[GodGunsGuts]

True to Darwinist form, I knew you guys would try to Wesley out of this one. The whole point is that the mutation was caused by the environment (the opposite of random mutation + natural selection) and was passed on to the offspring. This is the antithesis of the neo-Darwinian synthesis, and absolutely meets the qualification you laid down for falsifying the Darwinian ToE.

[UndauntedR]

True to Darwinist form

And true to IDist form, you label your opponent, ignore all arguments made by him, and attack a straw man of evolution.

The whole point is that the mutation was caused by the environment

First, methylation is not mutation. The article stated this explicitly, but you didn't read it: "...despite the fact that all offspring inherited exactly the same agouti gene (i.e., with no nucleotide differences), mice who received supplements had offspring with mostly brown fur..." Methylation only acts to control the level of gene expression. Methylation of the promoter of a gene will often lead to silencing that gene (by blocking DNA transcriptase). Alternatively, hypomethylation can cause over-expression of genes (e.g. oncogenes in human cancer). The reason the article was interesting was that they found a simple environmental factor which regulated the gene's expression via epigenetics (DNA methylation, which is inheritable). Again, this is not Lamarckism, but I'll let you figure out why.

(the opposite of random mutation + natural selection)

Any inheritable change in genetic expression is an evolutionary mechanism (not just random mutation - of which there are many types as well). For example, paramutation, bookmarking, imprinting, gene silencing, position effect, methylation, transvection, carcinogenesis, and histone and heterochromatin modifications all affect gene expression but do not change the actual DNA.

I also noticed that you avoided applying ID to some of the examples provided by nature. What kind of theory provides no answers when challenged?