Can Random Mutations Create New Complex Features?

Since posting our recent rebuttals to the TalkOrigins page on the Cambrian explosion (see hereand here), we've received some requests to respond to other pages on the TalkOrigins archive. One of these is a page purporting to respond to the claim that "Evolution cannot cause an increase in information."
Of course this title equivocates on the meaning of "information." As explained here, evolutionary mechanisms can generate new Shannon information, but that's is often a trivial accomplishment and doesn't at all necessarily mean you've generated any new functional biological feature. A random, garbled, functionless stretch of DNA can entail new "information" in the Shannon sense, but that's never going to explain how complex functional biological features arise. In any case, the TalkOrigins page responds as follows:
It is hard to understand how anyone could make this claim, since anything mutations can do, mutations can undo. Some mutations add information to a genome; some subtract it.
That bizarre statement reflects a gross misunderstanding of how Darwinian evolution works. A longstanding postulate in evolutionary biology, called Dollo's Law, holds that evolution is not reversible. Perhaps in some cases mutations can "undo" anything they "can do," but it's not at all clear that this is always the case.
There's a good reason for Dollo's Law. Darwinian evolution tends only to fix traits in a population when they confer some advantage upon the organism. Evolutionary biologist Jerry Coyne affirms this when he states: "It is indeed true that natural selection cannot build any feature in which intermediate steps do not confer a net benefit on the organism."1 So some mutations might provide an advantage, but "reversing" those mutations would presumably cancel the advantage. As far as the Darwinian mechanism is concerned, there isn't always a reason to expect that a mutation that "undoes" some advantageous trait will confer an advantage, get passed on to offspring, and be maintained in a population. So anything a mutation does cannot always be undone.

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