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7A16 Overshoot and collapse Simulation task Model Z405 “Ecosystem collapse” was developed to represent the historical collapse of a deer population after a population explosion following the extermination of predators. Processes of this type are frequent in many areas — not only in ecosystems. This typical system behavior is quite common wherever renewable resources are overused: overfishing, overgrazing, deforestation, firewood crisis. The same dynam- ics, based on similar structural relationships, also operates in the “world models” which describe the global development of human population, resource use, and envi- ronment (cf. models Z605, Z610, Z612 in Bossel 2007 System Zoo 3). The core of such systems consists of a population which depends on a renewable resource. If overused, the regeneration ability of the resource degenerates until a re- covery is no longer possible and the resource collapses along with the population that depends on it. The process is reduced to its essential components and processes in the following to examine dynamic behavior and development options. Overuse and Collapse ECOLOGICAL per cap CARRYING CAPACITY availability INITIAL ae INITIAL CONSUMERS renewable ep consumer 2— = regeneration | ‘SOUPS resource use growth population | igsses TIME es MIN REGENERATION RESOURCE SPECIFIC BIRTH DEATH or RATE REGENERATION RATE CONSUMPTION RATE = HARVEST RATE Figure Z416a: Simulation diagram for use of a renewable resource. Simulation model The simulation diagram is shown in Figure Z416a. The respective model equations are listed in the following. The two state variables renewable resource and consumer population are coupled to each other by resource use and by the growth of the con- sumer population that is made possible by resource use. The growth of the consumer population \s proportional to its size and the per cap availability of the renewable resource. Since per capita (food) consumption is limited, a Michaelis-Menten saturation is introduced (cf. model Z111 “Density dependent growth” in System Zoo 1). The resource use (e.g. food consumption) is proportional to consumer population and SPECIFIC CONSUMPTION as long as a sufficient amount of renewable resource is available. If this is not the case, resource use is restricted to the available amount. In the case of malnutrition of the consumer population, its rate of growth by BIRTH RATE drops below the rate of /osses by DEATH OR HARVEST RATE. 
