Negative frequency-dependent selection (ie, declining fitness with increased frequency in
the population) is thought to be one of the factors that maintains biological diversity. In this
paper, we give a concrete mathematical argument supporting this. Our model is as follows: A
collection of species derive their fitnesses via a rock-paper-scissors-type game whose
precise payoffs are a function of the environment. The new aspect of our model lies in
adding a feedback loop: the environment changes according to the relative fitnesses of the …

Negative frequency-dependent selection (ie, declining fitness with increased frequency in
the population) is widespread in biology, and is thought to be one of the main factors
maintaining biological diversity within a community [24, 30]. There are many different
mechanisms that reduce the fitness of common genotypes or species, but two interactions
are nearly ubiquitous, operating