On Jan 29, 11:57 am, Seanpit <sean...
The problem is that your math is modeled on a bogus search mechanism.
You yourself have likened it to a blind-folded man searching *total*
sequence space in which "targets" are randomly or uniformly placed.
Your model *assumes* that the field is completely "flat", that the
blind-folded man can, after a given period of time, wind up *anywhere*
in that sequence space with equal probability. That it is only time
that determines how far the search can go. That is an absurd
assumption when you compare it to the selective sequence space of real
evolutionary mechanisms. In real evolutionary landscapes, the
landscape does have "pathways" that are selectively neutral (flat
relative to the starting sequence). It also has, for a particular
organism in a particular environment, selective hill and valley
pathways that go either up or down from the flat pathways. The
steepness of these pathways varies from sheer cliff faces to sharp
declines. Unlike real landscapes, however, the steepness of the
slopes and inclinations are not static but *can* be different in
different environmental conditions. [We will, for our model's
purposes, switch the usual idea of a selective peak for a selective
valley, since going downhill is easier than going uphill.]
RM starts with a current sequence and changes that sequence only until
it reaches a block of lower reproductive success for the sequence
change (a strong upward slope, the steeper the slope and the more it
continues uphill, the less time will be spent in that direction and
the less frequently it will be visited -- unless there are
environments where the organism exists where the slope is changed, in
that case, some organisms, in that environment, may follow the
downward path, splitting the population into those that favor one
environment over another). What that means is that the probability of
frequent visitation to a new position depends on time, on what sorts
of "selective barriers" to reach that position existed, and whether
the local environmental condition caused the path to slope up or down
at the time a real attempt could be made.
None of that is considered in your mathematical model of sequence
If you were to plot the frequency of visitation of possible
positions after x amount of time, wrt sequence, you would never see a
random or uniform distribution of sites throughout total sequence
space, with every site having equal probabilities of visitation. You
would, instead, see fuzzy threads of change along branching
selectively neutral paths, where, at each new step of neutral change,
new side paths are tried, but not usually followed for any distance
(the further away in an upward direction, the less frequent visitation
will be). Over long time frames, such selectively neutral drift can
visit quite different areas of a sequence landscape arranged by
sequence similarity, but primarily along the threads of selective
neutrality. But again,along these threads, there will be a search of
other sequences making the thread a fuzzy one. Most of the time this
fuzziness along a thread of neutral change will be like the idea of
the position of electrons in an atom; a fuzzy cloud with some
positions being more probable and others less probable, but none
completely excluded from search. Unlike the cloud of possible
electron sites, however, some directions will be more probable than
others (slope matters).
Searches by the blind searcher in *real* sequence space where
selection exist and tests each change are much more constrained than
in your assumed flat plain. New downward paths in such a landscape
may be rare, but those are the ones that will be found and traveled
down. In general, it will be the target that is nearest some possible
neutral search thread that will be most likely to be found. The
closer a path of downward slope is to the fuzzy area around a neutral
thread that has been searched, the more probable that it will be
Even in your imaginary flat sequence space, it is the "target"
*closest* to the starting point that is most likely to be found by a
random search. The distance of the *closest* target is not, however,
what your math calculates. You cannot predict that number unless you
know, for each starting sequence, what the closest target sequence
with a modified, additional, emergent, or novel function is and when
it was first discovered (since target sequences change over time
neutrally -- and to optimize new function -- as well as the starting
sequence, current sequence positions are certainly not going to be the
same as sequence at discovery).
> > > Many sequences in sequence space are
> > > potential "targets" according to this definition of a "target".
> > And almost all of them are utterly irrelevant if you require them to
> > be found starting with a specific sequence. OTOH, new, modified,
> > emergent, or additional functions that are nearby the specified start
> > site *are* likely to be found. What is the probability that a "target
> > sequence" one aa change (or one mutational step) away will be found
> > compared to the probability that a target sequence in which almost all
> > the sequence is different will be found?
> That's not the important question here. The important question is,
> "What are the odds that a target sequence will happen to be one aa
> change away from any starting position?"
I have no idea because I can only observe the target sequences that
have been found. They represent the winners which did happen to be
close to some other pre-existing sequence. You cannot calculate
probability from a biased sample. Nor, as you do, from a bogus,
completely simple-minded, methodological idea of what RM/NS involves.
> That's the real question
> here, and the answer to that question depends upon the level of
> functional complexity under consideration.
No way to tell from your model. Higher levels of functional
complexity that you point to (all seemingly involve multiprotein
complexes) appear to arise by a completely different mechanism than a
random search through total sequence space where you change one aa at
a time to get to a new function within a single protein. You would
have to model a different sort of mutational space involving just
those mutations that affected specific protein-protein interactions
between different proteins without changing other sites in any major
functional way. Or a sequence space where you include chimeric protein
formation. Contact me when you have such a model. Hopefully one more
realistic than the flat total sequence space model you have been
> I have shown you several papers that clearly prove that even at very
> low levels of functional complexity the odds of a target being within
> a single aa change of any starting point are low.
Since most of the functional complexity you point to is due to protein-
protein interactions, is it your claim that those cannot be affected
by single aa changes? Again, your model of sequence space is for a
single sequence, not a model of protein-protein interaction.
> These odds only get
> exponentially lower and lower with each step up the ladder of
> functional complexity.
> I know, I know . . . your standard comeback is that evolution only
> happens when it can happen.
Wrong tense. Evolution only *happened* when it *could* happen.
Existing systems are the winners and do not represent a random sample
of anything. They are a decidedly biased sample. And one clearly
biased feature is the degree of similarity they have to other pre-
existing genes and systems. Your claim is that that bias is not a
causally relevant bias that helps explain how such systems evolve.
Instead we get a false dichotomy between complete randomness that
actually can search total sequence space and a magical invisible
untestable intelligent fairy.
> Well, Howard, that isn't very scientific
> of you. Science is about predicting the future -
That would be a surprise to all those archeologists, SETI researchers,
and forensic scientists you keep invoking. It would also be a
surprise to geologists, paleontologists, meterolgists, historians, and
many others that use the scientific method to understand the past to
*understand* the principles and mechanisms at work that may affect the
future but cannot necessarily allow us to predict it with specificity.
> about predicting
> when something is or isn't "likely" to happen in a given amount of
Which depends on the mechanism one is proposing. Which you understand
by asking if the proposed mechanism can explain what actually *has*
happened. Your total random walk math clearly cannot explain the
past, so it probably is not the mechanism that *did* cause the past
and is, thus, worthless in predicting the future. Now you have to
test alternative mechanisms that could explain the past. But how do
you test a model that an invisible untestable something did something
somehow (without leaving any traces of having done it) at some time
and some place to produce whatever I claim cannot be done by chance
alone. That leaves out a whole big range of alternative explanations
that do not involve long chains of completely chance changes *before*
selection is applied at the end.
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