Tuesday, June 9, 2009

The Long Tail of Life

In performing risk assessments we are often asked (or required) to make estimations of values. Typically once a risk is identified it needs to be rated for likelihood (how often) and severity (how bad). The ratings may be difficult to make in the absence of data or first-hand experience with the risk. We often therefore rely on “guesstimates”, calibrated against similar estimates by other colleagues or peers.

Here is a question to exercise your powers of estimation.

I recently came across an article by Carl Haub of the US Population Reference Bureau which seeks to answer the following question - How many people have ever lived? Put another way, over all time, how many people have been born? Haub says that he is asked this question frequently, and apparently there is something of an urban legend in population circles which maintains that 75% of all people who had lived were living in the 1970s. This figure sounds plausible to the lay person since we believe most aspects of the 20th century are characterised by exponential growth.

Haub sought to debunk this statement with an informed estimate. He observes that any estimate of the total number of people who have ever been born will depend basically on two factors: (1) the length of time humans are thought to have been on Earth and (2) the average size of the human population at different periods. Haub assumes that people appeared about 50,000 years ago, and from then till now he creates ten epochs (benchmarks) characterized by different birth rates


The period from 50,000 B.C. till 8,000 B.C., the dawn of agriculture, is a long struggle. Life expectancy at birth probably averaged only about 10 years for this period, and therefore most of human history. Infant mortality is thought to have been very high — perhaps 500 infant deaths per 1,000 births, or even higher. By 1 A.D. the population had risen to 300 million which represents results a meagre growth rate of only 0.0512 percent per year.

By 1650, world population rose to about 500 million, not a significant increase over the 1 A.D. estimate. Numbers were kept in check by the Black Plague which potentially killed 100 million people. By 1800 however, the world population had passed the 1 billion mark, and has increased rapidly to the current 6 or so billion.

The graph below shows another analysis which corroborates the estimates of Haub. The curve exhibits a long tail or power law with a steep increase in population from about the 18th century.


Looking at the curve above you may be tempted to believe the urban legend that 75% of all people ever born were in fact alive in the 70s. Haub in fact reports that in 2002 just under 6% of all people ever born were in fact living. Or put another way, approximately 106 billion people had been born over all time, of which 6 billion are currently living.

The key to this conclusion is the extremely high birth rate (80 per thousand) required to keep humans from becoming extinct between the period of 50,000 B.C. and 1 A.D. According to Haub there had been about 46 billion births by 1 A.D. but only a handful of people had survived. That is, the vast majority of people who have been born have also died.

How good was your estimate to the original question?

Interestingly, WolframAlpha returns the correct answer to the question. I was closer to 30% – 40% of all people being alive today, certainly no where near 6%.

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