Yes, biologists can do maths....but approximating solutions would never have gotten man to the moon and neither would probabilities. Sorry...not real science!!!
So what are you saying Wolf? Is evolutionary science like gravitational science? Or are you just here to be a fence sitter and pounce at every opportunity to strutt your stuff?
Wiki: Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying
fitness landscape; this generality is shown by successes in fields as diverse as
engineering,
art,
biology,
economics,
marketing,
genetics,
operations research,
robotics,
social sciences,
physics,
politics and
chemistry[
citation needed].
Apart from their use as mathematical optimizers, evolutionary computation and algorithms have also been used as an experimental framework within which to validate theories about
biological evolution and
natural selection, particularly through work in the field of
artificial life. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of
microevolutionary processes, however some computer simulations, such as
Tierra and
Avida, attempt to model
macroevolutionary dynamics.
In most of real applications of EAs, computational complexity is a prohibiting factor. In fact, this computational complexity is due to fitness function evaluation.
Fitness approximation is one of the solutions to overcome this difficulty.
Another possible limitation of many evolutionary algorithms is their lack of a clear
genotype-phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as
embryogenesis to become a mature phenotype. This indirect
encoding is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the
evolvability of the organism
[1][2]. Such indirect (aka generative or developmental) encodings also enable evolution to exploit the regularity in the environment
[3]. Recent work in the field of
artificial embryogeny, or artificial developmental systems, seeks to address these concerns.
Jukes and Cantor's one-parameter model
JC69 is the simplest of the models of nucleotide substitution.
[1] The model assumes that all nucleotides has the same rate (
μ) of change to any other nucleotides. The probability that any nucleotide
x remains the same from time 0 to time 1 is;
Pxx(1) = 1 − 3μPxx(t) must be read; probability (or proportion, in this case it is equivalent) that
x becomes
x at time
t. For the probability that any nucleotide
x changes to any other nucleotide
y we write
Pxy(t). The probability for time
t + 1 is;
Pxx(t + 1) = (1 − 3μPxx(t) + μ(1 − Pxx(t))The second part of the equation denotes the probability that the nucleotide was changed from time 0 and 1, but then got back to its initial states on time 2. The model can be rewritten in a differential equation with the solution;
Or if we want to know the probability of nuleotide
x to change to nucleotide
y;
With time, the probability will approach 0.25 (25%). Kimura's two-parameters model
Mostly known under the name
K80, this model was developed by Kimura in 1980 as it became clear that all nucleotides substitutions weren't occurring at an equal rate. Most often, transitions (changes between A and G or C and T) are more common than transversions.
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