"Anon."  wrote in
news:clh816$j0o$1{at}darwin.ediacara.org: 

> William Morse wrote:
>> "Anon."  wrote in
news:cl65sn$ave$1
>> {at}darwin.ediacara.org:
> 
>> John is something of a conundrum. He is neither stupid nor ignorant.
>> But he is singularly single-minded, and has an unfortunate tendency
>> (shared by many humans, including myself) to lapse into calumny when
>> his arguments are challenged.  I gave up responding to John some time
>> ago, even though he raises some good arguments, because of his
>> single- mindedness. I suggest you do the same. What we need to do is
>> get into some good arguments between ourselves so we can both satisfy
>> our desire for intellectual discussion. I think this may be difficult
>>  because we tend to agree, but here goes: bipedalism in humans is
>> simply a result of drift - our ancestors could have as easily
>> switched to knuckle-walking. 
>> 
> What?  We're bipedal?  No wonder I've been getting funny looks!
> 
> More seriously, I think the typical reaction to that would be "no way,
> nothing that complex could evolve by chance".  Which leads me to
> wonder what the chance is.
> 
> In trhe following discussion, I will ignore any possible developmental
> constraints: they could be included but the maths gets messy.
> 
> For drift to be the explanation, we have to posit that all of the
> genes involved in the shift to bipedalism have drifted to fixation. 
> So, we'll need to know how many genes are involved, the probabilities
> of fixation of neutral alleles (which depend on the population size
> and structure), and the mutation rate of these alleles.  We'll also
> need to know the time since the shift to bipedalism started.

In my drift scenario  I am counting heavily on sampling error as opposed 
to neutral drift to fix the alleles - so I need to have a small effective 
population size. I am also counting on our ancestors as having been 
primarily arboreal with brachiating locomotion, and using limited 
bipedalism when walking on the ground.  

 
> The probability of bipedalism evolving over that time scale is then
> the product of the probabilities for each allele.  The probability for
> each allele is approximately the probability of fixation divided by
> the mutation rate.

Again, my supposition is that bipedalism actually evolved over a 
relatively short time scale, when a small group of primates was faced 
with a choice of bipedalism vs. knuckle-walking in adapting to a primarly 
ground-based existence. 


 
> This is, of course, not what we want: we know that bipedalism has 
> evolved, and want to know whether it was by drift or something else. 
> To estimate the probability that it was drift wot done it, we have to 
> calculate the probability that it some other factor than drift caused 
> bipedalism, and then use Bayes formula to invert the probabilities. 
> At this point, I will only point out that probabilities of fixation of
> alleles can be increased by giving them a positive selection
> coefficient - we would need to know what the selection coefficients
> were to do the calculations.

Aye, there's the rub. I am assuming fairly steep selection against the 
switch from quadripedalism to bipedalism, i.e. a steep adaptive valley to 
cross, even though each peak is relatively stable. Many dinosaurs were 
obviously quite successful as bipeds, as are kangaroos. I would note that 
all of these examples had large tails, which presumably could help them 
balance during the switch. Primates had no such balancing aid, so it 
would seem to take a fairly strong positive selection coefficient in 
favor of bipedalism for it to evolve by selection from a large 
quadripedal population. This is why I am intrigued by the possibility 
that the correct explanation is sampling error in a small population that 
is already partly bipedal due to an arboreal existence.

 
> After all that, I can give you a list of 57 different parameters that 
> are necessary for the calculation, but are impossible to estimate.
> 
> There may be a different, and better approach to this analysis, if so 
> I'd be interested in hearing it.  One that needs only 32 
> impossible-to-estimate parameters would be fine.

Unfortunately I don't have a better approach. It might be possible to 
estimate some of the selection coefficients for bipedal vs. quadripedal 
locomotion based on biomechanical considerations (and I think there have 
been some studies on the energetics), but we would still need data on the  
ease of switching from brachiation to either bipedalism or quadripedalism 
from a developmental standpoint. This information will come in the future 
(the good lord willin' and the creek don't rise) but is not available 
now. And the effective population size might be a key variable, but one 
that will never be known. 

I suppose if I were serious about my hypothesis I should first try to 
narrow down the number of genes involved in hip development. You don't 
happen to have any grad students in need of a thesis project?


Yours,

Bill Morse
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