Statements (47)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:alsoKnownAs |
gptkb:Lotka–Volterra_equations
|
| gptkbp:application |
population dynamics
ecological modeling |
| gptkbp:assumes |
predator population declines exponentially in absence of prey
no immigration or emigration predators depend on prey for food prey population grows exponentially in absence of predators |
| gptkbp:category |
partial differential equations
mathematical modeling population ecology |
| gptkbp:consistsOf |
two first-order nonlinear differential equations
|
| gptkbp:describes |
dynamics of biological systems
|
| gptkbp:field |
ecology
mathematical biology |
| gptkbp:form |
dx/dt = αx - βxy
dy/dt = δxy - γy |
| gptkbp:hasModel |
interaction between predators and prey
|
| https://www.w3.org/2000/01/rdf-schema#label |
predator–prey equations
|
| gptkbp:influenced |
development of modern ecological modeling
|
| gptkbp:influencedBy |
chemical reaction kinetics
|
| gptkbp:introduced |
gptkb:Alfred_J._Lotka
gptkb:Vito_Volterra |
| gptkbp:introducedIn |
1920s
|
| gptkbp:limitation |
assumes constant environment
assumes linear functional response does not account for carrying capacity |
| gptkbp:notableExample |
lynx and hare populations in Canada
wolves and moose on Isle Royale |
| gptkbp:parameter |
α = natural growth rate of prey
β = predation rate coefficient γ = natural death rate of predators δ = efficiency of turning prey into predators |
| gptkbp:publishedIn |
gptkb:Journal_of_the_American_Chemical_Society
gptkb:Nature |
| gptkbp:relatedTo |
gptkb:competitive_Lotka–Volterra_equations
gptkb:SIR_model Rosenzweig–MacArthur model |
| gptkbp:solvedBy |
cyclic population oscillations
|
| gptkbp:usedIn |
epidemiology
fisheries management conservation biology theoretical ecology |
| gptkbp:variant |
x = number of prey
y = number of predators |
| gptkbp:bfsParent |
gptkb:competitive_Lotka–Volterra_equations
|
| gptkbp:bfsLayer |
7
|