Nonsynonymous to Synonymous Substitution Ratio ka/ks:
Measurement for Rate of Evolution in Evolutionary Computation
Ting Hu & Wolfgang Banzhaf
{tingh, banzhaf} @ cs.mun.ca
Memorial University of Newfoundland, Canada
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Abstract
we define the rate of evolution Re in an EC system based on
the rate of efficient genetic variations being accepted by the
E C p o p u l a t i o n . T h i s d e f i ni t i on is m otiv ate d b y th e
measurement of “amino acid to synonymous substitution ratio”
ka/ks in biology, which has been widely accepted to measure
the rate of gene sequence evolution. Experimental applications
to investigate the effects of four major configuration
parameters on our rate of evolution measurement show that Re
well reflects how evolution proceeds underneath fitness
function development and provides some insights into the
effectiveness of EC parameters in evolution acceleration.
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Simulation
A tree-based GP system for instance.
Quintic polynomial symbolic regression: f ( x) = x
z Truncation selection scheme
z Sub-tree replacement crossover/mutation
A) For a single run
Measure evolution rate of gene sequences
Biologists compare two homologous gene sequences
From two related species to measure evolution rate.
glutamine
lysine
lysine
B) Parameter comparison
z
Population size
z
Tournament selection size
z
Mutation rate
z
Crossover rate
(amino acids)
Gene sequence 1 : … … CAG … … AAA … … AAA … ...
Gene sequence 2 : … … CAG … … AAG … … AAT … ...
glutamine
lysine
aspartic
(amino acids)
Synonymous Nonsynonymous
substitution
substitution
ka : the number of nonsynonymous substitutions per site
(adaptive evolution rate)
ks : the number of synonymous substitutions per site
(background evolution rate)
ka / ks measures evolution rate!
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Measure evolution rate in EC
Similarity in EC individuals:
z
z
Not all genetic changes will be accepted
Two types of genetic substitutions
-- synonymous & nonsynonymous
Evolution rate Re definition:
The rate of genetic changes being accepted.
Measure Re :
For an EC population from generation t to t+1,
Ma(t) :
Ms(t) :
Na(t) :
Ns(t) :
number of nonsynonymous substitutions
number of synonymous substitutions
total nonsynonymous sensitivity (sites)
total synonymous sensitivity (sites)
ka(t) = Ma(t)/Na(t) : nonsynonymous substitution rate
ks(t) = Ms(t)/Ns(t) : synonymous substitution rate
Re(t) = ka(t)/ks(t): evolution rate
5
−
2 x3 + x