Rapid population increase at the arrival of Neolithic to Britain

In a new paper published at the Journal of Archaeological Science (paywall), Mark Collard et al. argue that the arrival of agriculture to Great Britain, some 6000 years ago, was followed by a rapid increase of the population.

From that they conclude somehow that the process involves a migration. I am not so sure because in optimal conditions a population can even double in one or two generations, but certainly implies some sort of rapid expansion of the farming economy that maybe is best explained with some level of migration.

Another problem I have is apparent lack of continuity between continental and insular cultures. Clearly it was not the Danubian farmers with their homogeneous culture who made that colonization but there are several other less defined cultures in Atlantic Europe by that time, including one just south of the Channel that would soon become the second center of Dolmenic Megalithism (but with a rather peculiar drift) at Brittany and Midwest France (classical Armorica). There had been other distinct farmer cultures in NW France and Belgium but were about then absorbed by the Rössen culture (Danubian). There was also another non-Danubian farmer culture in Denmark and agriculture was also penetrating gradually into SW Atlantic Europe at that time.

From what I gather from the abstract and the short article at New Scientist, the population quadrupled in four centuries, which is quite fast, and they think that the immigrants arrived from France. They also say that the first increase of the population happened in South England and then in Middle Scotland, which may have a different origin altogether.

Sincerely, I would not mind reading this one because my understanding of Neolithic Britain is very fragmented and this seems a serious attempt to systematize the knowledge of this major historical change.