the notion that the favorable variations arise from random genetic mutations.
In discussing the evidence for naturalistic evolution, this FAQ will focus mainly on neo-Darwinism, though other views will be discussed as appropriate.
 Stephen Jay Gould, Introduction, in Carl Zimmer, Evolution: The Triumph of an Idea (New York: HarperCollins Publishers, 2001), p. xii.