PREDATORPREY
MODELLING
CARLSSON KONG CHIE HAO
NG XIANG LOONG
GOH XUE HENG
INTRODUCTION
“Every morning in Africa, a gazelle wakes up. It
knows it must run faster than the fastest lion or
it will be killed. Every morning a lion wakes up.
It knows it must outrun the slowest gazelle or it
will starve to death. It doesn’t matter whether
you’re a lion or gazelle. When the sun comes
up, you’d better be running.”
PREDATOR-PREY
MODELLING
•
Describes the number (density) of prey consumed per predator
per unit of time for given quantities (densities) of prey and
predator.
•
Is also called a Volterra-Lotka model (or) Competition model
(One species will depend on other species for their food)
•
Information about competition between two species, which are
showing an identical ecological niche
01
USAGE
TO PROVE THE ECOLOGICAL
EQUILIBRIUM
Assumptions
Here’s what we first make assumptions:
●
the prey population will grow exponentially when the predator is absent;
●
the predator population will starve in the absence of the prey population (as
opposed to switching to another type of prey);
●
predators can consume infinite quantities of prey; and
●
there is no environmental complexity
●
The prey always has enough food
(There are only two species animals)
Causal Loop
Diagram of
PredatorPrey
As we can see…
One of the classic studies of predator-prey interactions is the 90-year data set of snowshoe hare and
lynx pelts hare-lynx data purchased by the Hudson's Bay Company of Canada. While this is an indirect
measure of predation, the assumption is that there is a direct relationship between the number of
pelts collected and the number of hare and lynx in the wild
Lotka-Volterra prey-predator
equations
Assume that, in the absence of predators, the prey will
grow exponentially according to 𝑑𝑥/𝑑𝑡=𝑎𝑥 for a certain a
> 0. We also assume that the death rate of the prey due
to interaction is proportional to 𝑥𝑦,
● Where,
x is the Prey population (Rabbits);
y is the Predator population (Foxes)
A set of fixed positive constants
a (the growth rate of prey),
b (the rate at which predators destroy prey),
So,
𝑑𝑥
𝑑𝑡
= 𝑎𝑥 − 𝑏𝑥𝑦
Lotka-Volterra predator-prey
equations
Without prey, predators will die exponentially according to 𝑑𝑦/𝑑𝑡=−
𝑟𝑦 for a certain r>0.
● Their birth strongly depends on both population sizes, so we
finally find for a certain c>0
●
A set of fixed positive constants r (the death rate of predators),
and c (the rate at which predators increase by consuming prey).
So,
𝑑𝑦
𝑑𝑡
= 𝑐𝑥𝑦 − 𝑟𝑦
Questions
𝑑𝑥
= −0.05𝑥 + 0.001𝑥𝑦
𝑑𝑡
𝑑𝑦
= 0.1𝑦 − 0.005𝑥𝑦
𝑑𝑡
Predator
:
𝒙
Prey
:
𝒚
Prey affected by
:
𝑷𝒓𝒆𝒅𝒂𝒕𝒐𝒓
Predator affected by
:
𝑷𝒓𝒆𝒚
Thank You!