The study's first author, Dr Anders Bergstrom, of the Francis Crick Institute and an alumnus of the Wellcome Sanger Institute, told Express.co.uk: "Our results imply that several Neanderthal individuals contributed genetic material, but it's difficult to say if it was a question of tens, or hundreds, or an even larger number.
"It's certainly possible that modern humans and Neanderthals lived side by side for some period of time, but it's also possible that these were only sporadic encounters.
"The genomes can simply not tell us much about the social dynamics behind this admixture.
"Likewise, genomes can not say much about the geographical location where the admixture occurred, but it is commonly assumed that it took place in the Middle East shortly after a group of modern humans had arrived there from Africa, about 50,000-60,000 years ago."
Comment: Some other recent research suggests that these interbreeding events could have begun as early as about 200,000 years ago.
By contrast, even though far less is known about them, there is evidence of more sustained interbreeding with Denisovans, with studies having indicated between three and five percent of the DNA of Melanesians and Aboriginal Australians, and around six percent in Papuans deriving from the extinct species.
Dr Bergstrom said: "We do not address the timing of Denisovan admixture in this paper, but previous research has estimated that it occurred shortly after Neanderthal admixture, so something like 45-55 kya.
"Present-day genomes tell us very little about where the admixture occurred geographically, but because Denisovan ancestry today is found in the highest proportions in Oceania it is commonly assumed that it took place somewhere in Southeast Asia."
The study also suggests some DNA from Neanderthals is also present in modern day people living in west Africa, albeit a much smaller percentage.
Dr Bergstrom said: "I think this finding speaks to a more general trend in the understanding of human prehistory, in that things are often more complex than they seem at first.
"While Neanderthal admixture likely occurred outside of Africa, some groups then migrated back into Africa much later and carried this Neanderthal ancestry with them.
"The patterns we see in genomes today are thus often the product of multiple layers of migration and admixture."
Assessing the importance of the research, Dr Bergstrom said it highlighted how, in order to understand the landscape of genetic variation in modern humans, it was necessary to understand the evolutionary history which shaped it.
He added: "Past processes of separation, migration, admixture and population size changes underlie why our genomes look the way they do today.
"There are definitely many further discoveries to be made about human evolution, particularly in Africa, where we are only just scratching the surface.
"Our findings in this study give some insight into the timescale over which present-day human populations diversified within Africa, but the details of this process are still a complete muddle.
"Ultimately, ancient DNA will likely be needed to further illuminate our complex past."
Dr Chris Tyler-Smith, recently retired from the Wellcome Sanger Institute, added: "Though this resource is just the beginning of many avenues of research, already we can glimpse several tantalising insights into human history.
"It will be particularly important for better understanding human evolution in Africa, as well as facilitating medical research for the full diversity of human ancestries."
...Did I just write that out loud?