An article by Ives and Carpenter
Understanding the dynamics of complex systems such as the human gut is challenging. Here is the background knowledge Ives and Carpenter suggest is necessary for beginning to develop an understanding of the diversity/stability relationship:
Before designing an empirical study, it is necessary to know enough about the dynamics of an ecosystem and the environmental perturbations that impinge upon it to select appropriate definitions of stability; there will often be several appropriate definitions. These concepts also identify key features—we will refer to them as mechanisms—that together dictate stability. These mechanisms involve the strength of interactions among species, the mode in which species interact (whether they are competitors, predators, mutualists, etc.) that gives the food-web topology, and the ways in which species experience different types of environmental perturbations. Because both species interactions and environmental perturbations can drive fluctuations in species densities, these must be sorted out and quantified to understand their mechanistic roles in diversity-stability relationships.
And, here is a excerpt from the recommendations they make at the end of the paper:
The human gut community does exhibit characteristics of a stable system such as the ability to resist perturbations. So, what are the mechanisms that maintain the diversity, what is the diversity stability relationship and how do we go about studying it.
The relationship between diversity and stability has interested ecologists since the inception of the discipline (35), and the absence of a resolution reflects the complexity of the problem. Much of the complexity derives from the multiplicity of diversity-stability relationships, depending on the definitions of diversity and stability and on the context in which an ecosystem is perturbed. We cannot expect a general conclusion about the diversity-stability relationship, and simply increasing the number of studies on different ecosystems will not generate one.Rather than search for generalities in patterns of diversity-stability relationships, we recommend investigating mechanisms. A given diversity-stability relationship may be driven by multiple mechanisms, and the same mechanisms may evoke different diversity-stability relationships depending on the definitions of diversity and stability. We need more studies revealing exactly what these mechanisms are. This requires models joined to empirical studies that can reproduce, in a statistically robust way, not only a diversity-stability relationship but also the dynamics exhibited by a system.