Here R0 is interpreted as the proliferation rate per generation and K = (R0 − 1) M is the carrying capacity of the environment. The Beverton–Holt model was introduced in the context of fisheries by Beverton & Holt (1957).
In this specific application, R0 denotes the rate at which a population grows per generation, and K = (R0 − 1) M represents the environmental limit beyond which the population cannot survive. The Beverton–Holt model was first introduced in the field of fisheries by Beverton & Holt (1957).