Your article with my comments:
Which didn't answer the "absolute minimum amount of time" question, but IS on topic.
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By Dr David Whitehouse
BBC News Online science editor
A new hypothesis about recent human evolution suggests that we came very close to extinction because of a "volcanic winter" that occurred 71,000 years ago.
Some scientists estimate that there may have been as few as 15,000 humans alive at one time.
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"new" hypothesis - a proposition, or set of propositions, set forth as an explanation for the occurrence of some specified group of phenomena, either asserted merely as a provisional conjecture to guide investigation (working hypothesis) or accepted as highly probable in the light of established facts.
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The volcanic winter lasted about six years. It was followed by 1,000 years of the coldest Ice Age on record.
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How do we know this?
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It brought widespread famine and death to human populations around the world. It also affected subsequent human evolution.
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Have we documented this?
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This was because of a so-called bottleneck effect. The rapid decrease, in our ancestors' populations, in turn, brought about the rapid differentiation - or genetic divergence - of the surviving populations.
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Please explain the mechanism by which the decrease of population results in an increase of differentiation, and why, if this is the case, going down to eight in "recent" history could not account for the genetic divergence we see today.
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The idea is being advocated by Professor Stanley Ambrose of the University of Illinois.
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Its nice he advocates his own idea. How much support does he have?
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He believes that the eruption of Mount Toba in Sumatra caused the bottleneck.
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I like that word believes.
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"Modern human races may have diverged abruptly, only 70,000 years ago," he writes in the Journal of Human Evolution.
Geneticists have thought for some time that humans passed through a recent evolutionary bottleneck but they had little idea what may have caused it.
Scientists believe that an eruption of Toba caused a volcanic winter that lasted six years and significantly altered global climate for the next 1,000 years.
During those six years, there was substantial lowering of global temperatures, drought and famine. No more than 15,000 people survived.
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How do we know that no more than 15,000 people survived?
Why not 14000? Why not eight?
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When better conditions returned, the human population was able to grow once more and develop the genetic diversity we see today.
"When our African recent ancestors passed through the prism of Toba's volcanic winter, a rainbow of differences appeared," Professor Ambrose said.
Nice conclusion, is it a fact?
The rate of mutation and genetic change is relatively constant. When you consider that you are looking at diversity not only in humans, but across the board in animals, you can make a pretty good estimate of when the most recent common ancestors could have lived.