Arditi–Ginzburg equations

The Arditi–Ginzburg equations describe ratio dependent predator–prey dynamics. Where N is the population of a prey species and P that of a predator, the population dynamics are described by the following two equations:^[1]

$\begin{align} \frac{dN}{dt} & = f(N)N-g\left(\frac N P \right)P \\[4pt] \frac{dP}{dt} & = e g\left(\frac N P \right)P-uP \end{align}$

Here f(N) captures any change in the prey population not due to predator activity including inherent birth and death rates. The per capita effect of predators on the prey population is modeled by a function g which is a function of the ratio of predators to prey, ${\textstyle N/P}$, making predator harvest prey in proportion to the ratio of predators to prey. e is the reproductive payoff the predators receive for consuming prey and finally u is the death rate of the predators. Making predation pressure a function of the ratio of prey to predators contrasts with the prey dependent Lotka–Volterra equations, where the effect of predators on the prey population is simply a function of the magnitude of the prey population g(N). Because the number of prey harvested by each predator decreases as predators become more dense, ratio dependent predation represents an example of trophic function. Ratio dependent predation may account for heterogeneity that occurs in large scale natural systems that could decrease predator efficiency when prey is scarce.^[1] The merit of ratio dependent predation over prey dependent models of predation has been the subject of much controversy especially between biologists Lev R. Ginzburg and Peter A. Abrams.^[2] Ginzburg purports that ratio dependent models more accurately depict predator prey interactions while Abrams maintains that said models make unwarranted complicating assumptions.^[2]

See also

• Lotka–Volterra equation
• Population dynamics

References

1. "Coupling in predator-prey dynamics: Ratio-Dependence" (PDF). ac.els-cdn.com. Retrieved 2015-09-28.
2. "The nature of predation: prey dependent, ratio dependent or neither?". www.sciencedirect.com. Retrieved 2015-09-28.