Does the information increase if there is no selection?

INTRODUCTION

Dembski stated in his book No Free Lunch (page 212):

The No Free Lunch theorems show that evolutionary algorithms, apart from careful fine-tuning by a programmer, are no better than blind search and thus no better than pure chance.

The ev program is an evolutionary algorithm that shows that without fine tuning the selection process leads to an information gain. To evaluate how much better than chance the ev results are, is we need to do a control. What happens in an ev simulation when there is no selection? One would expect there to be no information gain and any information gain under those circumstances should be "no better than chance". This then forms a baseline by which we can measure how much better the ev algorithm does using selection than it does on chance alone.

MATERIALS AND METHODS

The cleanest way to test this is to use the standard example from the ev paper. According to my notes in the ev program documentation 'see also' section, this is the "Parameter file for selective phase in the paper: evp.selection".

I set the parameters to run to 2000 generations where things should have stabilized.

evp parameter file evp.selection modified to turn off selection
mk script to run ev
mkgraph script to make graphs
xyplop control parameter file for the plotting program xyplo.
genhisp control parameter file for the histogram plotting program genhis.
genpicp control parameter file for the histogram to postscript conversion program genpic.
The postscript output was converted to jpg using convert, an www.imagemagick.org program, ps2jpg.
mkjpgs script to make jpgs
noselection.calc a 'calc' program used to determine the significance of the results. It is run by calc.

RESULTS

list The run with an initial seed of 0.30.
xyin raw data file for xyplo. This is linked to the list file.
This is a graph of the information content, Rsequence, as a function of the generation number.
The graph is also available in PostScript: xyout.ps.
We would expect the results to fluctuate around the predicted value, perhaps close to a Gaussian distribution. Using genhis we get the histog. Genpic converts that ascii file to postscript and 'convert' creates a jpg to show:

The results are indeed roughly Gaussian and close to zero. The histogram is also available in PostScript: histogram.ps

DISCUSSION

There is indeed a roughly Gaussian distribution around zero bits of information when the simulation is run with no selection. According to the histog the mean is 0.11092 bits with a standard deviation of 0.29928 bits. Using calc, we find (noselection.calc, mkcalc, noselection.result) that this is 12.99 standard deviations from 4.0 bits. It is hard to compute the probability because it is so low. Calc gives 0.00e+00 +/- 4.66e-10. That is, it is zero with a variation of 10^-10!

This control experiment shows that when the ev program is run without selection there is no information increase. Therefore we can attribute the information increases observed with selection on entirely to that selection. In other words, an evolutionary algorithm does far better (almost 13 standard deviations!) than 'pure chance' which is the situation when there is no selection. This falsifies Dembski's statement about No Free Lunch Theorems.

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Schneider Lab
origin: 2002 March 3
updated: 2002 March 7
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