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  Topic: Evolutionary Computation, Stuff that drives AEs nuts< Next Oldest | Next Newest >  
Wesley R. Elsberry



Posts: 4504
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: 4504
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: 4504
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: 10227
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: 4504
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.

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

    
Wesley R. Elsberry



Posts: 4504
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 = 0.00000

1000 runs, N=50, u=0.05000, K=27, C=0, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.00000

1000 runs, 01 correct : p_c2c calc = 0.95185, MC = 0.93800; p_c2i calc = 0.04815, MC = 0.06200

1000 runs, N=50, u=0.05000, K=27, C=1, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.04726

1000 runs, 02 correct : p_c2c calc = 0.90602, MC = 0.90400; p_c2i calc = 0.09398, MC = 0.09600

1000 runs, N=50, u=0.05000, K=27, C=2, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.09476

1000 runs, 03 correct : p_c2c calc = 0.86240, MC = 0.85900; p_c2i calc = 0.13760, MC = 0.14100

1000 runs, N=50, u=0.05000, K=27, C=3, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.13592

1000 runs, 04 correct : p_c2c calc = 0.82088, MC = 0.82400; p_c2i calc = 0.17912, MC = 0.17600

1000 runs, N=50, u=0.05000, K=27, C=4, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.17810

1000 runs, 05 correct : p_c2c calc = 0.78135, MC = 0.80400; p_c2i calc = 0.21865, MC = 0.19600

1000 runs, N=50, u=0.05000, K=27, C=5, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.21618

1000 runs, 06 correct : p_c2c calc = 0.74373, MC = 0.75900; p_c2i calc = 0.25627, MC = 0.24100

1000 runs, N=50, u=0.05000, K=27, C=6, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.25848

1000 runs, 07 correct : p_c2c calc = 0.70792, MC = 0.74400; p_c2i calc = 0.29208, MC = 0.25600

1000 runs, N=50, u=0.05000, K=27, C=7, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.29226

1000 runs, 08 correct : p_c2c calc = 0.67384, MC = 0.67200; p_c2i calc = 0.32616, MC = 0.32800

1000 runs, N=50, u=0.05000, K=27, C=8, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.32460

1000 runs, 09 correct : p_c2c calc = 0.64139, MC = 0.62100; p_c2i calc = 0.35861, MC = 0.37900

1000 runs, N=50, u=0.05000, K=27, C=9, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.36086

1000 runs, 10 correct : p_c2c calc = 0.61051, MC = 0.61000; p_c2i calc = 0.38949, MC = 0.39000

1000 runs, N=50, u=0.05000, K=27, C=10, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.38966

1000 runs, 11 correct : p_c2c calc = 0.58112, MC = 0.59500; p_c2i calc = 0.41888, MC = 0.40500

1000 runs, N=50, u=0.05000, K=27, C=11, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.42060

1000 runs, 12 correct : p_c2c calc = 0.55314, MC = 0.54600; p_c2i calc = 0.44686, MC = 0.45400

1000 runs, N=50, u=0.05000, K=27, C=12, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.44794

1000 runs, 13 correct : p_c2c calc = 0.52650, MC = 0.52000; p_c2i calc = 0.47350, MC = 0.48000

1000 runs, N=50, u=0.05000, K=27, C=13, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.47050

1000 runs, 14 correct : p_c2c calc = 0.50115, MC = 0.50900; p_c2i calc = 0.49885, MC = 0.49100

1000 runs, N=50, u=0.05000, K=27, C=14, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.50130

1000 runs, 15 correct : p_c2c calc = 0.47702, MC = 0.45800; p_c2i calc = 0.52298, MC = 0.54200

1000 runs, N=50, u=0.05000, K=27, C=15, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.51658

1000 runs, 16 correct : p_c2c calc = 0.45406, MC = 0.48200; p_c2i calc = 0.54594, MC = 0.51800

1000 runs, N=50, u=0.05000, K=27, C=16, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.54270

1000 runs, 17 correct : p_c2c calc = 0.43219, MC = 0.41800; p_c2i calc = 0.56781, MC = 0.58200

1000 runs, N=50, u=0.05000, K=27, C=17, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.56708

1000 runs, 18 correct : p_c2c calc = 0.41139, MC = 0.41200; p_c2i calc = 0.58861, MC = 0.58800

1000 runs, N=50, u=0.05000, K=27, C=18, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.59218

1000 runs, 19 correct : p_c2c calc = 0.39158, MC = 0.35000; p_c2i calc = 0.60842, MC = 0.65000

1000 runs, N=50, u=0.05000, K=27, C=19, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.61070

1000 runs, 20 correct : p_c2c calc = 0.37272, MC = 0.37200; p_c2i calc = 0.62728, MC = 0.62800

1000 runs, N=50, u=0.05000, K=27, C=20, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.62762

1000 runs, 21 correct : p_c2c calc = 0.35478, MC = 0.33300; p_c2i calc = 0.64522, MC = 0.66700

1000 runs, N=50, u=0.05000, K=27, C=21, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.64048

1000 runs, 22 correct : p_c2c calc = 0.33770, MC = 0.32200; p_c2i calc = 0.66230, MC = 0.67800

1000 runs, N=50, u=0.05000, K=27, C=22, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.66146

1000 runs, 23 correct : p_c2c calc = 0.32144, MC = 0.31500; p_c2i calc = 0.67856, MC = 0.68500

1000 runs, N=50, u=0.05000, K=27, C=23, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.67854

1000 runs, 24 correct : p_c2c calc = 0.30596, MC = 0.28900; p_c2i calc = 0.69404, MC = 0.71100

1000 runs, N=50, u=0.05000, K=27, C=24, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.69380

1000 runs, 25 correct : p_c2c calc = 0.29123, MC = 0.28000; p_c2i calc = 0.70877, MC = 0.72000

1000 runs, N=50, u=0.05000, K=27, C=25, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.70792

1000 runs, 26 correct : p_c2c calc = 0.27721, MC = 0.27700; p_c2i calc = 0.72279, MC = 0.72300

1000 runs, N=50, u=0.05000, K=27, C=26, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.72154

1000 runs, 27 correct : p_c2c calc = 0.26386, MC = 0.23500; p_c2i calc = 0.73614, MC = 0.76500

1000 runs, N=50, u=0.05000, K=27, C=27, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.73644

1000 runs, 28 correct : p_c2c calc = 0.25116, MC = 0.24500; p_c2i calc = 0.74884, MC = 0.75500

1000 runs, N=50, u=0.05000, K=27, C=28, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion 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 = 0.00000

1000 runs, N=12, u=0.18000, K=27, C=0, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.00000

1000 runs, 01 correct : p_c2c calc = 0.82667, MC = 0.82700; p_c2i calc = 0.17333, MC = 0.17300

1000 runs, N=12, u=0.18000, K=27, C=1, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.17058

1000 runs, 02 correct : p_c2c calc = 0.68338, MC = 0.69300; p_c2i calc = 0.31662, MC = 0.30700

1000 runs, N=12, u=0.18000, K=27, C=2, p_pop_c2c calc = 1.00000, MC = 1.00000
Proportion of candidates w/C2I bases = 0.32233

1000 runs, 03 correct : p_c2c calc = 0.56493, MC = 0.56600; p_c2i calc = 0.43507, MC = 0.43400

1000 runs, N=12, u=0.18000, K=27, C=3, p_pop_c2c calc = 0.99995, MC = 1.00000
Proportion of candidates w/C2I bases = 0.44117

1000 runs, 04 correct : p_c2c calc = 0.46701, MC = 0.48600; p_c2i calc = 0.53299, MC = 0.51400

1000 runs, N=12, u=0.18000, K=27, C=4, p_pop_c2c calc = 0.99947, MC = 1.00000
Proportion of candidates w/C2I bases = 0.53508

1000 runs, 05 correct : p_c2c calc = 0.38606, MC = 0.39800; p_c2i calc = 0.61394, MC = 0.60200

1000 runs, N=12, u=0.18000, K=27, C=5, p_pop_c2c calc = 0.99713, MC = 0.99700
Proportion of candidates w/C2I bases = 0.61167

1000 runs, 06 correct : p_c2c calc = 0.31914, MC = 0.32100; p_c2i calc = 0.68086, MC = 0.67900

1000 runs, N=12, u=0.18000, K=27, C=6, p_pop_c2c calc = 0.99008, MC = 0.99200
Proportion of candidates w/C2I bases = 0.67967

1000 runs, 07 correct : p_c2c calc = 0.26382, MC = 0.25100; p_c2i calc = 0.73618, MC = 0.74900

1000 runs, N=12, u=0.18000, K=27, C=7, p_pop_c2c calc = 0.97466, MC = 0.97200
Proportion of candidates w/C2I bases = 0.73475

1000 runs, 08 correct : p_c2c calc = 0.21809, MC = 0.23600; p_c2i calc = 0.78191, MC = 0.76400

1000 runs, N=12, u=0.18000, K=27, C=8, p_pop_c2c calc = 0.94778, MC = 0.95500
Proportion of candidates w/C2I bases = 0.78383

1000 runs, 09 correct : p_c2c calc = 0.18029, MC = 0.19100; p_c2i calc = 0.81971, MC = 0.80900

1000 runs, N=12, u=0.18000, K=27, C=9, p_pop_c2c calc = 0.90797, MC = 0.91400
Proportion of candidates w/C2I bases = 0.81492

1000 runs, 10 correct : p_c2c calc = 0.14904, MC = 0.16000; p_c2i calc = 0.85096, MC = 0.84000

1000 runs, N=12, u=0.18000, K=27, C=10, p_pop_c2c calc = 0.85582, MC = 0.85600
Proportion of candidates w/C2I bases = 0.85667

1000 runs, 11 correct : p_c2c calc = 0.12321, MC = 0.12900; p_c2i calc = 0.87679, MC = 0.87100

1000 runs, N=12, u=0.18000, K=27, C=11, p_pop_c2c calc = 0.79357, MC = 0.78600
Proportion of candidates w/C2I bases = 0.88083

1000 runs, 12 correct : p_c2c calc = 0.10185, MC = 0.09800; p_c2i calc = 0.89815, MC = 0.90200

1000 runs, N=12, u=0.18000, K=27, C=12, p_pop_c2c calc = 0.72446, MC = 0.72100
Proportion of candidates w/C2I bases = 0.89900

1000 runs, 13 correct : p_c2c calc = 0.08420, MC = 0.08100; p_c2i calc = 0.91580, MC = 0.91900

1000 runs, N=12, u=0.18000, K=27, C=13, p_pop_c2c calc = 0.65196, MC = 0.66100
Proportion of candidates w/C2I bases = 0.91458

1000 runs, 14 correct : p_c2c calc = 0.06960, MC = 0.07600; p_c2i calc = 0.93040, MC = 0.92400

1000 runs, N=12, u=0.18000, K=27, C=14, p_pop_c2c calc = 0.57925, MC = 0.55400
Proportion of candidates w/C2I bases = 0.93192

1000 runs, 15 correct : p_c2c calc = 0.05754, MC = 0.06100; p_c2i calc = 0.94246, MC = 0.93900

1000 runs, N=12, u=0.18000, K=27, C=15, p_pop_c2c calc = 0.50891, MC = 0.50000
Proportion of candidates w/C2I bases = 0.94333

1000 runs, 16 correct : p_c2c calc = 0.04756, MC = 0.03900; p_c2i calc = 0.95244, MC = 0.96100

1000 runs, N=12, u=0.18000, K=27, C=16, p_pop_c2c calc = 0.44278, MC = 0.45400
Proportion of candidates w/C2I bases = 0.95083

1000 runs, 17 correct : p_c2c calc = 0.03932, MC = 0.03800; p_c2i calc = 0.96068, MC = 0.96200

1000 runs, N=12, u=0.18000, K=27, C=17, p_pop_c2c calc = 0.38206, MC = 0.38200
Proportion of candidates w/C2I bases = 0.96183

1000 runs, 18 correct : p_c2c calc = 0.03250, MC = 0.03600; p_c2i calc = 0.96750, MC = 0.96400

1000 runs, N=12, u=0.18000, K=27, C=18, p_pop_c2c calc = 0.32736, MC = 0.32200
Proportion of candidates w/C2I bases = 0.96875

1000 runs, 19 correct : p_c2c calc = 0.02687, MC = 0.03200; p_c2i calc = 0.97313, MC = 0.96800

1000 runs, N=12, u=0.18000, K=27, C=19, p_pop_c2c calc = 0.27881, MC = 0.25300
Proportion of candidates w/C2I bases = 0.97600

1000 runs, 20 correct : p_c2c calc = 0.02221, MC = 0.02000; p_c2i calc = 0.97779, MC = 0.98000

1000 runs, N=12, u=0.18000, K=27, C=20, p_pop_c2c calc = 0.23629, MC = 0.23400
Proportion of candidates w/C2I bases = 0.97817

1000 runs, 21 correct : p_c2c calc = 0.01836, MC = 0.01800; p_c2i calc = 0.98164, MC = 0.98200

1000 runs, N=12, u=0.18000, K=27, C=21, p_pop_c2c calc = 0.19941, MC = 0.19100
Proportion of candidates w/C2I bases = 0.98308

1000 runs, 22 correct : p_c2c calc = 0.01518, MC = 0.01600; p_c2i calc = 0.98482, MC = 0.98400

1000 runs, N=12, u=0.18000, K=27, C=22, p_pop_c2c calc = 0.16769, MC = 0.17300
Proportion of candidates w/C2I bases = 0.98458

1000 runs, 23 correct : p_c2c calc = 0.01255, MC = 0.00600; p_c2i calc = 0.98745, MC = 0.99400

1000 runs, N=12, u=0.18000, K=27, C=23, p_pop_c2c calc = 0.14061, MC = 0.15400
Proportion of candidates w/C2I bases = 0.98617

1000 runs, 24 correct : p_c2c calc = 0.01037, MC = 0.01400; p_c2i calc = 0.98963, MC = 0.98600

1000 runs, N=12, u=0.18000, K=27, C=24, p_pop_c2c calc = 0.11762, MC = 0.11200
Proportion of candidates w/C2I bases = 0.99042

1000 runs, 25 correct : p_c2c calc = 0.00858, MC = 0.00600; p_c2i calc = 0.99142, MC = 0.99400

1000 runs, N=12, u=0.18000, K=27, C=25, p_pop_c2c calc = 0.09819, MC = 0.10400
Proportion of candidates w/C2I bases = 0.99075

1000 runs, 26 correct : p_c2c calc = 0.00709, MC = 0.01200; p_c2i calc = 0.99291, MC = 0.98800

1000 runs, N=12, u=0.18000, K=27, C=26, p_pop_c2c calc = 0.08183, MC = 0.08000
Proportion of candidates w/C2I bases = 0.99283

1000 runs, 27 correct : p_c2c calc = 0.00586, MC = 0.00700; p_c2i calc = 0.99414, MC = 0.99300

1000 runs, N=12, u=0.18000, K=27, C=27, p_pop_c2c calc = 0.06810, MC = 0.07400
Proportion of candidates w/C2I bases = 0.99358

1000 runs, 28 correct : p_c2c calc = 0.00484, MC = 0.00600; p_c2i calc = 0.99516, MC = 0.99400

1000 runs, N=12, u=0.18000, K=27, C=28, p_pop_c2c calc = 0.05661, MC = 0.04400
Proportion 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: 4504
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:




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

    
dvunkannon



Posts: 1377
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知 referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I知 not an evolutionist, I知 a change in allele frequentist! - Nakashima

  
Wesley R. Elsberry



Posts: 4504
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: 1377
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.

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

  
Wesley R. Elsberry



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(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



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(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知 referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I知 not an evolutionist, I知 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.

--------------
"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:



--------------
"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.

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

  
Wesley R. Elsberry



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Joined: May 2002

(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.

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

  
dvunkannon



Posts: 1377
Joined: June 2008

(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.

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

  
Wesley R. Elsberry



Posts: 4504
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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"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
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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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Joined: June 2008

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

  
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