The 2013 article is careful to define what is meant by random in the modern synthesis:

“I will use the definition that the changes are assumed to be random with respect to physiological function and could not therefore be influenced by such function or by functional changes in response to the environment. This is the assumption that excludes the phenotype from in any way influencing or guiding genetic change.”

Some have criticised the article and the videos on the grounds that the modern synthesis does not require DNA change to be equally likely everywhere in the genome. The article does not make that claim. On the contrary it states:

“The concept of a purely random event is not easy to define. The physico-chemical nature of biological molecules will, in any case, ensure that some changes are more likely to happen than others.”

Of course the modern synthesis can accept non-random change. That has been known ever since the identification of genome hotspots. What is completely contrary to the spirit of the modern synthesis is targeted DNA change that is functionally significant. We now have examples of that kind of change. To read more on those examples see the answer to the question on the relevance to physiology.

The relevant part of the IUPS2013 lecture starts at 7 minutes with the phrase “It is important to ask the question what we mean by random” followed at 7:18 by “rather by whether the changes are functionally relevant” before quoting the paragraph from the article shown above. The article and the lecture could not be clearer. See also Randomness and Function.

It is remarkable how often the same unthinking criticism of the article and the lecture turn up on blog websites. What this shows is that the writers have not taken the time to read the article or listen carefully to the video lectures. Having missed the target on this matter, the same bloggers usually go on to the further false accusation that I claim to have disproved “the theory of evolution”. Anyone who reads the article or watches the videos would find that laughable, so why do they do it? For some strange reason defenders of neo-Darwinism on blogs seem to think that anyone who questions neo-Darwinism is questioning the existence of evolution. The article clearly states:

“In some respects, my article returns to a more nuanced, less dogmatic view of evolutionary theory (see also Müller, 2007; Mesoudi et al. 2013), which is much more in keeping with the spirit of Darwin’s own ideas than is the Neo-Darwinist view.”

As I write in another answer (Answers-dogmatism.html): “It is perfectly possible to defend the virtual certainty that life has evolved while debating in the usual argumentative scientific way the uncertainties surrounding the question of mechanisms.” That is where the real debate is taking place: what are the relative contributions of the various mechanisms to the evolutionary process and the speed with which it has occurred (see Speed of Evolution).