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Animal Brain size, mass, and surface area

  1. Jan 13, 2012 #1
    Animal Brain size, body mass, and surface area

    S.J. Gould wrote a series of interesting articles (chapters 22-24 in Ever Since Darwin) about the ratio of body mass to brain mass among animal species. Bigger animals have bigger brains (of course) but the ratio is getting smaller: a human's brain is smaller than an ant's relative to body size. Gould conjectures that this is due to volume to surface area ratio: since volumes (and therefore masses) increase faster than surface areas, an ant has a larger surface area to body mass ratio. Therefore, the ant needs a relatively bigger brain to control and sense its body surface area, with its appendages, nerves, etc.

    Question: this explanation sounds reasonable, but Gould provides no evidence. Does anyone know of evidence to support that hypothesis, or of other hypotheses regarding that phenomenon?
    Last edited: Jan 13, 2012
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  3. Jan 13, 2012 #2

    jim mcnamara

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    You probably want to consider encephalization quotient, a relative calculation. It generally IS NOT considered applicable across classes (e.g., mammals vs reptiles vs annelids). See this article for a discussion

  4. Jan 15, 2012 #3
    Thanks, I looked it up and I also read one of the reviews referenced there. However, that doesn't answer the question. The enchephalization quotient quantifies a species' distance from the log-log regression line; it doesn't explain why the line has the slope it does (2/3), and it doesn't even explain why the slope is less than 1.
  5. Jan 15, 2012 #4


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    I don't really know why surface area would have that much of an influence on brain size. I guess I'd look at it more as a limit issue. When you're going from a teeny tiny ganglion to an actual brain and increasing in complexity, initially, I'd expect an increase in brain size with organism complexity, but I'd expect that to begin to plateau as function stabilizes although size increases. For example, if a cat and human have the same basic analogous muscles, while the neurons in a human may need more motor endplate branches than in a cat to control the larger muscles, there's no compelling reason why you'd need more neurons in the brain for that purpose. There are differences in size, but they become less proportional.

    Steven Gould is primarily an evolutionary biologist, not a neuroscientist, so when he begins to conjecture outside of his field, consider it just that, conjecture.
  6. Jan 16, 2012 #5

    1. I think your reasoning is similar to Gould's: a bigger (that is, heavier) body without much more sophistication would require a proportionally smaller brain. Gould made a similar argument going the other way around: the ant's smaller (lighter) body has larger relative surface area which requires a relatively bigger brain.

    2. This is not a limit issue. It's true for all animals from ants to blue whales, and doesn't level off at any point.

    3. Gould was not even an evolutionary biologist, as his detractors often mention. He was a paleontologist. The chapters I mentioned are so badly written that one wonders whether they were written by a child (he describes all animals as geometric cubes). Nevertheless, some of the most interesting research and conjectures come from those who step outside of their fields, e.g. Roger Penrose, Len Adleman, Schrödinger, etc.
  7. Jan 16, 2012 #6


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    The allometric scaling argument seems sound, though there is always the question of whether you can reduce the reason to some single factor like circulation efficiency in the case of metabolic rate (Kleiber's law) or neural mass to body surface area in this case. In a rough approximation at least, brain mass is going to grow by the cube while body surface grows by the square.

    So Gould was really applying a biological null hypothesis to the brain - it is standard thinking, the obvious place to start.

    But you were asking about slope. If it is just a surface/mass relationship, then slope would be 2/3.

    The slope is in fact different across the animal phyla. From http://si-pddr.si.edu/jspui/bitstre...llometry_of_Brain_Miniaturization_in_Ants.pdf

    The interesting finding of this study is that the relationship breaks down with extreme miniaturisation in the case of ants.

    But I think the honest answer with brain allometry studies is that there is a lot of speculation.

    For example, some say dolphins are "above the line" simply because they are pygmy whales rather than because they have evolved larger brains due to social intelligence or echolocation. One or other might be the dominant factor. It is quite easy to fit the same data to different explanations.

    However at the phyla level, the basic observation that brains follow some kind of scaling law goes right back to Haller in the 1700s. And Gould's reasoning would be the plausible starting point for most.
  8. Jan 16, 2012 #7
    That would only be true for a cube, and I think that was one of Gould's errors. Consider two cylinders of the same radius r, one of height h and the other of radius 2h. The second has twice the volume of the first, but what can you say about the ratio of their surface areas? It could be almost identical, if the height is far smaller than the radius (pancake), or it could approach 2 if height is far greater than radius (spaghetti). Unless I'm missing something, it's basic solid geometry. If I were to choose a simple geometric shape that approximates a living organism, I'd choose a cylinder or a rectangular cuboid other than a cube.
  9. Jan 16, 2012 #8


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    The brain grows by the cube - it does form a pretty circular lump because one of its design constraints is its need to be highly internally connected.

    Whereas the surface area of the body grows by the square (of any volume increase). But yes, this is an idealisation as bodies are not actually spherical blobs. They are far more varied.

    However within phyla, body plans would be similar enough so that some constant surface area relationship existed. Which would set things up for a ratio between the brain and body surface area.
  10. Jan 17, 2012 #9
    I'm sorry, but the more I think about this, the less it makes sense to me.

    What does volumes grow by the cube mean? What does area grows by the square mean? These are, I think, utterly meaningless statements from a mathematical and physical standpoint, except for the obvious: volume is three-dimensional, area is two-dimensional. I was wondering about this when I read Gould, but I was more interested in his biological insights, which are fascinating, than in his deeply flawed math (and politics, but we'll leave that alone).

    These statements only make sense if we say that the ratio of volume to surface area of a cube of side length x is x/6. Therefore, the ratio grows linearly with x. Outside that context, I see no sense in these statements.

    As for the human body, it's pretty far from a cube, and any approximation that treats it as such would perforce be way off. As a rough approximation, I'd say that the human body approximates a rectangular cuboid of dimensions roughly in a ratio of 9:2:1. For a dog, I'd go with 5:4:1.

    Then, we have to decide what growth occurs in each of the three dimensions.

    So, I retract all references to Gould and to surface area in my original post, but the original question remains: why do bigger bodies require proportional smaller brains?
    Moonbear made a reasonable hypothesis, but I wonder whether there are more.
  11. Jan 17, 2012 #10


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    Does this help?

  12. Jan 17, 2012 #11
    About as much as this does:

    I stated that the cube case is trivial four times already.
    Can you rigorously state volume grows by the cube for an arbitrary geometric shape?
  13. Jan 17, 2012 #12


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    In the general case, a general creature is going to scale up proportionally. It does not matter about the shape. The same could be said about an amoeba.

    Double its height and its length and breadth will double as well, preserving all dimensions.

    At least, ideally.

    If a man were scaled up to twice his height, so he's now 12ft tall, his weight won't double, it will octuple.

    Unfortunately, this won't happen in real life because of the square cube law (Google this). The mans' legs have a cross-sectional area, and in doubling all dimensions, his corss section has only squared not octupled. His legs are now supporting twice as much weight per unit area.

    Let's say a 6 ft man has the following dimensions:
    6ft tall, 2 ft across, 1 foot through, his mass is 100kg, and his leg cross section is 100cm2 (10cmx10cm)

    His legs are supporting 1kg per cm2

    Scale this man up to 12 ft and he is
    12ft tall, 4 ft across, 2 foot through, his mass is 800kg, and his leg cross section is 400cm2(20cmx20cm)

    His legs are supporting 2kg per cm2.

    This double-sized man will collapse under his own weight.
  14. Jan 17, 2012 #13


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    My above post was a little premature. You're not convinced about the linear-cube relationship.
    It does. Feel l free to pick a shape at whim and try it to prove it to yourself.
    A sphere octuples in volume when its radius doubles.
    Note that you can make any arbitrary shape built from a collection of small spheres. So, doubling the linear measurement of any shape will octuple its volume and mass.

    Look, uh, if you're just learning this, perhaps you could be a little less snarky and make fewer assertions about what is trivial and what is fundamental.
    Last edited: Jan 17, 2012
  15. Jan 17, 2012 #14


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    yes, Martin. This i why mechanical engineers know that giant insects are not possible as they are now structured. Compressing force of gravity goes with volume (cubed) while structural integrity goes with surface area (squared). So if you keep making an insect bigger and bigger, it gets to the point where it's weight can't be supported by the surface area.
  16. Jan 17, 2012 #15


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    Cross-sectional area.
  17. Jan 17, 2012 #16


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    You just seem to want a pointless argument.

    I already said....

  18. Jan 17, 2012 #17


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    oops, thanks.
  19. Jan 17, 2012 #18

    Don't patronize me. I'm not learning anything here, as nothing said in the last few posts is more than trivial and obvious. I get that 23=8. You spent a lot of words and numbers to demonstrate that, but I got it in the third grade or so.

    You, on the other hand, seem to assume that doubling one dimension will necessarily be accompanied by doubling of the two other dimensions, and that this holds across species. That may be true, but I see no reason to take it as obvious, and stating 23=8 for the eleventh time using nice pictures will not help to convince me.

    Besides, none of that has anything to do with my question, anyway.

    Indeed, the stingray and the elephant have very similar body plans...
  20. Jan 17, 2012 #19


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    Certainly not. You sure have a novel way of going about, getting irritable, demanding and insulting.

    Why are you annoyed with us exactly? Who do you think is responsible for your failing to grasp the principles we're sharing with you? Ours?

    It was you who asked:

    Don't get snarky because we provided you with the answer to a question you asked.

    In the general case, as I said - it is true. Once we have the general formula, we can consider what might change about a given animal.

    You had not grasped the general case. The principle involved.
    Last edited: Jan 17, 2012
  21. Jan 17, 2012 #20
    As much as I enjoy that intellectual exchange, the Snooker Masters is on, so that will be my last post here. The "general case", the "principle involved" of which you boast, is the third-grade statement that a three-dimensional object has three dimensions (gasp!), and thus doubling all three will lead to an eightfold increase in volume. I guess a small mind will capture that fact with the slogan "volume increases by the cube", but some of us aren't satisfied by slogans, as my cylinder examples show. Now go apply that brilliant slogan to a cobra, a stingray, and an elephant (same body plan, according to apeiron), and tell me how it worked out. I'm done arguing with you.
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