Fitness Requires A Constant Frame Of Reference.
John Edser
> Nature 459, 983-986 (18 June 2009) | doi:10.1038/nature08071; Received 13
> January 2009; Accepted 9 April 2009; Published online 27 May 2009
> Adaptation and the evolution of parasite virulence in a connected world
> Geoff Wild 1, Andy Gardner 2 & Stuart A. West 3
> 1.. Department of Applied Mathematics, University of Western Ontario,
> London, Ontario N6A 5B7, Canada
> 2.. Institute of Evolutionary Biology, University of Edinburgh, King's
> Buildings, Edinburgh EH9 3JT, UK
> 3.. Department of Zoology, University of Oxford, Oxford OX1 3PS, UK
> Abstract:
> Adaptation is conventionally regarded as occurring at the level of the
> individual organism, where it functions to maximize the individual's
> inclusive fitness.
JE:-
But individual fitness is not equivalent to inclusive fitness in any
form. Individual fitness, inclusive or not, remains entirely classically
Darwinian, i.e. this key concept of evolutionary theory only allows a
single fitness maximand at just the one level of selection: the fertile
form (parental) level. Any proposed maximand fitness must remain maximal
no-matter-what, i.e. a maximand fitness cannot be validly argued to be
selected to become reduced to something less than it could have been by
simply increasing the levels of selection (as is the case within
Hamilton's rule). A maximand fitness can only be defined within a
falsifiable evolutionary theory as: Total Darwinian Fitness (TDF). This
I define as: the TOTAL number of strictly FERTILE forms reproduced per
parent per population. On no account can TDF be selected to be reduced
to something less than a maximand fitness because reducing TDF means
that parent will be selected against.
Only one, single empirical way exists to 100% halt Darwinian evolution:
force every TDF to remain equivalent for each and every parent within
one natural population for as long as it remains possible to do so.
Inclusive fitness has no such empirical falsification. It was and
remains just a mathematical, polycentric argument. Inclusive fitness
allows more than a single fitness maximand simply by increasing the
level of selection to more than one. Specifically these are three: the
gene, the individual and the group. Hamilton's logic is only
mathematically valid. Inclusive fitness was only possible via firstly
Haldane's and then Hamilton's deletion of all genetic epistasis within
evolutionary theory. Correct this ongoing and simply massive
oversimplification and inclusive fitness ceases to exist, even just
mathematically.
Hamilton's Rule was and remains polycentric because it allows at least
three levels of selection. These are: a portion of the classically
Darwinian individual level of fitness as the donation c, a gene level
determined by r (relatedness at just the gene level) and a classically
group level measured by b. Note that empirically, only ONE of these
levels can possibly remain maximized because two of them r and c remain
SET NESTED, specifically r represents a nested sub fitness of c and not
the reverse. The proposed fitness b only represents the SET INTERSECTION
between Darwinian individuals, i.e. is simply, not the the fitness of
anything.
If K = TDF of the donor (the fitness altruistic individual) then
Hamilton's condition for any individually fitness altruistic gene to
spread (which remains equivalent within Hamilton's mathematics to a
"selfish gene" only because two and not just the one epistatic level of
gene fitness has been mathematically allowed) then Hamilton's Rule
becomes: rb>K-c. IOW, K does not represent a fitness maximand simply
because c (the donation) must be subtracted from it. The fact that this
can even take place within the rule means that K cannot possibly
represent a fitness maximand. Note that no other fitness maximand
replaces K within the rule. The net result of this is that Hamilton's
rule cannot be falsified only because all it contains are fitness
variables. A proposed fitness maximand can only be represented by a
constant. e.g. my proposition of the constant K representing the
falsifiable TDF of the donor representing a fitness frame of reference.
In short, Hamilton's argument was and remains classically post modern,
i.e. he simply deleted any requirement for a fitness constant which is
absolutely required to act as a falsifiable frame of reference for
inclusive fitness.
It was Galileo in the mid 1600's who was the first to prove that just a
bunch of variables, which is all Hamilton's Rule actually is, cannot
prove a thing without at least one defined constant acting as a critical
frame of reference, _even if the variables remain 100% mathematically
valid without a single constant_. What differentiates mathematics from
non mathematics is the proposal of at least one constant. Note that this
is only possible OUTSIDE of mathematics. Mathematics remains incapable
of defining a single constant. What separates just a common belief from
a bona fide theory of science is that at least one proposed constant
within the proposed scientific theory must remain unchanged and
empirically falsifiable.
Regards,
John Edser
Independent Researcher
Perplexed in Peoria
> What differentiates mathematics from
> non mathematics is the proposal of at least one constant. Note that this
> is only possible OUTSIDE of mathematics. Mathematics remains incapable
> of defining a single constant.
I'm pretty sure it can define one.
Entertained by my own EIMC Internetional Ptd. Lty.
countability) just for the sake of counting.
The word (concept) fitness may allow us to more realistically reflect on, or
to better focus on the fact, that from single-celled to complex
multicellular biological systems of functures (functional structures)
sometimes function in ways that more or less directly or indirectly promote
their procreative potential to the point of reproductive success.
Or, more specifically, it might funnel our attention onto facets of our and
our ancestors' existence from where there is self-insights and
social-insights to be had by indentifying traits that have promoted, and
still promote, the reproductive survival of individual cellular systems'
such as - not least importantly ;-) - us *human* individuals.