I was just looking at my tree and there are gnats all over it!  Mostly on the leaves.
I am leaving for work now, but I will check the site tonight for responses.

Thanks.

JoAnn
I am spraying with a peroxide/water mix, seems to help.

indoor tree or outdoor tree?  newly rooted, or more than a year or two old?

(Fungus) gnats are harmless on leaves.
They are a pest, pest in indoor/GH grown plants.
The larvae do damage the roots.

My guess?
You may be referring to them easy controlled aphids.
Soapy water spray will kill them all.

Dry-loving spider mites are tougher.

George makes a good point, you may have the wrong bug, can you post a pic?

The tree is outside - the LSU Purple I planted in the spring.  It is about 7ft tall with lots of new growth and figs!  I am praying for record breaking heat for them to start ripening by the end of Oct.  My Mom is coming for a visit from the 3rd -10th and would LOVE to have some fresh figs from my tree for her to try.

Pictures!?  Yikes!  They are small and have wings - they move quickly.  I googled images of gnats and found one on a man.  The caption mentioned cool nights with high humidity - I think that explains it.  Tonight is in the low 70s with 85% humidity. Should I just wait it out or introduce them to their demise?

Here's a picture of the tree before the gnats;)  Yeah - I like my tree!

Fungus gnats don't really hang out outdoors... at least I don't necessarily notice them much outside.  Not to the quantity you're describing.  Fungus gnats also usually keep to the soil line for me, not near the leaves.  Hope they aren't fruit flies... (the kind you get from the grocery store)

Definitely not aphids - they are small, black with wings, no ripe fruit yet. Maybe I could take a picture of the little buggers, they are about 1/8 inch long, maybe smaller.

This is the best I could do for pictures - they are tiny!!

Try spraying with listerine.  I never tried it, but I heard it works great on flying things. 

Not sure what they are as the pics don't really show much, but your leaves look perfectly healthy, no insect damage so maybe they are harmless? 

Based on your pictures, you do not have aphids or fungus gnats. The insects in your pictures are the wrong shape & size. I do not have a good guess as to what they might be. I agree with BLB. Don't do anything until you know they are causing a problem. If you really want an ID, I would bet the people at Texas A&M will do it.