This post is not the second post about shadeshifters that I mentioned in the first post on that subject. In case you missed that first one, it was about colour-changing animals; I reserved the word ’shadeshifters’ for animals that can change colour in seconds, minutes, or a few hours at most. The post asked the question whether shadeshifters elsewhere in the universe might be larger than the ones we have on Earth. The promised second post was to be about possible workarounds to allow large shadeshifters. Well, that will -probably- become the third post on this subject.
This new second post will be about the energy costs of colour changing, also called metachrosis. I had mentioned costs aspects without going into detail, for the simple reason that papers on the subject did not provide measurements of the energy bill of colour change.
What would a colour-changing system cost? If such a system on another world is similar to ones on Earth, four cost factors can be distinguished. The first factor is a ‘visual environment analysis centre’; this brain part makes use of an already existing good visual system and analyses environmental visual information in terms of colour, contrast, contours, etc. It then makes a sort of recipe that describes the visual environment. The second part, the ‘body mapper’ is also a brain centre, one that translates the recipe into a map fitting the animal precisely, holding instructions for all colour-producing skin cells (chromatophores). The third factor is the cost of firing neurones that run from the ‘mapping centre’ to every chromatophore, turning it on or off. The fourth factor deals with the chromatophores themselves: spreading or concentrating pigment granules must also cost something.
Anyway, back to shadeshifting. Lacking facts, we can still think about whether animal size would affect these costs. Let’s assume that a shadeshifter needs four layers of chromatophores of different colours to produce a wide range of colour effects. I see no need for a large animal to thicken each of these four layers. Whether the colours are visible will depend on the dead tissue above, not on the thickness of the colour-producing layers. A skin area of 10 square centimeter would therefore contain the same amount of chromatophores for a small as for a large animal. In other words, the total number of chromatophores and the number of neurons to turn them on and off are linearly related to the skin area of the animal. If a large animal has three times the skin area of the small one, it will have three times the number of chromatophores. Note that we just concluded that the third and fourth cost factors linearly depend on skin area.
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Click to enlarge; copyright Gert van Dijk |
Aha! Now we are back on familiar ground, meaning ‘scaling’. ‘Scaling’ has been discussed on this blog many times (***). Say we have a chameleon with a length of 25 cm; in other words, L=25. We increase its length, width and height all five times, so the animal become 5 times longer, wider and higher; its length will be 5L=125 cm. Now, surface area scales as a square, so the animal’s skin area becomes larger by the square of 5, meaning it becomes 5^2=25 times larger. The third and fourth cost factors of our larger shadeshifter are therefore 25 times those of the small one.
By itself this does not mean that much. A large animal would in general obviously have higher energy costs than a small one. The key question is how the costs of shadeshifting relate to the animal’s overall energy budget. To answer that, we need to know how metabolism scales with size.
First, we need to realise that each kg of animal will need an amount of energy, so we need to think about the mass of the animal. Mass is related to volume, and volume is easy to work out; it scales with the third power. Our super-chameleon, 5 times the length, width and height of the small one, has 5^3=125 times the volume of the small one, and therefore also about 125 times the mass.
You might think that the energy needed to sustain one kg of animal is the same for a large and a small animal. If that were true, then the larger animal, 125 times the mass of the smaller one, would also have 125 times more energy to spend. That would be very nice for shadeshifting, because the costs of shadeshifting would only become 25 times larger. Brilliant!
But no. It doesn’t work that way.
It actually costs more to sustain one kg of rabbit than one kg of elephant. Small animals have relatively high energy costs, which means that small animals run more quickly out of energy than large ones (this is why mice need to eat often). Mind you, the effect is relative: in total, an elephant of course needs more energy than a mouse; it’s just per kg than the elephants needs less energy. The relationship of metabolism to body mass is well known in zoology:
Minimal metabolic rate (MMR) = a M^0.75
‘Minimal metabolic rate’ means the animal does nothing besides being alive. The constant ‘a’ differs between groups of animals, and we can forget that for now. The exponent of 0.75 is less than one, which is another way of saying that large animals use relatively little energy. Can we now work out what scaling by length (L) does, rather than by mass (M)? Yes, we can: mass relates to volume and volume was length to the third power:
mass (M) ~ volume ~ L^3
We can now replace ‘M’ in the first equation with ‘L^3’, giving:
Minimal metabolic rate (MMR) = a (L^3)^0.75 = a L^2.25
This is the equation we need. It tells us what happens to MMR if we make the length of an animal 5 times larger. MMR then becomes 5^2.25 times larger, which is 37.4 times larger. Remember that the skin area became 25 times larger. In other words, the energy budget increased 37 times, and the costs for colour changing 25 times. That’s a comfortable margin! In short, large animals can more easily afford shadeshifting than small ones. .
But how about the first and second cost factors? I see no reason why analysing the visual environment should depend on animal size, so the first factor should not cost more. The second factor was making a map telling each chromatophore what to do. In its simplest form, the costs for such a map would also reflect the number of chromatophores, meaning skin area, which does not alter the reasoning above.
All in all, the relative costs of shadeshifting get smaller as size increases. That is good news for large shadeshifters! Of course, the problems posed by thicker dead skin layers are still there…
PS the video at the top of the video was made for the instagram channel I am trying out (j.gertvandijk)
8 comments:
Perhaps the shadeshifters use their shifting talents more as a supplementary than as a primary action. Imagine an shadeshifting elephant, keeping most of its skin under a layer of dust or mud; not much of the colorchanging would be visible under those conditions - bits and pieces visible around the ankles, maybe the ears and trunk, especially *while* the elephant postures and moves those ears and trunk around.
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On the other hand, if the shadeshifting elephant had just bathed itself or been cleaned by its keepers, then the entire body potentially becomes a canvas for whatever color changing it is doing.
{so maybe shadeshifting would be most useful in hippos and giant salamanders, keeping themselves moist and clean, while also avoiding sunburn}
This is a fascinating and useful analysis! You can probably assume that past a certain size camouflage becomes pointless for an animal, and thermoregulation and communication take over--but that would predict that very large animals would be more brightly colored, which we don't actually see on Earth. I wonder why?
The discussion of cephalopod nerves reminded me of a theory I read recently in the book "What is Intelligence?" By Blaise Aguera Y Arcas. He proposes that intelligence comes about in order to more accurately predict your environment, and that among social animals like humans our environment includes other humans, who are also predicting us, leading to a recursive feedback loop that favors runaway growth in brain size. Octopuses are solitary though, so why are they so intelligent for invertebrates?
His theory is that, because cephalopods have unmyelinated neurons, they can't have one big central node for processing sensory information--it would be too expensive to send signals from the tips of their tentacles all the way to a central brain. Instead, every tentacle, and even every sucker on every tentacle, does most of its sensory processing locally--which includes the task of predicting what neighboring suckers and tentacles are going to do in order to coordinate the entire octopus toward some goal like hunting or mating. As a result, the recursive intelligence intelligence improvement loop happens at the level of a single octopus trying to predict the behavior of its own body, rather than within a group of octopuses trying to predict each other's behaviors.
On large animals being overall less colourful than smaller ones, this probably has to do with the availability of carotenoids. Mark Witton discussed it a bit here https://markwitton-com.blogspot.com/2018/02/a-mural-for-dippy-restoring-celebrity.html?m=1
Great find!
>very large animals would be more brightly colored, which we don't actually see on Earth. I wonder why?
Possibly because most of the large-bodied animals are mammals, which for the most part don't see too much in the way of colors...and then you have the animals which are preyed upon by mammals. (note that some of the larger deer and antelope are red-furred, which their predators can't distinguish from floral colors)
Anthony: you raise the interesting point of how much of an animal’s skin is coated by dust or mud. Animals seem to apply such coats on purpose, and that purpose probably has nothing to do with camouflage (although a nice coat of mud would camouflage even a pink elephant). I wonder to which extent the skin of other animals is coated in such a way; many animals that do not wash themselves still have very visible colours (antelopes, giraffes), so my guess is that dirt coatings generally only ply a small role in visibility. No data though…
Waqualbus (Spugpow?): I also used to assume that ver6y large animals could not use camouflage, but a fascinating talk on last year’s DinoCon about camouflaging T. rex made me reconsider that. Well, to some extent: you cannot hide T. rex from view on an open plain, but in forests camouflage could still work. At present large animals are not brightly coloured, but they are all mammals, and perhaps their history of being small nocturnal creatures meant that their genetic colour gamut became limited to boring browns and greys. Now that the colours of dinosaurs are studied more en more, perhaps we will find that even large ones could be garish.
I like the theory of Aguera y Arcas! I have only now started to think about how the design of neurones must affect life in the universe to an enormous degree; there may be a post in there somewhere!
Davide: I never thought about carotenoid availability. But animals on other world could easily make their own interesting pigments, independent of outside sources. Mark Witton is working on a book on dinosaur colour (more on Patreon), by the way.
Anthony: Aha! You are correct: why have colours if you can only see greys? But in my future third post on the subject I plan to make the point that changing the brightness of the skin (the ‘value’ in painting terms) without changing colour (‘hue’) would still present a large advantage.
Yes, Waqualbus=Spugpow--it's what I default to when I can't be bothered to enter a personal URL to comment.
And indeed, the latency of neurons is probably a big source of variation in organisms. A species with much lower neuron latency and bandwidth than vertebrates could presumably maintain the same high level of responsiveness to its environment with far fewer neurons, and presumably much less intelligence as well. The more information the brain receives "directly," the less it has to creatively extrapolate from limited data, and the less useful intelligence becomes. So presumably a creature with better neurons would be much larger and stupider, while also being more agile and quick to respond to complex stimuli, like a giant housefly.
Apparently some crocodilians (including some decently-sized species) have the ability to make their skin darker or lighter in response to environmental conditions. (with changes in under 90 minutes)
https://www.nature.com/articles/s41598-018-24579-6 isn't the only article I've seen on the subject (and I haven't fully read through this one) but it seems to have both a good overview and some cool things past that.
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