Diversity and extinction in a lattice model of a population with fluctuating environment.

I study a lattice stochastic model of a mutating population sensitive to the influence of a fluctuating environment. The dynamics of the population stressed by linear and periodic disturbances is investigated. In agreement with previous studies of nonspatial models, I find a critical rate of change in the environmental variable beyond which the population becomes extinct, and I show explicitly that the presence of space in the model can affect the critical rate. Further, I study the diversity defined as the total number of different cell types present in the lattice as a function of intensity and frequency of the environmental disturbance. If the disturbance becomes fast and intense the population becomes extinct. Interestingly, I find that for moderate stresses the diversity increases with the intensity and frequency of disturbance. The transition between large diversity and extinction is sharp, implying that the populations with high diversity are generally the ones closest to the extinction threshold. When subjected to colored noise of increasing intensity the system grows in diversity but at the same time is more likely to become extinct.