Darwin was not without his critics. In his book, Darwinism: The Refutation of a Myth, Soren Lovtrup points out that "some critics turned against Darwin's teachings for religious reasons, but they were a minority; most of his opponents ... argued on a completely scientific basis." He goes on to explain:

"...the reasons for rejecting Darwin's proposal were many, but first of all that many innovations cannot possibly come into existence through accumulation of many small steps, and even if they can, natural selection cannot accomplish it, because incipient and intermediate stages are not advantageous."

Perhaps the most formidable of Darwin's critics was St. George Mivart. His major book, On the Genesis of Species, took aim at the notion that natural selection could account for the accumulation of the incipient stages of useful structures (Mivart, 1871). Stephen Jay Gould notes that

"Darwin offered strong, if grudging, praise and took Mivart far more seriously than any other critic...Mivart gathered, and illustrated "with admirable art and force" (Darwin's words), all objections to the theory of natural selection---"a formidable array" (Darwin's words again). Yet one particular theme, urged with special attention by Mivart, stood out as the centerpiece of his criticism. It remains today the primary stumbling block among thoughtful and friendly scrutinizers of Darwinism. No other criticism seems so troubling, so obviously and evidently "right" (against a Darwinian claim that seems intuitively paradoxical and improbable).

Mivart awarded this criticism a separate chapter in his book, right after the introduction. He also gave it a name, remembered ever since. He called it "The Incompetency of 'Natural Selection' to account for the Incipient Stages of Useful Structures." If this phrase sounds like a mouthful, consider the easy translation: we can readily understand how complex and full developed structures work and owe their maintenance and preservation to natural selection---a wing, an eye, the resemblance of a bittern to a branch or of an insect to a stick or dead leaf. But how do you get from nothing to such an elaborate something if evolution must proceed through a long sequence of intermediate stages, each favored by natural selection? You can't fly with 2% of a wing or gain much protection from an iota's similarity with a potentially concealing piece of vegetation. How, in other words, can natural selection explain these incipient stages of structures that can only be used (as we now observe them) in much more elaborated form?"

Gould goes on to point out that among the difficulties of Darwinian theory "one point stands high above the rest: the dilemma of incipient stages. Mivart identified this problem as primary and it remains so today."

Dr. Robert Macnab of Yale University concluded a major 50 page review of the sensory and motor mechanism of the bacterium, E. coli, with these remarks:

As a final comment, one can only marvel at the intricacy in a simple bacterium, of the total motor and sensory system which has been the subject of this review and remark that our concept of evolution by selective advantage must surely be an oversimplification. What advantage could derive, for example, from a "preflagellum" (meaning a subset of its components), and yet what is the probability of "simultaneous" development of the organelle at a level where it becomes advantageous (Macnab, 1978)?

Darwin's Black Box: The Biochemical Challenge to Evolution by Michael J. Behe (1996) offers an excellent analysis of the problem of irreducible complexity in biology. An overview of the problem may be found in his article, Molecular Machines:Experimental Support for the Design Inference.