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Super simple question, but I can't find the answer on the Internet (and I'm in a foreign country so the library is not English.) As the title says, what is the smallest scale at which blood vessels, nerves, lymphatic vessels, bronchi, renal structures, etc.. are deterministic (same for most of the population)? For example, I'd imagine capillaries are pretty much random, while (most?) people have an aorta, so where does the pattern break? Is there a scale at which an animal's body is probably similar to their siblings but dissimilar to a complete stranger? Or is it just a statistical distribution thing (the smaller you go the more standard deviation you get)?

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    $\begingroup$ Interesting question.. but I have no definitive answer.. All developmental structures arise because of some kind of morphogen gradient.. The smaller you go there are microgradients and there can be stochastic fluctuations there. It is not about capillaries being small.. Their branching results because of VEGF gradient in a very small area (I am guessing VEGF but there can be other morphogens too), which is not deterministic (or we can say the initial conditions are random). You can perhaps model it as each cell secreting some n VEGF molecules drawn from some distribution. $\endgroup$ – WYSIWYG Aug 18 '14 at 16:24
  • $\begingroup$ Even the major arteries and veins do not have a completely deterministic structure. They also have minor variability depending on the idiosyncrasies in the visceral structure. But yes their overall direction is more or less determined. $\endgroup$ – WYSIWYG Aug 19 '14 at 4:39
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Indeed a very good question. I'm afraid it might remain without a proper anatomy-based answer, but my intuition would tend towards agreeing with "the smaller you get, the more deviation you'll find".

Or rather, I would expect the same principle as in conservation of genetic patterns to apply here: the more central a tissue structure is to survival, i.e. the more downstream systems depend on it, the more likely it will grow in conserved patterns.

As an excellent example, the largest blood vessels including the aorta and its first- and second-degree branches are identical in branch number, approximate relative branch size and approximate branching location across probably all living humans (given that babies born with malformations on this scale would probably not survive without drastic surgery). Similarly, the largest-level nerves and nuclei are identical across the species. These are central systems that provide core functionality for survival.

On the other hand, teeth are quite important, but the odd tooth missing or additional doesn't harm terribly as no downstream systems depend on them. Indeed, it isn't uncommon for humans to be missing a permanent tooth and keep their primary (baby) tooth in that spot for decades; similarly, missing 8th teeth or additional 9th teeth also occur.

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  • $\begingroup$ Just a small note on "the smaller you get, the more deviation you'll find".. Small is for the system size (absolute number of interacting entities and limits of diffusion etc) and not the size of the objects in consideration. $\endgroup$ – WYSIWYG Aug 19 '14 at 10:50
  • $\begingroup$ I agree with your answer in general, but I feel that humans are more uniform than they need to be, just for the sake of survival. I wonder why eye color is far more variable than nail color, even though they're equally trivial. $\endgroup$ – Misha Aug 19 '14 at 15:16
  • $\begingroup$ Nail colour is much less relevant for sexual attraction? I'm sure you'll find equally useful examples in other animal species to illustrate the principle I mention :) $\endgroup$ – Armatus Aug 19 '14 at 16:15
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The answer is... basically none. The variability is high, and can also happen in the macroscopic range. If you want a quick-and-dirty idea of the fraction of the population presenting a certain variability in humans, I would suggest a good anatomy atlas or manual. A good resource would be Gray's Anatomy (the book, not the soap ;-).

Apart from that, @Armatus is in my opinion correct in assuming that variability is inversely proportional to scale. However I would like to point out that even the largest blood vessels can derive from the classical structure in many ways, and are certainly not identical among all living humans.

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  • $\begingroup$ Anatomy books wont answer this kind of a query.. Gray's anatomy has not included any new information since 50 years ago (that's an exaggeration but still) $\endgroup$ – WYSIWYG Aug 19 '14 at 4:33
  • $\begingroup$ @WYSIWYG Oh yeah... ? Well go tell that to all the anatomy researchers around the world, 'cause I am sure they will appreciate :-D Ok, I don't have Gray's at home, but I happen to have Sobotta's Atlas. Panel 86, tome 2: variable distribution of the coronary arteries; panel 116, tome 2: variability of the aortic arch. I'll admit there are just the clinically important variabilities in those books, though... $\endgroup$ – Raoul Aug 19 '14 at 10:38
  • $\begingroup$ When looking at anatomical drawings, I've wondered if the fine details (ex. small blood vessels) are just a random sample of one individual, or do they only draw features that are common to "most" of the population. I had no idea until now that anatomical atlases include variability data. $\endgroup$ – Misha Aug 19 '14 at 15:00
  • $\begingroup$ @Misha Yes, they do for commonly encountered variabilities. The medical staff has to be aware of some of them to treat patients correctly. BTW, you might find more variability data (in the macroscopic range) in surgical technique atlases, since knowledge of anatomical variability is mostly useful to surgeons. $\endgroup$ – Raoul Aug 19 '14 at 17:34
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Biology is not deterministic. Traits like this have variable expressivity.

A phenotype with 100% expression in a population with an allele is said to have complete penetrance. There is no gene which could specify a single blood vessel pattern that could have complete penetrance. Variable expressivity means the same genes yield a spectrum of forms of the same phenotype.

  1. A description of phenotype variability, penetrance and expressivity
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  • $\begingroup$ Nothing is deterministic.. But deterministic approximation works well under certain condition. System size is definitely one factor. With expanding size, stochastic systems approach thermodynamic limit and deterministic approximations are valid.Depends on what you are looking at. Deterministic modeling is easier and less computationally intensive. $\endgroup$ – WYSIWYG Aug 19 '14 at 10:46
  • $\begingroup$ Logic is deterministic. Not sure what you mean by approximately deterministic. I know fuzzy logic lets booleans be approximate. But Idk that fuzzy logic is defined as deterministic. Sounds like a good question for someone who studies logic. $\endgroup$ – 12345678910111213 Aug 19 '14 at 15:36

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