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12.6: Independent carrying capacities

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    Self-limitation or self-enhancement of population growth are within the \(r\,+\,sN\) framework. Below these terms are in red.



    The self-feedback term for the prey, \(s_{1,1}\), is typically negative, reflecting a carrying capacity for the prey in the absence of predators, \(K_1\,=\,-r_1\,/\,s_{1,1}\). This tends to stabilize the system, dampening oscillations and leading to a joint equilibrium of predator and prey.

    On the other hand, the self-feedback term for the predator, \(s_{2,2}\), is typically zero, meaning the predators vanish in the absence of prey. But it could be positive, indicating benefits from group hunting and the like. A positive value for \(s_{2,2}\) tends to destabilize the system, leading to enlarging oscillations.

    This page titled 12.6: Independent carrying capacities is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Clarence Lehman, Shelby Loberg, & Adam Clark (University of Minnesota Libraries Publishing) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.