Graphical Representation and Stability Conditions of Predator-Prey Interactions.¶
Rosenzweig, M. L., & MacArthur, R. H. (1963). Graphical Representation and Stability Conditions of Predator-Prey Interactions. The American Naturalist, 209-223.
Cited by¶
1 citation across 1 artifact.
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Primes¶
- Derivative Amplification
- Inventory replenishment: reorder-point logic that uses the rate of inventory drawdown to set replenishment quantities propagates the amplification through multi-echelon networks. Hiring and capacity cycles: organisations that hire in response to the growth rate of demand overshoot and then lay off, with chains of suppliers and customers driven by the same logic amplifying the cycle. Predator-prey ecosystems: predators whose reproductive investment responds to prey-population growth rate rather than level can produce limit-cycle oscillations that amplify when the trophic chain is extended.
This sourceGraphical (isocline) analysis of predator-prey dynamics whose enrichment/efficiency regime yields limit-cycle oscillations — the ecological instance of derivative-coupled amplification.
Supported in partVerified against the publisher's abstract
The abstract gives isocline stability conditions and oscillatory periods for predator-prey models; it says nothing about reproductive response to prey growth rate or trophic-chain amplification.
“The stability of the interaction close to equilibrium was found to depend exclusively, in the mathematically-continuous model, upon the slopes of two lines in the graph at equilibrium.”
- Inventory replenishment: reorder-point logic that uses the rate of inventory drawdown to set replenishment quantities propagates the amplification through multi-echelon networks. Hiring and capacity cycles: organisations that hire in response to the growth rate of demand overshoot and then lay off, with chains of suppliers and customers driven by the same logic amplifying the cycle. Predator-prey ecosystems: predators whose reproductive investment responds to prey-population growth rate rather than level can produce limit-cycle oscillations that amplify when the trophic chain is extended.
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