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Single-Step and Cumulative Selection

It is often said that a million monkeys, left to type on a keyboard at random, will eventually produce the complete works of Shakespeare. The principle involved here - that the complete works of Shakespeare could arise by chance, if given enough time - is true. However, the odds against such a phenomenon are absolutely astronomical. This argument is often used in debating evolution: that the odds against so complex a system as a life form, even the simplest bacterium, arising by chance are astronomical.

This argument reflects a common misconception about evolution in general. It is not based on chance or random happenstance. Instead, it is based on the power of cumulative selection to produce well-adapted, self-replicating organisms. The simulation you are about to view is a demonstration of the power of cumulative selection.

Simple Probability: Single-Step Selection

As stated above, the probability of the monkeys typing the complete works of Shakespeare are infinitesimal. What about the probability of randomly generating a simple 12-letter phrase? Given only 27 characters (the 26 letters and a space), the chance is (1/27)¹², or 1 in 150,094,635,296,999,121. Needless to say, even a simple 12-letter target phrase would take a long time to generate using simple single-step selection.

Cumulative Selection

We have seen that single-step selection is (to understate the situation) extremely inefficient. However, cumulative selection is capable of (relatively) quickly and efficiently selecting for a target phrase. Cumulative selection is the principle actually in operation in evolution. It does not involve repeated, isolated, single-step trials, but instead "breeds from" the most successful entities. In the 12-letter phrase example, cumulative selection begins with a start string and randomly alters the letters until the phrase is closer to the target. Each time the phrase is improved, that sequence of letters is kept and the remaining letters are selected for. The cumulative selection demonstration took an average of 239 attempts to breed the first 12 letters of the alphabet, "ABCDEFGHIJKL", from the phrase "RANDOMLETTER".

The Simulation: Instructions

Click the button below to launch the text breeder, which will open in a new window. Enter the text you want to breed in the top box and the text you would like to breed from in the second box. Then click OK and watch your phrase be generated!
Warning: the demonstration requires a Java 1.1 capable browser.

Words of Warning

This simulation is a powerful demonstration of cumulative selection at work. However, it is not a good simulation of actual evolution, since it operates by seeking a "target". Natural selection does not choose some organisms above others with a distant purpose or ideal form "in mind". It simply means that the best-adapted organisms will, on average, leave more progeny than less-adapted organisms. Natural selection is simply survival (and reproduction) of the fittest - not the search or quest for a target, as many suggest.

Credits and Acknowledgements

The underlying premise of this simulation was originally conceived by Richard Dawkins in his book The Blind Watchmaker (see pages 46-50), published by W.W. Norton. We have been kindly granted permission to utilize the concepts found in the book for this simulation.

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