Re: Sexual selection of disadvantageous traits


"John Harshman" <jharshman.diespamdie@xxxxxxxxxxx> wrote in message news:ZmCJg.4918$yO7.4861@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Perplexed in Peoria wrote:

"John Harshman" <jharshman.diespamdie@xxxxxxxxxxx> wrote in message news:lWqJg.4154$tU.1382@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Perplexed in Peoria wrote:


"John Harshman" <jharshman.diespamdie@xxxxxxxxxxx> wrote in message news:HXoJg.4132$tU.2558@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Perplexed in Peoria wrote:


"John Harshman" <jharshman.diespamdie@xxxxxxxxxxx> wrote in message news:_5nJg.21829$gY6.19405@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx



Perplexed in Peoria wrote:

[snip]


There are three ways a tail affects male fitness. First, it
really is (by assumption) a handicap - it decreases survival
chances over the period from birth to sexual maturity. Second,
due to the non-linear feature that Harshman insists on,
it is correlated (post-survival-selection) with other positive
genetic traits. [Third way - sexiness to females - snipped]

Actually, a non-linear relationship is not necessary for this to be
true. The statistical expectation for all surviving males is that they
will have some mean "survivability". Since the long tail is costly in
terms of survival, the expectation is that long-tailed birds will have
compensating average increased levels of "quality".

I think you are wrong here. Without non-linearity, there would be
no compensating correlation. The surviving long-tailed birds would
not be particularly high in quality - at least no more so than the
surviving short-tail birds. Both are impacted equally by quality,
if there is no non-linearity.

You have to remember that "quality" is specifically defined so as to
ignore the cost of the long tail. So if the expected survivability of
all surviving birds is S, the cost of long tails is C, and the quality
is Q, then for short-tailed birds S = Q, while for long-tailed birds S =
Q - C. But since we agreed that the expected S is the same for long- and
short-tailed birds, ...


I agreed to no such thing.

That was the entire original assumption of the handicap principle.
Perhaps you should go back and read Zahavi's original paper.


Ah! Zahavi's original paper. I'm not sure I have read the paper,
though I have read his later book. And I have read Maynard-Smith's
comments on Zahavi in which he initially rejected Zahavi's theory
because he (JMS) was assuming independence, and then later came
to understand that the handicap principle works if you add (as
Zahavi had without saying so explicitly) an assumption of
non-linearity. See "Animal Signals" by JMS and Harper.


... Q(short-tailed) = Q(long-tailed) - C. And thus the
long-tailed birds have higher expected quality. What you have noticed is
that expected S is the same for all birds, long-tailed and short-tailed.

I notice no such thing.

Unfortunate. I wonder what you have noticed.


But Q is indeed higher for the long-tailed birds.

I'm really quite surprised that you are making such an elementary
mistake. If selection on the tail handicap and selection on
'quality' are independent (which is another way of saying that
no non-linearity exists) then selection will not create a
correlation between these traits.

Of course it will. Let's suppose we have a mixture of four types, for
simplicity: the four combinations of long and short tails, high and low
quality. Suppose that the long tail has a cost, and that low quality has
a cost too, such that the costs are equal. So after a round of survival,
the population is enriched in short-tail, high-quality, depleted in
long-tail, low-quality birds. Try any numbers you like for the cost
itself. I'll say 10% each just for fun. So if we start with a population
of 100 males of each type, we end up with this table:

T
short long
high 100 90
Q
low 90 80


The low-long entry should be 81, not 80. 100 * 0.9 * 0.9 = 81.


But now take this 2 x 2 table and put yourself in the position of a
female trying to find a high-quality male but unable to see quality
directly. Using tails as a clue, is the female more likely to select a
high-quality mail by choosing a long-tailed or short-tailed male?
Answer: long-tailed: 9/17 (.529) vs. 10/19 (.526).


Correct answer: 10/19 vs 10/19.

Depends on the function you pick, I suppose. But where do you get your
10/19? "Corrected", the answer would be 90/171 (still .529).

90/171 = 10/19 (divide numerator and denominator by 9)
90/171 = .526... , not .529

And, in any case, even using your numbers, you haven't shown that
the better quality of the long tailed males comes close to
compensating for the handicap.

Of course it doesn't compensate for the handicap. We're still talking
past each other. My point here is that if you ignore the effects of the
handicap (which is what Zahavi originally did) we expect a surviving
long-tailed bird to be of higher quality than a surviving short-tailed
bird. Remember that quality is explicitly defined as not counting the
handicap.

I agree that if the surviving fraction of low-Q, long-T is small enough
(less than .81 in your example) then the surviving long-Ts will be
disproportunately high-Qs. A long tail will be evidence of high
quality. But, correcting what you said: "Actually, a non-linear
relationship is not necessary for this to be true.", I am claiming
that a non-linear relationship *is* necessary. And I offered the
corrected (81 vs 80) table as an example of a linear relationship
in which there is no post-selection correlation between tail and
quality. Which is where we started. But you seem to be trying to
morph the discussion into just what Zahavi erroneously said.

That is, expected S is not the
same for long-tails and short-tails.

It's the same for *surviving* long-tails and short-tails. Advantage in
tail-length is, on average, offset by disadvantage in quality, and vice
versa.

False and bizarre. More on this below.

Let's try something more extreme using your method:
short T long T
high Q 100 60
low Q 60 20

Nope. Still not enough. Of those 80 surviving long-tails,
only half (36 + 4) will make it through another round of selection.
But much more than half (136/160) of the short-tails will.

Irrelevant to the question of "quality", which ignores the handicap. So
is the subsequent, similar discussion. Let me repeat once again: the
original handicap theory doesn't work. It doesn't work because it
artificially separates "quality" from total survivability. While it's
true that a long-tailed bird that survives to breeding age is of better
mean quality than a short-tailed bird that survives (which for some
reason you don't understand), ...

I do understand it. I simply claim that it requires non-linearity.

...this result is due entirely to the
artificial definition of quality.

I also think you fail to understand what "non-linear" means in this
connection. What it means is that the cost of the ornament must not be
constant but must be a function of quality, such that high-quality birds
have a lower cost of producing the ornament than do low-quality birds.

Well, it is not just the cost of 'producing' the ornament. You also
have to count in the cost of carrying the ornament. Both cost
components - the physiological cost of producing and the cost of
carrying - can be rolled together into a single cost expressed as
a decreased probability of survival. If that cost (expressed as
a survival probability) is the same for high and low quality birds,
you get a table like this:
short T long T
high Q 100 90
low Q 90 81
and there is no correlation. But make the cost higher for low quality
birds (8/9 for low quality vs 9/10 for high quality) and you get
your original table in which, as you point out, there is a correlation.

[snip]

Or thinking of it
another way, all surviving birds have gone through an equal test of
their survivability. The expectation is that any given bad
characteristic is compensated for by some equal combination of good
characteristics. Here we are reducing all characteristics to two: tail
length and quality. If one character gets "better", the expectation is
for the other to get "worse".

I repeat that this (and Zahavi's original theory) relies on making an
artificial distinction between the handicap and quality, which there is
no reason to believe exists in nature.

I agree that the analysis requires that we make that distinction.

What the female is really looking
at would be survivability, and tail length is no clue to that.

Huh? That made no sense to me. I would have written that what
the female is looking at is tail-length (admittedly among survivors),
but what she is 'really interested in' is expected survival in the
next generation's round of selection. And I thought we were trying
to determine the conditions under which tail length would be a
clue.

I have no clear idea what you were doing. I was defending the main point
of Zahavi's original theory, which is that a long tail is evidence of
"quality". (I repeat this is of no interest as an explanation of nature,
and thus Zahavi's original theory is biologically useless, because
quality is artificially defined as excluding effects of the long tail.)
A deficit in one character is made up by expected advantages in other
characters, because birds that survive have equal expected
survivability. (That's what "survivability" means.)

And I have no clear idea what you are doing. Here you repeat your
claim of equal expected survivability of surviving birds. And that
strikes me as a gross error. So I apparently don't understand what
you are saying. And you repeat that a deficit in one character is
made up by expected advantages in other characters. But you seemed
to deny this above when you wrote "Of course it doesn't compensate
for the handicap".

I would say that survival results from two factors - an inherent
(and heritible) "survivability" factor, and a (non-heritible)
factor of sheer luck. All survivors have equal survival, but
they do not necessarily have equal survivability.

It is rather odd that two supposedly intelligent and informed
people are having such difficulty making themselves understood.

.

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