This version of the NDT definition is the result of discussions with my colleague Professor James F. Crow. He considers that this version is a fair representation of evolutionists' current thought.
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The Neo-Darwinian Theory: Version 2004

Part 1
All living organisms on Earth today are descended from inanimate matter.

Part 2
The processes of descent in Part 1 involved very large, but unknown, numbers of steps, mostly small.

Part 3
We do not yet know what steps led to the formation of the first self-replicating entity, but, from then on, the sole sources of novelty in Part 2 have been random, spontaneous, heritable, changes in genomes and other hereditary materials.

Part 4
Histories of descent, following these changes, involved, or depended on, one or more of the following factors:
The "Natural Selection List":
natural selection
genetic driftEvolution
recombination
population structure
population migration
sexual selection
transposable elements
horizontal transmission
neutral changes
selfish DNA
polyploidy
developmental constraints
cell organelles
and any others (excluding design) that future research might reveal.


Notes

Definition:  Mutation = heritable change in a genome or other hereditary material

Synonyms:  The Neo-Darwinian Theory of Evolution
                     The Synthetic Theory of Evolution
                     The Evolutionary Synthesis
END

The above formulation is incomplete until the term natural selection has been defined. I can find no agreed definition in the literature (see What is Natural Selection?). Books (e.g., Endler, Sober) have been written to answer this question!

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I have had some difficulty in finding out what people mean by the NDT. Norman Macbeth stated that "About 1930, they put together something that was generally known as the Synthetic Theory, and that has been the dominant idea ever since, for fifty years. It is rather strange to say this, but the Synthetic Theory has never been formulated. It was a vague consensus that was never formulated in any detail."  (Darwinism: A Time for Funerals, Broadside Edition, Robert Briggs Associates, San Francisco, 1982, p.3)

In the Preface (p.xiii, last paragraph) to The Evolutionary Synthesis (E. Mayr & W. B. Provine, Harvard University Press, 2nd Edition, 1998), Ernst Mayr wrote that "the synthesis is nothing but a confirmation of Darwin's original theory". I could find no definition of the NDT in this book. When I asked Will Provine (in 2001) for a definition, he replied that it was not easy to give a simple definition.

Elsewhere, Mayr also wrote: "Darwinism is not a simple theory that is either true or false but is rather a highly complex research program that is continuously being modified and improved". E. Mayr (1988) Toward a New Philosophy of Biology (Belknap Press of Harvard University Press, Cambridge, Massachusetts), p. 535.

Francisco Ayala writes: "The modern theory of evolution....is an amalgam of well-established theories and working hypotheses..." (Proc. Nat. Acad. Sci. vol. 102, suppl. 1, May 3, 2005, p.6515). I sent an email asking how many theories and hypotheses are in his amalgam. He replied to my emails, but did not give me any number in asnwer to this qiestion.

Douglas Futuyma (Evolutionary Biology, 3rd edition,1998, pp.26,27; Sinauer Associates, Sunderland MA) listed 20 items which he said were (a) "Major Tenets of the Evolutionary Synthesis" and (b) "the orthodox modern theory of evolution". The list cannot be complete, however, because it includes  no common ancestor postulate.

Michael Majerus (Melanism: Evolution in Action, Oxford University Press, 1998, p.78) gives a half-page, unreferenced definition of the NDT that differs from that given above; it contains no mention of common descent or random, spontaneous mutation. His NDT is apparently an adjustable theory, for he states "The Darwinian and neo-Darwinian theories have been amended in various ways, for specific cases or sets of cases". In an e-mail sent on May 7, 2002, I asked if it is possible to test the validity of an adjustable theory; I have not yet received a reply.

Elliott Sober (The Nature of Selection, University of Chicago Press, 1984, p.22, paragraph 2) and Philip Kitcher (Abusing Science, MIT Press, Cambridge MA, 1982, p.18) refer to the modern synthesis and state how it arose but do not define the NDT.

Mr Pun on a web site states that "the modern synthetic rheory version of the NDT was not formulated systematically until the publication of Dobzhansky's Genetics and the Origin of Species" (T. Dobzhansky, 3rd Edition, Columbia University Press, New York and London, 1951). This book contains a definition of the "Theory of Evolution" involving 4 and only 4 points with no mention of random mutation or natural selection (p.11, para.2); this is not. therefore, a definition of the NDT. Moreover, the book's index contains no mention of the NDT or any of its synonyms. I think, therefore, that Mr Pun is mistaken.

The Oxford English Dictionary and Webster's Dictionary do not define the NDT or neo-Darwinian.

The 2002 book Gene Avatars: the Neo-Darwinian Theory of Evolution does not formulate or define the NDT.

Phillip Johnson defines his use of the term Darwinism as "fully naturalistic evolution, involving chance mechanisms guided by natural selection."