In this lecture we will see how 
algorithmic probability can also shed light

on certain aspects of biological evolution

and how numerical results from the natural case

can be translated to optimization 
methods for artificial evolution

in techniques such as genetic 
and evolutionary algorithms.

Central to modern biological evolutionary theory
is the understanding that evolution is gradual

and is explained by some small genetic changes 
in large populations over time.

Genetic variation is commonly thought
to arise by chance, through mutation,

with small changes leading to major
evolutionary changes over time

when such changes provide 
some evolutionary advantage.

Often of interest in connection 
to the possible links

between the theory of biological evolution
and the theory of information

is the place and role 
of randomness in the process

that provides the variety necessary
to allow organisms to change and adapt.

Natural selection explains 
how life has evolved

over millions of years 
from more primitive forms.

The speed at which this happens, however,
has sometimes defied formal explanations

when based on random, uniformly distributed mutations.

The common creationist 
argument, for example,

is that there is no way to achieve
the level of design of an organism

by accumulation of random modifications.

But if one considers that mutations
are perturbations from the environment,

then it is clear that 
they may not distribute uniformly

and not be completely random.

So not all mutations 
would be equally probable.

In fact, this is already known in biology.

Not all DNA segments 
or regions in the genome

suffer the same rate of mutation.

And even in a person's lifetime,

mutation rates are very different.

So to explore mutation distributions
different from uniform distributions

should not be or come as a surprise.

It is not difficult to see how organisms

interacting with each other

is some sort of process that may be 
related to the universal distribution

if DNA is thought as living in software space,

with mutations actually algorithmic perturbations

something previously suggested by people

such as Gregory Chaitin himself
and his metabiology

and also by Stephen Wolfram.

What if we assumed that mutations 
are not uniformly distributed

but distributed with a strong 
algorithmic simplicity bias

if DNA is in this software space?

What would happen if we study evolution
from that point of view?

Here you have the way 
in which we performed an experiment

following a pipeline

in which we introduced 
the universal distribution

into the way in which mutation 
changes software such as DNA.

So before applying a mutation, 
we simulate every possible single-point mutation

and find which one would be the most simple,

according to algorithmic probability 
measured by BDM.

and then that would be the mutation
that we keep to the next generation.

Of course in reality, 
natural evolution mutations 
may not apply in this way,

but because mutations would not
be drawn from a uniform distribution,

they would come from something 
related to the universal distribution

so they don't have to be simulated 
and tested beforehand.

They are naturally favoured.

Results both on synthetic 
and on small biological examples

indicate an accelerated rate of convergence, 
evolutionary convergence,

when mutations are 
not statistically uniform

but algorithmically uniform,

that is, mutations distributed
according to the universal distribution.

We have also shown that algorithmic distributions 
can evolve modularity and genetic memory

because some structures of low complexity
will be preserved and carried over time,

creating batches of lower randomness,
sometimes living to an accelerated production of diversity,

but also to population extinctions,
because by following the universal distribution,

low complexity modules 
are unable to adapt fast enough,

thereby possibly explaining 
naturally occurring phenomena

such as diversity explosions as it happened
in, for example, the Cambrian period.

And massive extinctions 
such as the end Triassic,

whose origins are currently 
a cause for debate.

Here's an example of this speedup phenomena

with mutations following 
a universal distribution

when evolving a graph that is chasing
a non-random growing graph

such as a Zay-Kay graph that we saw 
in the last unit and several before.

But also the simple structures 
like kauri trees and stars.

Introducing a simplicity bias 
is thus translated

into a faster evolutionary convergence.

Graphs require way less number
of steps to reach those graphs

when applying algorithmic mutation

than when applying 
uniform distributed mutations.

Furthermore, introducing this bias

translates into being able to find
differentiated evolutionary pathways

with differing weights among genes,

which turn out to be 
commonly associated to cancer

in a well-known biological network.

This is because now not all 
evolutionary paths have the same weight

or have the same probability.

Some will be more likely according 
to the universal distribution mutations than others.

So the natural approach 
that we have introduced

appears to be a good approximation

to what we observe in biological evolution

than models based exclusively on random 
uniform mutations, for various reasons.

And it's also natural because those random mutations
are known to be not completely random

but the effect of different causes, which,
if they are thought to the algorithmic in a new way,

then they should obey algorithmic probability 
and be related to the universal distribution.

The results also validate 
suggestions in the direction

that computation may be an equally 
important driver of evolution.

We also show that inducing the method
and problems of optimization, such as genetic algorithms,

our approach has the potential to accelerate 
convergence in artificial evolutionary algorithms.

Finally, to show that these results could be translated back 
into the way we solve problems by algorithmic means,

we tested whether we could speed up 
evolutionary programming in specific examples

using, for example, a genetic 
algorithm, using the same ideas,

that is, drawing mutations from 
universal distribution instead of uniform.

What we found is that for 
classical benchmark experiments

convergence results using genetic 
algorithms were significantly sped up,

thereby strengthening what 
we also think underlies nature itself,

that it doesn't draw mutation 
from uniform distributions.

So the concept behind is that if you're trying
to approximate something that is far from random,

which organisms under environments are,

then mutations biased toward 
algorithmic simplicity will give you an edge.

And it is very likely that this mechanism is
in operation for natural algorithmic causes

and the way in which evolution 
drives biological creativity.

Our results also provide a formal framework

and a version of open-ended 
evolution based on these ideas.

Open-ended evolution is somehow the idea 
that evolution never ends and has no objective,

so it keeps changing over time 
as it is necessary.

Here is some bibliography 
about this subject from our group.

I am sure you would have 
never guessed how, for example,

the BCB (ph) which I think is a mega number

would be connected whatsoever 
to biological evolution,

but this is just a taste of how we have connected
these apparently disparate ideas

into a very beautiful and elegant theory.

In the next unit we will see an application 
of logical depth into image classification.