Text 979, 175 rader
Skriven 2004-12-10 21:34:00 av Perplexed In Peoria (1:278/230)
Ärende: Re: The "fuel" of evoluti
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"William Morse" <wdmorse@twcny.rr.com> wrote in message
news:cp67ut$2uf0$1@darwin.ediacara.org...
> "Perplexed in Peoria" <jimmenegay@sbcglobal.net> wrote in
> news:cp5748$2jln$1@darwin.ediacara.org:
>
> >
> > "William Morse" <wdmorse@twcny.rr.com> wrote in message
> > news:cp0pte$1909$1@darwin.ediacara.org...
> >> an588@freenet.carleton.ca (Catherine Woodgold) wrote in
> >> news:coebn4$1m2i$1@darwin.ediacara.org:
> >>
> >> > phillip smith (deletethis-phills@ihug.co.nz) writes:
> >> >> I should have said I am working on a replacement for fitness( see
> >> >> reply to JE). I think fitness has fatal errors. We keep using it
> >> >> because we have had no choice. Not that I am sure I an do better.
> >> >
> >> > Here is a definition of the fitness of a given gene in context.
> >> > For this definition to make sense, I assume a multiple-universe
> >> > model:  that due to quantum-mechanical fluctuations, a given
> >> > universe at a given point in time develops into multiple future
> >> > versions (possbilities), over which a meaningful probability metric
> >> > can be defined.
> >> >
> >> > Consider a gene A in a particular individual X in a particular
> >> > environment.  Consider also all the copies of gene A, for
> >> > example in siblings, cousins, and other members of the population.
> >> >
> >> > Consider the universe U containing individual X.  Consider also
> >> > the fictional universe U-prime which is exactly like U except that
> >> > individual X does not exist.
> >> >
> >> > Go forward in time 5 generations, and count up
> >> > the average number of copies of gene A in the population, averaged
> >> > over the alternate universes with a probabilistic weighting.
> >> >
> >> > The fitness of gene A in individual X is the average number
> >> > of copies of A in the futures of universe U, minus the average
> >> > number of copies of A in the futures of universe U-prime.
> >> > Descendents of cousins etc. are also included in the count.
> >>
> >> That's a great definition - up to 5 generations. What happens if all
> >> the descendants at 6 generations die without issue? Is the fitness 0,
> >> or do we have an arbitrary cutooff at 4 generations?
> >>
> >> So what we would like to have is a definition that, like yours, takes
> >> into account alternate future environments, but that can be extended
> >> farther into the future. I have a rather fuzzy mathematical intuition
> >> that if you somehow combine Markov chains with a discount factor for
> >> expected future gains you might come up with a reasonable
> >> approximation of a fitness function - recognising that fitness is
> >> always going to be ultimately only definable in retrospect.
> >
> > I think that you are on the wrong track with your talk of a "discount
> > factor".  It seems to me that what we have are a sequence of fitness
> > definitions.  There is first the traditional simple one-generation
> > definition - count direct offspring (with a factor of 1/2 if the
> > organism is sexual).  Then there is the two-generation definition -
> > count grand children, then take the square root to get average growth
> > per generation.  Take the cube root for the three-generation
> > definition.  And so on.  Now, once you have this infinite sequence of
> > fitness
> > numbers, you may wish to take some kind of weighted average.  Perhaps
> > that is what you mean by a discount factor - you intend to give the
> > greatest weight to the short term fitness numbers.  But, depending on
> > your application, there may be some reason to use some other
> > "envelope" rather than an exponentially declining one.
> >
> > In economics, a "discount factor" is used to come up with a "current
> > value" of some infinite stream.  But if you recall that any fitness
> > must be some kind of growth rate per unit time, you will realize that
> > the growth *rate* is automatically finite, even if the growth is
> > unbounded.
>
> (Josh - sorry for not abbreviating the post, but I wanted to leave in the
> original spark for my suggestion)
>
> [moderator's note: Cool dat. - JAH]
>
> What I was trying to get at was how to make a reasonable approximation of
> current fitness given that the future is uncertain - which was in
> response to Catherine Woodgold's interesting idea to try to use multiple-
> universe models to calculate a fitness value.
>
> Future uncertainty, in my limited understanding of economics, is what the
> discount factor is for. Even with zero inflation, a dollar tomorrow is
> not worth a dollar today. If it were, banks would charge you a fixed fee
> rather than compound interest for a loan. Markov chains alone do not
> provide for this - they only provide a prediction for expected future
> variation - and it is the unexpected future variation (an asteroid
> impact, the evolution of flight) that cheapens the current value of
> future fitness.
>
> Catherine Woodgold chose an arbitrary cut-off point of 5 generations, and
> this may in fact be a valid way of "discounting" future fitness - the
> additional fitness after 5 generations may in general be minimal. I think
> this ignores the very high fitness associated with certain phenotypes,
> e.g. flying ability or eusocialism, which is why I suggested a discount
> rate. Now I was not thinking of fitness as a growth rate, and perhaps I
> should be, but I still don't see how that resolves the problem of
> incorporating future uncertainty into a current measure. As Guy noted in
> another follow, fitness is not really a measurable quantity so much as a
> concept useful in modeling evolution. I believe it is grounded in reality
> but, as I noted above, can only really be measured in retrospect. I also
> believe that defining fitness only over the short term is not
> particularly helpful in understanding evolution, so it is worthwhile to
> try to develop a definition that takes into account expected future
> variation.

Like you, I am not sure what context to cut, so I will leave the whole
thing.  It appears that I did misinterpret what you were trying to
do with your "discount factor".

Future uncertainty, in my understanding (BA 1972) of economics is only
a small part of what the discount factor is for.  More significant is
the fact that resources available now can be productively employed to
generate more resources in the future.  Another aspect, even for those
who don't know how to utilize resources productively, is Keynes's
observation that "in the long run we are all dead".  Homo economicus
would prefer to enjoy the use of the resources now, because he may
not be around to enjoy them later.

Homo biologicus, on the other hand, draws a different moral from Keynes's
bon mot.  Since we are all dead in the long term, the short term is
meaningless.  It is only the long term persistence of our lineages that
is significant.  Homo biologicus is a long-term thinker.

Now to "fitness".  I am enough of a Machian to believe that any useful
scientific concept must ultimately be related to something you can measure.
Any concept of fitness must thus be based on a clear cut mathematical or
statistical manipulation of real physical measurements.  For fitness,
this means that the base reality is individual organism fitness, which
is measured by counting descendents.  However, as Fisher shows, the
more useful concept for theory is derived from this base reality.  In
theory, we are not interested so much in individual fitnesses as in the
fitness of types - that is, the average fitnesses of individuals that
share some characteristic.  Furthermore, in cases where there is some
variation in the time of a generation, it turns out that the more useful
concept is the growth rate per year, rather than the growth rate per
generation.  Fisher provides the conceptual machinery for measuring this,
in the section in which he talks about demographics and "reproductive
value".  Both I and Bob originally assumed that this is what you were
getting at with your talk of Markov processes.

So far, I have been talking about various forms of actual measurable
fitness.  However, it can only be measured retrospectively.  In this
sense, NS really is a tautology - the fittest types spread because the
fact that they have spread is converted into a measurement of fitness.

The empirical content of evolutionary theory appears when we make the
non-tautological statement that past fitness is a good predictor of
present and future fitness.  Organisms ARE adapted because they WERE
adapted, as proved by their survival, and because the environment
PROBABLY hasn't changed enough so that that past adaptation is no longer
relevant.

Now, the question arises as to whether we get a better prediction of
future fitness by measuring fitness (ie. growth) over the past year, or
over the past century.  There is clearly a trade-off here.  The
environment fluctuates, so using too short a baseline may provide
a bad sample - last year may have been anomalously dry.  On the other
hand, the environment does change in some long term trends, so we don't
want to give too much weight to the distant past.  And that is pretty
close to what you are saying about a discount factor to account for
future uncertainty.  I am just looking at the problem in a time-reversed
fashion.
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