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monty;115438 said:
Sure, but you've gotta admit, two data points works a lot better than one data point: at least then you can judge whether drawing a line of slope beak/mantle from the 2003 animal matches up with beak/mantle for the new one, and if it does then have a bit of confidence about guessing the mantle size from the biggest beak...

welllllll marginally, problem is, that often the relationship is not linear, it may be a power curve or some other (mine is a ln relationship)!

j
 
Jean;115459 said:
welllllll marginally, problem is, that often the relationship is not linear, it may be a power curve or some other (mine is a ln relationship)!

j

That's sort of why I said 2 points is a lot better than one point. It's really sort of more than 2 points, because you have (size of 2003) and (size of new) and (beak of 2003) and (beak of new) so you can either plot how the ratio changes as a function of size, in some very limited way, or test if it's also a log relationship by trying it with (log size)/beak or size/(log beak) or (log size)/(log beak), but it could easily be some wacky curve, and having 2 points lets you fit things a bit better than 1. Of course, 3, 10, 100, or 1000 points is a lot better, though... I just think the guess of the size of the one that left the biggest beak starts to get a lot less wild with 2 data points than one, is all...
 
Clem;115455 said:
:alarm::alarm::alarm::alarm::alarm:

Monty! No! Gaahhh! That's not what I was saying! I was merely using the appearance of tendons on the back of a human hand to illustrate my (speculative!) musings on the arm musculature, and how those muscles might extend from the buccal plane all the way to the back of the brachial crown, not unlike the configuration of a bullpup rifle. I've attached a pic to show where this notion came from. I've outlined in green the arms IV pair. Now, perhaps it's an accident of debriding and abuse from longliners, but it certainly appears that both arms IV share a connection to a single distinct muscular structure that terminates at the posterior of the brachial crown. My purposes aren't nefarious, but if all the arms are so anchored, I wonder how their actions would impact the eyes, which appear to be nestled between the muscular bases of arms II and III, and what advantage, if any, would be conferred on an animal that could squeeze with its arms and its head.

Now I'll go read those things you linked to.

Clem

I didn't mean to suggest you thought they had tendons... but I did want to clarify that for other people. I'm starting to get more of what you're saying, though. The hard part is that the arms and the head are mostly muscle, so in some ways where the "arm muscles" end and the "head muscles" start is sort of arbitrary. They don't seem to like to deform their heads as much as their arms, obviously, so I'd think that any extension of arm musculature into the head is primarily to anchor the bases of the arms. I'd expect there to be some sort of support muscles around the brachial crown all the way back, so I'm pretty sure that the head can't be thought of as a bundle of arm muscles held together by connective tissue... but there might well be some arm-muscle-bits mixed in going back quite a distance.

It's also, of course, quite possible that I'm just confused. I've tried to figure this out from diagrams and histology slides for a while, but I haven't seen it well-documented anywhere. JZ Young published some amazing books of histology, but they focus almost entirely on the neuroanatomy, so they don't really address this... in Nixon & Young, in fact, Kier is the only one referenced for arm musculature, except as related to suckers, at least for the loliginid overview (yeah, I know Mesonychoteuthis isn't a loliginid). I've got some xeroxes of JZ Young histology stuff, particularly The Anatomy and Nervous System of Octopus vulgaris, that shows this area in regards to the interbrachial commissure, that's the cross-connection between the nerves going down each arm. There's a 1908 monograph by Joseph Guérin that shows a bit just as the arms enter the brachial crown, that (insofar as my rusty French comprehends) shows that the basic arm muscle profile extends into the head a bit, and then there are some cross-connecting muscles that give some support. He doesn't discuss the eyes at all, though, and neither follows the arms back into the head. It seems, though, that the extension of the arms that go back to form the head are mostly anchors for the arms that are held pretty rigid.

I did find that Nixon & Young show some relevant stuff, but it varies a lot between species, and even among cranchiids... I'll scan some pics and report back.
 
monty;115488 said:
That's sort of why I said 2 points is a lot better than one point. It's really sort of more than 2 points, because you have (size of 2003) and (size of new) and (beak of 2003) and (beak of new) so you can either plot how the ratio changes as a function of size, in some very limited way, or test if it's also a log relationship by trying it with (log size)/beak or size/(log beak) or (log size)/(log beak), but it could easily be some wacky curve, and having 2 points lets you fit things a bit better than 1. Of course, 3, 10, 100, or 1000 points is a lot better, though... I just think the guess of the size of the one that left the biggest beak starts to get a lot less wild with 2 data points than one, is all...

it's just not that easy unfortunately, here's a fake regression (cos I don't have any real Messie data) and all it tells you is that one is bigger than the other! the pedantic scientist in me just won't allow for any meaningful conclusions to be drawn from this. And you can play with it all you want but you can't predict or draw conclusions from what simply isn't there. What happens in the younger/smaller sizes? Is there an ontogenetic change in growth form, do the older ones reach an asymptote (rare in squid but........), does the growth speed up/slow down?????? and so on, it's very dangerous to extrapolate based on only two sets of measurements!

Argumentatively yours

J
 

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Jean;115499 said:
it's just not that easy unfortunately, here's a fake regression (cos I don't have any real Messie data) and all it tells you is that one is bigger than the other! the pedantic scientist in me just won't allow for any meaningful conclusions to be drawn from this. And you can play with it all you want but you can't predict or draw conclusions from what simply isn't there. What happens in the younger/smaller sizes? Is there an ontogenetic change in growth form, do the older ones reach an asymptote (rare in squid but........), does the growth speed up/slow down?????? and so on, it's very dangerous to extrapolate based on only two sets of measurements!

Argumentatively yours

J

"Oh, this is abuse. Arguments are down the hall." - Monty (Python):tongue:

Are you arguing that having 2 data points is just as bad as having one? I didn't mean to argue that it would allow a high-confidence guess, just that it's a big improvement over one... mostly, because you can at least estimate how wrong the 1 point approximation is. I entirely concede that it will be a lousy guestimate anyway... but I think we *can* say some fairly reasonable things, like ML is monotonically increasing with beak length, that they won't be wildly uncoupled, and so forth. And since we want one as a function of the other, we can get ML(b) and and an estimate of dML(b)/db for each squid, so there are (kinda) 4 measurements, the value and derivative at each squid's beak size. I think it's not too awful to imagine that both the ML(b) and dML/db are monotonic and kinda smooth over the range, so it's at least possible to fit a curve made of two terms of the Taylor series instead of one. Is this a good estimate? Meh, not really, unless you make a lot of assumptions, but I think they're not completely insane assumptions.

So I put forth that the "best" assumption from one squid with ML=ML0 and b = b0 is:

ML(b - b0) = ML0 + (ML0/b0)(b-b0)

and with 2 squids, with the other having ML=ML1 > ML0 and b=b1 > b0

ML(b - b0) = ML0 + (ML0/b0)(b-b0) +
((ML1/(2b1(b1-b0))) - (ML0/(2b0(b1-b0))))(b-b0)^2

(unless I screwed up the algebra)
which is "better" assuming all the usual Taylor approximation stuff applies.

I did cheat a little, and assume that the line from (0,0) to (b,ML(b)) is a good enough approximation of the derivative, though, too.

Note that "better" doesn't imply "particularly good" but I think the curve is monotonic and pretty smooth and otherwise well-behaved over this range.

It is quite true that this makes some horribly naive assumptions, and whether to use naive assumptions to get an answer or to say "I refuse to endorse and answer that I know is naive so it's probably wrong" is sort of a judgment call... I wouldn't bet my reputation on it, but it's not completely unbelievable. You could possibly do better by assuming some other form rather than a Taylor polynomial, like whatever the log relationship you found in Nototodarus looked like and trying to fit different constants to that, and maybe using (ML1 - ML0) / (b1 - b0) as the derivative estimate for the bigger squid, and stuff like that, too. In fact, I should have done the latter, and as penance I re-solved it:

ML(b - b0) = ML0 + (ML0/b0)(b-b0) +
(((ML1-ML0)/(2(b1-b0)^2)) - (ML0/(2b0(b1-b0))))(b-b0)^2

Of course, this is, in some sense, all completely :tomato: rather than :grad: but people use these sorts of naive models for things all the time. And they sometimes kinda get the right answer, approximately.

And it's not like there are dire consequences for guessing wrong :sink:

p.s. I realized as I was going to sleep that I forgot to correct the ML(b1) value in the 1st deriv equation, on the unlikely chance that anyone is referring to this for some real reason.
 
a few pics for Clem

All pics from Nixon & Young:

A histology slice through Sepia officinalis that shows that the arm musculature does go back to the eyes:


A diagram of the muscles for those eyes, so you can guess how the eye muscles interact with the above:



I don't see the same arm musculature apparently extending into the head in this Mesonychoteuthis picture in an obvious way:



Other cranchiids are weird enough that I wouldn't extrapolate too much from the above, though (although the sepia pics are similar to sepioteuthis, for what that may be worth):

 

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Wow. What happened here? I spend a day away and all of this has happened.

Ok, first things first (and the last I'll say tonight).... we will have many more than 2 data points for the beak biomass regression equations. Cat's out of the bag - we'll have ~ 10. Now I shut up; 10 is better than 2; 2 is better than 1.
 
With 10, there must be at least one eye intact, one would hope :fingerscrossed:
 
Not all are large (as in colossal sized); a number fit into buckets and were preserved at sea. I'll be able to post more information in week or so (I have yet to see them yet).

The best part about this is that they'll not be deformed as a consequence of freezing; the worst part is that I didn't get an opportunity to display them properly - it's hard to know what they'll look like.
 
aaaaaaaaaawwwwwwwwwwwwww I was having fun arguing 2 vs 1 :biggrin2:

yes Monty 2 is better than 1 (marginally :biggrin2:) BUT more is always better....'tis the universal plaintive cry of the scientist "MORE DATA....I........NEED.........MORE .........DATA"

And I wouldn't like to try and get a regression based on so few past a journal editor (I've had one tell me my 1100 were too few :mad: fortunately I'm not submitting my paper to that journal!)

J
 
Steve O'Shea;115556 said:
Not all are large (as in colossal sized); a number fit into buckets and were preserved at sea. I'll be able to post more information in week or so (I have yet to see them yet).

The best part about this is that they'll not be deformed as a consequence of freezing; the worst part is that I didn't get an opportunity to display them properly - it's hard to know what they'll look like.

Hmmm I wonder if there's an ontogenetic shift in growth, will look forward to hearing about this. Which beak parameters are you using? Just rostral length or are you planning to use hood, crest etc?????

Are you going to age them????????


So many questions!!!!

J
 
Jean;115693 said:
aaaaaaaaaawwwwwwwwwwwwww I was having fun arguing 2 vs 1 :biggrin2:

yes Monty 2 is better than 1 (marginally :biggrin2:) BUT more is always better....'tis the universal plaintive cry of the scientist "MORE DATA....I........NEED.........MORE .........DATA"

And I wouldn't like to try and get a regression based on so few past a journal editor (I've had one tell me my 1100 were too few :mad: fortunately I'm not submitting my paper to that journal!)

J

I wouldn't even try to describe what I propose as a regression, it's just an ad hoc derivative estimate leading to a guess. Still, people who get too fascinated with "the right way to do data analysis" sometimes can't see the forest for the trees.

Continuing the trend from Monty -> Monty Python -> Monty Hall, I wrote up a blog post about an article suggesting that psychologists have been introducing a bias into their results for years, and the embarrassing observation that us computer graphics weenies were doing something analogous for quite a few years, too (but we caught it on our own faster than the psychologists :tongue:):

Monty Hall vs. Psychologists

Anyway, 1100 seems like a rather high threshold, unless there's some reason to believe that the sampling is horribly biased.

Oh, yeah. This is a humorous take on the perils of data analysis and presentation:

http://www.nbb.cornell.edu/neurobio/land/images/CTC/viz-o-matic.wmv
 

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