Do energy costs affect the size of colour-changing animals? (Shadeshifting II)

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. 

The first three factors have to do with neurons, and on Earth neurons are expensive (for example, the human brain requires some 20% of all blood pumped out by the heart while having a mass of only about 1.5% of the body). I do not know whether neurons on all planets will also be expensive, but let’s assume so. Mind you, if neurons would be really cheap somewhere, an organism would not be punished for throwing brain power at any problem; would that allow a runaway evolution of intelligence? In reverse, are we perhaps hampered by overly expensive neurones? If so, we are perhaps more stupid than the rest of the universe; no wonder they don’t come visiting...

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. 

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) 

 

Shadeshifters: colour-changing animals for speculative biology

This video shows an ocopus changing colour;

 I recommend its author's Youtube channel 

Not many animal behaviours on Earth attract more interest than the quick colour changes of octopuses and other cephalopods, who clearly outperforms chameleons and other vertebrates that also change colour. Then again, it depends on what exactly you mean by ‘colour changing animals’. What I mean largely is the ability to use your skin as a high-resolution display screen. That is both attractive and weird, so you would think that many people would use that capability for their speculative biology projects, but that doesn’t seem to be the case (at present anyway). Perhaps the lack of colour-changing is another example of the difficulty of abandoning mammal stereotypes, similar to the automatism of equipping every large animal on any planet with typical mammal front and hind legs? Perhaps...

This post will explore which factors could affect the likelihood of colour changing animals on other worlds. There already is a technical term for this ability: ‘metachrosis’. I admit I wasn’t aware of this term and am probably not the only one: ‘metachrosis’ occurred only four times in PubMed and only 321 times in Google Scholar at the time of writing. ‘Metachrosis’ describes the phenomenon, but we also need a name for animals that do so. The phrase ‘colour-changing animals’ is not precise enough, as we shall see, and also sounds awkward, so I will propose ‘shadeshifters’.

click to enlarge; from Duarte (see reading list)

Not just any kind of colour change

Let’s narrow down the field of colour change in animals. The skin of most humans becomes a bit darker after prolonged exposure to sunlight (in some, short exposure can elicit an unfortunate bright red phase), and human hair tends to turn grey or white if you wait long enough. Many animals change colour twice a year to prepare for summer and winter. Some animals change colour for a few weeks only in the breeding season. The mechanism of these slow changes is usually straightforward in that the amount or nature of pigments in the skin change (not a ‘red’ sunburn though; that is increased blood flow). Such pigment changes are probably universal, i.e. they happen all over the universe, but those are not I mean. I do mean quick changes on a timescale of seconds or minutes, at most hours. I propose to use ‘shadeshifters’ only for animals with this quick type of colour change: cephalopods can change colour within a second, and chameleons take something like 10 to 30 seconds.

Apart from the speed for colour change, the resolution of the display needs to be considered too. In this aspect cephalopods are the undisputed masters, being able to mimic small pebbles, sand, coral, etc. because their skin displays have a very high resolution. But that doesn’t mean that a low-resolution display would be useless or boring. Suppose some animal walks around in a shaded forest without direct sunlight, in which the environment offers little colour contrast as well as little dark-to-light contrast. That animals would do well if it had a slightly mottled almost monochrome colour pattern. But when that animal walks out into bright sunlight, it would benefit from counter shading, with the shaded areas of its body much lighter than the sunlit areas. In both environments the spatial resolution of the skin display could be low, but the change would camouflage the animal well in both surroundings. This suggests that shadeshifting does not need to be limited to high resolution displays to be effective.  

What would you use metachrosis for?

It pays to keep in mind why animals have colours in the first place. Depending on which source you use to answer that question, you may distinguish three or more different purposes. Here is a simple threefold scheme: colours serve thermoregulation, communication or camouflage. Colours for thermoregulation can offer protection from heat, for which being white and reflective helps, or from cold, for which being dark helps. Camouflage is not limited to prey animals that try to escape predation by mimicking the background or breaking up their outlines. Predator can use the same techniques to get closer to their prey too. Animal can also mimic very conspicuous objects to fool others into not recognising them, such as a mantis that looks like a bright flower. As for communication, animals can use colours to signal all kinds of messages to one another, from ‘I am now sexually receptive’, through ‘I am flashy, I am fit!’ to ‘Do NOT mess with me’.

If you think about metachrosis from the point of view of shadeshifters, you start to feel sorry for animals that have no metachrosis, because they must settle for some sad compromise between thermoregulation, communication and camouflage. Think about a snow hare: for thermoregulatory purposes black might be the better colour, but being white in snow offers obvious camouflage benefits (of course, evolution will probably start tinkering with that white pelt to improve its thermoregulatory performance. All this suggests that a major benefit of metachrosis is that an animal can switch between colour purposes. There are indications that chameleons indeed choose different camouflage patterns depending on which predator they face. The mimic octopus uses its colours along with the position of its arms and its behaviour to mimic different animals, and it probably does not choose which animal it mimics at random.

click to enlarge; form wallin (see reading list)

What does it take to change colour quickly?

On Earth, the most common way to achieve metachrosis is to have ‘chromatophores’ with pigment transportation. A chromatophore is a cell that contains particles of pigment. These cells are named for their colours (melanophores for brown to black, xantho- and erythrophores for yellow and red, etc.). Some cells reflect light (irido- and leucophores). When the particles are clumped together, their combined colour effect is weak, but when the particles are spread out, the colour becomes stronger.

click to enlarge; How cephalopods produce colour; from Figon (see reading list)

To choose a particular colour requires turning different cells on or off. Hormones can be used for that but cannot switch a specific yellow cell on while turning the next yellow off. High resolution metachrosis  require a well-developed nervous system than allows ways to control those ‘pixel cells’. This can only be done if the animals has a sort of map, or an instruction tree, to tell which parts should have which colours. That map has to be designed based on the visual characteristics of the environment, and for that you need a high-resolution visual system and appropriate processing power. In short, shadeshifters need a good brain and a good visual system. Don’t expect hi-res metachrosis in animals with poor visual processing capability!

But the rub is that both chromatophores and the nerve endings that control them must be alive. Skins typically consist of layers of living cells that are covered by dead material, such as dead epidermis cells. That dead layer helps provide mechanical protection (and also helps as an osmotic and chemical barrier). It will not surprise anyone that larger animals have thicker skin than small animals, meaning the dead layer is thicker too. That dead epidermis scatters and absorbs light, which ruins the colours of the deeper lying chromatophores. Obviously, metachrosis can only work if the skin is visible! Hair, feathers and thick scales add so much dead tissue that metachrosis becomes pointless. This is probably why the chromatophores of mammals and birds lost the ability to move pigment particles around in the cells: that would be pointless. Fish, amphibians and reptiles do have such cells and do have metachrosis.

Limiting factors

The maximum size of a shadeshifter probably depends on how thick that dead skin layer is. Of course, if colour-changing is very advantageous, you would expect evolution to come up with a way to make those dead cells as transparent as possible, and for the dead skin to be thinner than holds for comparable species of similar size. I tried to find papers comparing the thickness and transparency of the epidermis between chameleons and lizards of comparable size but could not find any. On Earth, large chameleons, about the size of a cat, are the largest terrestrial shadeshifters. It is of course quite possible that chameleon size is limited by reasons that have nothing to do with their colours.    

Animals living in water may not need a thick dead epidermis as much as land animals do, perhaps because there is less mechanical abrasion under water. The largest aquatic shadeshifter appears to be the Giant Pacific Octopus, with a mass of some 15 kg. Again, I have no idea whether octopus size is limited by metachrosis; this does not seem likely, but hi-res metachrosis will have an energy cost.          
           
In conclusion, shadeshifters would be animals with excellent visual processing capability whose skin is open to view, not covered with hairs, feathers or anything like that. Terrestrial ones would probably be fairly small and aquatic ones may be bigger. That size limit is a pity but the remaining restrictions leave  enough leeway to play with. Still, I am thinking of workarounds that would allow larger shadeshifters. Are there ways to make the dead epidermis tougher and more transparent without thickening it? Thinking more out of the box, can the colours from deep in the skin be transported to superficial layers? Farther out of the box, is it possible to change the colour of dead tissue, which probably requires abandoning chromatophores as the engine of colour change? Now that I have already let some cats out of that same box, I would not be surprised if the readers of this blog come up with solutions well before I am ready to write another post on the subject.

Reading list

Wallin M Nature’s palette. How animals, including humans, produce colours. Www. Biosicioence explained 2002

Duarte RC, Flores AAV, Stevens M. 2017 Camouflage through colour change: mechanisms, adaptive value and ecological significance. Phil. Trans. R. Soc. B 372: 20160342. http://dx.doi.org/10.1098/rstb.2016.0342

Figon, Florent and Casas, Jérôme (August 2018) Morphological and Physiological Colour Changes in the Animal Kingdom. In: eLS. John Wiley & Sons, Ltd: Chichester. DOI: 10.1002/9780470015902.a0028065

Stuart-Fox D, Moussali A. Camouflage, communication and thermoregulation: lessons from colour changing organisms. Phil. Trans. R. Soc. B (2009) 364, 463–470 doi:10.1098/rstb.2008.0254

Meyer W, Schmidt J, Kacza J et al. Basic structural and functional characteristics of the epidermal barrier in wild mammals living in different habitats and climates. European Journal of Wildlife Research, 2011, 57 (4), pp.873-885. ?10.1007/s10344-011-0499-9?. ?hal-00664099?

Akat E et al. Comparison of vertebrate skin structure at class level: A review. Anat Rec. 2022;305:3543–3608.