Download presentation

Presentation is loading. Please wait.

1
**Pedro Ribeiro de Andrade Gilberto Câmara**

Predator-Prey Models Pedro Ribeiro de Andrade Gilberto Câmara

2
**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)

3
**“nature red in tooth and claw”**

4
**One species uses another as a food resource: lynx and hare.**

5
**The Hudson’s Bay Company**

6
**hare and lynx populations (Canada)**

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

7
**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.

8
**Predator-prey systems**

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

9
**predator population decreases predator population increases**

Predator-prey cycles normal prey population prey population increases prey population increases predator population decreases as less food predator population increases as more food prey population decreases because of more predators

10
**Generic Model f(x) prey growth term g(y) predator mortality term**

h(x,y) predation term e - prey into predator biomass conversion coefficient MTBI summer 2008

11
**Lotka-Volterra Model 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 MTBI summer 2008

12
**Predator-prey population fluctuations in Lotka-Volterra model**

13
**Predator-prey systems**

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 = The time t is measured in months. There are 40 wolfes and 1000 rabbits

14
Phase plane Variation of one species in relation to the other

15
**Phase trajectories: solution curve**

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

16
Equilibrium point The point (1000, 80) is inside all the solution curves. It corresponds to the equilibrium solution R = 1000, W = 80.

17
Hare-lynx data

18
Hare-lynx data

Similar presentations

OK

Predation (Chapter 18) Predator-prey cycles Models of predation

Predation (Chapter 18) Predator-prey cycles Models of predation

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on blood stain pattern analysis equation Ppt on domestic robots of the future Ppt on gestational diabetes mellitus Ppt on different types of forests in world Convert doc to ppt online Ppt on security attacks in information security Ppt on nitrogen cycle and nitrogen fixation cycle Ppt on machine translation patent Ppt on understanding body language Ppt on indian national parks