Answer: Alyssum spreads by underground roots and also by seeds. Your best defense is to keep the plants cut back so they don't flower (and produce seeds) and to dig the roots and stems out of the soil. If you keep the green sprouts cut back so they can't manufacture energy, the roots will eventually die out. An additional measure is to lay 3"-4" of organic mulch material over the soil to exclude light which will keep any seeds from germinating. Alyssum makes a wonderful groundcover, as long as it behaves itself!
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