The question at issue is not whether gradual transitions are conceivable (and existent), but whether they can be explained by the assumption that they are caused by random mutations.
Take the case of humans after their separation from chimps some million years ago. An upper limit to the number of individuals having been born since then is 10^16 (i.e. 10^9 newborns per year for 10^7 years).
10^16 is an extremely small number when compared with the number of possible mutations in the genetic code. Let us assume that the number of relevant base pairs (i.e. without junk DNA) is 100'000'000 pairs per chromosome set. This results in three hundred million possible point-replacement mutations (because every base pair can be replaced by three alternatives).
The number of possible combinations of two such point mutations is already 10^17, i.e. higher than the number of all "humans" ever born since our separation from chimps. The number of all possible single-step mutations is even much higher than the number of point-replacement mutations.
So evolutionary advantages depending on two or more single-step mutations cannot have had a relevant impact (at least for human evolution). If we believe in neo-Darwinism we must assume that every innovation is produced by a sequence of single-step mutations, each of which alone responsible for a relevant increase in fitness.
Let us assume that three factors must be affected for an increase in fitness to emerge. So even if the probability of a beneficial mutation in a newborn were as high as 10^-5 for each factor, the probability that beneficial mutations occur for all three factors is 10^-15, i.e. extremely improbable.
So neo-Darwinism requires essentially this hypothesis:
Every evolutionary innovation can produced by a sequence of single-step mutations, each of which alone responsible for a relevant increase in fitness.
Because this hypothesis is obviously wrong, neo-Darwinism is refuted.
If we take into account that many properties depending each on more than one single genetic factor must evolve at the same time, it becomes even more obvious that the neo-Darwinian explanation of evolution is simply untenable.
The upright gait
was only one of many traits which had to evolve in us after our separation from chimps. For that to happen, the structures of bones, of muscles and of tendons had to gradually change. Let us ignore that in fact the bone structure (involved in the upright-gait evolution) alone consists of several bones with each several traits.
So let us make the completely unrealistic assumption that one 'progressive' single-step mutation in the genetic factor of each (i.e. bone, muscle and tendon) structure is enough to entail a relevant increase in fitness.
Let us further assume that the probability of such progressive mutations in newborns is each as high as 10^-5. So we conclude that among 10^15 newborns (i.e. a billion newborns of a million generations), only one individual will carry all three necessary mutations.
Because a change in only one or two of the three involved structures cannot lead to a relevant increase in fitness (rather the contrary), it becomes obvious that the upright gait cannot have evolved in a neo-Darwinian way.
The above is a composition of extracts from posts to talk.origins from November 2000