Answer: Though they do not have pure white bark, river birch (B. nigra) is quite resistant to attack and gray birch (B. populifolia) is moderately resistant. However, gray birch is very susceptible to leaf miners and river birch is attacked by leaf aphids. Probably the best species is the Monarch birch (B. maximowicziana) which has white bark on older trees and is only moderately susceptible to leafminers and aphids.
As with most wood boring insects, the bronze birch borer is extremely difficult to control, especially if an infestation is established. This pest seems to prefer birches located in unsuitable habitats. Birches generally grow in shady, cool and moist wooded areas. Thus, when birches are planted as an accent plant in sunny, dry urban lawns, they are rapidly attacked.
If you decide to replant a birch, keep the soil moist, fertilize regularly and control aphids and leafminers to help keep your birch vigorous and better able to withstand borers.
I can find only one source of these trees in California: Sonoma Horticultural Nursery in Sebastopol. Perhaps a phone call to them can lead to a source closer to your home. (707-823-6832).
Best wishes with your landscape!
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