Behavioral catastrophes in biological systems

Catastrophic behavior of systems of animal organism populations is analyzed in relation to energy inputs into the system. In unconstrained systems, steady state equilibrium behavior is only possible if energy use rates equal input rates, while catastrophic explosions and collapses can occur when energy is drawn from an accumulated pool. In constrained systems, where negative feedback mechanisms regulate proliferation below the energy input rate, catastrophic behavior can occur if the regulative mechanisms saturate or are weakened by external stresses. Such systems are often characterized by breakpoints or thresholds, and we may observe single stable point-equilibria, dual stable point-equilibria, metastable point-equilibria, or cyclic-equilibria. Application of theory to management problems is addressed, with particular reference to an insect pest infesting coniferous forests. Because the risk of undesirable behavior (pest outbreaks) is proportional to the distance from the unstable breakpoint (outbreak threshold), risk can be estimated if the threshold function is known. In the example, the threshold is approximated as a function of forest variables which determine insect numbers and tree resistance to infection.