How does the environment influence farming?

Question

So I've noticed that certain plants haven't been growing in a timely manner. On my starting world I had a toxic biome near the teleport point and got a bunch of toxic top seeds, but after 3-4 cycles of growing and harvesting the wheat right next to them, the toxic tops I'd planted hadn't grown at all.

I've since moved on to an arid biome world. I placed some dirt near the teleport point, tilled it, and planted some wheat, a crystal plant, and a toxic top. None of them have grown.

My inference is that plants will either grow or not grow depending on planet biome; is this correct? If so, which plants grow on which planets?

Another plausible guess is that the tilled block matters - some plants may grow in tilled dirt while others require mud. Is this correct? If so, which plants grow on which blocks?

Answer 1

According to currently available sources, farming is not affected by any external factors (soil type, rainfall, biome, temperature etc.). The only factor that affects plant growth is the growth rate of the particular crop. Toxic Tops require roughly 280 growth cycles, whereas Wheat only requires 27 cycles (a growth cycle represents the interval at which the game calculates growth, and is 20 seconds).

Taken from the Starbound Wikia site: http://starbound.wikia.com/wiki/Farming

Obviously, as the game is still in beta, there is room for this to change.

Answer 2

Update Oct. 2015 (Stable development branch): Crops will not grow in the absence of rain and/or of a player character.

Even though this is an update, I'm submitting this as an answer rather than a comment because the answer has changed: yes, the environment does influence crop growth. For some elaboration, please see my answer at this link.