Ayurveda, India’s 5,000-year-old system of natural medicine, has followers around the world, including in Hollywood. American pop star Katy Perry uses a gut-cleansing treatment rooted in Ayurveda, for instance, and Colombia-born US TV star Sofia Vergara takes capsules of Indian gooseberry – amla – to boost immunity. Scientists estimate that over 30 trillion tiny organisms, collectively known as the microbiome,...