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Wars, drought, famine, pestilence, locusts, cattle-plague! Why so many calamities in succession? Why?" This missionary lament is, in a sense, the theme of John Iliffe's excellent book. Let it be said right away that this is almost certainly the best single volume history of Africa extant and it should enjoy a large success. Like all such volumes, however, one tends to skim through the later chapters because of the almost impossible task of saying anything new or different about the colonial era or modern South Africa in such highly summarised form. This book's tremendous strength lies earlier, in the seamless way he takes us from the very earliest days of man on the planet - for the first traces of modern man, 100,000 years ago, are to be found in Ethiopia and South Africa - through the Roman, Christian and Muslim eras to modern Africa, all with an equally sure touch.

The great mystery of Africa is that for millions of years human development was at its most advanced there but that gradually it fell behind all other continents. The first hominids appeared there 4.4 million years ago and thereafter it saw the first humans, the first traces of Homo erectus, then of Homosapiens, then of neanderthal man. The first stone tools seem to have been used in south Africa 45,000 years ago and the first underground mining in the Nile Valley 35,000 years ago. Far later than that, during the apogee of Egyptian or Carthaginian civilisation or the golden age of Muslim north Africa, for example, it would have seemed a far safer bet that Africans would pillage and colonise Europe rather than the other way round.

Some would say this developmental failure was due to Africa's failure to develop its own script (but then most countries borrowed their script from others); or was because of its peripheral position vis-a-vis major world trade routes (but why not see Europe as peripheral to Africa?); or the fact that it merely traded things that grew (animals, produce, slaves) or that men dug up (but why did manufactures not develop?).

The easy way out has always been to blame outsiders, to focus on the terrible devastation wrought by the Atlantic slave trade, for example. But slavery was old in Africa when Europeans arrived and it was only because Africa was so weak in relation to Europe (ie that its developmental lag had already occurred) that European slavers could pillage there with such impunity.

Iliffe's answer is that the sheer vastness of Africa and the aridity of much of its climate hindered the development of transport networks and thus of state formation. When oppressive rulers came to power the best and most feasible response was simply to trek out of their reach. But what made these handicaps truly operative was the crucial extra factor of Africa's "unique population history", which is the great theme of his book.

As he points out, the expansion of Islam after 632 ad was "the central process in world history for the next 400 years" and north and west Africa were key foci of this insurgent Muslim world. But the arrival of the Black Death, which killed between a quarter and a third of all Egyptians in 18 months, plunged north Africa into a 500-year decline. The scale of the collapse was almost unimaginable: in 1517 the Egyptian state was able to collect less than one-fifth of the land tax paid in 1315. Moreover, 28 successive outbreaks of pneumonic plague thereafter meant that by the early 19th century Egypt's population may still have been only half what it had been 600 years before: and what was true of Egypt applied equally right across the Maghreb.

Similar demographic disasters characterised what Iliffe rightly calls "the world's most hostile disease environment". West Africa was plagued by endemic syphilis, yaws, malaria, sleeping sickness, Guinea worm and other intestinal parasitic maladies. Moreover, plagues such as these generally eventuated in famines, and these not infrequently carried off anything up to half the population of whole regions. Angola, for example, experienced a famine which killed between a third and a half of the population roughly every 70 years from the 16th century on.

This not only meant that life expectancy was probably less than 25 years, but that much of African society was obsessed with the procurement of women and children and the great tension between male age grades. To extract surplus the rulers often adopted methods which damaged its very production, most notably slavery: even the experienced David Livingstone saw such misery in east Africa that he had the "impression of being in Hell".

Colonialism at first brought a new slavery of its own and, with it, smallpox, but ultimately led to a prodigious demographic take-off as modern health measures were applied to a continent bent on frantic reproduction for mere survival. Africa's population increased from 142 million in 1920 to over 200 million by 1950, since when it has raced towards a billion - the most rapid population growth ever.

In 1948 the British colonial secretary, Creech-Jones, spoke with considerable foresight: "We apply better health arrangements only to be faced with a population problem of appalling dimensions . . . they employ agricultural methods and ways of living hopelessly inadequate for such numbers . . . They cannot on their present economies enjoy all the services which they begin to demand . . . We cannot . . . hope to satisfy all these new appetites . . . and consequently there must be discomfort and agitation."

Discomfort and agitation there have certainly been, although Iliffe sees hope in a possible near-term demographic stabilisation. Whether the still growing Aids epidemic will allow one to speak of "stabilisation" is a moot point. If this book has one lesson it is that the one thing Africa has never really enjoyed is stability: it seems as elusive as ever today.

R. W. Johnson is the director of the Helen Suzman Foundation, Johannesburg, and an emeritus fellow of Magdalen College, Oxford.