chapter  4
62 Pages

Interacting populations

The Lotka-Volterra model takes its name from the authors of the first investigations of interacting populations. Volterra (1926a; 1926b; 1931) based his considerations on the unexpected results of the field observations of the biologist D’Ancona (1954) on the fishing catches in the Adriatic sea after the First World War. Other models were developed later to avoid the main drawback of the original Lotka-Volterra model, namely, the neutral stability of its interior equilibrium point. This makes the solutions sensitive to variations of the initial conditions of the system, and therefore biologically they are not very satisfactory. These modifications include at first quadratic models, which incorporate a logistic growth term for at least one of the two populations, and then also other nonlinear terms, such as the effect of satiation in feeding.