An iterative continuous-event model of the population outbreak of a phytophagous Hemipteran

Resumo

A model scenario of a drastic increase in the number of a phytophagous species (jumping plant lice) at the expense of primary and secondary Encyrtidae parasites (a large family of parasitic microwasps) has been developed based on the case study of changes in the local density of a Psyllidae species in Australia. A phenomenological model differentially describes the reproduction efficiency in several ranges of the population state. A continuous-event structure is proposed where the rate of decrease in the abundance of generations is uneven at different developmental stages of the insect with an incomplete metamorphosis and the points where it changes are determined by the state of internal variables in the auxiliary equation for the continuous system. A spontaneous time-limited local outbreak occurs after overcoming the threshold equilibrium in the iterative dynamic system, which reduces the effect of normal regulatory mechanisms of psyllid reproduction and changes the rate of the decrease in the abundance of generations. The method of supplementing the right-hand part of the first equation by special functional with a limited range of values simulates a drastic decrease in survival with depletion of resources. This modification causes a backward tangent bifurcation. Several generations after the bifurcation, the population switches to the mode of fluctuations without any pronounced cyclic component, which is common for small insects with a low abundance.