Transcript Predator-Prey Model

A Systems Dynamics Approach
Introduction
• 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, plantherbivore, parasite-host, tumor cells (virus)-immune
system, susceptible-infectious interactions, etc. (Scholarpedia)
Elements of the Model
Wo l f
Rabbit
AREA
Grass
WOLF Model
Wolf Model
(Wolf)
Birth rate Wolf
c natality Wolf
(Wolf)
Death by human
Wolf
Natural death Wolf
Death Rate Wolf
Starvation Wolf
TIME STEP
i Wolf Population
RABBIT Model
Rabbit Model
(Rabbits)
Birth rate rabbits
c natality rabbits
(Rabbits)
actual number of rabbits caught by wolf
Rabbits
Natural death rabbits
Death rate rabbits
Starvation rabbits
TIME STEP
i Rabbits
GRASS Model
Grass Model
(Grass)
Death rate grass
grass eaten by rabbits
natural death
TIME STEP
c density grass nom
Grass
i Grass
i Area
(Grass)
grass untouched
natality grass
Spread rate grass
Wolf, Rabbit, Grass Interaction
Explanation
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.
The wolves will almost completely
cut off the rabbits’ food supply.
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Internet Sources
• http://www.cs.uwyo.edu/~wspears/courses/CS501
0/frey/rabbits.pdf
• http://www.scholarpedia.org/article/Predatorprey_model