The Arditi–Ginzburg equations describe

ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

-dependent

predator–prey Predation is a biological interaction in which one organism, the predator, kills and eats another organism, its prey. It is one of a family of common List of feeding behaviours, feeding behaviours that includes parasitism and micropredation ...

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:

\frac & = e \,gP-uP \end

Here ''f''(''N'') captures any change in the prey population not due to predator activity including inherent

birth Birth is the act or process of bearing or bringing forth offspring, also referred to in technical contexts as parturition. In mammals, the process is initiated by hormones which cause the muscular walls of the uterus to contract, expelling the f ...

and death rates. The per capita effect of predators on the prey population (the harvest rate) is modeled by a function ''g'' which is a function of the

''N''/''P'' of prey to predators. Predators receive a reproductive payoff, ''e,'' for consuming prey, and die at rate ''u''. Making predation pressure a function of the ratio of prey to predators contrasts with the prey-dependent Lotka–Volterra equations, where the per capita 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 Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be use ...

, ratio-dependent predation is a way of incorporating predator

intraspecific competition Intraspecific competition is an interaction in population ecology, whereby members of the same species compete for limited resources. This leads to a reduction in fitness for both individuals, but the more fit individual survives and is able to ...

for food. Ratio-dependent predation may account for

heterogeneity Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...

in large-scale natural systems in which predator efficiency decreases when prey is scarce. The merit of ratio-dependent versus prey-dependent models of predation has been the subject of much controversy, especially between the biologists Lev R. Ginzburg and Peter A. Abrams. Ginzburg purports that ratio-dependent models more accurately depict predator-prey interactions while Abrams maintains that these models make unwarranted complicating assumptions. A later review critically examines the claims made about ratio-dependent predation to find that the added value of the ratio-dependent predation models is unclear and concludes that "As empirical evidence is often lacking on both functional responses and the importance of functional responses for population dynamics, there is no need to strongly favor one limit model over the others." A recent ecology undergraduate textbook devotes about equal space to Lotka-Volterra and Arditi-Ginzburg equations. Neither prey-dependent nor ratio-dependent models can claim universal accuracy but the issue is to identify which is least wrong.

See also

References

Further reading