The construction of this model is described in two papers by Wilensky & Reisman (1998 2006) referenced below. The classic LV models though assume the populations can take on real values, but in small populations these models underestimate extinctions and agent-based models such as the ones here, provide more realistic results. It is a closer match to the classic Lotka Volterra population oscillation models. This variation is more complex than the first, but it is generally stable. Once grass is eaten it will only regrow after a fixed amount of time. The behavior of the wolves is identical to the first variation, however this time the sheep must eat grass in order to maintain their energy - when they run out of energy they die. The second variation, the "sheep-wolves-grass" version explictly models grass (green) in addition to wolves and sheep. This variation of the model is particularly well-suited to interacting species in a rich nutrient environment, such as two strains of bacteria in a petri dish (Gause, 1934). This variation produces interesting population dynamics, but is ultimately unstable. ![]() As such, sheep don't either gain or lose energy by eating or moving. ![]() In this variation, we model the grass as "infinite" so that sheep always have enough to eat, and we don't explicitly model the eating or growing of grass. To allow the population to continue, each wolf or sheep has a fixed probability of reproducing at each time step. Each step costs the wolves energy, and they must eat sheep in order to replenish their energy - when they run out of energy they die. In the first variation, the "sheep-wolves" version, wolves and sheep wander randomly around the landscape, while the wolves look for sheep to prey on. There are two main variations to this model. In contrast, a system is stable if it tends to maintain itself over time, despite fluctuations in population sizes. Such a system is called unstable if it tends to result in extinction for one or more species involved. This model explores the stability of predator-prey ecosystems. You can also Try running it in NetLogo Web If you download the NetLogo application, this model is included. (back to the library) Wolf Sheep Predation ![]() NetLogo Models Library: Wolf Sheep Predation
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