Fig. 1. Cooperation breaks down in diverse and long-lived microbiomes.

a Cartoon of the model: Both hosts and microbiota can invest in cooperation. Host can also invest in host control that preferentially benefits more cooperative symbionts. Microbes migrate into the system at rate M from a fixed environmental pool of largely uncooperative microbes between host generations, and at rate m each symbiont generation within host generations (Methods, Table 1). b Example dynamics from the model. Cooperation evolves when the benefits of cooperation are high, symbiont relatedness is high (i.e. within-species diversity is low) and the microbiome is short lived (the ratio of symbiont to host generations is 1). Increasing the number of symbiont generations within a single host generation (generation ratio) increases symbiont competition within the host and cooperation with the host collapses (unless stated, parameters are x = y = 2, R = 0.5, f = 0.02, g = 0.1, m = 1 × 10⁻⁶, M = 0.05). c Effect of relatedness and benefit to cost ratio of the evolution of cooperation. Cooperation is only stable at high relatedness, high benefit to cost ratio and low generation ratio. Increasing the generation ratio leads to the collapse of cooperation across a wide parameter space.