The form of reproduction you are referring to is called vegetative propagation. In vegetative propagation, new plants derive from the stem, root, or leaves of existing plants, without involving the production of seeds or spores. The offspring are genetically identical to the parent plant since they are produced asexually, resulting in a clone of the original plant. Examples of vegetative propagation include runners (e.g., strawberry plants), bulbs (e.g., onion plants), and tubers (e.g., potato plants).
