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Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 17 2009,11:00

This thread is for comments on evolutionary computation.

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"You can't teach an old dogma new tricks." - Dorothy Parker

Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 17 2009,11:15

"weasel" math

Given:

Base set size K (number of possible characters at each position)

Target string length L

Mutation rate (per site) u

Population size N

here are some basic probabilities to go with a "weasel" run.

Per base:

Pincorrect to correct = 1 / K

Pcorrect to incorrect = (K - 1) / K

Blind search:

Ptry is all correct = K-L

Pa try in the population is all correct = N * K-L

Expected number of correct bases when all bases are changed = L  / K

Expected number of correct bases when a genome is produced via copy with mutation = u * L  / K

In "weasel" run:

Expected number of correct bases given a partially matching string:
Given C as number of correct matching bases

expected correct bases after mutation = C + (u * (L - C) / K) - (u * C * (K - 1) / K)

There's a few more items to derive to pull in the population parameter, but I need to go now.

Edit: Equations for Ptry is all correct and dependencies per PT comment by Mike Elzinga.

Edited by Wesley R. Elsberry on Mar. 19 2009,19:40

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"You can't teach an old dogma new tricks." - Dorothy Parker

Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 18 2009,11:03

More "weasel" math

Probability that a candidate will retain all the correct letters from its parent: (1 - (u * (k - 1) / k))C

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"You can't teach an old dogma new tricks." - Dorothy Parker

Richardthughes

Posts: 9723
Joined: Jan. 2006

 (Permalink) Posted: Mar. 18 2009,11:24

Can you derive an optimal mutation rate?

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Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 18 2009,11:47

 Quote (Richardthughes @ Mar. 18 2009,11:24) Can you derive an optimal mutation rate?

I'll have to think about that some. Later.

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"You can't teach an old dogma new tricks." - Dorothy Parker

Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 18 2009,13:19

More "weasel" math:

Probability of a candidate changing a parent's correct base to an incorrect base = PCandidate_C2I =

(1 - (1 - (u * (K - 1) / K))C)

Probability that a population will have at least one candidate that preserves all the correct bases from the parent of the previous generation = PPopulation_C2C =

1 - (PCandidate_C2I )N

Checked via Monte Carlo methods, and using the N=50 and u=0.05 values that (IIRC) ROb was often using:

 Code Sample 1000 runs, 00 correct : p_c2c calc = 1.00000, MC = 1.00000; p_c2i calc = 0.00000, MC = 0.000001000 runs, N=50, u=0.05000, K=27, C=0, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.000001000 runs, 01 correct : p_c2c calc = 0.95185, MC = 0.93800; p_c2i calc = 0.04815, MC = 0.062001000 runs, N=50, u=0.05000, K=27, C=1, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.047261000 runs, 02 correct : p_c2c calc = 0.90602, MC = 0.90400; p_c2i calc = 0.09398, MC = 0.096001000 runs, N=50, u=0.05000, K=27, C=2, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.094761000 runs, 03 correct : p_c2c calc = 0.86240, MC = 0.85900; p_c2i calc = 0.13760, MC = 0.141001000 runs, N=50, u=0.05000, K=27, C=3, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.135921000 runs, 04 correct : p_c2c calc = 0.82088, MC = 0.82400; p_c2i calc = 0.17912, MC = 0.176001000 runs, N=50, u=0.05000, K=27, C=4, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.178101000 runs, 05 correct : p_c2c calc = 0.78135, MC = 0.80400; p_c2i calc = 0.21865, MC = 0.196001000 runs, N=50, u=0.05000, K=27, C=5, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.216181000 runs, 06 correct : p_c2c calc = 0.74373, MC = 0.75900; p_c2i calc = 0.25627, MC = 0.241001000 runs, N=50, u=0.05000, K=27, C=6, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.258481000 runs, 07 correct : p_c2c calc = 0.70792, MC = 0.74400; p_c2i calc = 0.29208, MC = 0.256001000 runs, N=50, u=0.05000, K=27, C=7, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.292261000 runs, 08 correct : p_c2c calc = 0.67384, MC = 0.67200; p_c2i calc = 0.32616, MC = 0.328001000 runs, N=50, u=0.05000, K=27, C=8, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.324601000 runs, 09 correct : p_c2c calc = 0.64139, MC = 0.62100; p_c2i calc = 0.35861, MC = 0.379001000 runs, N=50, u=0.05000, K=27, C=9, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.360861000 runs, 10 correct : p_c2c calc = 0.61051, MC = 0.61000; p_c2i calc = 0.38949, MC = 0.390001000 runs, N=50, u=0.05000, K=27, C=10, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.389661000 runs, 11 correct : p_c2c calc = 0.58112, MC = 0.59500; p_c2i calc = 0.41888, MC = 0.405001000 runs, N=50, u=0.05000, K=27, C=11, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.420601000 runs, 12 correct : p_c2c calc = 0.55314, MC = 0.54600; p_c2i calc = 0.44686, MC = 0.454001000 runs, N=50, u=0.05000, K=27, C=12, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.447941000 runs, 13 correct : p_c2c calc = 0.52650, MC = 0.52000; p_c2i calc = 0.47350, MC = 0.480001000 runs, N=50, u=0.05000, K=27, C=13, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.470501000 runs, 14 correct : p_c2c calc = 0.50115, MC = 0.50900; p_c2i calc = 0.49885, MC = 0.491001000 runs, N=50, u=0.05000, K=27, C=14, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.501301000 runs, 15 correct : p_c2c calc = 0.47702, MC = 0.45800; p_c2i calc = 0.52298, MC = 0.542001000 runs, N=50, u=0.05000, K=27, C=15, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.516581000 runs, 16 correct : p_c2c calc = 0.45406, MC = 0.48200; p_c2i calc = 0.54594, MC = 0.518001000 runs, N=50, u=0.05000, K=27, C=16, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.542701000 runs, 17 correct : p_c2c calc = 0.43219, MC = 0.41800; p_c2i calc = 0.56781, MC = 0.582001000 runs, N=50, u=0.05000, K=27, C=17, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.567081000 runs, 18 correct : p_c2c calc = 0.41139, MC = 0.41200; p_c2i calc = 0.58861, MC = 0.588001000 runs, N=50, u=0.05000, K=27, C=18, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.592181000 runs, 19 correct : p_c2c calc = 0.39158, MC = 0.35000; p_c2i calc = 0.60842, MC = 0.650001000 runs, N=50, u=0.05000, K=27, C=19, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.610701000 runs, 20 correct : p_c2c calc = 0.37272, MC = 0.37200; p_c2i calc = 0.62728, MC = 0.628001000 runs, N=50, u=0.05000, K=27, C=20, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.627621000 runs, 21 correct : p_c2c calc = 0.35478, MC = 0.33300; p_c2i calc = 0.64522, MC = 0.667001000 runs, N=50, u=0.05000, K=27, C=21, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.640481000 runs, 22 correct : p_c2c calc = 0.33770, MC = 0.32200; p_c2i calc = 0.66230, MC = 0.678001000 runs, N=50, u=0.05000, K=27, C=22, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.661461000 runs, 23 correct : p_c2c calc = 0.32144, MC = 0.31500; p_c2i calc = 0.67856, MC = 0.685001000 runs, N=50, u=0.05000, K=27, C=23, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.678541000 runs, 24 correct : p_c2c calc = 0.30596, MC = 0.28900; p_c2i calc = 0.69404, MC = 0.711001000 runs, N=50, u=0.05000, K=27, C=24, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.693801000 runs, 25 correct : p_c2c calc = 0.29123, MC = 0.28000; p_c2i calc = 0.70877, MC = 0.720001000 runs, N=50, u=0.05000, K=27, C=25, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.707921000 runs, 26 correct : p_c2c calc = 0.27721, MC = 0.27700; p_c2i calc = 0.72279, MC = 0.723001000 runs, N=50, u=0.05000, K=27, C=26, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.721541000 runs, 27 correct : p_c2c calc = 0.26386, MC = 0.23500; p_c2i calc = 0.73614, MC = 0.765001000 runs, N=50, u=0.05000, K=27, C=27, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.736441000 runs, 28 correct : p_c2c calc = 0.25116, MC = 0.24500; p_c2i calc = 0.74884, MC = 0.755001000 runs, N=50, u=0.05000, K=27, C=28, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.74932

The above completely explains why a list showing the best candidate from each generation is highly unlikely to show any change in a correct character when a candidate bearing it was selected as best in a previous generation. The proportion of candidates that had a change of a correct character to an incorrect one nonetheless rises to almost three-quarters of each generation when almost all characters are correct.

Now doing the Monte Carlo methods on the situation with N=12 and u=0.18, where I picked N and u in order to get a range of values for the population that went down to a relatively small probability.

 Code Sample 1000 runs, 00 correct : p_c2c calc = 1.00000, MC = 1.00000; p_c2i calc = 0.00000, MC = 0.000001000 runs, N=12, u=0.18000, K=27, C=0, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.000001000 runs, 01 correct : p_c2c calc = 0.82667, MC = 0.82700; p_c2i calc = 0.17333, MC = 0.173001000 runs, N=12, u=0.18000, K=27, C=1, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.170581000 runs, 02 correct : p_c2c calc = 0.68338, MC = 0.69300; p_c2i calc = 0.31662, MC = 0.307001000 runs, N=12, u=0.18000, K=27, C=2, p_pop_c2c calc = 1.00000, MC = 1.00000Proportion of candidates w/C2I bases = 0.322331000 runs, 03 correct : p_c2c calc = 0.56493, MC = 0.56600; p_c2i calc = 0.43507, MC = 0.434001000 runs, N=12, u=0.18000, K=27, C=3, p_pop_c2c calc = 0.99995, MC = 1.00000Proportion of candidates w/C2I bases = 0.441171000 runs, 04 correct : p_c2c calc = 0.46701, MC = 0.48600; p_c2i calc = 0.53299, MC = 0.514001000 runs, N=12, u=0.18000, K=27, C=4, p_pop_c2c calc = 0.99947, MC = 1.00000Proportion of candidates w/C2I bases = 0.535081000 runs, 05 correct : p_c2c calc = 0.38606, MC = 0.39800; p_c2i calc = 0.61394, MC = 0.602001000 runs, N=12, u=0.18000, K=27, C=5, p_pop_c2c calc = 0.99713, MC = 0.99700Proportion of candidates w/C2I bases = 0.611671000 runs, 06 correct : p_c2c calc = 0.31914, MC = 0.32100; p_c2i calc = 0.68086, MC = 0.679001000 runs, N=12, u=0.18000, K=27, C=6, p_pop_c2c calc = 0.99008, MC = 0.99200Proportion of candidates w/C2I bases = 0.679671000 runs, 07 correct : p_c2c calc = 0.26382, MC = 0.25100; p_c2i calc = 0.73618, MC = 0.749001000 runs, N=12, u=0.18000, K=27, C=7, p_pop_c2c calc = 0.97466, MC = 0.97200Proportion of candidates w/C2I bases = 0.734751000 runs, 08 correct : p_c2c calc = 0.21809, MC = 0.23600; p_c2i calc = 0.78191, MC = 0.764001000 runs, N=12, u=0.18000, K=27, C=8, p_pop_c2c calc = 0.94778, MC = 0.95500Proportion of candidates w/C2I bases = 0.783831000 runs, 09 correct : p_c2c calc = 0.18029, MC = 0.19100; p_c2i calc = 0.81971, MC = 0.809001000 runs, N=12, u=0.18000, K=27, C=9, p_pop_c2c calc = 0.90797, MC = 0.91400Proportion of candidates w/C2I bases = 0.814921000 runs, 10 correct : p_c2c calc = 0.14904, MC = 0.16000; p_c2i calc = 0.85096, MC = 0.840001000 runs, N=12, u=0.18000, K=27, C=10, p_pop_c2c calc = 0.85582, MC = 0.85600Proportion of candidates w/C2I bases = 0.856671000 runs, 11 correct : p_c2c calc = 0.12321, MC = 0.12900; p_c2i calc = 0.87679, MC = 0.871001000 runs, N=12, u=0.18000, K=27, C=11, p_pop_c2c calc = 0.79357, MC = 0.78600Proportion of candidates w/C2I bases = 0.880831000 runs, 12 correct : p_c2c calc = 0.10185, MC = 0.09800; p_c2i calc = 0.89815, MC = 0.902001000 runs, N=12, u=0.18000, K=27, C=12, p_pop_c2c calc = 0.72446, MC = 0.72100Proportion of candidates w/C2I bases = 0.899001000 runs, 13 correct : p_c2c calc = 0.08420, MC = 0.08100; p_c2i calc = 0.91580, MC = 0.919001000 runs, N=12, u=0.18000, K=27, C=13, p_pop_c2c calc = 0.65196, MC = 0.66100Proportion of candidates w/C2I bases = 0.914581000 runs, 14 correct : p_c2c calc = 0.06960, MC = 0.07600; p_c2i calc = 0.93040, MC = 0.924001000 runs, N=12, u=0.18000, K=27, C=14, p_pop_c2c calc = 0.57925, MC = 0.55400Proportion of candidates w/C2I bases = 0.931921000 runs, 15 correct : p_c2c calc = 0.05754, MC = 0.06100; p_c2i calc = 0.94246, MC = 0.939001000 runs, N=12, u=0.18000, K=27, C=15, p_pop_c2c calc = 0.50891, MC = 0.50000Proportion of candidates w/C2I bases = 0.943331000 runs, 16 correct : p_c2c calc = 0.04756, MC = 0.03900; p_c2i calc = 0.95244, MC = 0.961001000 runs, N=12, u=0.18000, K=27, C=16, p_pop_c2c calc = 0.44278, MC = 0.45400Proportion of candidates w/C2I bases = 0.950831000 runs, 17 correct : p_c2c calc = 0.03932, MC = 0.03800; p_c2i calc = 0.96068, MC = 0.962001000 runs, N=12, u=0.18000, K=27, C=17, p_pop_c2c calc = 0.38206, MC = 0.38200Proportion of candidates w/C2I bases = 0.961831000 runs, 18 correct : p_c2c calc = 0.03250, MC = 0.03600; p_c2i calc = 0.96750, MC = 0.964001000 runs, N=12, u=0.18000, K=27, C=18, p_pop_c2c calc = 0.32736, MC = 0.32200Proportion of candidates w/C2I bases = 0.968751000 runs, 19 correct : p_c2c calc = 0.02687, MC = 0.03200; p_c2i calc = 0.97313, MC = 0.968001000 runs, N=12, u=0.18000, K=27, C=19, p_pop_c2c calc = 0.27881, MC = 0.25300Proportion of candidates w/C2I bases = 0.976001000 runs, 20 correct : p_c2c calc = 0.02221, MC = 0.02000; p_c2i calc = 0.97779, MC = 0.980001000 runs, N=12, u=0.18000, K=27, C=20, p_pop_c2c calc = 0.23629, MC = 0.23400Proportion of candidates w/C2I bases = 0.978171000 runs, 21 correct : p_c2c calc = 0.01836, MC = 0.01800; p_c2i calc = 0.98164, MC = 0.982001000 runs, N=12, u=0.18000, K=27, C=21, p_pop_c2c calc = 0.19941, MC = 0.19100Proportion of candidates w/C2I bases = 0.983081000 runs, 22 correct : p_c2c calc = 0.01518, MC = 0.01600; p_c2i calc = 0.98482, MC = 0.984001000 runs, N=12, u=0.18000, K=27, C=22, p_pop_c2c calc = 0.16769, MC = 0.17300Proportion of candidates w/C2I bases = 0.984581000 runs, 23 correct : p_c2c calc = 0.01255, MC = 0.00600; p_c2i calc = 0.98745, MC = 0.994001000 runs, N=12, u=0.18000, K=27, C=23, p_pop_c2c calc = 0.14061, MC = 0.15400Proportion of candidates w/C2I bases = 0.986171000 runs, 24 correct : p_c2c calc = 0.01037, MC = 0.01400; p_c2i calc = 0.98963, MC = 0.986001000 runs, N=12, u=0.18000, K=27, C=24, p_pop_c2c calc = 0.11762, MC = 0.11200Proportion of candidates w/C2I bases = 0.990421000 runs, 25 correct : p_c2c calc = 0.00858, MC = 0.00600; p_c2i calc = 0.99142, MC = 0.994001000 runs, N=12, u=0.18000, K=27, C=25, p_pop_c2c calc = 0.09819, MC = 0.10400Proportion of candidates w/C2I bases = 0.990751000 runs, 26 correct : p_c2c calc = 0.00709, MC = 0.01200; p_c2i calc = 0.99291, MC = 0.988001000 runs, N=12, u=0.18000, K=27, C=26, p_pop_c2c calc = 0.08183, MC = 0.08000Proportion of candidates w/C2I bases = 0.992831000 runs, 27 correct : p_c2c calc = 0.00586, MC = 0.00700; p_c2i calc = 0.99414, MC = 0.993001000 runs, N=12, u=0.18000, K=27, C=27, p_pop_c2c calc = 0.06810, MC = 0.07400Proportion of candidates w/C2I bases = 0.993581000 runs, 28 correct : p_c2c calc = 0.00484, MC = 0.00600; p_c2i calc = 0.99516, MC = 0.994001000 runs, N=12, u=0.18000, K=27, C=28, p_pop_c2c calc = 0.05661, MC = 0.04400Proportion of candidates w/C2I bases = 0.99617

The above shows that in order to have low probabilities that the best candidate in a generation will retain all the characters that were correct in the parent, one must have small N and relatively high u values.

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"You can't teach an old dogma new tricks." - Dorothy Parker

Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 18 2009,14:17

Here's something for David...

Population size is on the X axis, running from 1 to 500. Mutation rate is on the Y axis, running from 0.0 (bottom of image) to 1.0. The lighter the pixel, the better the chance of convergence. This was generated by finding the PPopulation_C2C(K-1) for each condition represented by the pixel and scaling that probability over 1,024 grayscale values.

As expected, there is no local sensitivity to change in parameters.

Expanding the population scale by ten gives this:

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"You can't teach an old dogma new tricks." - Dorothy Parker

dvunkannon

Posts: 1376
Joined: June 2008

 (Permalink) Posted: Mar. 18 2009,14:57

Some Id-ists have trouble understanding why abstractions like GA/EC are relevant - ie. but it ain't wet! An important point for these folks (and others) is that GA isn't a model of evolution, it _IS_ evolution.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 18 2009,15:45

Huh... I just realized that I should have done the graphs up for (L-1) instead of (K-1). It's the difference between 26 and 27, so it won't make a big shift, but I'll generate those later when I get a chance.

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"You can't teach an old dogma new tricks." - Dorothy Parker

AmandaHuginKiss

Posts: 150
Joined: Dec. 2008

 (Permalink) Posted: Mar. 18 2009,16:33

 Quote (dvunkannon @ Mar. 19 2009,07:57) Some Id-ists have trouble understanding why abstractions like GA/EC are relevant - ie. but it ain't wet! An important point for these folks (and others) is that GA isn't a model of evolution, it _IS_ evolution.

That's one thing that I would like to try if I had time is to model the wet evolution.

dvunkannon

Posts: 1376
Joined: June 2008

 (Permalink) Posted: Mar. 18 2009,17:01

 Quote (Wesley R. Elsberry @ Mar. 18 2009,15:17) Here's something for David...Population size is on the X axis, running from 1 to 500. Mutation rate is on the Y axis, running from 0.0 (bottom of image) to 1.0. The lighter the pixel, the better the chance of convergence. This was generated by finding the PPopulation_C2C(K-1) for each condition represented by the pixel and scaling that probability over 1,024 grayscale values.As expected, there is no local sensitivity to change in parameters. Expanding the population scale by ten gives this:

Thank you Wes!

Sometimes people are stunned by complexity, but these images are so simple that most people don't see the significance. Evolution just works.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

Wesley R. Elsberry

Posts: 4303
Joined: May 2002

 (Permalink) Posted: Mar. 19 2009,09:33

"weasel" graph of PPopulation_C2C(L-1):

ETA: Again, population from 1 to 500 is on the X axis, and mutation probability from 0 to 1.0 is on the Y axis.

Comparison of (K-1) v. (L-1) versions of the graph (lighter is less different):

Edited by Wesley R. Elsberry on Mar. 19 2009,12:57

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"You can't teach an old dogma new tricks." - Dorothy Parker

Freelurker

Posts: 80
Joined: Oct. 2006

 (Permalink) Posted: Mar. 19 2009,11:35

 Quote (dvunkannon @ Mar. 18 2009,15:57) Some Id-ists have trouble understanding why abstractions like GA/EC are relevant - ie. but it ain't wet! An important point for these folks (and others) is that GA isn't a model of evolution, it _IS_ evolution.

This is true in one sense, but let's not lose the distinction between genetic optimization algorithms and simulations of biological evolution.

It seems to me that Dembski makes mischief in just this way. All this criticism of modelers "sneaking in" information just isn't relevant to simulation models. The entire model, every bit of it, came from the modeler. The real issue is the fidelity of the model; does it match reality sufficiently to justify any conclusions one makes based on the model.

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Invoking intelligent design in science is like invoking gremlins in engineering. [after Mark Isaak.]
All models are wrong, some models are useful. - George E. P. Box

dvunkannon

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 (Permalink) Posted: Mar. 19 2009,11:48

Quote (Freelurker @ Mar. 19 2009,12:35)
 Quote (dvunkannon @ Mar. 18 2009,15:57) Some Id-ists have trouble understanding why abstractions like GA/EC are relevant - ie. but it ain't wet! An important point for these folks (and others) is that GA isn't a model of evolution, it _IS_ evolution.

This is true in one sense, but let's not lose the distinction between genetic optimization algorithms and simulations of biological evolution.

It seems to me that Dembski makes mischief in just this way. All this criticism of modelers "sneaking in" information just isn't relevant to simulation models. The entire model, every bit of it, came from the modeler. The real issue is the fidelity of the model; does it match reality sufficiently to justify any conclusions one makes based on the model.

I agree. There are folks who deny evolution can exist at all, and there are those who deny what biology does is evolution.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

Richardthughes

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 (Permalink) Posted: Mar. 19 2009,16:05

EIL's math page for 'Weasel':

http://www.evoinfo.org/WeaselMath.html

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Wesley R. Elsberry

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 (Permalink) Posted: Mar. 19 2009,18:39

Did you notice that there wasn't any math there for the "weasel" as described by Dawkins? Just Dembski/Marks "partitioned search" and "deterministic search".

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"You can't teach an old dogma new tricks." - Dorothy Parker

Richardthughes

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 (Permalink) Posted: Mar. 19 2009,18:50

 Quote (Wesley R. Elsberry @ Mar. 19 2009,18:39) Did you notice that there wasn't any math there for the "weasel" as described by Dawkins? Just Dembski/Marks "partitioned search" and "deterministic search".

Yes. They're very keen to frame it as it isn't. I'm convinced Dembski still doesn't 'get' GAs.

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"Richardthughes, you magnificent bastard, I stand in awe of you..." : Arden Chatfield
"You magnificent bastard! " : Louis
"ATBC poster child", "I have to agree with Rich.." : DaveTard
"I bow to your superior skills" : deadman_932
"...it was Richardthughes making me lie in bed.." : Kristine

Wesley R. Elsberry

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 (Permalink) Posted: Mar. 20 2009,00:30

Here's an interesting graph:

I've put a 20 pixel border around this. On the X axis, there is the number of correct letters (treated as a continuous scale), and mutation rate is on the Y axis. I've taken terms from the "expected number of correct letters in a mutated string" calculation and subtracted the term for expected conversion of correct to incorrect from the expected conversion of incorrect to correct. Black is a net 28 expected new incorrect letters, white is a net 2 expected new correct letters, and the border color is where the two terms cancel each other out. One can see at a glance that as one considers candidates with more matching letters, only lower mutation rates are going to give a good chance of matching all the letters.

And here's the same graph, but with the net 1 expected new incorrect values shifted to black, too, making a contour visible, and showing how the mutation rate interacts with expectations for new candidate strings:

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"You can't teach an old dogma new tricks." - Dorothy Parker

Wesley R. Elsberry

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 (Permalink) Posted: Mar. 25 2009,15:25

"weasel" versus "partitioned search"

I derived an equation for expectation of correct bases following mutation in "weasel" (see above for earlier reference):

 Quote expected correct bases after mutation in "weasel" = C + (u * (L - C) / K) - (u * C * (K - 1) / K)

"Partitioned search" would be the case where:

 Quote expected correct bases after mutation in PS = C + (u * (L - C) / K) - (0 * u * C * (K - 1) / K)= C + (u * (L - C) / K) - 0= C + (u * (L - C) / K)

"Locking" or "latching" is the same as removing the term that allows for correct bases to mutate to incorrect ones. What remains is an expectation that the number of correct bases can only monotonically increase.

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"You can't teach an old dogma new tricks." - Dorothy Parker

Jkrebs

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 (Permalink) Posted: Mar. 25 2009,15:53

Hi.

dvunkannon

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 (Permalink) Posted: Mar. 25 2009,18:49

 Quote (Richardthughes @ Mar. 18 2009,12:24) Can you derive an optimal mutation rate?

Start with an optimal population size. Goldberg's research suggests  N= 1.4L, where L is the length of the problem description (and therefore the population members) in bits. That is a good bit higher than the commonplace 50.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

Wesley R. Elsberry

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 (Permalink) Posted: Mar. 25 2009,18:59

I get N=178 for that. Is that what you get?

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dvunkannon

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 (Permalink) Posted: Mar. 25 2009,20:09

 Quote (Wesley R. Elsberry @ Mar. 25 2009,19:59) I get N=178 for that. Is that what you get?

Yeah, I guessed 27 log 2 was around 4.5 so I got 177.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

dvunkannon

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 (Permalink) Posted: Mar. 26 2009,09:22

Quote (dvunkannon @ Mar. 25 2009,21:09)
 Quote (Wesley R. Elsberry @ Mar. 25 2009,19:59) I get N=178 for that. Is that what you get?

Yeah, I guessed 27 log 2 was around 4.5 so I got 177.

I should mention that most of Goldberg's research is in GAs using only a selection operator and a recombination operator, no mutation. This despite publishing papers (see the "Ready to Rumble" series) that show mutation is the more efficient operator in some broad classes of problems.

Since Weasel is really a (1,n)-ES, not a selectorecombinative GA, that population sizing heuristic might not be completely appropriate. But I don't know of other work with as firm a footing.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

Wesley R. Elsberry

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Joined: May 2002

 (Permalink) Posted: Mar. 26 2009,09:33

While statistically unlikely, successive recombination operations can produce the same changes as point mutation can (this is dependent on having a population with good diversity, of course), so it isn't surprising that recombination might be used as a sole mechanism for change.

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"You can't teach an old dogma new tricks." - Dorothy Parker

Wesley R. Elsberry

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 (Permalink) Posted: Mar. 26 2009,17:23

Avida applied to evolutionary biology

The Beneficial Effect of Deleterious Mutations

If they put something up on the work experimenting to test Sewall Wright's shifting-balance theory, I'll post the link.

Edited by Wesley R. Elsberry on Mar. 27 2009,20:29

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Henry J

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 (Permalink) Posted: Mar. 27 2009,13:28

But wouldn't recombination by itself continually reduce the amount of diversity in the gene pool, and eventually producing a deficit of it?

Henry

Richardthughes

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 (Permalink) Posted: Mar. 27 2009,17:08

Pharyngula on "Weasel":

http://scienceblogs.com/pharyng....put.php

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"You magnificent bastard! " : Louis
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Wesley R. Elsberry

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 (Permalink) Posted: Mar. 27 2009,20:49

 Quote (Henry J @ Mar. 27 2009,13:28) But wouldn't recombination by itself continually reduce the amount of diversity in the gene pool, and eventually producing a deficit of it?Henry

Both genetic drift and natural selection reduce variation, but I wouldn't think it is primarily the choice of mutation modality that affects that.

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"You can't teach an old dogma new tricks." - Dorothy Parker

dvunkannon

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 (Permalink) Posted: Mar. 27 2009,23:40

 Quote (Henry J @ Mar. 27 2009,14:28) But wouldn't recombination by itself continually reduce the amount of diversity in the gene pool, and eventually producing a deficit of it?Henry

Yes, recombination and selection lead to convergence, hopefully on the correct allele. Goldberg's Design of innovation is a great resource on these issues in GAs.

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

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