Editing Lotka–Volterra equations (section)

== Biological relevance of the model ==
[[File:Milliers fourrures vendues en environ 90 ans odum 1953 en.jpg|upright=1.5|thumb|Numbers of [[Lepus americanus|snowshoe hare]] (yellow, background) and [[Canada lynx]] (black line, foreground) furs sold to the [[Hudson's Bay Company]]. Canada lynxes eat snowshoe hares.]]

None of the assumptions above are likely to hold for natural populations. Nevertheless, the Lotka–Volterra model shows two important properties of predator and prey populations and these properties often extend to variants of the model in which these assumptions are relaxed:

Firstly, the dynamics of predator and prey populations have a tendency to oscillate. Fluctuating numbers of predators and prey have been observed in natural populations, such as the [[lynx]] and [[snowshoe hare]] data of the [[Hudson's Bay Company]]<ref>{{cite journal|last=Gilpin|first=M. E.| year=1973|title=Do hares eat lynx?|journal=American Naturalist|issue=957|pages=727–730|doi=10.1086/282870| volume=107| s2cid=84794121}}</ref> and the moose and wolf populations in [[Isle Royale National Park]].<ref>{{cite journal|last1=Jost| first1=C.|last2=Devulder|first2=G.|last3=Vucetich|first3=J.A.| last4=Peterson|first4=R.|last5=Arditi|first5=R.| doi=10.1111/j.1365-2656.2005.00977.x|title=The wolves of Isle Royale display scale-invariant satiation and density dependent predation on moose|journal=J. Anim. Ecol.|volume=74|issue=5|pages=809–816| year=2005}}</ref>

Secondly, the population equilibrium of this model has the property that the prey equilibrium density (given by <math> x = \gamma/\delta </math>) depends on the predator's parameters, and the predator equilibrium density (given by <math> y =  \alpha/\beta </math>) on the prey's parameters. This has as a consequence that an increase in, for instance, the prey growth rate, <math> \alpha</math>, leads to an increase in the predator equilibrium density, but not the prey equilibrium density. Making the environment better for the prey benefits the predator, not the prey (this is related to the [[paradox of the pesticides]] and to the [[paradox of enrichment]]). A demonstration of this phenomenon is provided by the increased percentage of predatory fish caught had increased during the years of [[World War I]] (1914–18), when prey growth rate was increased due to a reduced fishing effort.

A further example is provided by the experimental [[iron fertilization]] of the ocean. In several [[iron fertilization#Experiments|experiments]] large amounts of iron salts were dissolved in the ocean. The expectation was that iron, which is a limiting nutrient for phytoplankton, would boost growth of phytoplankton and that it would sequester carbon dioxide from the atmosphere. The addition of iron typically leads to a short bloom in phytoplankton, which is quickly consumed by other organisms (such as small fish or [[zooplankton]]) and limits the effect of enrichment mainly to increased predator density, which in turn limits the [[carbon sequestration]]. This is as predicted by the equilibrium population densities of the Lotka–Volterra predator-prey model, and is a feature that carries over to more elaborate models in which the restrictive assumptions of the simple model are relaxed.<ref>{{Cite journal | 
last1=Pan |first1=A. |last2=Pourziaei |first2=B.|last3=Huang|first3=H.|date=2015-06-03|title= Effect of Ocean Iron Fertilization on the Phytoplankton Biological Carbon Pump.|volume=3 |issue=1 |pages=52–64|doi=10.4208/aamm.10-m1023|journal=Advances in Applied Mathematics and Mechanics|s2cid=124606355 }}</ref>