Re: 2. Nested Verses Intersecting Sets of Fitness
- From: John Edser <edser@xxxxxxxxxxxxxx>
- Date: Thu, 9 Apr 2009 13:35:26 -0400 (EDT)
Hi John,
Again I don't fully understand what you are saying but my main,
immediate concern is to try to grasp the possible relationship between
your perspective on evolution ond my own, which is bioepistemic
evolution.
Bioepistemic evolution is a multilevel selection scheme, though I use
the word rank to avoid the rather arbitrary definitions of levels that
are sometimes used in the scientific literature. There are five ranks
to bioepistemic evolution, running from rank0 to rank4 - in sequence
they are prebiotic evolution and the origin of life, genetic evolution
based on nucleotide base sequence data, darwinian machines, associated
with the brain and sense organs and the origin of sensory knowledge,
social evolution, where the selecting agent deliberately transmits
information to another group member and the origin of social
knowledge, such as language, and selection via agreed codes, which is
evolution as the origin of knowledge validated through those agreed
codes.
JE:-
Hi John H,
What you may need to address more specifically are the fitness
relationships between your proposed five levels. I argue that only two
basic i.e. 100% contradictory fitness relationships can be defined:
1) Fitness Dependent: which is always in the form of a single nested
set. This can be represented as a single set of concentric circles such
that each nested circle represents one dependently associated fitness
within a nested set of fitnesses. In your case all or some of the
proposed 5 levels remain dependent on the largest (undefined by you)
concentric circle which can alone represent the most significant
fitness. It should be apparent that nested associated sets cannot be
reversed, i.e. their order cannot be changed. If A is nested subset of B
then B cannot be a nested subset of A. To be able to select any one set
ALL of them have to be selected via just the fitness of largest set.
IOW, a nested set can only have ONE fitness via which everything in each
set can be selected.
2) Fitness independent: associated fitnesses which only intersect, i.e.
they cannot be described as one nested set of circles but as a number of
reversibly intersected and therefore fitness independent circles as
described by a Venn diagram. Set intersection is a much more simple
relationship because it remains reversible: if A intersects B then B
intersects A allowing either to be selected independent of the other.
Contrast this with nested sets: If A is a nested subset of B then B
cannot be a nested subset of A. Here, if you want to select A then you
can only do this by selecting B. IOW, they cannot be selected
independent of each other. Their difference with regards to selection
could not be more stark.
IF we begin discussion with your 5th level "social evolution" you will
have to define social relationships as EITHER fitness dependent or
fitness independent because they cannot be both.
These various levels are designed so that they necessarily run
in temporal sequence and are differentiated by the type and source of
data input used by the evolving system in question and by the location
and nature of the selective agent involved.
Incidentally, because of its relationship to my own work, I have
thought about this question of nesting but I currently lean to the
view that I do not think the ranks of evolution I describe can be
entirely nested - even though I do think that they can be treated as
being approximately nested for some purposes.
JE:
Nesting is a bit like pregnancy: either you are or you are not,
pregnant. IOW set nesting presents an out-of-fashion "black and white"
proposition. In today's Post Modern world everything is supposed to
remain gray. This is mostly because of a gross misuse mathematics.
What I want to elicit from you is the relationship between the kind of
rank ordering that I describe in bioepistemic evolution and the
selection scheme implicit in your own nested sets. You seem to be
saying, as do I and several other people, that evolutionary data
processes can be can be arranged into some sort of hierarchy
Nested sets of fitness remain IRREVERSIBLY hierarchic simply because
circles within the same nested set cannot be of the same same size. OTOH
intersecting sets can be the same size and can form entirely REVERSIBLE
hierarchies. Intersecting sets of fitness remain critically independent
of each other. Nested sets can be characterized as "multiplicative"
whereas intersecting sets are more simply, "additive". Empirically,
multiplication is not the same as addition. In mathematics
multiplication has become oversimplified to become equal with addition
via the commutative law which simply disregards the non reversible
nature of nested sets.
The
problem I am trying to get clear about is the definition of your
hierarchy and how you apply that to understanding the real world
products of evolution.
I propose that each Darwinian unit of selection, i.e. each parent
is comprised of _a single nested hierarchy of fitnesses_. This can be
represented as a single set of concentric circles in which each circle
presents a non reversible hierarchical fitness for each body part. The
SMALLEST nested circle represents genetic fitness, i.e. genes represent
the smallest body part which has a dependent fitness. OTOH a Darwinian
evolving population of contesting parents represents the set
intersection of the total fitness of each and every organism parent
within the same population, i.e. the 100% set intersection of just the
largest (most outer) circle of each parental nested set of fitnesses.
This alone contains all the nested (fitness dependent body parts) of
each parent. Only the largest circle can validly represent the total
fitness of each Darwinian selectee _and all of its parts_. It should be
apparent that once completed the number of adult forms reproduced by
each parent stands as a constant for all time. This allows TDF to act as
THE critical fitness falsifiable frame of reference for Darwinism.
I would like to know how many levels of nesting you need for human
evolution and how you define the boundaries around each of your nested
sets.
JE:-
Empirically, we simply don't know. However if nested fitnesses remain
non differentiated from intersecting fitness within Neo Darwinistic
models then nobody will even think to look.
As a MINIMAL model I propose a population comprised of two competing
adult forms, i.e. two nested sets of fitness where the the number of
nested sets of fitness in each adult remains the same. In this minimal
population only the two largest (outermost)circles representing TDF 100%
intersect allowing the natural selection of the largest within that
population.
Also, I would like to know how you approach the definition of
the separate elements that exist within each of those sets; it occurs
to me that these elements might include the units of selection, which
you mention; they might also include describing the fundamental data
processes that are applicable to each level, though in the latter case
I would not be comfortable with describing a data process as an
element in a set.
JE:-
In my proposed minimal nested model each nested set is comprised of only
three nested fitnesses. These are, in the order of smallest to largest:
1) Genetic fitness
2) Organism fitness
3) TDF (total Darwinian Fitness)
Note that TDF is a "data" process.
Finally, I would note that your comments about Hamilton did not
identify any specific, biological phenomena that could be interpreted
by your proposal but which were incompatible with the conventional,
competing alternatives.
JE:-
Using my minimal nested model, Hamilton only describes two intersecting
sets of fitnesses i.e. not three nested fitnesses: a genetic fitness
intersecting with an organism fitness allowing both to remain fitness
independent. In Hamilton's case the fitness of genes is allowed as
independent of the fitness of the body it remains within. Empirically,
all fitnesses are epistatic, i.e. remain multiplicative and additive.
This being the case any one gene fitness must remain a part of a nested
set of fitnesses i.e. they cannot lust intersect with the body fitness
they are within as Hamilton supposed. Gene fitnesses must remain nested
within body fitnesses OR the reverse. Empirically, the fitness of any
one gene remains nested within the fitness if the body it finds itself
within. The fact that genes can independently segregate at meiosis does
NOT allow Hamilton's model of independent gene fitness association
allowing "selfish genes" to provide fertile organism fitness altruism
via just a mythical selected reduction in TDF.
Regards,
John Edser
Independent Researcher
.
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