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At least among more complex organisms, I cannot think of any examples of highly mobile species (like animals) that also incorporate photosynthesis. Perhaps there are examples that I'm unaware of, but even so it seems to be exceedingly rare.

Is there some good reason for this, or is it a mere chance of evolution?

I could speculate, perhaps, in that photosynthesis just doesn't provide enough energy for the relatively high metabolism of mobile species; but even then, there seems there should be a "sweet spot" where some level of mobility would still be "worth it" for a photosynthesizing species, rather than the strict dichotomy that seems to be observable, so I naïvely find that explanation somewhat dissatisfactory. There just seems to be little reason for animals to not practice photosynthesis, if only to be able to eat less than they need to without it.

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    $\begingroup$ Interesting question. I would think that if you are mobile, and able to eat other non-mobile organisms that can't run away, then there's a pretty strong reason not to do photosynthesis: it's way faster to just swallow a bunch of carbohydrates in one bite rather than synthesize them all from scratch. $\endgroup$
    – Roland
    Jul 22, 2015 at 17:34
  • $\begingroup$ @Roland, I think nature shows that it's not always easy to "just swallow a bunch of carbohydrates". ;) $\endgroup$
    – Dolda2000
    Jul 22, 2015 at 18:23

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The difference in energy requirements of a motile species make photosynthesis an unsuitable form of primary energy generation for them.

Since plants are sessile, their energy consumption rates are lower. Plants have approximate respiration:photosynthesis rates of 0.35-0.9, as can be seen in this table (click to enlarge):

enter image description here

Once the energy consumption rates exceed 1, the organisms will, by definition, no longer be full autotrophs, as they will need to obtain their energy from alternative sources. Therefore, the relative low energy content of sunlight makes it impossible for motile animals, which have a larger energy requirement, to survive fully via photosynthesis.

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Why be mobile? To follow the sun?

Plants are mobile. Their seeds are. We have plants living on other plants.

Once they have a spot on the sun though moving does not necessarily improve your situation, being stationary and defending your territory though does. (Growing taller, deeper roots, wider crowns)

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There is at least one species of highly mobile animal that can photosynthesize, depending on your definition of "highly mobile":

Sea Sheep? This Adorable Sea Slug Eats So Much Algae It Can Photosynthesize

The catch is that this animal does not produce its own chloroplast.

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There are unicellular eukaryotes that photosynthesize and are very mobile. Many are in the phylum Chlorophyta. This one mentioned below is used for research and protein production, and can live on eating organic compounds in the dark. In the lab you dont need to stir small containers growing them - they move themselves to the light.

https://en.wikipedia.org/wiki/Chlamydomonas_reinhardtii

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