Bedbugs undergo incomplete metamorphosis, a type of development characterized by three life stages: egg, nymph, and adult. Unlike complete metamorphosis, where a larval stage is present and the insect undergoes a significant transformation (including a pupal stage), incomplete metamorphosis involves gradual growth and development where nymphs resemble miniature adults. They molt several times before reaching the adult stage, thus showing minor changes in form and size rather than a dramatic transformation.
The other options each represent pests that do not undergo incomplete metamorphosis. Carpenter ants, for example, experience complete metamorphosis, including distinct larval and pupal stages. Brown recluse spiders and American dog ticks are also not insects undergoing metamorphosis; spiders belong to arachnids and do not follow the metamorphosis pattern seen in insects, whereas ticks, as arachnids as well, develop through a larval stage, followed by nymphal and adult stages, also not fitting the definition of incomplete metamorphosis.