If some twisted genius vaporized all 10 trillion cells in your body — along with the hair, the fingernails, and other tissue they create — it would not leave empty space behind. A body-shaped cloud made of bacteria, viruses, and other former stowaways would hover briefly in the air. The cloud would outline your skin, delineate your lungs, trace your digestive tract. You might be gone for good, but your shadow biosphere would remain.

We got our first glimpse of these tiny tenants — now known collectively as the microbiome — in the late 17th century, when a Dutch lens grinder named Anton van Lee...