Re: Can variation and natural selection add or create new
Tue, 24 Aug 1999 16:50:58 EDT

In a message dated 8/21/99 7:12:02 AM Mountain Daylight Time, writes:

> But for starters, I would be happy for Tim to demonstrate how "variation
> and natural selection" can "add or create new information" in the sense
> *Tim himself* understands the term, when he answered his own question
> "Can variation and natural selection add or create new information?" with
> "I think so".

There is a theory of biological information created by Daniel Brooks, Edward
Wiley and John Collier that defines information in the terms of the entropy
of a physical array. It divides biological information into two concepts:
information capacity and information content. Information capacity
represents the total information a particular biological system can possess,
which is usually referred to as the potential diversity of the system. It is
defined as Hmax, the maximal entropy of that system. Information content
represents the actual information possessed by a biological system, which is
usually referred to as realized diversity. If is defined as Hobs, the
observed entropy of the system. A biological system is then made up of a
collection of entities. If the form of diversity that any random entity can
possess is equal probable, then Hobs = Hmax; that is, the realized diversity
of the system is equal to the potential diversity. If, however, there are
certain constraints on the system that make the probablities different for
each form of diversity, then Hobs < Hmax; that is, the realized diversity of
the system is less than the potential diversity. The difference between Hmax
and Hobs then becomes a measure of both the constraints on the system and the
organization within the system. In any event, as the diversity of the system
increases, so does its entropy and thus so does its information content.

As an example, imagine a system consisting of a population of 100 animals.
Within this population let's say that there is a locus on one chromosome that
contains a single allele. We can determine the information capacity of this
system by using the following formula:

Hmax = N k log M

where N is the population size, M is the amount of diversity in the system
(in this case, the number of different genotypes) and k is a constant used to
derive an answer in bits; for our purposes we will ignore it. If a locus has
only a single allele A, then there is only one different genotype possible --
AA. As such, the information capacity of the population for that one locus

Hmax = (100) log 1 = 0.

Now, imagine that at some point one member of the poulation undergoes a
mutation in one of the two copies of allele A that it possesses, making a new
allele B. Let's further assume that this new mutation becomes fixed within
the population. Now the population has 3 different genotypes -- AA, AB, BB
-- and so its information capacity increases to

Hmax = (100) log 3 = 47.7.

Now, imagine that a new allele C is created by mutation and becomes fixed;
this would create 6 different genotypes -- AA, AB, AC, BB, BC, CC -- and
increase information capacity to 77.8. You can see how this trend will
continue to progess: 4 alleles produces 10 different genotypes for an
information capacity of 100; 5 alleles, 15 genotypes, Hmax = 118; 6 alleles,
21 genotypes, Hmax = 132; and so on. As you can see, whenever a mutation
creates a new allele, the information capacity of the system increases,
regardless of whether the mutation increases, decreases or simply reshuffles
the information within the gene itself. In other words, as long as the
mutation increases diversity, even if the new allele is detrimental in
certain genotypical combinations, the information capacity of the system
always increases.

So this is how "variation" (through mutation) "can 'add or create new

But what about natural selection? This is trickier to show, because it
really requires a graph to understand it best. Natural selection is one of
the constraints on the population that prevent it's information content from
becoming equal to the information capacity, or which prevents the realized
diversity from being as great as the potential diversity. Some genotypical
combinations are simply less fit than others, so while the alleles themselves
may be fixed within the population, the probability that a specific genotype
having that allele appearing in a member of the population may be low.
Remember that realized diversity (Hobs) equals potential diversity (Hmax)
only when the probability that a random member of the population will possess
a specific genotype is equally probable for all genotypes. Natural selection
constrains the population so that each genotype has a different probability;
this results in an observed information content (Hobs) that is lower than the
information capacity.

This does not, however, constitute a decrease in information for three
reasons (and this is where the graph would be helpful). First of all, while
Hobs represents less information than Hmax, it does not represent a reduction
in information, because Hobs simply tells you how much of the potential
diversity has been realized by the population. And the purpose of natural
selection is to realize as much of the potential diversity as the environment
and other factors will permit. Hypothetically, a population with 4 alleles
may have a potential diversity of 10 genotypes, but current conditions may
only permit 4 genotypes to predominate. If, however, the conditions change
so that 6 or even 8 genotypes can predominate, natural selection will act to
bring those extra genotypes to prominence. In other words, the potential
diversity may not have changed, but natural selection acted to increase the
realized diversity.

The second reason is much like the first, except that Hobs increases as Hmax
increases. This is because as more potential diversity becomes available,
natural selection uses this to work towards increase the realized diversity
within the constraints imposed by the environment and other factors. The
third reason is that the difference between Hmax and Hobs is a measure of the
information content of the system due to the organization imposed on the
system by the constraints. In essence, it is a measure of the organizing
power of natural selection itself. The greater the difference between the
potential diversity and the realized diversity, the greater the organization,
and hence the greater the information content due to that organization.
Since the sum of the organized information and Hobs must always be equal to
Hmax, organized information can only increase at the expense of realized
diversity, and vice versa, but since natural selection determines both the
amount of realized diversity and the amount of organization, natural
selection can add or create new information regardless of whether it is in
the form of increased realized diversity or increased organization.

In conclusion, Brooks/Wiley/Collier theory provides an answer to the question
of "how 'variation and natural selection' can 'add or create new

Kevin L. O'Brien