[For the entire collection see Zbl 0565.00008.]
This paper outlines a formal model of evolution processes: the continuous Lotka-Volterra model. This model works with a continuous set of species represented by a vector q, whose components represent measurements associated to the species such as height, weight, position etc.. The density x(q,t) of the species over the state space is assumed to satisfy the partial differential equation \[ \partial_ tx(q,t)=x(q,t)\cdot w(q,t;x)+\nabla \cdot D(q)\nabla x(q,t) \] where w(q,t;x(t)) is a function representing the interaction of the species and is given by an integral formula.
The system is analysed using methods similar to those used for the Schrödinger equation. It is concluded that Darwinian selection induces a collapse process tending to localize the species in the spaces of possible phenotypic properties.