'Bitrophy' II (that's animals with photosynthesis)

In the previous post on this subject, I discussed some basic aspects of the feasibility of an animal using photosynthesis as an auxiliary energy source. Mind you, I never said that it would work! It is too early to reach a conclusion yet, and if you expect this post to finally answer that, sorry, no, not yet...

This post will have a look at some other factors that would have influence the efficacy of ‘bitrophy’, and I plan to try to pull it all together in a third post on this subject. So how do you judge whether or not bitrophy is of value for an animal? I thought that the ‘leaf area’ needed to catch light in relation body size might be a suitable measure: a very large leaf would be expensive in terms of material and metabolic costs as well as mechanical unwieldiness.   

So here we go; let’s walk through some factors.

1. Photosynthesis is inefficient
The inefficiency of photosynthesis, as we know it in Earth plants, is well known and was discussed previously in this blog. To summarise: many wavelengths present in visible light are not used in photosynthesis at all and are thus wasted. Photosynthesis has an inbuilt maximum, meaning that above a certain point increasing the level of light will not lead to more carbohydrate production. Finally, the chemical reaction runs almost as easily backwards as it does forwards, and given the fact that there is much less CO2 (0.04%) in the air than O2 (20%), taking out CO2 and adding O2 was an uphill struggle to start with.        

2. Let there be light
How much light falls on a plant on a planet's surface? Well, obvious influences are how bright the star is, and how far away the planet is from that star. If the orbit is circular, the amount of light reaching the planet as a whole will constant during a year, but it will vary considerably if the orbit is highly elliptical. Then there is axial tilt: if the planet's axis is not perpendicular to the plane of that orbit, the planet will have seasons, and the amount of light will fluctuate during a year. The planet will rotate around its axis, and with day and night comes a halving of the amount of light on any point of the surface (except if there is 'tidal locking’: then one half will be perpetually lit and the other dark).
 
Finally, part of the surface will receive rays of light at a glancing angle, while others receive sunlight perpendicular to the ground, delivering much more energy. You can estimate that the average amount of light is only about one quarter of the maximum (I can expand with some fingures later). And that is at the top of the atmosphere. Below that, you have atmospheric scatter, clouds, and the shade of mountains, other plants, of being under water, etc., etc.

In the previous blog I used the local maximum amount of light to calculate how large a 'leaf' an animal would need to power its 'minimal metabolic rate' (MMR). Well, if you wish to account for the average amount of light, you should make that area four times as large! That means doubling the length of its side, if the leaf is square, or its radius, if it is circular. Of course, you can decide that such large leaves are unworkable, and you can limit the animal to the tropics. Or you can have it shut down and 'hibernate' through the night. 

3. Energy for an active lifestyle
The MMR only powers the energy needs of an animal ding nothing except being alive. More activity requires more energy, and Alexander's book mentions that the average energy need is about three times the MMR. So, if you wish to cater for that, you should increase the leaf area three times; that means increasing the radius by a factor 1.7.

4. More active animals
In the previous post, we learned that the MMR depends on body mass through an exponential function. The exponent was close to 0.75 for all animals, so that doesn’t matter. However, a multiplication factor differed greatly between animal types: mammals (and birds) need much more energy than some other animals.

Click to enlarge; copyright Gert van Dijk

The image above shows three schematic animals: a mammal, a -warm- lizard and a crustacean, all with a mass of 1 kg. I did not bother to refine the shapes, but they should be recognisable.

Click to enlarge; copyright Gert van Dijk

Here they are again, but now with leaves of the right size to cater for an MMR under maximum light. Remember that if you wish to take astronomical and activity problems into consideration, the radius of the leaf should be made 3.4 times as large (1.7 times 2). However, even with the not-adapted leaf, it is obvious that the mammal needs a ridiculously large impractical leaf. The crustacean's leaf looks more acceptable.  

5. Body size
MMR depends on the mass of an animal, and we have set leaf area to follow MMR. But mass is itself a function of size: increasing the size of an animal by a factor x will increase its mass by a factor of x to the third power. For instance, doubling the size will increase the mass eightfold. In reality things are more complicated, as you cannot simply increase all dimensions of an animal by the same amount and expect it to work. For instance, legs need to become thicker. This was explained in earlier posts, here, here and here. If you want more, here and here are posts on the same them devoted to the giants of  Game of Thrones.

Is anyone still there? If you are, we can work out how MMR responds to size as opposed to mass. First, mass is length to the power of three, and second, MMR depends on mass to the power of 0.75, so MMR increases with length to the power of 0.75 x 3 = 2.25.

Does this matter? Yes: say we double all aspects of an animal’s size. The radius of its leaf is doubled, and the area of the leaf becomes four times as large. Its mass increases by a factor 8, but its MMR only by a factor 4.76 (that’s two to the power of 2.25). That particular MMR would require an increase of the radius of the leaf of a factor 2.18 (that’s the square root of 4.75). But doubling the size yielded an increase of the radius of a factor 2.0, slightly too little. So, larger animals need extra large leaves, but the additional increase is not dramatically large. The influence of size on relative leaf area is not all that strong, but still, if you want your bitroph to have a relatively small leaf, the animal itself should be small.

Click to enlarge; copyright Gert van Dijk

The image above shows three sizes of mammal, warm lizard and crustacean, if 0.1 kg, 1 kg and 10 kg. You can see that the leaves are relatively larger for the big animals than their smaller cousins, but the differences between the three sizes are not impressive.            

Well, that concludes this post. It seems that the required 'leaf area' needs to be very large, and I doubt that having such a large structure would be worth it under most circumstances. But what about other circumstances? I will think it over and try to find solutions. No doubt, readers will have suggestions too.

Tabulae Mortuae II (Archives XII)

While I am preparing figures for the next instalment of the ‘bitroph’ series of posts, I thought I would post another ‘dead painting’, again an example of a plant with leaves as large as the sails on a sailing boat.

Click to enlarge; copyright Gert van Dijk

The painting is basically static: there is not a single animal about to enliven the scene, the horizon is completely flat, and the landscape is not exactly spectacular. There are some puddles on the ground, suggesting recent rain in an otherwise dry environment. Only the somewhat unnatural looking clouds add a bit of drama. All this may sound as if I am reviewing someone else’s work, not my own. That is because the painting is old enough to mean that I no longer have a strong image in mind of what I was aiming for. For painters such an ‘intended image’ can obscure judgement of the actual painting. I used to hold paintings up to a mirror to get a fresh look (I now do that digitally, without an actual mirror).

So it is up to the plants together with the clouds to provide any visual drama. The plants grow from underground roots, forming a regular succession of stems resembling telephone poles. In the scene, two roots met and formed special variants of their normal stem. The two entwine one another, and now form a botanic union.

I guess that we are looking at sexual reproduction. I have no idea what happens next; seeds drifting on the wind? Nuts borne by animals? I do remember that new plants form numerous roots that grow out in all directions.

I still like the idea of these underground roots traversing the landscape with maniacal precision, although such linearity looks unnatural. The scientific name of this species, by the way, was ‘Mania predictabilis’. Perhaps I should have envisaged a landscape where these plants are more numerous, and they all criss-cross the otherwise empty landscape.

Unfortunately, the large ‘unileaves’ won’t work for reasons outlined previously. If I do use the idea again, it will be easier to start a whole new painting than to alter this one. That’s why this is a tabula mortua: this painting is dead; it’s no more; it’s expired; it’s an ex-painting.