Our species' origins have been a source of fascination for millennia and account for the huge range of creation myths that are recorded in different cultures. Linnaeus, that great classifier of living things, gave us our biological name Homo sapiens (meaning "wise man") and our high rounded skulls certainly make us distinctive, as do our small brow ridges and chins. However, we are also remarkable for our language, art and complex technology.

The question is: where did these features evolve? Where can humanity place its homeland? In terms of our earliest ancestors, the answer is generally agreed to be Africa. It was here that our first ape-like ancestors began to make their homes on the savannah. However, a fierce debate has continued about whether it was also the ultimate birthplace of our own species.

Forty years ago, no one believed that modern humans could have originated in Africa. In some cases this idea was based on fading racist agendas. For example, in 1962, the American anthropologist Carleton Coon claimed that "If Africa was the cradle of mankind, it was only an indifferent kindergarten. Europe and Asia were our principal schools."

Part of the confusion was due to the lack of well-dated fossil and archaeological evidence. In the intervening years, however, I have been privileged to be involved in helping to accumulate data – fossil, chronological, archaeological and genetic – that show our species did have a recent African origin. But as the latest evidence shows, this origin was complex and in my new book, The Origin of Our Species, I try to make it clear what it means to be human and change perceptions about our origins.

I had been fascinated by ancient humans called Neanderthals even as a 10-year-old, and in 1971, as a 23-year-old student, I left London on a four-month research trip to museums and institutes in 10 European countries to gather data on the shapes of skulls of Neanderthals and of their modern-looking successors in Europe, the Cro-Magnons. My purpose was to test the then popular theory which held that Neanderthals and people like them in each region of the ancient world were the ancestors of people in those same regions today. I had only a modest grant, and so I drove my old car, sleeping in it, camping or staying in youth hostels – in Belgium I even spent one night in a shelter for the homeless. I survived border confrontations and two robberies, but by the end of my 5,000-mile trip I had collected one of the largest data sets of Neanderthal and early modern skull measurements assembled up to that time.

Over the next three years I added data on other ancient and modern samples, and the results were clear: Neanderthals had evolved their own special characteristics, and did not look like ancestors for the Cro-Magnons or for any modern people. The issue was: where had our species evolved? In 1974 I was unable to say, but taking up a research post at the Natural History Museum meant I could continue the quest.

My research uncovered clues, however, and over the next decade my work – along with that of a few others – focused on Africa as the most likely homeland of our species. We remained an isolated minority until 1987, when the paper "Mitochondrial DNA and Human Evolution", was published by Rebecca Cann, Mark Stoneking and Allan Wilson. It put modern human origins on the front pages of newspapers all over the world for the first time for it showed that a tiny and peculiar part of our genome, inherited only through mothers and daughters, derived from an African ancestor about 200,000 years ago. This woman became known as Mitochondrial Eve. A furore followed, as anthropologists rowed over the implications for human evolution.

After that, the "out of Africa" theory – or as I prefer to call it "the recent African origin" model for our origins – really took off. My version depicted the following background. The ancient species Homo erectus survived in East Asia and Indonesia but evolved into Homo heidelbergensis in Europe and Africa. (This last species had been named from a 600,000-year-old jawbone found in Germany in 1907.) Then, about 400,000 years ago, H. heidelbergensis underwent an evolutionary split: north of the Mediterranean it developed into the Neanderthals, while to the south, in Africa, it became us, modern humans. Finally, about 60,000 years ago Homo sapiens began to leave Africa and by 40,000 years ago, with the advantages of more complex tools and behaviours, spread into Asia and Europe, where we replaced the Neanderthals and all the other archaic people outside of Africa. In other words, under our skins, we are all Africans.

Not every scientist agreed, however. One group continued to support the idea of multiregional evolution, an updated version of ideas from the 1930s. It envisaged deep parallel lines of evolution in each inhabited region of Africa, Europe, Asia and Australasia, stretching from local variants of H. erectus right through to living people in the same areas today. These lines did not diverge through time, since they were glued together by interbreeding across the ancient world, so modern features could gradually evolve, spread and accumulate, alongside long-term regional differences in things like the shape of the face and the size of the nose.

A different model, known as the assimilation model, took the new fossil and genetic data on board and gave Africa a key role in the evolution of modern features. However, this model envisaged a much more gradual spread of those features from Africa than did mine. Neanderthals and archaic people like them were assimilated through widespread interbreeding. Thus the evolutionary establishment of modern features was a blending process rather than a rapid replacement.

So who was right? Genetic data continued to accumulate through the 1990s in support of the recent African origin model, both from recent human populations and Neanderthal fossils. Recent massive improvements in recovery and analysis of ancient DNA have produced even more information, some of it very surprising. Fossil fragments from Croatia have yielded up a nearly entire Neanderthal genome, providing rich data that promise insights into their biology – from eye colour and hair type through to skull shape and brain functions. These latest results have largely confirmed a separation from our lineage about 350,000 years ago. But when the new Neanderthal genome was compared in detail with modern humans from different continents, the results produced an intriguing twist to our evolutionary story: the genomes of people from Europe, China and New Guinea lay slightly closer to the Neanderthal sequence than did those of Africans. Thus if you are European, Asian or New Guinean, you could have 2.5% of Neanderthal DNA in your genetic make-up.

The most likely explanation for this discovery is that the ancestors of today's Europeans, Asians and New Guineans interbred with Neanderthals (or at least with a population that had a component of Neanderthal genes) in North Africa, Arabia or the Middle East, as they exited Africa about 60,000 years ago. That ancient human exodus may have involved only a few thousand people, so it would have taken the absorption of only a few Neanderthals into a group of H. sapiens for the genetic effect – greatly magnified as modern human numbers exploded – to be felt tens of thousands of years later.

The breakthrough in reconstructing a Neanderthal genome has been mirrored across Asia in equally remarkable work on the human group that has become known as the "Denisovans". A fossil finger bone, about 40,000 years old, found in Denisova Cave, Siberia, together with a huge molar tooth, could not be assigned to a particular human species, though it has also had much of its genome reconstructed. This has revealed a previously unrecognised Asian offshoot of the Neanderthal line, but again with a twist. These Denisovans are also related to one group of living humans – the Melanesians of southeast Asia (and probably their Australian neighbours too). These groups also carry about 5% of Denisovan DNA from another interbreeding event that must have happened as their ancestors passed through southern Asia over 40,000 years ago.

So where does this added complexity and evidence of interbreeding with Neanderthals and Denisovans leave my favoured Recent African Origins model? Has it been disproved in favour of the multiregional model, as some have claimed? I don't think so. As we have seen, back in 1970, no scientists held the view that Africa was the evolutionary home of modern humans; the region was considered backward and largely irrelevant, with the pendulum of scientific opinion strongly swinging towards non-African and Neanderthal ancestry models. Twenty years later, the pendulum was starting to move in favour of our African origins, as fossil evidence began to be reinforced by the clear signals of mitochondrial DNA. The pendulum swung even further with growing fossil, archaeological and genetic data in the 1990s.

Now, the advent of huge amounts of DNA data, including the Neanderthal and Denisovan genomes, has halted and even reversed that pendulum swing, away from absolute replacement. Instead we are looking at a mixed replacement-hybridisation or "leaky replacement" model. This dynamism is what makes studying human evolution so fascinating. Science is not about being right or wrong, but about gradually approaching truth about the natural world.

The big picture is that we are still predominantly of recent African origin (more than 90% of our genetic ancestry). But is there a special reason for this observation? Overall, the pre-eminence of Africa in the story of our origins does not involve a special evolutionary pathway but is a question of the continent's consistently large habitable areas which gave greater opportunities for morphological and behavioural variations, and for genetic and behavioural innovations to develop and be conserved. "Modernity" was not a package that had an origin in one African time, place and population, but was a composite whose elements appeared at different times and places, and then gradually coalesced to assume the form we recognise today.

My studies have led me to a greater recognition in recent human evolution of the forces of demography (the need for large populations and social networks to make progress), drift and contingency (chance events), and cultural rather than natural selection than I had considered before. It seems that cultural "progress" was a stop-start affair for much of our evolution, until human groups were large, had long-lived individuals, and wide social networks, all helping to maximise the chances that innovations would survive and accumulate.

Linnaeus said of Homo sapiens "know thyself". Knowing ourselves means a recognition that becoming modern is the path we perceive when looking back on our own evolutionary history. That history seems special to us, of course, because we owe our very existence to it. Those figures of human species (usually males, who become increasingly hairless and light-skinned) marching boldly across the page have illustrated our evolution in many popular articles, but they have wrongly enshrined the view that evolution was simply a progression leading to us, its pinnacle and final achievement.

Nothing could be further from the truth. There were plenty of other paths that could have been taken; many would have led to no humans at all, others to extinction, and yet others to a different version of "modernity". We can inhabit only one version of being human – the only version that survives today – but what is fascinating is that palaeoanthropology shows us those other paths to becoming human, their successes and their eventual demise, whether through failure or just sheer bad luck.

Sometimes the difference between failure and success in evolution is a narrow one. We are certainly on a knife-edge now, as we confront an overpopulated planet and the prospect of global climate change on a scale that humans have never faced before. Let's hope our species is up to the challenge.

Professor Chris Stringer is the research leader in human origins at the Natural History Museum, London