A Volterra-Hamilton system describing the evolution of a dimorphic clone in the presence of inner developmental noise is considered as an open system in interaction with a fluctuating environment, subject to optimum growth conditions.
In the case of constant environment considered previously by Antonelli and Křivan the system is confined to an invariant set of a stationary diffusion process, which provides a model of growth canalization. Different invariant sets can be identified with different clonal types of a given species. The probability distribution of the diffusion over an invariant set accounts for the variability within the corresponding clonal type.
In this paper, the external noise in a non-constant environment is shown to trigger transitions between invariant sets as it interacts with the inner developmental noise. Such transitions from one clonal type to another, which do not involve any genetic alterations, are known in biology as plastic responses to the environment.
This is an entirely different mechanism than genetic mutations, which can disturb the equilibrium of the system. If after such a mutation the system settles down in a new stationary state with its own invariant sets and probability distribution, then one or more new genetically altered species will emerge.