Predator prey models
Download
1 / 18

Predator-Prey Models - PowerPoint PPT Presentation


  • 67 Views
  • Uploaded on

Predator-Prey Models. Pedro Ribeiro de Andrade Gilberto Câmara. Acknowledgments and thanks. Many thanks to the following professors for making slides available on the internet that were reused by us Abdessamad Tridane (ASU) Gleen Ledder (Univ of Nebraska)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Predator-Prey Models' - feryal


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Predator prey models

Predator-Prey Models

Pedro Ribeiro de Andrade

Gilberto Câmara


Acknowledgments and thanks
Acknowledgments and thanks

  • Many thanks to the following professors for making slides available on the internet that were reused by us

  • Abdessamad Tridane (ASU)

  • Gleen Ledder (Univ of Nebraska)

  • Roger Day (Illinois State University)


Nature red in tooth and claw
nature red in tooth and claw”



The hudson s bay company
The Hudson ’s Bay Company


Hare and lynx populations canada
hare and lynx populations (Canada)

Note regular periodicity, and lag by lynx population peaks just after hare peaks


Predator prey systems

The principal cause of death among the prey is being eaten by a predator.

The birth and survival rates of the predators depend on their available food supply—namely, the prey.

Predator-prey systems


Predator prey systems1

Two species encounter each other at a rate that is proportional to both populations

Predator-prey systems


Predator prey cycles

prey population proportional to both populations

increases

prey population

increases

predator population decreases

as less food

predator population increases

as more food

prey population decreases

because of more predators

Predator-prey cycles

normal prey population


Generic model
Generic Model proportional to both populations

  • f(x) prey growth term

  • g(y) predator mortality term

  • h(x,y) predation term

  • e - prey into predator biomass conversion coefficient


Lotka volterra model
Lotka-Volterra Model proportional to both populations

r - prey growth rate : Malthus law

m - predator mortality rate : natural mortality

a and b predation coefficients : b=ea

e prey into predator biomass conversion coefficient


Predator prey population fluctuations in lotka volterra model
Predator-prey population fluctuations in proportional to both populations Lotka-Volterra model


Predator prey systems2

Suppose that populations of rabbits and wolves are described by the Lotka-Volterra equations with: k = 0.08, a = 0.001, r = 0.02, b = 0.00002

The time t is measured in months.

There are 40 wolfes and 1000 rabbits

Predator-prey systems


Phase plane

V by the ariation of one species in relation to the other

Phase plane


Phase trajectories solution curve

A phase trajectory is a path traced out by solutions ( by the R, W) as time goes by.

Phase trajectories: solution curve


Equilibrium point

T by the he point (1000, 80) is inside all the solution curves. It corresponds to the equilibrium solution R = 1000, W = 80.

Equilibrium point




ad