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In this fantasy world there is no day/night but a constant mild light. There are also no seasons and the mild light is akin to the light at dawn or dusk. The sun doesn't really exist.

How would the plants and animals differ?

I assume sleep would look pretty different as well as photosynthesis.

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    $\begingroup$ Can it be a perpetual Saturday evening, as on Ursa Minor Beta? :-) $\endgroup$ – HDE 226868 Mar 21 '15 at 1:10
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    $\begingroup$ I am no expert on sleep (as my roommate will attest), but I think that light is the factor with the largest effect on circadian rhythm for most animals. If there are no daily temperature variations to keep time, then animals and plants may not have synchronized cycles. There would be no separation between diurnal, crepuscular, and nocturnal species, decreasing the number of biological niches in the environment. $\endgroup$ – 2012rcampion Mar 21 '15 at 2:14
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Since in your world, there are no natural time cycles, life will not have an external synchronization. Therefore the main changes in your world will be to changing weather (unless your world doesn't have that either). Instead of day-active and night-active animals, you might have dry-active and rain-active animals.

Some processes will still be cyclical because the cycles are not imposed but inherent in the process. For example, the predator-prey relation can lead to periodic cycles. Also biological processes often come in cycles not synchronized to external triggers (the most obvious one being menstruation). However, the complexity of ecosystems and biological systems probably means that the whole timing relations would be more chaotic, with several different cycles overlaying with more complex time behaviour.

I could imagine that animals would not have fixed, synchronized sleep cycles. While the brain needs sleep, some animals like dolphins can put parts of their brain to sleep. I imagine in a constant light world, such mechanisms would be more common also to land animals. In herd animals, it might also be that different animals sleep at different times, so that at any time some animals are awake and can react if predators arrive (which also can happen at any time). To minimize the risk that all members of the herd sleep at the same time, those animals would likely have different sleep cycles, so that a synchronization is excluded.

If the average light intensity is the same as in our world (just without the variations), photosynthesis would not be much affected; the plants would simply do it all the time, instead of only half of the time. However, neither plants nor animals would need to protect against intense sunlight.

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There is such an environment on Earth, called the Twilight Zone or more formally the Mesopelagic Zone. Notably, it is insufficient for photosynthesis. But how dim do you intend? Earth is rather dim according the the residents of Bellerophon or OGLE-TR-56b. Hal Clement was prescient with Iceworld in 1951.

An environment is ruled by available energy. Having far less energy on an absolute scale could be abundant if the chemistry is designed to work at that energy level. Such molecules are fragile by our standards, and the lower temperature is required so as not to smash them apart with random motion and nearby molecules rocketing through it.

Just as the natives of Sarr, breathing sulfer and drinking copper chloride, consider Earth to be impossibly cold and too dim to see well, Nadreck’s kind finds Earth to be inhospitable with blood-boiling temperatures, vast oceans of solvent and highly corrosive atmosphere.

If there are a suitable suite of reactions at the proper energy scale for life to exist using them, then that scale will be normal and comfortable.

If not, then it will be too energy-poor for life to take hold. Where low light is an extreme environment that can be explored by life that finds something else more optimal, then it is seen to be impoverished and harsh for that life.

In your case, the whole world is like that, so, it won’t be colonized by a biosphere that is comfortable somewhere else. It will be comfortable there, if it exists at all.

To get the kind of situation you want, perhaps life evolved and thrived under different conditions; then the conditions changed globally, leaving non-optimal biochemistry to cling to existence.

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