Lotka Volterra Model

## Lotka-Volterra Model

- Designed to predict oscillations in abundance of predator and prey populations
- Rate of Change in Prey Population=Intrinsic growth rate of prey population - removal of prey by predators
- DN/Dt= rN - cNP Rate of Change of Prey Population
- r= growth rate of prey
- N= population size of prey
- c= capture efficiency (rate of predation)
- P= population of predators

- DP/Dt= acNP-dP Rate of Change of Predator Population
- a=efficiency of food conversion (what % of each prey is transformed into new babies)
- c= capture efficiency
- N= prey population
- P=predator populaion
- d= death rate of predator

### Graph of Lotka-Volterra

Lotka-Volterra represents the population fluxes between predator and prey as a circular cycle.

* The model starts with low populations of predators and prey (bottom left quadrant)

* Because of low predator populations prey populations increase, but predator populations remain low (bottom right quadrant)

* As prey populations increase predator populations begin to increase (top right quadrant)

* Eventually a threshold is passed DP/Dt where predators eat enough prey causing prey populations to begin to decrease (top left quadrant

* Eventually predator populations decrease due to the declining prey population, this leads us back to the lower left quadrant with low predator and prey populations

Link to LV Model You Can Manipulate

### Limitations of Lotka-Volterra

- No time lag between predator and prey population responses
- Neutrally Stable= there is no attraction to some equilibrium point
- Any perturbation in the model will have it continue to cycle at a new amplitude until a new force acts on the model
- Eventually one of the populations oscillations may reach an axis signaling that a population has died out

- Based off of a Type I Functional response which is the least realistic type of functional response
- Type I response does not have any density dependence factors, therefore predator populations are linearly related to prey populations without any consideration of the density of the predator population

page revision: 9, last edited: 11 Nov 2009 02:04