Post on 23-Feb-2016
description
Predator-Prey ModelA Systems Dynamics Approach
• Predator-prey models are arguably the building blocks of the bio- and ecosystems as biomasses are grown out of their resource masses.
• Species compete, evolve and disperse simply for the purpose of seeking resources to sustain their struggle for their very existence.
• Depending on their specific settings of applications, they can take the forms of resource-consumer, plant-herbivore, parasite-host, tumor cells (virus)-immune system, susceptible-infectious interactions, etc. (Scholarpedia)
Introduction
The System Dynamics Model
AREA
Wol f Rabbit Grass
Elements of the Model
WOLF Model
Wolf Model
Wolf
Birth rate Wolf
(Wolf)
c natality Wolf
Death Rate Wolf
(Wolf)
Death by human
Natural death Wolf
Starvation Wolf
TIME STEP
i Wolf Population
RABBIT Model
Rabbit Model
Rabbits
Birth rate rabbits
(Rabbits)
c natality rabbits
Death rate rabbits
(Rabbits)
actual number of rabbits caught by wolf
Natural death rabbits
Starvation rabbits
TIME STEP
i Rabbits
GRASS Model
Grass Model
Grass
Death rate grassgrass eaten by rabbits
natural death
i Grass
c density grass nom
i Area
Spread rate grass
(Grass)
natality grass
grass untouched
(Grass)
TIME STEP
Wolf, Rabbit, Grass Interaction
As the amount of grass increases, so does the number of rabbits.
When grass is low, rabbit population also becomes low – which means not enough food to support the wolves.
As the secondary predator (the wolves) would dramatically increase in population, and then crash hard when the primary predator (the rabbits) were nearly extinct.
Then, the rabbits would go around eating and reproducing, while the wolves would catch up, after nearly going extinct themselves.
Explanation
The danger is when either population fluctuates so much that population dips down to zero.
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Explanation
The wolves will almost completely cut off the rabbits’ food supply.
Internet Sources• http://www.cs.uwyo.edu/~wspears/courses/CS501
0/frey/rabbits.pdf• http://www.scholarpedia.org/article/Predator-prey_
model