It could be mold and/or mildew. If the roof is shaded, all or in part, any dampness/water/wetness up there will 'stick around' and do this.
To test it out, mix a solution of 1 cup Household Bleach w/1 gallon of water. 2 cups for 2 gallons, and so on. (You can 'up' the Bleach if you want a stronger mix but it MAY kill/damage your vegetation wherever it runs.) W/O the sun around, 'broom on' some of the mix on the streak. (Start w/a conspicious part, perhaps in the back of the house or towards the peak of the roof.) Let it sit. Let it sit for about 15 minutes. If it disappears w/the use of a garden hose when you rinse, then it's mold/mildew. If not, it could be plain, old dirt.
Unfortunately, if the cleaning w/bleach works, you'll need to wash the ENTIRE roof. Otherwise, you'll notice the clean parts from down below. (It may look silly.) To kinda 'permanently' stop the mold/mildew, you need to trim back the trees and such. Mold/mildew like dampness, shade, and warm temperatures. By allowing the sun in and adding the extra airflow, you shouldn't get this problem.
My best to ya and hope this helps.
Jay J -Moderator
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