Answer: Once the seeds have sprouted you should remove the dome. The top is there just to keep the seedbed moist during the germination process. If you keep the dome on after the seedlings have begun to grow things will be too moist and you'll be inviting the fungal disease called damping-off.
Once the seedlings have emerged, place the trays under a source of artificial light to encourage growth, and thin the seedlings as they grow so there's plenty of room between them to provide good air circulation.
I start my tree seedlings in individual pots, but starting them in a tray is fine, too. When started in peat pots, the entire pot can be planted when the trees have outgrown the space available for their roots. Planting pots and all reduces transplanting stress.
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