Prior work has shown a positive scaling relationship between vertebrate body size, human height, and gut microbiome alpha diversity. This observation mirrors commonly observed species area relationships (SAR) in many other ecosystems. Here, we expand these observations to several large data sets, showing that this size-diversity scaling relationship is independent of relevant covariates, like diet, body mass index, age, sex, bowel movement frequency, antibiotic usage, and cardiometabolic health markers. Island biogeography theory (IBT), which predicts that larger islands tend to harbor greater species diversity through neutral demographic processes, provides a simple mechanism for positive SARs. Using gut-adapted IBT model, we demonstrated that increasing the length of a flow-through ecosystem led to increased species diversity, closely matching our empirical observations. We delve into the possible clinical implications of these SARs in the American Gut cohort. Consistent with prior observations that lower alpha diversity is a risk factor for Clostridioides difficile infection (CDI), we found that individuals who reported a history of CDI were shorter than those who did not and that this relationship was mediated by alpha diversity. We observed that vegetable consumption had a much stronger association with CDI history, which was also partially mediated by alpha diversity. In summary, we find that the positive scaling observed between body size and gut alpha diversity can be plausibly explained by a gut-adapted IBT model, may be related to CDI risk, and vegetable intake appears to independently mitigate this risk, although additional work is needed to validate the potential disease risk implications.